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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mater.</journal-id>
<journal-title>Frontiers in Materials</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mater.</abbrev-journal-title>
<issn pub-type="epub">2296-8016</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1129850</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2023.1129850</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Materials</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Resource environment load prediction method for metal material machining based on process condition similarity matching</article-title>
<alt-title alt-title-type="left-running-head">Xing et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fmats.2023.1129850">10.3389/fmats.2023.1129850</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Xing</surname>
<given-names>Zhipeng</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Dai</surname>
<given-names>Haicong</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Xiong</surname>
<given-names>Jiaji</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Jiong</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Li</surname>
<given-names>Yufeng</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2148964/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Institute for Advanced Materials and Technology</institution>, <institution>University of Science and Technology Beijing</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>CETC Information Science Academy</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Shanghai Aerospace Equipments Manufacturer Co., Ltd.</institution>, <addr-line>Shanghai</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>State Key Laboratory of Mechanical Transmission</institution>, <institution>Chongqing University</institution>, <addr-line>Chongqing</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1776428/overview">Chen Wang</ext-link>, Tsinghua University, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2150304/overview">Peixun Fan</ext-link>, Tsinghua University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/970703/overview">Ke Bi</ext-link>, Beijing University of Posts and Telecommunications (BUPT), China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2150827/overview">Kuan Lu</ext-link>, Northwestern Polytechnical University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2150849/overview">Chuanzhen Huang</ext-link>, Yanshan University, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Yufeng Li, <email>liyufengcqu@cqu.edu.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Semiconducting Materials and Devices, a section of the journal Frontiers in Materials</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>01</day>
<month>02</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>10</volume>
<elocation-id>1129850</elocation-id>
<history>
<date date-type="received">
<day>22</day>
<month>12</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>20</day>
<month>01</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Xing, Dai, Xiong, Zhang and Li.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Xing, Dai, Xiong, Zhang and Li</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>
<bold>Introduction:</bold> Resource environment load data are important for analyzing and improving the environmental performance, which are affected by the process condition of metal material machining processes. However, the environmental performance assessment in previous research focused on the results under the specific process conditions. The resource environment load data need to be re-collected when the process conditions are changed for a credible assessment, which is time- consuming and tedious.</p>
<p>
<bold>Methods:</bold> This paper proposed a process condition- oriented prediction method of resource environment load data with limited samples. The significance of process condition elements on the resource environment load data was analyzed, and then the resource environment load was predicted according to the similarity between the process condition to be predicted and the existing process conditions.</p>
<p>
<bold>Results and Dicussion:</bold> The results show that the average prediction accuracy of this method exceeds 90%, and further the accuracy for predicting the environmental performances using the predicted data is more than 93% which would help process designers to choose the better process condition for machining the metal materials.</p>
</abstract>
<kwd-group>
<kwd>environment performance</kwd>
<kwd>process condition</kwd>
<kwd>resource environment load</kwd>
<kwd>similarity matching</kwd>
<kwd>machining</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The manufacturing industry is the important pillar of world&#x2019;s economic development. Simultaneously, metal machining process also results in significant resource and energy depletion, accompanied the generation of a large amount of environmental waste in the form of solids, liquid, gas and airborne particulates (<xref ref-type="bibr" rid="B6">Du et al., 2020</xref>; <xref ref-type="bibr" rid="B9">He Y. et al., 2022</xref>). International Energy Agency (IEA) had reported that it is responsible for approximately 30% of global final energy consumption and over 20% of global CO<sub>2</sub> emissions (<xref ref-type="bibr" rid="B2">Agency, 2008</xref>). Consequently, to address on the environmental issues, environmental performances are evaluated based on the life cycle assessment (LCA) methodology which has been widely applied in the metal machining process to guide enterprises toward Green Manufacturing. The accuracy of the environmental performance results directly depends on the resource environment load data in life cycle inventory (LCI) which is the second of four phases of the LCA methodology regulated by the ISO 14040 and ISO 14044 series of international technical standards (<xref ref-type="bibr" rid="B7">Ferrari et al., 2021</xref>). Therefore, it has become a crucial concern to obtain the reliable resource environment load data.</p>
<p>Resource environment load data in LCI for evaluating the environmental performances of metal machining process can be divided into primary data (when the data are obtained directly at the production sites and associated to the related process units) and secondary data (when the data come from databases, literature, estimates) (<xref ref-type="bibr" rid="B7">Ferrari et al., 2021</xref>). Some researchers have evaluated the environmental performances based on the secondary data. Bekker et al. evaluated the environmental performances of computer numerical control (CNC) milling according to the resource environment load data entries in SimaPro software (<xref ref-type="bibr" rid="B3">Bekker and Verlinden, 2018</xref>). He et al. investigated the environmental performances of an automotive fuel-line clip produced with recycled polyamide 12 from the selective laser sintering process in comparison to the conventional polyamide 66 counterpart, based on commercial LCA databases (<xref ref-type="bibr" rid="B8">He D. et al., 2022</xref>). Soares et al. conducted a comparative environment performance assessment between hobbing 20MnCr5 with minimum quantity lubrication and flood lubrication based on the data obtained from database provided by GaBi (<xref ref-type="bibr" rid="B20">Soares et al., 2022</xref>). Vukelic et al. monitored the negative environment impact of cutting processes through midpoint and endpoint assessment based on Ecoinvent database (<xref ref-type="bibr" rid="B22">Vukelic et al., 2020</xref>). In the above research, the environmental performances were predicted with the secondary data which mainly depend on material and process types (<xref ref-type="bibr" rid="B17">Narita et al., 2008</xref>). Once the material and process types are determined, the resource environment load data would be predicted to be the constant value. However, during the metal machining process, the resource environment load data are associated with the specific process conditions (<xref ref-type="bibr" rid="B16">Liu et al., 2022</xref>), which not only relate to the process type and material type, but also depend on process parameters, equipment, etc., (<xref ref-type="bibr" rid="B14">Khettabi et al., 2007</xref>; <xref ref-type="bibr" rid="B5">de Souza Zanuto et al., 2019</xref>; <xref ref-type="bibr" rid="B23">Wang et al., 2021</xref>). The change of process conditions will lead to the change of resource environment load. For example, the disc mechanism consumes 478% more energy than the two-cylinder mechanism on average to grind the single 2-m-long timber beams made of three wood species: ash, pine and spruce. (<xref ref-type="bibr" rid="B24">Wargu&#x142;a et al., 2022</xref>). Therefore, the secondary data without considering specific process conditions is unsuitable for accurate environmental impact assessment for the actual metal machining process (<xref ref-type="bibr" rid="B4">Dai et al., 2022</xref>).</p>
<p>Employing the reliable primary data obtained directly at production or experiment sites is critical for obtaining credible assessment results (<xref ref-type="bibr" rid="B12">Kalverkamp et al., 2020</xref>). Some researchers focused on the environmental performances considering the primary data. Afzal et al. had analyzed the environmental performances of three different welding processes based on the resource environment load data collected on site for welding 1&#xa0;m long and 2.5 thick AISI 304 stainless steel sheets under given experimental conditions (<xref ref-type="bibr" rid="B1">Afzal et al., 2021</xref>). Pittner et al. conducted an environmental impact assessment using the resource environment load data obtained from experiments for different fusion welding processes of the shear test specimens and automotive cap profile under specified parameter settings, and the results showed that laser beam welding brings about up to 60% reduced environmental performances for both cases in comparison to the resistance spot welding (<xref ref-type="bibr" rid="B18">Pittner and Rethmeier, 2022</xref>). Khanna et al. presented the comparison of dry and cryogenic LCO2 machining based on the collected data on the consumption of electricity and LCO2 for milling a slot with 1,000&#xa0;mm. And the results show that considering all impact categories, more than 95% higher impacts have been generated in the case of LCO2 condition in comparison with dry machining (<xref ref-type="bibr" rid="B13">Khanna et al., 2022</xref>). Shah et al. evaluated the environment performance for drilling the Inconel 718 using cryogenic cutting fluids based on the collected primary data in each cutting test, and the representative impact category results at three different cutting speeds between the two cryogenic environments were obtained (<xref ref-type="bibr" rid="B19">Shah et al., 2021</xref>). However, these studies performed the environmental performance assessment using the primary data and these data are directly obtained under the given process conditions. Further, the resource environment load data in LCI is changeable in different process conditions. When the process condition change, new resource environment load data are required to assess the environmental impact of the metal machining process. Using the above methods, the resource environment load data needs to be re-collected when the process conditions are changed for a credible assessment, which is time-consuming and tedious. Therefore, the motivation for this research was to investigate the resource environment load data prediction under the new process condition for evaluating the environmental performances and further promoting the efficient improvement of metal machining process conditions.</p>
<p>Therefore, the major aim and novelty of this research is to effectively predict the resource environment load under changeable process condition and accurately evaluate the environmental performance. In this method, the process condition is introduced to comprehensively describe the process type, materials, processing mode, equipment, process parameters and other information during the metal machining process. And then, the resource environment load database is constructed based on the concept of process condition to store the collected data. Moreover, a process condition similarity matching method based on weighted Euclidean distance is proposed for predicting the resource environment load data of new process conditions with limited sample data. Finally, a case study was conducted to validate the proposed method. The predicted data can be used for assessing the environment performance under the new process condition for machining the metal materials.</p>
</sec>
<sec sec-type="materials|methods" id="s2">
<title>2 Materials and methods</title>
<sec id="s2-1">
<title>2.1 Resource environment load database construction</title>
<p>The actual production processes are complex and diverse, the process conditions are not identical in different processes. For example, in the cutting process, the type of material and processing method may be the same, while process parameter and equipment are different. However, different process conditions such as Equipment, Processing Modes, Material Types, Process Parameters, etc., may lead to different energy requirement, processing time, etc., These differences would further result in the changes of resource environment load data. Taking the same product as an example, the energy consumption and emissions generated by a small lathe and a large CNC lathe are different, while other process conditions are the same. Therefore, it is necessary to define and store the process conditions corresponding to the current resource environment load. The concept of process condition is used to comprehensively describe process conditions including information related to material, process parameters, processing mode, processing method, equipment and condition description. <xref ref-type="table" rid="T1">Table 1</xref> shows the elements of the machining process condition and its explanation in detail as an example.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Process condition elements of machining process and the explanations.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left"/>
<th align="center">Process condition elements</th>
<th align="center">Explanation</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">1</td>
<td align="left">Processing Type</td>
<td align="left">Turning, Milling &#x2026;</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">Material Types</td>
<td align="left">Steel, Aluminum &#x2026;</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">Equipment</td>
<td align="left">Lathes, Milling machines &#x2026;</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">Processing Modes</td>
<td align="left">Dry cut, Wet cut &#x2026;</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">Process Parameters</td>
<td align="left">Feed speed, Cutting force &#x2026;</td>
</tr>
<tr>
<td align="left">6</td>
<td align="left">Condition description</td>
<td align="left">Time, Location &#x2026;</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>As shown in <xref ref-type="table" rid="T1">Table 1</xref>, the processing methods include milling, turning, etc., The processing materials include steel, aluminum, etc., The processing equipment may use lathes, milling machines, etc., The processing modes include wet cutting, dry cutting, etc., while the processing parameters in the processing process include Feed speed, Cutting force, etc., and the description of the current processing location and time.</p>
<p>Further, the ultimate purpose of the resource environment load in LCI is to evaluate the environmental problems caused by actual production, and reduce the degree which harm to the human body and the environment, and further to provide scientific and accurate evidences for process designers. Based on process condition description, the resource environment load can be analyzed in detail. The resource environment load usually includes the input of resources, energy and environmental output. Resource and energy input include the amount of process objects, the amount of auxiliary materials, and energy consumption; Environmental outputs include air pollution, water pollution, solid waste, and occupational health. The resource environment load is shown in <xref ref-type="fig" rid="F1">Figure 1</xref>.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Resource environment load.</p>
</caption>
<graphic xlink:href="fmats-10-1129850-g001.tif"/>
</fig>
<p>Specifically, the resource environment load under a process condition is mainly represented by the input and output model (IPO). For example, in the machining process, resource inputs include raw materials, energy inputs (mainly refer to electrical energy), and the output mainly includes finished workpieces, and some environmental pollutants (such as waste liquid, Gaseous waste, occupational hazards and so on). The above information is presented using the IPO diagram, as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>IPO model of the machining processes.</p>
</caption>
<graphic xlink:href="fmats-10-1129850-g002.tif"/>
</fig>
<p>The type of resource environment load in the target condition can be clarified through the IPO diagram. When evaluating the environmental performances, the resource environment load data can be selected according to the demand for analyzing and assessing the resource environment load in the target condition. For example, if the purpose of studying resource environment load is to reduce human body damage, the main research resource environmental load indicators are occupational health, air pollution, etc., The selection of resource environment load indicators should follow a few principles.<list list-type="simple">
<list-item>
<p>&#x2022; Systematic principle: the selection of indicators must be reasonable in hierarchy, which can comprehensively characterize the process environmental problems.</p>
</list-item>
<list-item>
<p>&#x2022; The principle of quantification: the selection of indicators needs to consider the quantification of resource environment load, and the purpose of assessing environmental problems in actual process conditions can be achieved through monitoring and collecting the basic data of resource environment load.</p>
</list-item>
<list-item>
<p>&#x2022; The principle of operability: During the selection of resource environment load indicators, it is necessary to take into account the operability to facilitate the evaluation of environmental indicators.</p>
</list-item>
<list-item>
<p>&#x2022; The principle of independence: the indicators should avoid the intercorrelation. If they are related to each other, it will lead to unreasonable selection of indicators, which will increase the basic data collection workload of resource environment load, and ultimately affect the accuracy of resource environment load evaluation results.</p>
</list-item>
</list>
</p>
<p>Further, in order to ensure the accuracy of the environmental performances results, primary data at the production site are usually the basis of the evaluation. According to the input and output information described in the IPO diagram, the corresponding data are collected by sensors equipment such as power meters (measuring energy consumption), dust sensors (measuring the dust or oil mist, noise sensors, gas testers, etc.,). However, the resource environment load data collected by the sensor are difficult to structure in the actual process. Therefore, there is an urgent need to build a resource environment load database to manage resource environment load data.</p>
<p>In order to solve the above problems, this paper adopts B/S architecture to achieve WEB-based data access, and decouples the development of the front and back ends. The front-end page adopts Html, Css and JavaScript development, and the progressive development framework Vue is selected to simplify the development process. The Vue framework abstracts the state and behavior of the view based on the MVVM model. The back-end mainly uses the Springboot development framework, and the data storage uses MySQL and MogoDB for data persistence. Implement user-oriented data sharing services and applications, and support dynamic data update and structured management. The database development technology system is shown in <xref ref-type="fig" rid="F3">Figure 3</xref>.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Database development technology system.</p>
</caption>
<graphic xlink:href="fmats-10-1129850-g003.tif"/>
</fig>
</sec>
<sec id="s2-2">
<title>2.2 Resource environment load prediction method</title>
<sec id="s2-2-1">
<title>2.2.1 Prediction method framework</title>
<p>Considering the similarity of resource environment load data in homogeneous process conditions, this paper evaluates the resource environment load corresponding to the target condition by matching the existing data. Based on this, a framework of evaluating the resource environment load for process conditions is constructed and shown in <xref ref-type="fig" rid="F4">Figure 4</xref>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>The framework of resource environment load prediction.</p>
</caption>
<graphic xlink:href="fmats-10-1129850-g004.tif"/>
</fig>
<p>The resource environment load prediction method for process condition flow is as follows: Firstly, select the data from the resource environment database and environmental indicators. Secondly, analyze the significance of each resource environment load indicators according to the data. Thirdly, according to the significance of the resource environment load indicator, set the relative weight of each indicator. Fourthly, the weighted Euclidean distance and similarity are calculated between the target condition and the reference condition according to the resource environment load indicators and the corresponding weights. Fifthly, select the resource environment load data corresponding to the process condition with the greatest similarity as the evaluation value of the new process condition. And then, verify the evaluation values and giving an explanation. Finally, store reasonable evaluation results.</p>
</sec>
<sec id="s2-2-2">
<title>2.2.2 Significance analysis of process condition</title>
<p>Different process condition elements have different impacts on resource environment load. Therefore, significance analysis is used to explore the significant impact of process condition elements on resource environment load. Assume that there is correlation between resource environment load <inline-formula id="inf1">
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<mml:mi>&#x3b2;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is an unknown parameter unrelated to <inline-formula id="inf5">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf6">
<mml:math id="m7">
<mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is an unobservable random variable.</p>
<p>In general, if there is no linear relationship between <inline-formula id="inf7">
<mml:math id="m8">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, then all the <inline-formula id="inf9">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1,2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> in the model are 0. Therefore, to test that there is linear relationship between <inline-formula id="inf10">
<mml:math id="m11">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf11">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is to verify whether the hypothesis <inline-formula id="inf12">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>:</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> is true.</p>
<p>It can be seen from <inline-formula id="inf13">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>E</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> that the larger <inline-formula id="inf14">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>E</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is, the smaller <inline-formula id="inf15">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is, which means the closer the linear relationship between a and b is, where <inline-formula id="inf16">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf17">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf18">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>E</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represent sum of square of deviations, Residual Sum of Squares, Explained Sum of Squares respectively. Therefore, it is conceived to test hypothesis <inline-formula id="inf19">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> with the ratio of <inline-formula id="inf20">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>E</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> as a statistic. So it is necessary to determine the distribution of the test statistics.<disp-formula id="e2">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mover accent="true">
<mml:mi>Y</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi>T</mml:mi>
</mml:msup>
<mml:mover accent="true">
<mml:mi>Y</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="&#x2016;" close="&#x2016;" separators="|">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>Y</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:mi>y</mml:mi>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
<disp-formula id="e3">
<mml:math id="m23">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
<disp-formula id="e4">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>E</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:mi>y</mml:mi>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>In this model, if the hypothesis <inline-formula id="inf21">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is true, where the following is true:<disp-formula id="equ1">
<mml:math id="m26">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi mathvariant="normal">E</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x223c;</mml:mo>
<mml:msup>
<mml:mi>&#x3c7;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="equ2">
<mml:math id="m27">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x223c;</mml:mo>
<mml:msup>
<mml:mi>&#x3c7;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="e5">
<mml:math id="m28">
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi mathvariant="normal">E</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mrow>
<mml:mfrac>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi mathvariant="normal">E</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x22c5;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>m</mml:mi>
</mml:mfrac>
<mml:mo>&#x223c;</mml:mo>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>n</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>Where F is the statistic that tests hypothesis <inline-formula id="inf22">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, so for a given significance level <inline-formula id="inf23">
<mml:math id="m30">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, the F-value calculated from the sample detection value. If <inline-formula id="inf24">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2265;</mml:mo>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>n</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, the tests hypothesis <inline-formula id="inf25">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> will be rejected, that is, the regression effect is considered significant; Otherwise, accept <inline-formula id="inf26">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, that is, the regression effect is considered not significant. When the overall regression effect is verified, it is also necessary to test whether each process condition element <inline-formula id="inf27">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> has a significant linear impact on the resource environment load data.</p>
</sec>
<sec id="s2-2-3">
<title>2.2.3 Process condition similarity matching based on weighted euclidean distance</title>
<p>Euclidean distance method can reflect the absolute difference of different sample characteristics, which mostly used to analyze the difference in the size of dimension values (<xref ref-type="bibr" rid="B21">Terrados-Cristos et al., 2021</xref>). In a multidimensional data spatial structure, Euclidean distance is a method for measuring the spatial distance of two vectors. The magnitude of the Euclidean distance reflects the degree of similarity between the two vectors, i.e. the smaller the value, the smaller the difference between the two vectors (<xref ref-type="bibr" rid="B11">Ji and Ni, 2022</xref>).</p>
<p>First of all, the coordinates of the p-dimensional vector (i.e., the vector composed of process condition factors) of the reference condition M and the target condition N as follows:<disp-formula id="e6">
<mml:math id="m35">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
<disp-formula id="e7">
<mml:math id="m36">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>According to the concept of Euclidean distance, the distance <inline-formula id="inf28">
<mml:math id="m37">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> between the reference condition and the target condition can be obtained, as expressed in <xref ref-type="disp-formula" rid="e8">formula 8</xref>. Further, the process condition similarity (PCS) is used to describe the similar between the reference condition and the target condition as expressed in <xref ref-type="disp-formula" rid="e9">formula 9</xref> (<xref ref-type="bibr" rid="B25">Xu and Zhen-jun, 2005</xref>):<disp-formula id="e8">
<mml:math id="m38">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msqrt>
<mml:mrow>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>p</mml:mi>
</mml:munderover>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
<disp-formula id="e9">
<mml:math id="m39">
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>S</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
</p>
<p>However, in the traditional Euclidean distance method, all variables in the similarity matching model are treated equally and consistently. In fact, the similarity between the corresponding elements should be fully considered. For example, in the machining process, the cutting speed has a greater impact on noise and significantly less on carbon emissions. Therefore, it is more practical to consider the weight based on the significance of each variable.</p>
<p>Assuming that there are q resource environment load indicators corresponding to process conditions M and N, which are represented by <inline-formula id="inf29">
<mml:math id="m40">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1,2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. The weighted Euclidean distance between process conditions M and N can be expressed as follows:<disp-formula id="e10">
<mml:math id="m41">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msqrt>
<mml:mrow>
<mml:mrow>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>p</mml:mi>
</mml:munderover>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>where <inline-formula id="inf30">
<mml:math id="m42">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the weight that <inline-formula id="inf31">
<mml:math id="m43">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> corresponds to the resource environment load indicator <inline-formula id="inf32">
<mml:math id="m44">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf33">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1,2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mi>p</mml:mi>
<mml:mo>;</mml:mo>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1,2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>; <inline-formula id="inf34">
<mml:math id="m46">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the standard deviation of each dimension; <inline-formula id="inf35">
<mml:math id="m47">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the normalized indicator value, which can be expressed as follows:<disp-formula id="e11">
<mml:math id="m48">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>m</mml:mi>
</mml:mrow>
<mml:mi>s</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>where <inline-formula id="inf36">
<mml:math id="m49">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the original data value, <inline-formula id="inf37">
<mml:math id="m50">
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the mean of each dimension, and <inline-formula id="inf38">
<mml:math id="m51">
<mml:mrow>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is its standard deviation.</p>
<p>It can be seen from the <xref ref-type="disp-formula" rid="e10">formula 10</xref> that under the condition of sample determination, the calculation result of the Euclidean distance is proportional to the corresponding weight. However, giving weights to individual variables characterizes the subjectivity of the decision maker to the variables, but the completely subjective Euclidean distance calculation lacks the professionalism and credibility in the field. Therefore, objective weights need to be given to individual variables.</p>
<p>Taking the analysis result as the objective basis for determining the weight of each variable, if the range <inline-formula id="inf39">
<mml:math id="m52">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the value of the <inline-formula id="inf40">
<mml:math id="m53">
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> variable corresponding to the <inline-formula id="inf41">
<mml:math id="m54">
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> resource environment load indictor, the weight that the <inline-formula id="inf42">
<mml:math id="m55">
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> variable corresponding to the <inline-formula id="inf43">
<mml:math id="m56">
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> resource environment load indicator and the similarity between the reference condition and the target condition can be expressed as follows:<disp-formula id="e12">
<mml:math id="m57">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>p</mml:mi>
</mml:munderover>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
<disp-formula id="e13">
<mml:math id="m58">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>
</p>
<p>According to the results of similarity calculation, the data of resource environment load corresponding to the process condition with maximum similarity is used as the evaluation value of the new process condition. With the continuous enrichment and expansion of the process condition library, the accuracy of matching results can be further improved.</p>
</sec>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>3 Results</title>
<sec id="s3-1">
<title>3.1 Resource environment load data collection</title>
<p>Aluminum alloy materials are widely used metal material in the manufacturing industry, and it is of great significance to conduct environmental performance assessment during machining process. Therefore, in order to verify the accuracy and effectiveness of proposed method, an experiment which use VCML850 to mill aluminum alloy Al6061 on a CNC machine tool was conducted.</p>
<p>Due to the equipment is generally selected according to the process type, the resource environment load data is collected considering the process parameters, processing methods and other factors when processing aluminum alloy Al6061. Therefore, according to the systematic principle, quantitative principle, independence principle and operability principle of resource environment load data, noise, dust and carbon emission are selected as the resource environment load data in this case study. During the experimental, milling speed <italic>Vc</italic>, feed speed <italic>f</italic>, milling depth <italic>ap</italic>, milling width <italic>ae</italic>, two types of cutting condition (<italic>CC</italic>), dry cut and wet cut (represented by 1 and 2, respectively), were selected as the process condition elements. The resource environment load data under the different process conditions are shown in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Resource environment load data with different process conditions.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="center">
<italic>V</italic>
<sub>
<italic>c</italic>
</sub> (m/min)</th>
<th align="center">
<italic>f</italic> (mm/r)</th>
<th align="center">
<italic>ap</italic> (mm)</th>
<th align="center">
<italic>ae</italic> (mm)</th>
<th align="center">CC</th>
<th align="center">Noise (dB)</th>
<th align="center">PM (g)</th>
<th align="center">Carbon emission (g)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">M1</td>
<td align="center">90</td>
<td align="center">0.2</td>
<td align="center">0.8</td>
<td align="center">2.5</td>
<td align="center">1</td>
<td align="center">82</td>
<td align="center">108.00</td>
<td align="center">114.23</td>
</tr>
<tr>
<td align="center">M2</td>
<td align="center">165</td>
<td align="center">0.2</td>
<td align="center">1.2</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">82</td>
<td align="center">138.33</td>
<td align="center">49.00</td>
</tr>
<tr>
<td align="center">M3</td>
<td align="center">115</td>
<td align="center">0.28</td>
<td align="center">0.8</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">85</td>
<td align="center">118.00</td>
<td align="center">77.43</td>
</tr>
<tr>
<td align="center">M4</td>
<td align="center">140</td>
<td align="center">0.2</td>
<td align="center">2</td>
<td align="center">3.5</td>
<td align="center">1</td>
<td align="center">86</td>
<td align="center">134.67</td>
<td align="center">51.75</td>
</tr>
<tr>
<td align="center">M5</td>
<td align="center">140</td>
<td align="center">0.24</td>
<td align="center">1.6</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">89</td>
<td align="center">101.33</td>
<td align="center">88.67</td>
</tr>
<tr>
<td align="center">M6</td>
<td align="center">90</td>
<td align="center">0.24</td>
<td align="center">1.2</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="center">84</td>
<td align="center">100.00</td>
<td align="center">66.40</td>
</tr>
<tr>
<td align="center">M7</td>
<td align="center">140</td>
<td align="center">0.28</td>
<td align="center">1.2</td>
<td align="center">2.5</td>
<td align="center">1</td>
<td align="center">85</td>
<td align="center">95.30</td>
<td align="center">79.78</td>
</tr>
<tr>
<td align="center">M8</td>
<td align="center">115</td>
<td align="center">0.32</td>
<td align="center">1.2</td>
<td align="center">3.5</td>
<td align="center">1</td>
<td align="center">86</td>
<td align="center">88.67</td>
<td align="center">62.77</td>
</tr>
<tr>
<td align="center">M9</td>
<td align="center">165</td>
<td align="center">0.24</td>
<td align="center">0.8</td>
<td align="center">3.5</td>
<td align="center">1</td>
<td align="center">84</td>
<td align="center">98.33</td>
<td align="center">70.80</td>
</tr>
<tr>
<td align="center">M10</td>
<td align="center">165</td>
<td align="center">0.32</td>
<td align="center">1.6</td>
<td align="center">2.5</td>
<td align="center">1</td>
<td align="center">87</td>
<td align="center">92.00</td>
<td align="center">104.95</td>
</tr>
<tr>
<td align="center">M11</td>
<td align="center">90</td>
<td align="center">0.28</td>
<td align="center">1.6</td>
<td align="center">3.5</td>
<td align="center">1</td>
<td align="center">85</td>
<td align="center">90.30</td>
<td align="center">154.08</td>
</tr>
<tr>
<td align="center">M12</td>
<td align="center">140</td>
<td align="center">0.32</td>
<td align="center">0.8</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="center">96</td>
<td align="center">98.00</td>
<td align="center">55.80</td>
</tr>
<tr>
<td align="center">M13</td>
<td align="center">115</td>
<td align="center">0.2</td>
<td align="center">1.6</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="center">84</td>
<td align="center">88.33</td>
<td align="center">62.95</td>
</tr>
<tr>
<td align="center">M14</td>
<td align="center">90</td>
<td align="center">0.32</td>
<td align="center">2</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">90</td>
<td align="center">78.00</td>
<td align="center">76.01</td>
</tr>
<tr>
<td align="center">M15</td>
<td align="center">115</td>
<td align="center">0.24</td>
<td align="center">2</td>
<td align="center">2.5</td>
<td align="center">1</td>
<td align="center">88</td>
<td align="center">86.00</td>
<td align="center">64.96</td>
</tr>
<tr>
<td align="center">M16</td>
<td align="center">165</td>
<td align="center">0.28</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="center">89</td>
<td align="center">112.33</td>
<td align="center">37.21</td>
</tr>
<tr>
<td align="center">M17</td>
<td align="center">90</td>
<td align="center">0.2</td>
<td align="center">0.8</td>
<td align="center">2.5</td>
<td align="center">2</td>
<td align="center">94</td>
<td align="center">90.67</td>
<td align="center">230.08</td>
</tr>
<tr>
<td align="center">M18</td>
<td align="center">165</td>
<td align="center">0.2</td>
<td align="center">1.2</td>
<td align="center">4</td>
<td align="center">2</td>
<td align="center">106</td>
<td align="center">101.00</td>
<td align="center">100.49</td>
</tr>
<tr>
<td align="center">M19</td>
<td align="center">115</td>
<td align="center">0.28</td>
<td align="center">0.8</td>
<td align="center">4</td>
<td align="center">2</td>
<td align="center">90</td>
<td align="center">90.33</td>
<td align="center">173.11</td>
</tr>
<tr>
<td align="center">M20</td>
<td align="center">140</td>
<td align="center">0.2</td>
<td align="center">2</td>
<td align="center">3.5</td>
<td align="center">2</td>
<td align="center">104</td>
<td align="center">88.67</td>
<td align="center">181.81</td>
</tr>
<tr>
<td align="center">M21</td>
<td align="center">140</td>
<td align="center">0.24</td>
<td align="center">1.6</td>
<td align="center">4</td>
<td align="center">2</td>
<td align="center">102</td>
<td align="center">84.67</td>
<td align="center">101.20</td>
</tr>
<tr>
<td align="center">M22</td>
<td align="center">90</td>
<td align="center">0.24</td>
<td align="center">1.2</td>
<td align="center">3</td>
<td align="center">2</td>
<td align="center">88</td>
<td align="center">79.00</td>
<td align="center">185.53</td>
</tr>
<tr>
<td align="center">M23</td>
<td align="center">140</td>
<td align="center">0.28</td>
<td align="center">1.2</td>
<td align="center">2.5</td>
<td align="center">2</td>
<td align="center">101</td>
<td align="center">85.67</td>
<td align="center">240.80</td>
</tr>
<tr>
<td align="center">M24</td>
<td align="center">115</td>
<td align="center">0.32</td>
<td align="center">1.2</td>
<td align="center">3.5</td>
<td align="center">2</td>
<td align="center">100</td>
<td align="center">88.00</td>
<td align="center">161.91</td>
</tr>
<tr>
<td align="center">M25</td>
<td align="center">165</td>
<td align="center">0.24</td>
<td align="center">0.8</td>
<td align="center">3.5</td>
<td align="center">2</td>
<td align="center">97</td>
<td align="center">98.00</td>
<td align="center">157.98</td>
</tr>
<tr>
<td align="center">M26</td>
<td align="center">165</td>
<td align="center">0.32</td>
<td align="center">1.6</td>
<td align="center">2.5</td>
<td align="center">2</td>
<td align="center">106</td>
<td align="center">85.67</td>
<td align="center">185.94</td>
</tr>
<tr>
<td align="center">M27</td>
<td align="center">90</td>
<td align="center">0.28</td>
<td align="center">1.6</td>
<td align="center">3.5</td>
<td align="center">2</td>
<td align="center">89</td>
<td align="center">89.33</td>
<td align="center">165.25</td>
</tr>
<tr>
<td align="center">M28</td>
<td align="center">140</td>
<td align="center">0.32</td>
<td align="center">0.8</td>
<td align="center">3</td>
<td align="center">2</td>
<td align="center">92</td>
<td align="center">99.00</td>
<td align="center">154.69</td>
</tr>
<tr>
<td align="center">M29</td>
<td align="center">115</td>
<td align="center">0.2</td>
<td align="center">1.6</td>
<td align="center">3</td>
<td align="center">2</td>
<td align="center">88</td>
<td align="center">85.67</td>
<td align="center">282.19</td>
</tr>
<tr>
<td align="center">M30</td>
<td align="center">90</td>
<td align="center">0.32</td>
<td align="center">2</td>
<td align="center">4</td>
<td align="center">2</td>
<td align="center">101</td>
<td align="center">83.33</td>
<td align="center">157.50</td>
</tr>
<tr>
<td align="center">M31</td>
<td align="center">115</td>
<td align="center">0.24</td>
<td align="center">2</td>
<td align="center">2.5</td>
<td align="center">2</td>
<td align="center">94</td>
<td align="center">93.67</td>
<td align="center">138.67</td>
</tr>
<tr>
<td align="center">M32</td>
<td align="center">165</td>
<td align="center">0.28</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="center">2</td>
<td align="center">105</td>
<td align="center">106.67</td>
<td align="center">165.51</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Further, the resource environment load database interface is shown in <xref ref-type="fig" rid="F5">Figure 5</xref>. The data can be stored in the database after transmitting to the data processing analysis system. The role of the database is mainly to realize the management of the basic data of the resource environment load by using a graphical user interface, which can be more intuitive to manage the data. When it is necessary to evaluate the resource environment load of the actual process condition or optimize the process condition, the database can provide a reference base data inventory.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Resource environment load database interface.</p>
</caption>
<graphic xlink:href="fmats-10-1129850-g005.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Resource environment load prediction results</title>
<sec id="s3-2-1">
<title>3.2.1 Significance analysis results</title>
<p>According to the framework in <xref ref-type="sec" rid="s2-2">Section 2.2</xref>, it is first necessary to analyze the significance of the elements on the resource environment load in the process condition. Milling Al6061 process condition data is analyzed for significance and extreme range analysis, and the results are collated as shown in <xref ref-type="table" rid="T3">Table 3</xref>. Through the analysis of the range value, it can be seen that the influence of process condition elements on the carbon emission is shown as follows: <italic>CC</italic> &#x3e; <italic>ae</italic> &#x3e; <italic>Vc</italic> &#x3e; <italic>ap</italic> &#x3e; <italic>f</italic> for carbon emission; For noise, <italic>CC</italic> &#x3e; <italic>Vc</italic> &#x3e; <italic>ap</italic> &#x3e; <italic>f</italic> &#x3e; <italic>ae</italic>; With regard to PM, <italic>Vc</italic> &#x3e; <italic>f</italic> &#x3e; <italic>CC</italic> &#x3e; <italic>ap</italic> &#x3e; <italic>ae</italic>. Therefore, the reasonable process condition must be taken seriously to reduce the resource environment load.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>The range analysis results of resource environment load corresponding to Al6061 process condition.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Resource environment load</th>
<th align="center">
<inline-formula id="inf44">
<mml:math id="m59">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">
<inline-formula id="inf45">
<mml:math id="m60">
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">
<inline-formula id="inf46">
<mml:math id="m61">
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">
<inline-formula id="inf47">
<mml:math id="m62">
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">CC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Carbon Emission (g)</td>
<td align="center">34.6</td>
<td align="center">27.4</td>
<td align="center">34</td>
<td align="center">42</td>
<td align="center">97</td>
</tr>
<tr>
<td align="center">Noise (dB)</td>
<td align="center">5.4</td>
<td align="center">4</td>
<td align="center">4.6</td>
<td align="center">2.4</td>
<td align="center">10.9</td>
</tr>
<tr>
<td align="center">PM (g)</td>
<td align="center">14.2</td>
<td align="center">11.9</td>
<td align="center">10.4</td>
<td align="center">3.2</td>
<td align="center">11.1</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>According to the <xref ref-type="disp-formula" rid="e12">formula 12</xref>, the significance of variable <inline-formula id="inf48">
<mml:math id="m63">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> of each dimension on each resource environment load can be calculated. The weight of variable <inline-formula id="inf49">
<mml:math id="m64">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> corresponds to the resource environment load <inline-formula id="inf50">
<mml:math id="m65">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is <inline-formula id="inf51">
<mml:math id="m66">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and the weight set of each factor corresponding to the process condition is shown in <xref ref-type="fig" rid="F6">Figure 6</xref>. For carbon emission, the maximum weight is given to <italic>CC</italic> with 41%, and the minimum weight of milling width is 12%; For noise, the <italic>CC</italic> has the greatest impact on it, with a weight of 40%, while the milling speed has the lowest impact, with a weight of 9%. As for PM, feed speed has the highest impact, accounting for 28%, while spindle speed has the lowest impact, with a weight of 6%.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>The weight set of process condition factors for Al6061.</p>
</caption>
<graphic xlink:href="fmats-10-1129850-g006.tif"/>
</fig>
</sec>
<sec id="s3-2-2">
<title>3.2.2 Process condition similarity calculation results</title>
<p>Process condition similarity calculation is the premise and core of resource environment load prediction. Before calculating similarity, it is necessary to determine the raw data of the reference condition, and standardize the raw data according to the <xref ref-type="disp-formula" rid="e11">formula 11</xref>. Taking the reference condition sample M1 shown in <xref ref-type="table" rid="T2">Table 2</xref> as an example, the information can be expressed as M1 &#x3d; (90, 0.2, 0.8, 2.5, 1).</p>
<p>With Al6061 as the processing material, the set of process condition N1 &#x3d; (130, 0.26, 1.4, 3.25, 1), were selected as object process condition. The resource environment data under different process conditions stored in database are selected. Then, the weighted Euclidean distance results are used to represent the similarity between the object process condition to be predicted and the reference process conditions. The matching result is shown in <xref ref-type="table" rid="T4">Table 4</xref>. According to the matching results, the reference process conditions with the greatest similarity to the condition N1 is M6 when predicting the carbon emission. The reference process conditions with the greatest similarity for noise and PM are both M5.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>The matching results corresponding to N1.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Reference condition</th>
<th colspan="2" align="center">Carbon emission</th>
<th colspan="2" align="center">Noise</th>
<th colspan="2" align="center">PM</th>
</tr>
<tr>
<th align="center">
<inline-formula id="inf52">
<mml:math id="m67">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
<th align="center">
<inline-formula id="inf53">
<mml:math id="m68">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
<th align="center">
<inline-formula id="inf54">
<mml:math id="m69">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">M1- N1</td>
<td align="center">0.381</td>
<td align="center">0.619</td>
<td align="center">0.396</td>
<td align="center">0.604</td>
<td align="center">0.453</td>
<td align="center">0.547</td>
</tr>
<tr>
<td align="center">M2- N1</td>
<td align="center">0.323</td>
<td align="center">0.677</td>
<td align="center">0.326</td>
<td align="center">0.674</td>
<td align="center">0.375</td>
<td align="center">0.625</td>
</tr>
<tr>
<td align="center">M3- N1</td>
<td align="center">0.303</td>
<td align="center">0.697</td>
<td align="center">0.276</td>
<td align="center">0.724</td>
<td align="center">0.291</td>
<td align="center">0.709</td>
</tr>
<tr>
<td align="center">M4- N1</td>
<td align="center">0.274</td>
<td align="center">0.726</td>
<td align="center">0.291</td>
<td align="center">0.709</td>
<td align="center">0.341</td>
<td align="center">0.659</td>
</tr>
<tr>
<td align="center">M5- N1</td>
<td align="center">0.237</td>
<td align="center">0.763</td>
<td align="center">0.185</td>
<td align="center">0.815</td>
<td align="center">0.181</td>
<td align="center">0.819</td>
</tr>
<tr>
<td align="center">M6- N1</td>
<td align="center">0.208</td>
<td align="center">0.792</td>
<td align="center">0.260</td>
<td align="center">0.740</td>
<td align="center">0.306</td>
<td align="center">0.694</td>
</tr>
<tr>
<td align="center">M7- N1</td>
<td align="center">0.237</td>
<td align="center">0.763</td>
<td align="center">0.187</td>
<td align="center">0.813</td>
<td align="center">0.182</td>
<td align="center">0.818</td>
</tr>
<tr>
<td align="center">M8- N1</td>
<td align="center">0.210</td>
<td align="center">0.790</td>
<td align="center">0.227</td>
<td align="center">0.773</td>
<td align="center">0.278</td>
<td align="center">0.722</td>
</tr>
<tr>
<td align="center">M9- N1</td>
<td align="center">0.264</td>
<td align="center">0.736</td>
<td align="center">0.303</td>
<td align="center">0.697</td>
<td align="center">0.347</td>
<td align="center">0.653</td>
</tr>
<tr>
<td align="center">M10- N1</td>
<td align="center">0.323</td>
<td align="center">0.677</td>
<td align="center">0.326</td>
<td align="center">0.674</td>
<td align="center">0.375</td>
<td align="center">0.625</td>
</tr>
<tr>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
</tr>
<tr>
<td align="center">M31- N1</td>
<td align="center">0.725</td>
<td align="center">0.275</td>
<td align="center">0.690</td>
<td align="center">0.311</td>
<td align="center">0.551</td>
<td align="center">0.449</td>
</tr>
<tr>
<td align="center">M32- N1</td>
<td align="center">0.710</td>
<td align="center">0.290</td>
<td align="center">0.701</td>
<td align="center">0.299</td>
<td align="center">0.582</td>
<td align="center">0.418</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In order to demonstrate the accuracy of the proposed prediction method, the prediction values of each indicator are compared to the experimental values as shown in <xref ref-type="table" rid="T5">Table 5</xref>. The prediction accuracy of carbon emissions, noise, and PM for N1 are 92.5%, 91.5%, and 88.1% respectively. Besides, the Ecoinvent database was taken as reference to estimate the resource environmental data for N1. The result showed that the carbon emission is 46.3&#xa0;g. Accordingly, the accuracy of the proposed method for predicting the carbon emission is more than the one of Ecoinvent database. However, Ecoinvent database lacks the noise and PM data which results in that these two types of resource environment load cannot be predicted. Therefore, the proposed prediction method has the higher accuracy for predicting the resource environment load and more types can be analyzed, comparing to the Ecoinvent database.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Prediction accuracy for N1.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="center">Prediction value</th>
<th align="center">Experimental value</th>
<th align="center">Matched condition</th>
<th align="center">Accuracy (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Carbon Emission (g)</td>
<td align="center">66.4</td>
<td align="center">71.8</td>
<td align="center">M6</td>
<td align="left">92.5</td>
</tr>
<tr>
<td align="center">Noise (dB)</td>
<td align="center">89</td>
<td align="center">82</td>
<td align="center">M5</td>
<td align="left">91.5</td>
</tr>
<tr>
<td align="center">PM (g)</td>
<td align="center">101.3</td>
<td align="center">115</td>
<td align="center">M5</td>
<td align="left">88.1</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>4 Discussion</title>
<sec id="s4-1">
<title>4.1 Robust of the prediction method</title>
<p>In order to prove the robust of the proposed prediction method, another two sets of process conditions N2 &#x3d; (150, 0.3, 1.8, 3.75, 1), and N3 &#x3d; (130, 0.26, 1.4, 3.25, 2) were selected as object process conditions to test the effectiveness of the method. The weighted Euclidean distance results are used to represent the similarity between three process conditions to be predicted and the reference process conditions. The calculation results are shown in <xref ref-type="table" rid="T6">Tables 6</xref>, <xref ref-type="table" rid="T7">7</xref>.</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>The matching results corresponding to N2.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Reference condition</th>
<th colspan="2" align="center">Carbon emission</th>
<th colspan="2" align="center">Noise</th>
<th colspan="2" align="center">PM</th>
</tr>
<tr>
<th align="center">
<inline-formula id="inf55">
<mml:math id="m70">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
<th align="center">
<inline-formula id="inf56">
<mml:math id="m71">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
<th align="center">
<inline-formula id="inf57">
<mml:math id="m72">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">M1- N2</td>
<td align="center">0.622</td>
<td align="center">0.378</td>
<td align="center">0.638</td>
<td align="center">0.363</td>
<td align="center">0.726</td>
<td align="center">0.274</td>
</tr>
<tr>
<td align="center">M2- N2</td>
<td align="center">0.363</td>
<td align="center">0.638</td>
<td align="center">0.393</td>
<td align="center">0.607</td>
<td align="center">0.476</td>
<td align="center">0.524</td>
</tr>
<tr>
<td align="center">M3- N2</td>
<td align="center">0.370</td>
<td align="center">0.630</td>
<td align="center">0.408</td>
<td align="center">0.592</td>
<td align="center">0.460</td>
<td align="center">0.540</td>
</tr>
<tr>
<td align="center">M4- N2</td>
<td align="center">0.309</td>
<td align="center">0.691</td>
<td align="center">0.335</td>
<td align="center">0.665</td>
<td align="center">0.419</td>
<td align="center">0.582</td>
</tr>
<tr>
<td align="center">M5- N2</td>
<td align="center">0.204</td>
<td align="center">0.796</td>
<td align="center">0.217</td>
<td align="center">0.783</td>
<td align="center">0.266</td>
<td align="center">0.734</td>
</tr>
<tr>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
</tr>
<tr>
<td align="center">M16- N2</td>
<td align="center">0.242</td>
<td align="center">0.758</td>
<td align="center">0.197</td>
<td align="center">0.803</td>
<td align="center">0.198</td>
<td align="center">0.802</td>
</tr>
<tr>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
</tr>
<tr>
<td align="center">M31- N2</td>
<td align="center">0.788</td>
<td align="center">0.212</td>
<td align="center">0.738</td>
<td align="center">0.262</td>
<td align="center">0.622</td>
<td align="center">0.378</td>
</tr>
<tr>
<td align="center">M32- N2</td>
<td align="center">0.702</td>
<td align="center">0.298</td>
<td align="center">0.662</td>
<td align="center">0.338</td>
<td align="center">0.508</td>
<td align="center">0.492</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>The matching results corresponding to N3.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Reference condition</th>
<th colspan="2" align="center">Carbon emission</th>
<th colspan="2" align="center">Noise</th>
<th colspan="2" align="center">PM</th>
</tr>
<tr>
<th align="center">
<inline-formula id="inf58">
<mml:math id="m73">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
<th align="center">
<inline-formula id="inf59">
<mml:math id="m74">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
<th align="center">
<inline-formula id="inf60">
<mml:math id="m75">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Similarity</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">M1- N3</td>
<td align="center">0.761</td>
<td align="center">0.239</td>
<td align="center">0.746</td>
<td align="center">0.254</td>
<td align="center">0.651</td>
<td align="center">0.349</td>
</tr>
<tr>
<td align="center">M2- N3</td>
<td align="center">0.734</td>
<td align="center">0.266</td>
<td align="center">0.711</td>
<td align="center">0.289</td>
<td align="center">0.600</td>
<td align="center">0.401</td>
</tr>
<tr>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
</tr>
<tr>
<td align="center">M20- N3</td>
<td align="center">0.274</td>
<td align="center">0.726</td>
<td align="center">0.291</td>
<td align="center">0.709</td>
<td align="center">0.341</td>
<td align="center">0.659</td>
</tr>
<tr>
<td align="center">M21- N3</td>
<td align="center">0.237</td>
<td align="center">0.763</td>
<td align="center">0.185</td>
<td align="center">0.815</td>
<td align="center">0.181</td>
<td align="center">0.819</td>
</tr>
<tr>
<td align="center">M22- N3</td>
<td align="center">0.208</td>
<td align="center">0.792</td>
<td align="center">0.260</td>
<td align="center">0.740</td>
<td align="center">0.306</td>
<td align="center">0.694</td>
</tr>
<tr>
<td align="center">M23- N3</td>
<td align="center">0.237</td>
<td align="center">0.763</td>
<td align="center">0.185</td>
<td align="center">0.815</td>
<td align="center">0.183</td>
<td align="center">0.817</td>
</tr>
<tr>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
<td align="center">&#x2026;</td>
</tr>
<tr>
<td align="center">M31- N3</td>
<td align="center">0.303</td>
<td align="center">0.697</td>
<td align="center">0.276</td>
<td align="center">0.724</td>
<td align="center">0.291</td>
<td align="center">0.709</td>
</tr>
<tr>
<td align="center">M32- N3</td>
<td align="center">0.264</td>
<td align="center">0.736</td>
<td align="center">0.303</td>
<td align="center">0.697</td>
<td align="center">0.347</td>
<td align="center">0.653</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>According to the matching results in <xref ref-type="table" rid="T6">Tables 6</xref>, <xref ref-type="table" rid="T7">7</xref>, the reference process conditions with the greatest similarity to the conditions N2 and N3 are M5 and M22, respectively when predicting the carbon emission. When predicting noise, the reference process conditions with the greatest similarity with the conditions N2 and N3 are M16 and M21 respectively. When predicting PM, the reference process conditions with the greatest similarity with the conditions N2 and N3 are M16 and M21, respectively. The similarity matching results of the process conditions to be predicted, along with predicted and experimental values of their resource environment loads are shown in <xref ref-type="table" rid="T8">Table 8</xref>.</p>
<table-wrap id="T8" position="float">
<label>TABLE 8</label>
<caption>
<p>The resource environment load evaluation results for N2 and N3.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Process condition</th>
<th colspan="3" align="center">N2</th>
<th colspan="3" align="center">N3</th>
</tr>
<tr>
<th align="center">Prediction value</th>
<th align="center">Experimental values</th>
<th align="center">Matched condition</th>
<th align="center">Prediction value</th>
<th align="center">Experimental values</th>
<th align="center">Matched condition</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Carbon Emission (g)</td>
<td align="center">88.7</td>
<td align="center">83.7</td>
<td align="center">M5</td>
<td align="center">185.5</td>
<td align="center">172.7</td>
<td align="center">M22</td>
</tr>
<tr>
<td align="center">Noise (dB)</td>
<td align="center">89</td>
<td align="center">82</td>
<td align="center">M16</td>
<td align="center">102</td>
<td align="center">94</td>
<td align="center">M21</td>
</tr>
<tr>
<td align="center">PM (g)</td>
<td align="center">112.3</td>
<td align="center">106</td>
<td align="center">M16</td>
<td align="center">84.7</td>
<td align="center">76.3</td>
<td align="center">M21</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>After experimental verification, <xref ref-type="table" rid="T9">Table 9</xref> shows the accuracy verification results of the prediction method. The average prediction accuracy of carbon emissions, noise, and PM was 93%, 91.5%, and 90.4% respectively, all exceeding 90%. It can be seen that the proposed prediction method is efficient and robust for predicting the resource environmental data of different process condition.</p>
<table-wrap id="T9" position="float">
<label>TABLE 9</label>
<caption>
<p>The accuracy verification results of prediction method.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Process conditions</th>
<th align="center">N1</th>
<th align="center">N2</th>
<th align="center">N3</th>
<th rowspan="2" align="center">Average accuracy (%)</th>
</tr>
<tr>
<th align="center">Accuracy (%)</th>
<th align="center">Accuracy (%)</th>
<th align="center">Accuracy (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Carbon Emission</td>
<td align="center">92.5</td>
<td align="center">94.1</td>
<td align="center">92.6</td>
<td align="center">93.0</td>
</tr>
<tr>
<td align="center">Noise</td>
<td align="center">91.5</td>
<td align="center">91.5</td>
<td align="center">91.5</td>
<td align="center">91.5</td>
</tr>
<tr>
<td align="center">PM</td>
<td align="center">88.1</td>
<td align="center">94.0</td>
<td align="center">89.0</td>
<td align="center">90.4</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4-2">
<title>4.2 Environmental impact analysis with the predicted resource environmental data</title>
<p>According to the existing resource environment load data obtained for the new process conditions, the environmental performances of the new process conditions are assessed by using the LCA methodology, which is a widely used method of conducting environmental impact assessments of products or processes standardized in ISO14040 and ISO14044 (<xref ref-type="bibr" rid="B10">International Organization for Standardization, 2006</xref>; <xref ref-type="bibr" rid="B15">La Rosa et al., 2018</xref>). Accordingly, the environmental performances are evaluated by prediction data and experimental data, and the normalized results of six environmental impact categories are shown in <xref ref-type="table" rid="T10">Table 10</xref>.</p>
<table-wrap id="T10" position="float">
<label>TABLE 10</label>
<caption>
<p>Environmental performances of N1,N2,N3.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Category</th>
<th colspan="2" align="center">
<italic>N1</italic>
</th>
<th colspan="2" align="center">
<italic>N2</italic>
</th>
<th colspan="2" align="center">
<italic>N3</italic>
</th>
</tr>
<tr>
<th align="center">Result using predict data</th>
<th align="center">Result using actual data</th>
<th align="center">Result using predict data</th>
<th align="center">Result using actual data</th>
<th align="center">Result using predict data</th>
<th align="center">Result using actual data</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">ADP fossil</td>
<td align="center">1.73 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">1.63 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">3.40 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">3.12 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">5.73 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">5.11 &#xd7; 10<sup>&#x2212;13</sup>
</td>
</tr>
<tr>
<td align="center">AP</td>
<td align="center">1.41 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">1.33 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">2.48 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">2.33 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">4.04 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">3.76 &#xd7; 10<sup>&#x2212;13</sup>
</td>
</tr>
<tr>
<td align="center">FAETP</td>
<td align="center">2.53 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">2.38 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">4.43 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">4.15 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">7.23 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">6.74 &#xd7; 10<sup>&#x2212;14</sup>
</td>
</tr>
<tr>
<td align="center">GW</td>
<td align="center">1.66 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">1.57 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">3.02 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">2.81 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">4.96 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">4.56 &#xd7; 10<sup>&#x2212;13</sup>
</td>
</tr>
<tr>
<td align="center">HTP</td>
<td align="center">1.70 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">1.60 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">2.88 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">2.71 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">4.62 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">4.38 &#xd7; 10<sup>&#x2212;12</sup>
</td>
</tr>
<tr>
<td align="center">TETP</td>
<td align="center">4.44 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">4.17 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">7.56 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">7.12 &#xd7; 10<sup>&#x2212;14</sup>
</td>
<td align="center">1.22 &#xd7; 10<sup>&#x2212;13</sup>
</td>
<td align="center">1.15 &#xd7; 10<sup>&#x2212;13</sup>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>&#x2a;ADP, Fossil: Abiotic Depletion; AP, acidification potential; FAETP, freshwater aquatic ecotoxicity pot; GW, global warming potential; HTP, human toxicity potential; TETP, terrestric ecotoxicity potential.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>
<xref ref-type="table" rid="T11">Table 11</xref> illustrates the results of total environment performance assessment using resource environment load predict data and actual data respectively for process conditions N1, N2 and N3. It could be seen that the total environmental impact assessment result using the prediction value is close to the assessment result using the actual value. The accuracy of the total environmental impact assessment results using the prediction values for the three scenarios N1, N2 and N3 are 93.81%, 93.39% and 93.53% respectively. The results show that the method has a high accuracy and the data which predicted by similarity matching can be used to conduct environmental impact assessment.</p>
<table-wrap id="T11" position="float">
<label>TABLE 11</label>
<caption>
<p>The accuracy of total environmental impact using resource environment loading prediction data and actual data.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Process condition</th>
<th align="center">The total environmental performances using prediction values</th>
<th align="center">The total environmental performances using actual values</th>
<th align="center">Accuracy (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">N1</td>
<td align="center">2.25 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">2.12 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">93.81</td>
</tr>
<tr>
<td align="center">N2</td>
<td align="center">3.89 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">3.65 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">93.39</td>
</tr>
<tr>
<td align="center">N3</td>
<td align="center">6.29 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">5.91 &#xd7; 10<sup>&#x2212;12</sup>
</td>
<td align="center">93.53</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Based on the data in <xref ref-type="table" rid="T10">Table 10</xref> and <xref ref-type="fig" rid="F7">Figure 7</xref> shows the comparison of the percentage of various environment impact categories. Taking the process condition N1 as an example, it is seen that the evaluated percentage for each environment impact category is almost equal to the actual one, as shown in the <xref ref-type="fig" rid="F7">Figures 7A, 7D</xref>. The maximum environment impact category under process condition N1 is HTP, which accounts for about 75.6% of the total environmental impact. About 7.7% of the total environmental impact is consumed by the ADP fossil, which is the secondary maximum impact category. The impact of the GW and AP cannot be ignored due to environment performance of about 7.4% and 6.3% respectively, while the environment performance for the FAETP is the lowest. The process condition N2, N3 can be analyzed in the same way.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Comparison of assessment results for various environment impact categories using the prediction and actual values under different process conditions. <bold>(A)</bold>, <bold>(B)</bold> and <bold>(C)</bold> represent the environmental performances results of N1, N2 and N3 using the prediction data, respectively <bold>(D)</bold>, <bold>(E)</bold>, <bold>(F)</bold> represent the environmental performances results of N1, N2 and N3 using the actual data, respectively.</p>
</caption>
<graphic xlink:href="fmats-10-1129850-g007.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F8">Figure 8</xref> shows sensitivity analysis of environment impact categories under different process conditions using the data in <xref ref-type="table" rid="T10">Table 10</xref>. It can be drawn that the change proportion of environmental impact category under different process conditions presents the similar results. As can be seen from <xref ref-type="fig" rid="F8">Figure 8A</xref>, the maximal variation indicates that the ADP Fossil is most sensitive to the change of conditions from N1 to N2. Moreover, the same conclusion is obtained corresponding to the change of conditions from N2 to N3. However, the influence of the change of conditions from N3 to N1 on several environment impact categories are similar. These analyses can provide guidance for adjusting process conditions to improve certain environment performance.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Sensitivity analysis of environment impact categories under different process conditions: <bold>(A)</bold>. Change of environment impact category of process condition N2 relative to N1. <bold>(B)</bold>. Change of environment impact category of process condition N3 relative to N1. <bold>(C)</bold>. Change of environment impact category of process condition N2 relative to N3.</p>
</caption>
<graphic xlink:href="fmats-10-1129850-g008.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="conclusion" id="s5">
<title>5 Conclusion</title>
<p>Resource environment load data are very important for predicting environmental performances of the metal machining process. In this paper, a method based on process condition is proposed to predict the resource environment load data. In the proposed method, the process condition is introduced to comprehensively describe the process type, materials, processing mode, equipment, process parameters and other information of the metal machining process. A resource environment load database based on process condition is developed to store the collected data. After that, a process condition-oriented resource environment load prediction method is proposed, which uses the weighted Euclidean distance method for evaluating the resource environment load data. The results shows that the proposed method is effectively applied to predict the resource environment load under changeable process condition, providing basic data for analyzing and optimizing process condition. In addition, for the evaluated results of environmental performances of the metal material machining process, the accuracy for predicting total environmental performances using the predicted data is more than 93%. Considering the three different process conditions, it can be seen that the largest total environmental performances using the prediction values is under the N3 which agrees with the experimental values. The method is efficient and practical to evaluate the environment performances of different process conditions to help process designers make robust decisions in choosing a better process condition for machining the metal materials. Further, the future work may focus on the influence of quantities of the data sets on the prediction results and the comparison with different data-driven methods.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s7">
<title>Author contributions</title>
<p>Writing&#x2014;original draft, ZX and HD; Writing&#x2014;review and editing, YL and HD; methodology and investigation, JX, ZX, and JZ; conceptualization, project administration, supervision, ZX and YL All authors have read and agreed to the published version of the manuscript.</p>
</sec>
<sec id="s8">
<title>Funding</title>
<p>This research is supported by the Science Fund for Distinguished Young Scholars of Chongqing (Grant No. cstc2020jcyj-jqX0011).</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>HD was employed by Shanghai Aerospace Equipments Manufacturer Co., Ltd.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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