This paper mainly analyzes the maximum resistance that the isotonic muscle strength can overcome when the knuckle moves in full amplitude in the process of upper limb rehabilitation in the state of grade 4 muscle strength. Through the upper limb rehabilitation training robot, the muscle strength data of patients in the active rehabilitation process was collected in real time and evaluated by scientific evaluation method. This assessment includes the Maximum resistance to do a Repetition, called an I Repetition Maximum (IRM), and the maximum resistance to overcome at the completion of 10 repetitions (10 IRM). Assessment results can be used by rehabilitation therapists in the following ways:

1. Aid rehabilitation therapists in assessing the current upper limb strength of patients.

Therefore, by continuously collecting real-time muscle strength data and other relevant rehabilitation information, and integrating it with the expertise of rehabilitation therapists, this study will incorporate a method for assessing muscle strength into an upper limb rehabilitation training robot. This method will categorize data, establish a muscle strength database for different patient profiles, and provide tailored resistance levels and scientifically-based muscle strength ratings. The grading system for upper limb muscle strength is presented in Table 2 (Naghdi et al., 2010).

The input parameters for this study primarily encompass basic patient information and upper limb characteristic data collected via the rehabilitation robot. Specifically: Basic patient information includes age, gender, medical history, etc. Upper limb characteristic data: Collected using the upper limb robot system shown in Figure 2, covering health indicators such as active resistance torque and recovery time. These data are obtained through methods like marker matching, motion capture technology, and electromyography (EMG) sensor testing.

To ensure the accuracy and reliability of the research results, all patients participating in this experiment must meet the following criteria: 1. Able to independently complete specified movements during moderate-intensity upper limb muscle strength training; 2. The onset time is between 1 week to 3 months; 3. Age range is between 20 and 70 years old; 4. No history of cognitive impairment or neurological diseases such as epilepsy; 5. All patients have signed informed consent forms.

Based on the aforementioned patient criteria, all subjects in this study met the Level 5 requirements of the Brunnstrom scale. Consequently, three different experiments were designed with varying levels of active resistance torque for the upper limbs, denoted as E1, E2, and, E3. The specific experiments are shown in Table 3. It is assumed that under these three sets of experiments, the health statuses of the patients’ upper limbs correspond to First-degree Fault, Second-degree Fault, Third-degree Fault, and Fourth-degree Fault, respectively.

In the table, each experiment represents the patient’s rehabilitation training action under the specified upper limb active resistance moment. Each action is completed, and the number of actions is recorded as 1. When the patient completes 50 actions, it indicates that the patient has completed the experiment.

During the experimental process, muscle patches were affixed to the upper limbs of each patient, as illustrated in Figure 3. Daily training sessions involving E1, E2, and E3 were conducted based on the patients’ rehabilitation status.

The upper limb feature data collected by the rehabilitation robot will be used as the input of the BRB model, that is, the prerequisite attribute. By combining these characteristic quantities, confidence rules can be formed to infer the recovery status of the patient’s upper limb. In this process, the qualitative knowledge of the rehabilitation physician can be used to determine the importance and reference values of characteristic quantities such as active resistance moment and recovery time, and serve as inputs to the BRB model. Therefore, BRB theory can be effectively applied to the evaluation of upper limb rehabilitation status. On the basis of in-depth study of BRB theory system, this paper focuses on the evaluation and prediction of upper limb rehabilitation of patients, and expands the application of BRB theory in the assessment of upper rehabilitation status.

The evaluation block diagram of the human upper limb rehabilitation effect based on BRB is shown in Figure 4. First of all, data collection was carried out in Jilin Electric Power Hospital to collect real and effective quantitative test data and expert qualitative knowledge. Based on quantitative rehabilitation evaluation indicators, constraint conditions of characteristic quantity were set up, combined with rehabilitation exercise mechanism, and on the basis of quantitative rehabilitation evaluation parameters, a rehabilitation degree evaluation model was established by using beleif rule base theory.

In order to evaluate the rehabilitation state of the patient’s upper limb, this section will establish the relationship between the health state of the patient’s upper limb and the characteristic quantity based on the BRB theory by using the nonlinear relationship model f. The specific relationship model is shown in Formula 1: H = f x 1 t , x 2 t , … . , x M t , V (1) where H represents the health state of the patient’s upper limb predicted by the BRB model; x represents the characteristic quantity of the evaluation system; f Represents nonlinear function; V represents the weight parameters set inside the model. The characteristic quantity includes the characteristic quantity, such as the active resistance moment and active recovery time collected by the system.

In the process of establishing the patient’s upper limb health assessment model based on BRB, firstly, the feature quantity representing the patient’s upper limb health state is extracted, and the feature quantity of the upper limb health state is segmented and used as the input of the BRB model. Secondly, the parameter optimization model of BRB is established, and the parameters of the model are optimized and updated by computer algorithm to improve the accuracy of BRB model in predicting the rehabilitation state of upper limbs. Finally, the rehabilitation status of patients’ upper limbs was evaluated through the trained model.

In the BRB model of patient upper limb health assessment, rule k of BRB is shown in Formula 2: R k : i f x 1 i s A 1 k ∧ x 2 i s A 2 k ∧ ⋯ ∧ x M i s A M k (2) T h e n D 1 , β 1 , k , D 2 , β 2 , k , … , D N , β N , k w i t h a n e w r u l e w e i g h t θ k a n d a t t r i b u t e w e i g h t δ 1 , δ 2 , … , δ M where x i 1,2 , … , M is BRB input, that is, the quantity of the patient’s upper limb health characteristics collected by the upper limb rehabilitation robot; k indicates the number of BRB rules; A i k 1,2 , … , M represents the reference value of the ith premise attribute; R k represents the kth evaluation result of the rule; M and N represent the number of prerequisite attributes and the number of evaluation results respectively; β j , k represents the belief of the first evaluation result j; θ k represents the weight of rule k, and represents the weight of the δ i epresents the weight of the ith premise attribute.

In the process of BRB rule Reasoning, Evidential Reasoning (ER) algorithm is used to combine the confidence rules to get the final system output, which is the beleif rule base reasoning method based on evidence reasoning algorithm (Belief Rule-base Inference Methodology Using the Evidential Reasoning Approach) (Yang et al., 2006; Yang and Singh, 1994). The whole reasoning process consists of three main steps (Zhijie et al., 2017).

Step 1: calculate the matching degree of the prerequisite attribute of the belief rule base model, that is, the matching degree of the feature quantity. The matching degree reflects the matching degree between the feature quantity and the rule. The formula for calculating the matching degree of the prerequisite attribute of rule k is shown in Formula 3: a i k = A i l + 1 − x i A i l + 1 − A i l k = l A i l ≤ x i ≤ A i l + 1 1 − a i k k = l + 1 0 k = 1 ,   L , N k ≠ l , l + 1 (3) where, a i k represents the matching degree of the i premise attribute in rule k; A i l and A i l + 1 represent the i - th prerequisite attribute reference value in the two adjacent rules, respectively.

Step 2: Calculate the activation weight.

This process is used to determine which rules should be activated and considered during reasoning, better reflecting the uncertainties and fuzziness in expert knowledge, thereby improving the model’s adaptability to unknown situations to further determine the final output of the system. The degree to which different rules are activated depends on how well they match the input data. According to the BRB model, in order to facilitate the understanding and interpretation of the decision-making process of the model, the setting of the activation weights should be transparent and adjustable, and the relative relationship between them should be consistent. By calculating the activation weights, the contribution degree of different rules can be evaluated, and the reasoning basis based on the matching degree can be provided for the system. The formula for calculating the activation weight of Rule k is shown in Formula 4: ω k = θ k ∏ i = 1 N a i k δ ̄ i ∑ l = 1 L θ l ∏ i = 1 N a i l δ ̄ i (4) where δ ̄ i indicates attribute weight; a i k represents the matching degree of the input feature quantity relative to the ith attribute; θ k represents the corresponding rule weight.

Step 3: Use the ER algorithm for rule reasoning.

ER algorithm can deal with the combination of expert knowledge, deal with uncertainty, and is suitable for a variety of scenarios. ER algorithm can effectively synthesize the inference results of multiple rules, considering the weight and correlation between them, so as to reach a more accurate conclusion. By using the ER algorithm, the limitation of single-rule reasoning can be overcome, and the performance and effect of the system in decision-making and evaluation tasks can be improved. All rules in the BRB model are reasoned and analyzed by using the ER algorithm, and the final output result is obtained as shown in Formula 5: S x = D j , β ̂ j , j = 1,2 , … , L , N (5) where, β j ̂ indicates the belief degree of the evaluation result D j , as shown in Formula 6: β ̂ j = μ × ∏ k = 1 L ω k β j , k + 1 − ω k ∑ i = 1 N β i , k − ∏ k = 1 L 1 − ω k ∑ i = 1 N β i , k 1 − μ × ∏ k = 1 L 1 − ω k (6)

Formula 7 serves as a regulator in the ER model handling process, responsible for adjusting the evaluation result model. When μ increases, the evaluation result will be more conservative; when μ decreases, the evaluation result will be more aggressive. μ = ∑ j = 1 N ∏ k = 1 L ω k β j , k + 1 − ω k ∑ i = 1 N β i , k − M − 1 ∏ k = 1 L 1 − ω k ∑ i = 1 N β i , k − 1 (7) where N represents the number of evaluation results; β j ̂ Is a function of rule weights θ k , attribute weights δ i ̄ , and belief β j , k .

Assuming that D j the utility of the evaluation result is μ D j , then the expected utility is S ( X ) as shown in Formula 8: μ S X = ∑ j = 1 M μ D j β j (8) where β j indicates the belief of the output relative to D j .

Therefore, the output of the BRB-based health assessment model y ̂ is expressed as shown in Formula 9: y ̂ = μ S X (9)

In general, the rehabilitation specialist gives the initial BRB parameters based on the collection of historical information and empirical knowledge of the patient’s upper limb status. However, in special cases, it is difficult for rehabilitation specialists to accurately determine the value of these parameters due to differences in the patient’s physical condition and diagnostic requirements. This can lead to deviations between the initial BRB output and the actual results, thus reducing the accuracy of the evaluation of the upper limb rehabilitation effect. Fmincon is a nonlinear multivariable function with constraints Sreeraj (2013), which is often used to solve the minimum value of a nonlinear multivariate function. Therefore, this paper adopts Fmincon as an optimization function, takes mean square error as the input objective function for parameter optimization, and trains the BRB model to obtain the optimal model parameters. To minimize the error between the actual output result and the initial BRB output result, improve the evaluation accuracy of upper limb rehabilitation effect.

In the process of parameter optimization of BRB rehabilitation evaluation model, the following optimization objective function is established as shown in Formula 10: M s = θ 1 ⋯ θ k ⋯ δ 1 ⋯ δ m ⋯ β 1 k ⋯ β n k T min M S E y θ k , δ m , β n k 0 ≤ θ k ≤ 1 0 ≤ β n k ≤ 1 ∑ n = 1 N β n k ≤ 1 , k = 1,2 , ⋯ L (10) Where as shown in Formula 11: M S E = 1 T ∑ i = 1 T y i − y i r 2 (11) where, T represents the rehabilitation data volume, y i represent output of rehabilitation evaluation model for patients, and y i r represent output results of actual rehabilitation state of patients.

In the process of establishing the health assessment model of upper limb active rehabilitation, it is very important to select the reference index of upper limb rehabilitation state. According to the communication of rehabilitation experts in Jilin Electric Power Hospital, combined with the muscle strength sensor of rehabilitation robot. Finally, the active resistance torque of upper limb (ARTUL), Rehabilitation Training Time (RTT) and Mean Amplitude of Muscle Strength (MAMS) were selected as the reference indexes of upper limb rehabilitation, and three reference values were selected for every three reference indexes. These indicators will be used as the main basis for evaluating the health status of upper limbs, and verified by simulation verification data. In order to verify the evaluation model, because the main research object of this paper is the patients with grade 5 in Brunnstrom muscle strength table, after patient screening and training, 40 patients with grade 5 in Brunnstrom muscle strength table are finally determined for follow-up testing. According to the actual training of patients and communication with rehabilitation experts, Brunnstrom muscle strength is subdivided into 4 grades again for evaluation example verification as shown in formula 15.

For ARTUL, take 3 reference values, Small, Normal and Big, denoted by S , N and B , respectively as shown in Formula 12: A 1 k ∈ S , N , B (12)

Similarly, for RTT, take 3 reference values, Small, Normal and Long, denoted by S , N and L , respectively as shown in Formula 13: A 2 k ∈ S , N , L (13)

Similarly, for MAMS, take 3 reference values, Small, Normal and High, denoted by S , N and H , respectively as shown in Formula 14: A 3 k ∈ S , N , H (14)

As for the evaluation results, it can be seen from the experiment that there are 4 health states, respectively represented as I,II, III and IV, namely as shown in Formula 15: D = D 1 D 2 D 3 D 4 = I I I I I I I V (15)

The input feature quantity of the BRB has 3 reference indicators, and each reference indicator has 3 reference values, from which 27 initial confidence rules can be established to evaluate the health state of the system. Taking ARTUL as S as an example, the following rules are established according to expert knowledge as shown in Formula 16: R 1 : I f A T R U L i s S ∧ R T T i s S ∧ M A M S i s S , T h e n 1,0,0,0,0 R 2 : I f A T R U L i s S ∧ R T T i s S ∧ M A M S i s N , T h e n 0.9 , 0.1 , 0,0,0 R 3 : I f A T R U L i s S ∧ R T T i s S ∧ M A M S i s H , T h e n 0.8 , 0.2 , 0,0,0 R 4 : I f A T R U L i s S ∧ R T T i s N ∧ M A M S i s S , T h e n 0.9 , 0.1 , 0.0 , 0,0 R 5 : I f A T R U L i s S ∧ R T T i s N ∧ M A M S i s N , T h e n 0.8 , 0.2 , 0,0,0 R 6 : I f A T R U L i s S ∧ R T T i s N ∧ M A M S i s H , T h e n 0.7 , 0.3 , 0,0,0 R 7 : I f A T R U L i s S ∧ R T T i s L ∧ M A M S i s S , T h e n 0.6 , 0.3 , 0.1 , 0,0 R 8 : I f A T R U L i s S ∧ R T T i s L ∧ M A M S i s N , T h e n 0.5 , 0.4 , 0.1 , 0,0 R 9 : I f A T R U L i s S ∧ R T T i s L ∧ M A M S i s H , T h e n 0,0.9 , 0.1 , 0,0 (16)

Taking the above rules as an example, a systematic BRB rehabilitation evaluation model is established. The kth rule is as shown in Formula 17: R k : i f A T R U L i s A 1 k ∧ R T T i s A 2 k ∧ M A M S i s A 3 k , (17) T h e n H e a l t h − c o n d i t i o n i s I , β 1 , k , I I , β 2 , k , I I I , β 3 , k , I V , β 4 , k w i t h r u l e w e i g h t θ k a n d a t t r i b u t e w e i g h t δ 1 , δ 2 , … , δ 4

The validity of the health assessment model established in this section is verified by simulation analysis. During the experiment, 2,000 groups of characteristic values in three states were collected, of which 1,600 groups were used as training sets and 400 groups as test sets.

First of all, according to the reference values given by the rehabilitation therapist of Jilin Electric Power Hospital and the analysis of the characteristics of the sampled data, the semantic reference values of the characteristic quantities and evaluation results are quantified, as shown in Tables 4–6.

In the rehabilitation evaluation model, since each feature has 3 reference values, there are a total of 27 rules when evaluating the health status of these features. According to expert knowledge, the initial confidence of the three characteristic quantities is shown in Table 7.

According to the initial parameters given by the experts, regardless of the weight of the characteristic quantity δ i and θ k set to 1, the health evaluation result can be obtained, as shown in Figure 5. In Figure 5, the blue distribution represents the initial BRB health assessment results, and black represents the true health assessment results. As can be seen from the figure, the degree of fitting between the evaluation results and the training data is not high.

In order to improve the evaluation accuracy of the evaluation model, the parameters of the initial BRB were updated based on the established optimization model and the Fmincon optimization algorithm. The BRB parameters after training are shown in Table 8, and the evaluation results are shown in Figure 6. As can be seen from Figure 6. In Figure 6, the blue distribution represents the initial BRB health assessment results, black represents the real health assessment results, and red represents the BRB health assessment results optimized by Fmincon function, with an accuracy of 92.6%. It can be seen that the BRB health assessment results optimized by Fmincon function have a higher accuracy.

In order to further verify the advanced nature of the proposed model, BP and SVM were used for comparative analysis. BP and SVM algorithms are widely used in diagnosis, classification, prediction and other problems. Similar to BRB model simulation analysis, the SVM and BP algorithm evaluation model were trained and tested 1:1 with 1,600 sets of data. Figures 7, 8 show the results of the rehabilitation degree evaluation model based on support vector machine SVM and BP. It can be observed from the figure that the accuracy of BP neural network in the evaluation of upper limb health status is low for grade 2 and grade 4 health status, and the accuracy of overall rehabilitation evaluation is only 67%, while the overall evaluation stability is poor when SVM evaluates upper limb health status, and the assessed health status fluctuates poorly, and the evaluation accuracy is only 53%. Through the analysis of experimental results, it can be seen that the BRB-based upper limb health evaluation model of patients proposed in this chapter has higher accuracy and effectiveness than the rehabilitation evaluation model based on SVM and BP algorithm.