Performance degradation evaluation method for harmonic reducer for industrial robot

Abstract

The invention provides a harmonic reducer performance degradation evaluation method for an industrial robot, and the method comprises the steps: setting an experiment operation condition and a data collection strategy, and obtaining a whole-life-cycle sound emission and micro-vibration synchronous data set; extracting characteristics of the acoustic emission signal and the vibration signal by using the strong sensitivity of the acoustic emission signal to the early damage of the harmonic reducer and the accurate capturing capability of the micro-vibration signal to the middle and later damage; according to monotonicity, correlation, predictability and robustness indexes of the features, performing linear weighting on each index through an entropy weight method to construct a comprehensive evaluation index, and screening an optimal feature according to a highest score; a differential evolution (DE) method is adopted to fuse the optimal acoustic emission and micro-vibration characteristics, and a multi-stage health index (HI) capable of effectively representing the health state of the harmonic reducer is constructed.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial robots, and particularly relates to a method for evaluating the performance degradation of a harmonic reducer for industrial robots. Background Art

[0002] The harmonic reducer is the core transmission component of the joints of industrial robots, and its performance directly determines the running stability and safety of the robots. The flexspline with a thin-wall structure and the flexible bearing will continuously bear the action of high-frequency alternating stress loads during long-term operation, which is extremely easy to cause internal damage. The aggravation of the damage will lead to the performance decline of the harmonic reducer, thus affecting the overall performance of the robot, and even causing failures, resulting in the paralysis of the entire production line and huge economic losses.

[0003] Since the harmonic reducer is assembled from multiple components, the damage generated during the degradation process mostly appears in a coupled form, with concealment, randomness and concurrency, making it difficult to accurately describe its running performance and health state. In order to effectively control the occurrence of failures, it is necessary to grasp the damage inflection points at each stage of the harmonic reducer as early as possible, reveal the inherent trend characteristics of its degradation process, and accurately evaluate its performance evolution process in the whole life cycle.

[0004] Existing performance degradation evaluation methods mostly rely on a single signal, such as vibration signals, acoustic emission signals, etc. Among them, vibration signals are often used to reveal the fault characteristics such as wear, looseness and cracks of mechanical components due to their high sensitivity, strong reliability and good real-time performance, especially having a strong perception ability for macroscopic damage visible to the naked eye in the later stage of damage. Different from this, acoustic emission signals are more sensitive to weak damage in the early stage of performance degradation. However, although these methods have their own characteristics, since they all use a single signal for performance degradation evaluation, it is difficult to comprehensively capture the potential key information in the degradation process, and at present, there has not yet been a damage perception method using composite signals throughout the whole life cycle from the initiation of early weak damage to complete failure. Summary of the Invention

[0005] The purpose of the technical solution of the present invention is to design a method for evaluating the performance degradation of a harmonic reducer for industrial robots, so as to accurately capture the damage inflection points at each degradation stage, effectively reveal the inherent approximate monotonic trend of the damage evolution process, and realize the comprehensive tracking of the performance degradation process in the whole life cycle.

[0006] In order to achieve the above invention purpose, the technical solution of the present invention provides a method for evaluating the performance degradation of a harmonic reducer for industrial robots, including the following steps:

[0007] Run the experiment at the rated speed according to the preset acoustic emission sampling frequency, preset micro-vibration sampling frequency, and preset multiple rated torque loads, record data according to the preset acquisition strategy, and generate a synchronous dataset of acoustic emission and micro-vibration in the whole life cycle;

[0008] Extract the standard deviation, variance, maximum value, and negative entropy of the acoustic emission signal, as well as the mean value, standard deviation, negative entropy, and smoothness index of the micro-vibration signal from the synchronous dataset of acoustic emission and micro-vibration in the whole life cycle as acoustic emission features and micro-vibration features, and perform normalization processing to obtain multiple normalized acoustic emission feature sequences and multiple normalized micro-vibration feature sequences;

[0009] Calculate the monotonicity index, correlation index, predictability index, and robustness index of multiple normalized acoustic emission feature sequences and multiple normalized micro-vibration feature sequences respectively, establish a linear weighted comprehensive evaluation index for acoustic emission features and a linear weighted comprehensive evaluation index for micro-vibration features, and screen the optimal features according to the highest score to obtain the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence;

[0010] Calculate the mutual information and Euclidean distance between the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence, combine with the fitness function to fuse the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence to obtain the optimal objective fusion function, and then obtain the multi-stage health indicators of the harmonic reducer health state, realizing the evaluation of the performance degradation of the harmonic reducer.

[0011] Preferably, the expression of the monotonicity index is as follows:

[0012]

[0013] In the formula, f i represents the i-th normalized acoustic emission feature sequence or normalized micro-vibration feature sequence, and respectively represent the number of times the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence f i rises and falls, N is the total number of data points of the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence f i , represents the change amplitude of the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence f i between adjacent monitoring points k + 1 and k.

[0014] Preferably, the expression of the correlation index is as follows:

[0015]

[0016] In the formula, fi represents the i-th normalized acoustic emission feature sequence or normalized micro-vibration feature sequence, Cov(f i , T) represents the covariance between the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence f i and the time vector T, and σ(f i ) and σ(T) are the standard deviations of the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence and the time vector T respectively.

[0017] Preferably, the expression of the predictability index is as follows:

[0018]

[0019] In the formula, f i represents the i-th normalized acoustic emission feature sequence or normalized micro-vibration feature sequence, std(f i,begin ) represents the standard deviation of the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence f i in the healthy stage, |f i,end -f i,begin | represents the difference between the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence f i in the rapid degradation stage and the initial stage.

[0020] Preferably, the expression of the robustness index is as follows:

[0021]

[0022] In the formula, f i represents the i-th normalized acoustic emission feature sequence or normalized micro-vibration feature sequence, represents the mean value of the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence f i , exp(·) is the exponential function, used to ensure that the robustness index is positive, and N is the total number of data points of the normalized acoustic emission feature sequence or normalized micro-vibration feature sequence f i .

[0023] Preferably, when calculating the linear weighted comprehensive evaluation index of the acoustic emission feature and the linear weighted comprehensive evaluation index of the micro-vibration feature, the formula of the linear weighted comprehensive evaluation index used is as follows:

[0024] C = w1Mon + w2Corr + w3Rob + w4Pro

[0025]

[0026] Wherein, C is the linearly weighted comprehensive evaluation index, j represents the jth performance evaluation index, including the monotonicity index, the correlation index, the predictability index and the robustness index, w1 is the weight of the monotonicity index, w2 is the weight of the correlation index, w3 is the weight of the predictability index, and w4 is the weight of the robustness index.

[0027] Preferably, the multi-stage health index formula is as follows:

[0028]

[0029] Wherein, represents the optimal objective fusion function, represents the mutual information, represents the Euclidean distance, represents the optimal acoustic emission feature sequence, represents the optimal micro-vibration feature sequence, l(·) represents the fitness function in the differential evolution algorithm, max indicates that the optimization objective of the fitness function is the maximum, and γ∈[0,1] is a parameter for adjusting the relative weights of the mutual information and the Euclidean distance.

[0030] The technical solution of the present invention proposes a method for evaluating the performance degradation of a harmonic reducer for an industrial robot, including: setting experimental operating conditions and data acquisition strategies to obtain a synchronous data set of acoustic emission and micro-vibration in the whole life cycle; using the strong sensitivity of the acoustic emission signal to early damage of the harmonic reducer and the accurate capture ability of the micro-vibration signal to mid- and late-stage damage to extract the features of the acoustic emission signal and the vibration signal; according to the monotonicity, correlation, predictability and robustness indexes of the features, linearly weight each index by the entropy weight method to construct a comprehensive evaluation index, and screen the optimal features according to the highest score; adopt the differential evolution (DE) method to fuse the optimal acoustic emission and micro-vibration features to construct a multi-stage health indicator (HI) that can effectively characterize the health state of the harmonic reducer. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a schematic flow chart of the performance degradation evaluation of the harmonic reducer provided by the embodiment of the present invention;

[0032] Figure 2 is a schematic diagram of the evolution trend of the acoustic emission and micro-vibration features of the harmonic reducer provided by the embodiment of the present invention;

[0033] Figure 3 is a schematic diagram of the scores of the monotonicity, correlation, predictability, robustness indexes and the comprehensive evaluation index of the acoustic emission feature and the micro-vibration feature provided by the embodiment of the present invention;

[0034] Figure 4Schematic diagram of the optimal acoustic emission features, optimal micro-vibration features, and multi-stage HI based on DE fusion provided by the embodiments of the present invention. Detailed implementation manners

[0035] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of this application.

[0036] As Figure 1 shown, the embodiments of the present invention provide a method for evaluating the performance degradation of a harmonic reducer for an industrial robot, including the following steps:

[0037] Step 1: Run the experiment at the rated speed according to the preset acoustic emission sampling frequency, preset micro-vibration sampling frequency, and preset multiple of the rated torque load, record data according to the preset acquisition strategy, and generate a synchronous dataset of acoustic emission and micro-vibration for the entire life cycle.

[0038] For example, in the experiment, the acoustic emission sampling frequency is set to 1 MHz, the preset micro-vibration sampling frequency is set to 25.6 kHz, the preset multiple of the rated torque load is set to 3 times the rated torque load, and it runs at the rated speed of 2000 rpm. The preset acquisition strategy is to record 0.5 seconds of data every 10 minutes. The entire experimental cycle is 114 hours, and a total of 678 files are generated and saved as an independent file as the synchronous dataset of acoustic emission and micro-vibration for the entire life cycle.

[0039] As Figure 2 shown, Step 2: Extract the standard deviation, variance, maximum value, and negative entropy of the acoustic emission signal in the synchronous dataset of acoustic emission and micro-vibration for the entire life cycle, as shown in (a) of Figure 2 , and the mean value, standard deviation, negative entropy, and smoothness index of the micro-vibration signal, as shown in (b) of Figure 2 , as acoustic emission features and micro-vibration features, and perform maximum-minimum normalization processing to obtain multiple normalized acoustic emission feature sequences and multiple normalized micro-vibration feature sequences to eliminate the dimensional differences between features. As can be seen from Figure 2 , the acoustic emission signal shows higher sensitivity in the early damage stage, and its initial damage inflection point is effectively identified at the observation period of 130, 23 observation periods earlier than the micro-vibration signal. The micro-vibration signal has more advantages in detecting damage in the middle and late stages, and captures the severe damage inflection point at the observation period of 318, 58 observation periods earlier than the acoustic emission signal.

[0040] The high-quality HI of the harmonic reducer should map the monotonic and irreversible characteristics inherent in the degradation process, be closely related to the overall degradation state of the entire life cycle, facilitate subsequent prediction and analysis, and have a certain noise resistance. Therefore, monotonicity, correlation, predictability, and robustness are used to measure the superiority of HI.

[0041] As Figure 3 shown, Step 3: Calculate the monotonicity index, correlation index, predictability index, and robustness index of multiple normalized acoustic emission feature sequences and multiple normalized micro-vibration feature sequences respectively, establish a linear weighted comprehensive evaluation index of acoustic emission features and a linear weighted comprehensive evaluation index of micro-vibration features based on the entropy weight method, and screen the optimal features according to the highest score to obtain the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence. Figure 3 Figure (a) in Figure 3 is a schematic diagram of the monotonicity index, correlation index, predictability index, robustness index, and linear weighted comprehensive evaluation index of the acoustic emission feature sequence after normalization.

[0042] Among them, monotonicity means that under the drive of the inherent physical characteristics of the harmonic reducer, the degradation process shows a monotonic and irreversible trend, which is mainly manifested as the continuous rise or fall of the eigenvalue. The monotonicity index Mon(f i ) is expressed as follows:

[0043]

[0044] In the formula, f [ represents the i-th normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence, and respectively represent the number of times the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i rises and falls. N is the total number of data points of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i , represents the change amplitude between adjacent monitoring points k + 1 and k of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i .

[0045] Correlation is a measure of the degree of association between the degradation feature vectors of the harmonic reducer over time. The higher the correlation, the more significant the association between the two. On the contrary, it indicates a weak association. The correlation index Corr(f i ,T) is expressed as follows:

[0046]

[0047] In the formula, Cov(f i , T) represents the covariance between the AE feature sequence after normalization or the micro-vibration feature sequence after normalization f i and the time vector T, and σ(f i ) and σ(T) are the standard deviations of the AE feature sequence after normalization or the micro-vibration feature sequence after normalization and the standard deviation of the time vector T, respectively.

[0048] Predictability is used to evaluate whether the constructed HI is beneficial to subsequent performance prediction. An ideal HI should have good degradation characterization ability and provide a reliable basis for the life prediction of the harmonic reducer. The predictability index Pro(f i ) is expressed as follows:

[0049]

[0050] In the formula, std(f i,begin ) represents the standard deviation of the AE feature sequence after normalization or the micro-vibration feature sequence after normalization f i in the healthy stage, which is used to measure the volatility of this stage. |f i,end -f i,begin | represents the difference between the AE feature sequence after normalization or the micro-vibration feature sequence after normalization f i in the rapid degradation stage and the initial stage, representing the amplitude of system degradation.

[0051] Robustness describes the tolerance of the harmonic reducer to uncertain factors and random perturbations during the degradation measurement process, effectively reflecting the resistance of HI to random noise and outliers. The robustness index Rob(f i ) is expressed as follows:

[0052]

[0053] In the formula, represents the mean value of the AE feature sequence after normalization or the micro-vibration feature sequence after normalization f i , exp(·) is the exponential function, which is used to ensure that the robustness index is positive, and N is the total number of data points of the AE feature sequence after normalization or the micro-vibration feature sequence after normalization f i .

[0054] A single evaluation index has certain biases in evaluating performance degradation. Considering monotonicity index, correlation index, predictability index, and robustness index comprehensively, a linear weighted comprehensive evaluation index is constructed to calculate the linear weighted comprehensive evaluation index of acoustic emission features and the linear weighted comprehensive evaluation index of micro-vibration features corresponding to multiple normalized acoustic emission feature sequences and multiple normalized micro-vibration feature sequences. The expression of the linear weighted comprehensive evaluation index C is as follows:

[0055] C = w1Mon + w2Corr + w3Rob + w4Pro

[0056]

[0057] In the formula, C is the linear weighted comprehensive evaluation index, j represents the jth performance evaluation index, including monotonicity index, correlation index, predictability index, and robustness index, w1 is the weight of the monotonicity index, w2 is the weight of the correlation index, w3 is the weight of the predictability index, and w4 is the weight of the robustness index.

[0058] The entropy weight method is used to determine the weights of each performance evaluation index. The greater the information entropy of the index, the richer the information provided, the greater the contribution to the comprehensive evaluation, and the greater the corresponding weight.

[0059] First, perform proportional normalization on each evaluation index. Then, the specific value of the jth performance evaluation index of the ith acoustic emission feature sequence or micro-vibration feature sequence can be expressed as:

[0060]

[0061] In the formula, f ij represents the specific value of the jth performance evaluation index of the ith acoustic emission feature sequence or micro-vibration feature sequence, F ij represents the specific value of the jth performance evaluation index of the ith normalized acoustic emission feature sequence or normalized micro-vibration feature sequence after proportional normalization, and m represents the total number of features in the acoustic emission feature sequence or micro-vibration feature sequence.

[0062] The information entropy of the jth performance evaluation index can be expressed as:

[0063]

[0064] In the formula, K is a normalization factor used to normalize the information entropy value to the [0, 1] interval for facilitating the comparison of the amount of information between different evaluation indexes.

[0065] The weight of the jth performance evaluation index can be expressed as:

[0066]

[0067] Step 4: Based on the adaptive feature fusion strategy of the DE algorithm, fuse the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence to obtain the optimal target fusion function, and its formula is as follows:

[0068]

[0069] In the formula, represents the optimal acoustic emission feature sequence, represents the optimal micro-vibration feature sequence, l(·) represents the fitness function in the DE algorithm, and max represents the optimization objective of the DE algorithm, which maximizes the fitness function value.

[0070] To effectively capture the implicit coupling features and explicit state offsets of performance degradation in the whole life cycle of the harmonic reducer, mutual information and Euclidean distance are introduced to jointly construct multi-stage health indicators of the harmonic reducer's health state, so as to realize the assessment of the performance degradation of the harmonic reducer.

[0071] Among them, mutual information is used to measure the non-linear correlation between the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence, and its mathematical expression is:

[0072]

[0073] In the formula, p(a,v) represents the joint probability density function, and p(a) and p(v) are their respective marginal probability density functions. Mutual information reflects and The degree of information sharing between them, and the larger the value, the stronger the correlation.

[0074] Euclidean distance is used to measure the distance relationship between the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence, and its mathematical expression is:

[0075]

[0076] In the formula, and respectively represent the optimal acoustic emission feature value and the optimal micro-vibration feature value at the observation time k, and N is the total number of data points in the eigenvalue sequence.

[0077] The optimal target fusion function is equivalent to the weighted sum of mutual information and Euclidean distance. Among them, the goal of mutual information is to maximize, while the goal of Euclidean distance is to minimize. Then the multi-stage health indicator can be expressed as:

[0078]

[0079] In the formula, I(·,·) and Edist(·,·) are mutual information and Euclidean distance respectively, γ ∈ [0,1] is a parameter for adjusting the relative weights of mutual information and Euclidean distance in the optimal objective fusion function, and the value of γ being 0.5 is determined through multiple experiments to ensure the balance of the relative weights of mutual information and Euclidean distance in the optimal objective fusion function.

[0080] Among them, the weights of the monotonicity, correlation, predictability, and robustness indexes corresponding to the calculated acoustic emission and micro-vibration characteristics are 0.04, 0.3704, 0.5, 0.0893 and 0.0869, 0.3861, 0.5237, 0.0033 respectively. Figure 4 In (a) of [reference], it is a schematic diagram of the maximum value of the acoustic emission signal. Figure 4 In (b) of [reference], it is a schematic diagram of the mean value of the micro-vibration signal. Figure 4 In (c) of [reference], it is a schematic diagram of the multi-stage HI constructed by adaptively fusing these two optimal features using the DE algorithm.

[0081] From Figure 4 it can be seen that the comprehensive evaluation indexes corresponding to the maximum value of the acoustic emission signal and the mean value of the micro-vibration signal are the highest, indicating that these two characteristics have more advantages in reflecting the health state of the harmonic reducer. Therefore, these two optimal characteristics are selected as the basis for subsequent feature fusion. The maximum value of the acoustic emission signal identifies the initial damage inflection point and the severe damage inflection point at the observation cycles 130 and 376 respectively, and the mean value of the micro-vibration signal detects the corresponding damage inflection points at the observation cycles 153 and 318. The degradation inflection points identified by the HI obtained based on the DE fusion method are located at the cycles 130 and 318 respectively, fully combining the strong sensitivity of the acoustic emission signal in the identification of early weak damage and the accurate capture ability of the micro-vibration signal for medium and late damage, and can timely detect the evolution inflection points of different damage stages in the whole life cycle of the harmonic reducer. In addition, compared with the degradation trends provided by the single optimal acoustic emission and micro-vibration characteristics, the multi-stage HI based on DE fusion effectively reveals the inherent approximate monotonic trend in the degradation process of the harmonic reducer, further improving the accuracy and reliability of the performance degradation assessment.

[0082] The beneficial effects of the present invention are as follows: The micro-vibration sensor has high sensitivity in signal monitoring, with a 5-10 times improvement in amplitude perception compared to general vibration sensors, and has more advantages in capturing damage characteristics in the middle and late stages. Therefore, the embodiments of the present invention fully combine the strong sensitivity of acoustic emission signals in early weak damage identification and the accurate capture ability of micro-vibration signals for middle and late stage damage, and can timely detect the evolution inflection points of different damage stages in the whole life cycle of the harmonic reducer, realizing the accurate characterization of the damage characteristics of the harmonic reducer in the whole life cycle. In addition, compared with the degradation trends provided by single optimal acoustic emission and micro-vibration characteristics, the multi-stage HI based on DE fusion effectively reveals the inherent approximate monotonic trend in the degradation process of the harmonic reducer, further improving the accuracy and reliability of performance degradation assessment.

Claims

1. A method for evaluating the performance degradation of a harmonic reducer for an industrial robot, characterized in that, Including the following steps: Run the experiment at the rated speed according to the preset acoustic emission sampling frequency, preset micro-vibration sampling frequency, and preset multiple of the rated torque load, record the data according to the preset acquisition strategy, and generate a synchronous dataset of acoustic emission and micro-vibration in the full life cycle; Extract the standard deviation, variance, maximum value, and negative entropy of the acoustic emission signal, as well as the mean value, standard deviation, negative entropy, and smoothness index of the micro-vibration signal from the synchronous dataset of acoustic emission and micro-vibration in the full life cycle as acoustic emission features and micro-vibration features, and perform normalization processing to obtain multiple normalized acoustic emission feature sequences and multiple normalized micro-vibration feature sequences; Calculate the monotonicity index, correlation index, predictability index, and robustness index of multiple normalized acoustic emission feature sequences and multiple normalized micro-vibration feature sequences respectively, establish a linear weighted comprehensive evaluation index for acoustic emission features and a linear weighted comprehensive evaluation index for micro-vibration features, and screen the optimal features according to the highest score to obtain the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence; Calculate the mutual information and Euclidean distance between the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence, combine the fitness function to fuse the optimal acoustic emission feature sequence and the optimal micro-vibration feature sequence to obtain the optimal target fusion function, and then obtain the multi-stage health index of the harmonic reducer health state to realize the evaluation of the performance degradation of the harmonic reducer.

2. The performance degradation evaluation method of a harmonic reducer for an industrial robot according to claim 1, characterized in that The expression of the monotonicity index is as follows: where f i represents the i-th normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence, and represent the number of upward and downward changes of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i respectively, N is the total number of data points of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i , represents the change amplitude of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i between adjacent monitoring points k + 1 and k.

3. The performance degradation evaluation method of a harmonic reducer for an industrial robot according to claim 1, wherein The expression of the correlation index is as follows: where f i represents the i-th normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence, and Conv(f i , T) represents the covariance of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i and the time vector T, and σ(f i ) and σ(T) are the standard deviations of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence and the standard deviation of the time vector T, respectively.

4. The performance degradation evaluation method of a harmonic reducer for an industrial robot according to claim 1, wherein The expression of the predictability index is as follows: where, f i represents the i-th normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence, and std(f i,begin ) represents the standard deviation of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i in the healthy stage, and |f i,end - f i,begin | represents the difference between the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i in the rapid degradation stage and the initial stage.

5. The performance degradation evaluation method of a harmonic reducer for an industrial robot according to claim 1, characterized in that, The expression of the robustness index is as follows: where f i represents the i-th normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence, represents the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i of the mean value, exp(·) is the exponential function, used to ensure that the robustness index is positive, and N is the total number of data points of the normalized acoustic emission feature sequence or the normalized micro-vibration feature sequence f i of.

6. The performance degradation evaluation method of a harmonic reducer for an industrial robot according to claim 1, characterized in that When calculating the linear weighted comprehensive evaluation index of acoustic emission features and the linear weighted comprehensive evaluation index of micro-vibration features, the formula of the linear weighted comprehensive evaluation index used is as follows: C = w1Mon + w2Corr + w3Rob + w4Pro In the formula, C is the linear weighted comprehensive evaluation index, j represents the jth performance evaluation index, including the monotonicity index, correlation index, predictability index, and robustness index, w1 is the weight of the monotonicity index, w2 is the weight of the correlation index, w3 is the weight of the predictability index, and w4 is the weight of the robustness index.

7. The performance degradation evaluation method of a harmonic reducer for an industrial robot according to claim 1, wherein The formula for the multi-stage health index is as follows: In the formula, represents the optimal objective fusion function, represents the mutual information, represents the Euclidean distance, represents the optimal acoustic emission feature sequence, represents the optimal micro-vibration feature sequence, l(·) represents the fitness function in the differential evolution algorithm, max indicates that the optimization objective of the fitness function is the maximum, and γ∈[0,1] is a parameter for adjusting the relative weights of the mutual information and the Euclidean distance.

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