Soybean roasting is a crucial stage in the production of soy-based foods and biofuels. This complex thermochemical process allows for the deep modification of the physical, chemical, and organoleptic properties of soybeans, thus improving their flavor, texture, color, and digestibility (Saravacos and Kostaropoulos, 2002; Mujumdar, 2006; Toledo et al., 2007). However, potential failures in these soybean thermal processing operations can have devastating consequences in terms of finished product quality, energy efficiency, and operator safety. As Grau et al. (2014) rightly point out, “breakdowns in roasting equipment lead to high maintenance costs and can seriously compromise product quality and worker safety”.

Early and accurate diagnosis of failures in soybean roasters is therefore crucial to ensure the reliability, durability, and optimal performance of these complex industrial installations. According to Roos and Drusch (2015), “real-time monitoring of critical roasting process parameters is essential to quickly detect any operational deviations and effectively prevent failures”. However, conventional methods of monitoring and preventive maintenance are rapidly reaching their limits in the face of the growing complexity of these transformation processes (Fellows, 2022; Singh and Heldman, 2001; Valentas et al., 1997; Brennan and Grandison, 2012; Geankoplis, 2003; Ray, 2023). Innovative new approaches are therefore needed to meet these industrial challenges.

The method proposed in this work uses particle swarm optimization (PSO) as the main optimization algorithm. Kennedy and Eberhart (1995) introduced particle swarm optimization, an optimization technique inspired by the social behavior of birds and fish. Poli et al. (2007) published a paper detailing the theoretical principles and mathematical foundations of particle swarm optimization.

Shi and Eberhart (1998) proposed a modified version of the original PSO algorithm, which has shown better performance in certain applications. Clerc (2010) wrote a comprehensive book on particle swarm optimization, describing in detail the different variants of the algorithm and their advantages and limitations.

The use of particle swarm optimization in this method allows for the efficient solution of nonlinear, non-smooth, and non-convex optimization problems, as demonstrated by the work of Niknam (2012) on economic dispatch optimization. Niknam and Amiri (2010) also successfully used a hybrid approach based on PSO, ACO, and k-means for cluster analysis.

Furthermore, the theoretical foundations of swarm intelligence are described in the work of Engelbrecht (2005). This understanding of the mechanisms of particle swarm optimization enables the improvement of its implementation and performance for the applications targeted in this work.

Brennan and Grandison (2012) have published a reference work on food processing, providing in-depth knowledge on food processes. Fellows (2022) wrote a book on food processing technologies, including principles and practices. Geankoplis (2003) published a manual on unit operations and separation processes in transport, providing useful knowledge for process optimization. Grau et al. (2014) studied predictive maintenance strategies for industrial applications, providing relevant information for improving process performance.

Mujumdar (2006) edited a compendium on industrial drying, Ray (2023) described the principles of food processing in a recent work, and Roos and Drusch (2015) published a book on phase transitions in foods, all providing specialized knowledge in the key areas of this method. Sandeep (2011) edited a work on thermal food processing, its control, and automation, Saravacos and Kostaropoulos (2002) wrote a manual on food processing equipment, and Singh and Heldman (2001) published an introduction to food engineering, offering complementary insight on food processes.

Finally, Toledo et al. (2007) dealt with thermal food processing, its control, and automation, while Valentas et al. (1997) edited a manual on food engineering practices, providing in-depth expertise on the optimization of food processes.

Soybean roasting is a key step in the transformation of soybean seeds into food products such as tofu, soy milk, or soy sauce. This process involves several successive steps aimed at modifying the physical and chemical properties of the soybean seeds.

As described by Roos and Drusch (2015), soybeans initially contain a high moisture content, generally between 10% and 15%. The first step of the process is therefore a preliminary drying process aimed at reducing this moisture content to around 5%–7%, as highlighted by Singh and Heldman (2001) in their introduction to food engineering. Table 1 presents the typical parameters for drying soybean seeds.

Next, the soybean seeds are subjected to a roasting process, as described by Mujumdar (2006) in his reference work on industrial drying. This step involves heating the seeds to temperatures between 150°C and 200°C for a duration of 10–30 min, thus causing complex chemical reactions. Saravacos and Kostaropoulos (2002) explain that these reactions lead to modifications of the protein, lipid, and carbohydrate compounds present in the soybeans. Figure 1 illustrates the schematic diagram of the soybean roasting process.

As reported by Fellows (2022) and Valentas et al. (1997), roasting helps inactivate antinutritional factors such as protease inhibitors, improve protein digestibility, and develop the characteristic flavor of roasted soybean. Geankoplis (2003) also emphasizes that the physicochemical transformations induced improve the texture and water-holding capacity of the roasted seeds.

After this roasting step, the soybean seeds generally undergo a controlled cooling process, as described by Brennan and Grandison (2012) in their book on food processing. This cooling helps stabilize the properties of the finished product and prepares the seeds for further processing steps, such as grinding or extraction of the components of interest.

Several parameters of the soybean roasting process have a significant impact on the physical, chemical, and organoleptic properties of the final product. As emphasized by Fellows (2022), the control of these parameters is essential to obtain high-quality, consistent products that meet consumer expectations.

The roasting temperature is one of the most critical parameters. According to Mujumdar (2006), excessively high temperatures can lead to excessive degradation of the compounds of interest and the development of undesirable flavors, while too low temperatures do not allow the desired transformations to be achieved. Saravacos and Kostaropoulos (2002) thus recommend temperatures between 150°C and 200°C to obtain an optimal balance between changes in texture, color, and flavor.

Another important parameter is the roasting duration. As explained by Brennan and Grandison (2012), a treatment time that is too short does not allow the complete realization of the chemical reactions, while a time that is too long can lead to excessive degradation of the compounds. According to these authors, durations of 10–30 min seem to offer the best compromise to develop the characteristic flavor while preserving the nutritional qualities of the soybean, as shown in Table 2.

The initial moisture content of the soybean seeds also plays an essential role, as highlighted by Singh and Heldman (2001). A too high moisture content slows down heat and mass transfers, while a too low content can lead to excessive drying and loss of quality. These authors thus recommend a residual moisture content between 5% and 7% at the end of the preliminary drying step.

Finally, the control of the post-roasting cooling conditions, particularly the cooling rate, is also a key parameter for preserving the organoleptic and functional qualities of the product, as described by Roos and Drusch (2015).

By controlling these various process parameters, it is possible to optimize the quality of the roasted soybean and obtain a product that meets the requirements of consumers and the food industry.

Particle Swarm Optimization (PSO) is a stochastic optimization method developed by Russell Eberhart and James Kennedy in 1995. Inspired by social behaviors observed in nature, such as the flight of birds, PSO allows a set of particles to represent candidate solutions moving through a search space. Each particle adjusts its position based on its personal experience (best personal position) and the collective experience of the swarm (global best position) (Eberhart and Shi, 2000; Elbeltagi et al., 2005; Kennedy and Eberhart, 1995; Parsopoulos and Vrahatis, 2002; Poli et al., 2007; Trelea, 2003; Yang, 2010).

The proposed method must be able to adapt to potential roaster failures. Indeed, proper roaster operation is essential to ensure consistent and reproducible roasting of coffee beans. However, various malfunctions or operating parameter drifts can occur, impacting the final quality of the roasted coffee.

One of the most common failures of a roaster is temperature drift during the roasting cycle. This may be due to thermal control problems, heating element wear, or variations in thermal load. In this case, the actual temperature in the roasting drum T(t) may deviate from the programmed setpoint T c t .

In order to adapt to these variations, the proposed kinetic model must integrate the actual roasting temperature T(t) rather than the setpoint T c t , as emphasized by Illy and Viani (1995). Joët et al. (2010) also stress the importance of taking environmental factors into account when analyzing the biochemical composition of green coffee.

To this end, the actual temperature T(t) can be expressed as a function of the setpoint T c t and a corrective term ΔT(t) (Equation 3): T t = T c t + Δ T t (3) where ΔT(t) represents the difference between the actual temperature and the setpoint, which may vary over time. This corrective term can be estimated from in-situ temperature measurements in the roasting drum.

Sunarharum et al. (2014), for example, propose an approach where ΔT(t) is modeled as a time-dependent stochastic process of the form (Equation 4): Δ T t = a + b . t + σ . W t (4) with a, b and σ parameters to be identified, and W(t) a Wiener process (white noise). By integrating this expression of T(t) into the kinetic model, we then obtain a more realistic description of temperature evolution during roasting, taking into account potential drifts and fluctuations. “This ensures the model’s robustness in the face of variations in roaster temperature”, emphasize Fabbri et al. (2011). Schenker and Rothgeb (2017), Borém et al. (2013) and Kreuml et al. (2013) also provide further evidence on the impact of roasting and storage conditions on coffee sensory quality and color.

In addition to the global temperature variations over time, the temperature can also exhibit spatial inhomogeneities within the roasting drum itself. Indeed, the circulation of hot air, the agitation of the grain bed, and the geometry of the drum generally induce thermal gradients, with hotter or colder zones.

To integrate these spatial effects into the model, one can, for example, consider that the temperature follows a statistical distribution within the volume of the drum. Joët et al. (2010) propose to model the local temperature T x , t as a random variable following a normal distribution with mean T t and standard deviation σ T t (Equation 5): T x , t = N T t , σ T 2 (5) where T t is the average temperature, which is itself time-dependent as seen previously, and σ T t characterizes the amplitude of the thermal inhomogeneities.

Similarly, Sunarharum et al. (2014) consider that the corrective term Δ T t also follows a normal distribution (Equation 6): Δ T t = N a + b . t , σ 2 (6)

with a, b and σ the parameters of this distribution.

By averaging the kinetic properties over the temperature distribution, we then obtain a model that takes spatial variations into account, as pointed out by Fabbri et al. (2011) (Equation 7): d C d t = ∫ k T x , t . C x , t . p T x , t d T (7) where p (T (x,t)) is the probability density function of the local temperature T (x,t). This approach better represents the physical reality of the process, with more or less reactive zones within the drum. Borém et al. (2013) and Kreuml et al. (2013) also provide further evidence on the impact of temperature inhomogeneities on the final properties of roasted coffee.

Another important phenomenon to take into account is the variation in the mass of coffee beans during roasting. Indeed, the chemical and physical reactions occurring during this process induce a significant loss of mass, which can reach 15%–20% of the initial mass.

This evolution of grain mass m t can be modelled empirically, as proposed by Illy and Viani (1995) (Equation 8): m t = m 0 . e − k . m . t (8) where m 0 is the initial mass of the green beans, and k m is a kinetic coefficient of mass loss, dependent on the temperature.

More specifically, Sunarharum et al. (2014) decompose this mass loss into several contributions (Equation 9): d m d t = − m 0 . k H 2 O . X H 2 O + k C 2 O . X C 2 O + k v o l t a t . X v o l t a t (9) with:

• X H 2 O the mass fraction of water evaporated

Joët et al. (2010) also point out that these mass loss phenomena influence the concentration of various biochemical compounds within the grains. It is therefore important to couple this mass evolution to the degradation/formation kinetics of the compounds of interest.

Fabbri et al. (2011) propose for example, to express concentrations C t as a function of mass m t (Equation 10): C t = C 0 . m 0 m t (10) where C 0 is the initial concentration in the green beans.

This approach makes it possible to obtain a global model that takes into account variations in mass and composition during roasting. Borém et al. (2013) and Kreuml et al. (2013) also provide further evidence on the impact of mass loss on the final properties of roasted coffee.

In conclusion, the proposed kinetic model must be able to adapt to the various potential failures of the roaster, in particular:

• Global temperature variations in the drum,

This will ensure the robustness of the quality control method, regardless of the operating stability of the roaster used, as highlighted by Joët et al. (2010), Sunarharum et al. (2014), Fabbri et al. (2011), Schenker and Rothgeb (2017), Borém et al. (2013) and Kreuml et al. (2013).

In order to assess the performance of the roasting process and detect potential problems, it is necessary to define relevant indicators and associated trigger thresholds. These can be based on physico-chemical, sensory or economic measurements.

Commonly used physico-chemical indicators include (Illy and Viani, 1995; Fabbri et al., 2011):

• The mass loss m t / m 0 described above, with a threshold of 15%–20%, for example,

On the sensory level, indicators such as (Meilgaard et al., 1999; Kreuml et al., 2013):

• Overall aromatic intensity, assessed by a trained panel on a scale of 0–10.

Provide a more detailed view of the impact of roasting parameters. Threshold limits can be defined for each of these attributes.

Finally, economic indicators such as (Yeretzian et al., 2002):

• Yield m t / m 0 .

All these indicators can then be combined in a multi-criteria function F to be maximized, under threshold constraints (Equation 11): F = w 1 ( m t m 0 + w 2 . L * + w 3 . ∑ C i t + w 4 . Aromatic intensity + w 5 . Overall quality − w 6 . Energy costs ) (11) with w i the relative weights of each criterion, to be adjusted according to the manufacturer’s priorities.

The test bench used for this study consists of a pilot roaster with a capacity of 10 kg of green coffee. The roasting drum, with a diameter of 50 cm and a length of 80 cm, is made of stainless steel and is driven by an electric motor that allows the rotation speed to be adjusted between 5 and 15 revolutions per minute (Figure 2).

The heating system is provided by a set of 12 electric heaters with a total power of 15 kW, evenly distributed around the drum. These heaters are temperature-regulated using a control system that maintains the drum temperature between 200°C and 240°C during the roasting process, which varies from 10 to 20 min.

To monitor the evolution of the main process parameters in real-time, the test bench is equipped with temperature sensors (thermocouples), pressure sensors (differential pressure sensors), and air flow meters (mass flow meters) installed at different key locations in the process, especially at the inlet and outlet of the roasting drum.

The tests were carried out with an Arabica coffee from Cameroon. The operating conditions tested cover a temperature range of 200°C–240°C, roasting durations of 10–20 min, and drum rotation speeds of 5–15 revolutions per minute.

In order to test the diagnostic system’s ability to detect different types of failure, faults were simulated in a controlled manner on the test bench. The faults studied included.

• Partial or total failure of the heating system

Failure scenarios were programmed into the control system in order to accurately reproduce these operating hazards, and to evaluate the process response and the diagnostic system’s ability to identify them.

Figure 3 shows the recognition rate of the main faults simulated by the innovative diagnostic method developed, based on the particle swarm optimization (PSO) algorithm. These results were obtained from tests carried out on the laboratory test bench, where different types of failure were deliberately introduced.

For each type of failure, numerous tests were carried out to statistically evaluate the diagnostic system’s ability to detect them correctly. The diagnosis accuracy corresponds to the percentage of cases in which the fault was successfully identified by the algorithm.

This figure clearly shows the performance of the diagnostic method developed for the main identified failures. The high diagnosis accuracy, exceeding 90% in some cases, demonstrate the effectiveness of the proposed approach.

Moreover, the analysis of the fault signatures allows us to trace back to the probable causes and estimate the severity degree of the failure.

The results of the numerical simulation of the roasting process are presented in Figure 4.

This figure shows the predicted evolution of the product temperature over time, as a function of the main physical phenomena involved. This prediction was obtained using a numerical model developed in MATLAB, which is based on the thermal balance equations of the process.

The model takes into account the main physical phenomena involved in roasting, such as heat transfer, chemical reactions, and product mass variations. The model parameters have been adjusted based on the experimental measurements made on the test bench described earlier.

It can be observed that the temperature increases gradually until it reaches a plateau around 200°C during the cooking phase.

Beyond these simulation results, the performance of the prediction of the product mass loss during roasting has been evaluated. Table 3 summarizes the average errors obtained for the three roasting modes studied: light, medium, and dark.

This table shows that the model developed can predict the evolution of mass loss with good accuracy, with errors of less than 5.5% for the different roasting profiles. These results demonstrate the reliability of the numerical model for optimizing the roasting process.

The in-depth analysis of the results of the accelerated aging tests has made it possible to identify the most frequently encountered failures on the roasting system. These failures can have a significant impact on the performance and reliability of the process.

Partial failure of the heating system was detected in 92% of cases. This type of failure can be manifested by a local drop in temperature in the roasting chamber, leading to uneven cooking of the product. The causes can be multiple, such as an electrical problem, deterioration of the heating resistors, or a malfunction of the temperature control system.

Partial obstruction of the air inlets/outlets was observed in 88% of the tests. This phenomenon can be due to the progressive accumulation of fine particles or deposits on the ventilation grids and ducts, thus reducing the air flows necessary for the homogeneity of drying and cooking.

Finally, leaks at the level of the sealing gaskets were detected in 85% of the cases. These failures can lead to hot air losses and therefore a decrease in the energy efficiency of the process. They can be caused by the aging or degradation of the sealing materials under the effect of thermal and mechanical stresses.

Table 4 summarizes the frequencies of occurrence of these three main types of failures identified during the accelerated aging tests.

Analysis of fault signatures, optimized by the PSO algorithm, has made it possible to identify the most relevant indicators for each type of fault, offering avenues for process improvement and predictive maintenance.

In order to position the performance of the fault signature-based diagnostic method developed in this study (i.e., the PSO method), it is interesting to compare it to other classical monitoring and fault detection techniques for roasting systems.

In the context of diagnosing faults in roasting machines, two major challenges emerge: label noise and data decentralization. These issues can significantly affect the reliability and effectiveness of current diagnostic methods.

This study introduced an innovative method for diagnosing and predicting failures in the soybean roasting process, utilizing Particle Swarm Optimization (PSO). Unlike traditional methods that rely on fixed thresholds, our approach is based on a dynamic analysis of the signatures of key variables, allowing for more precise and adaptive anomaly detection. With a fault recognition rate exceeding 90%, this method provides unparalleled robustness in identifying failures such as heating issues and air obstructions. By integrating a real-time adaptation mechanism, the prediction error for remaining useful life was reduced to 15%, compared to 35% for conventional techniques, highlighting the efficiency and innovation of this approach. Additionally, the comparison of this method with other diagnostic techniques revealed significant advantages in terms of accuracy and responsiveness, reinforcing its position as a preferred tool for the industry.

The implications of this method are extensive and could significantly transform the food industry, particularly in the areas of coffee and soybean roasting. The ability to quickly and accurately detect failures allows for the optimization of the final product’s quality while minimizing maintenance costs and improving operational safety. By integrating this method into existing production systems, companies can achieve substantial savings by reducing unexpected downtime and enhancing operational efficiency. Moreover, the PSO method has demonstrated superior performance compared to other diagnostic techniques, such as threshold-based or statistical methods, by offering increased adaptability and accuracy to manage the complexities of industrial processes. This paves the way for widespread adoption in other sectors where equipment reliability is crucial.

Future research should focus on extending the application of the PSO method to other food processing operations, taking into account the specificities and challenges of each sector. In addition, the integration of Labeling Noise and Data Decentralization could transform our method into an even more powerful tool, capable of adapting to the current challenges of the food processing sector, particularly in the soybean roasting process. Future research will be needed to explore these challenges in greater depth. Finally, research could also explore the environmental and economic impacts of this method, assessing how it can contribute to more sustainable practices in the food industry. This research could also lead to practical recommendations for the implementation of these technologies in real industrial environments.