Residual life prediction method based on multi-evaluation index and multi-feature mutual influence

Abstract

The invention discloses a residual life prediction method based on mutual influence of multiple evaluation indexes and multiple features, and belongs to the technical field of residual life prediction of large castings and forgings. Aiming at the problem that the prediction result is inaccurate due to the influence of the external environment in the operation process of the slewing bearing of the wind turbine, the importance degree of features is comprehensively evaluated from multiple indexes, objective weights are comprehensively evaluated by utilizing a CRITIC method, comprehensive optimization function values of the features are obtained, mutual information amounts are respectively calculated, and the prediction result is accurate. And self-adaptive weight feature selection is realized according to a continuous change trend of a mutual information amount increment sum. A nonlinear state space model considering multi-degradation state interaction and multi-feature random correlation is proposed to be established, and online RUL prediction is achieved. According to more obtained monitoring data, estimation of each degradation state is achieved through an APF algorithm, distributed state fusion is achieved through a diagonal matrix weighting algorithm, unknown parameters in the model are estimated through MLE, and finally the effectiveness of the method is verified through monitored vibration data and temperature data.

Description

Technical Field

[0001] The present invention belongs to the technical field of remaining life prediction of large castings and forgings, and particularly relates to a remaining life prediction method based on the mutual influence of multiple evaluation indicators and multiple features. Background Art

[0002] Large castings and forgings have a harsh working environment and complex load changes. The resulting failures can easily lead to serious accidents, resulting in significant economic losses and even casualties. Excessive maintenance and replacement also have a significant impact on economic operations. Therefore, effective analysis of the remaining life (RUL) of large castings and forgings can ensure the healthy operation of large mechanical equipment while reducing maintenance costs, which is of great research significance. At present, research on wind turbine slewing bearings has mainly focused on fault prediction and diagnosis, and the literature in the field of RUL prediction is still very limited. The Outline of the National Medium- and Long-Term Science and Technology Development Plan also established the reliability of complex and major equipment and RUL prediction technology as a priority development goal.

[20] These also provide new ideas for the operation and maintenance of system components.

[0003] Compared to physical models, data-driven approaches attempt to derive life prediction models directly from monitored degradation data, rather than relying solely on physical failure mechanisms. By adding sensors to mechanical equipment, rich, real-time observational data reflecting equipment degradation is acquired, driving the rapid development of data-driven RUL prediction technology. Data-driven approaches primarily include statistical, artificial intelligence, and fusion methods. Statistical methods primarily rely on collected monitoring data and model it using stochastic or statistical models to achieve RUL prediction.

[0004] Using a single variable or a characteristic value within a certain domain to evaluate the degradation state of the equipment cannot accurately represent the degradation state. In order to accurately reflect the overall operating status, it is necessary to extract multiple features from multiple sensor data and conduct a comprehensive analysis to predict the RUL of the wind turbine slewing bearing. Summary of the Invention

[0005] In order to address the problem that the prediction results of wind turbine slewing bearings are inaccurate due to the influence of the external environment during operation, the present invention provides a remaining life prediction method based on the interaction of multiple evaluation indicators and multiple features, extracting more sensitive features suitable for characterizing the original data to improve parameter estimation and RUL prediction accuracy.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] The remaining life prediction method based on the interaction of multiple evaluation indicators and multiple features includes the following steps:

[0008] Step 1: Randomly select different features of different sensor data from multiple dimensions, and use three evaluation indicators: correlation, monotonicity, and robustness to comprehensively analyze the importance of the features;

[0009] The Spearman correlation coefficient is calculated in step 1, and the formula is: ,

[0010] Where, is the total feature quantity, is the corresponding monitoring time series.

[0011] The monotonicity index describes the consistency of data performance degradation, which depends on the overall strength of the monotonic non-decreasing or monotonic non-increasing trend. The closer the monotonicity index is to 1, the better the monotonicity trend of this type of feature. Its formula is: ,

[0012] Where, is a unit step function;

[0013] The robustness index is defined as: .

[0014] Step 2: The CRITIC method is used to calculate the weight of each evaluation index to obtain the comprehensive optimization function value of the feature. The random correlation between different features of different sensor data and the interaction between different degradation states are considered to establish a nonlinear state space prediction model.

[0015] The specific operations of step 2 are:

[0016] The CRITIC method is based on the volatility and correlation of data to comprehensively measure the objective weight of indicators, which is better than the entropy weight method and standard deviation method. The CRITIC method is used to calculate the weight of each indicator. Assuming that Features, evaluation indicators to form an indicator data matrix: , where Represents a sample Middle evaluation index value.

[0017] (1) Dimensionless processing

[0018] In order to eliminate the influence of different dimensions on the evaluation results, it is necessary to perform dimensionless processing on each indicator. The CRITIC weight method does not recommend the use of standardization because if standardization is used, the standard deviations of all indicators are basically the same, which makes the subsequent variability indicators meaningless. The formula is: ;

[0019] (2) Indicator variability

[0020] The level of fluctuation in the values ​​of each indicator is measured by the standard deviation. The larger the standard deviation, the more obvious the fluctuation in the indicator value, which better reflects the diversity of information, indicating that the indicator is more important in the evaluation and should be given a greater weight. The formula is:

[0021] , ;

[0022] Where, Indicates the The standard deviation of an indicator.

[0023] (3) Conflicting indicators

[0024] The Spearman correlation coefficient is used to measure indicator conflict. A high correlation between an indicator and other indicators indicates that the conflict between the indicators is small, and more identical information can be obtained, which may reduce the importance of the indicator in the overall evaluation. Therefore, a relatively small weight should be given to the indicator to avoid information duplication. The formula is: , where Indicates evaluation indicators and The correlation coefficient between .

[0025] (4) The formula for information volume is:

[0026] , The larger the The more important an evaluation indicator is in the entire evaluation indicator system, the greater the weight it needs to be assigned.

[0027] (5) Objective weight

[0028] No. Objective weights assigned to evaluation indicators for:

[0029] ;

[0030] The comprehensive evaluation equation constructed will Substitute into the comprehensive evaluation equation to calculate the comprehensive evaluation function value , the formula is as follows:

[0031] ,

[0032] Calculate the weight of each indicator according to Sort the values ​​in descending order to obtain the features with the largest comprehensive evaluation function value. The order is: ;

[0033] Comprehensive evaluation function value The largest feature is the benchmark feature, and the comprehensive evaluation function value , calculate the mutual information between the benchmark features and other features in turn, and calculate the sum of the mutual information increments in turn to obtain its changing trend. The sum of the mutual information increments starts, and when the continuous change trend is less than the set value, it is considered that the Feature pair The combination of the features has little effect, so the first Features form a feature combination.

[0034] The mutual information equation is: , where yes and The joint probability distribution function of and They are and The marginal probability distribution function of

[0035] In the state space model, the state transition function is used to describe the degradation process of the state, and the measurement function analyzes the relationship between multiple features and the state. The formula is: , where is the measurement function; is the state transition function, 、 Represent the degenerate state and The characteristics of the moment, and represent state transition noise and measurement noise respectively, , , Drift coefficient, is the diffusion coefficient, It is a standard Brownian motion. is the measurement matrix, ;

[0036] exist Introducing hidden correlations between multiple degenerate states Matrix, the state transfer equation is: , where Features in Degraded state ,Right now , Extract the total number of features from the data collected by a single sensor, , , express The corresponding drift coefficient, the drift coefficient changes randomly, . , , , different Expressing different diffusion processes, ;

[0037] In the observation equation, the correlation is introduced Matrix, where , , therefore, the established observation equation is:

[0038] ;

[0039] Assume that the observation error , are independent of each other, and their observation functions are fused to construct the following multi-source observation function:

[0040] , where To monitor the time, , for the The feature vector of the group observation data; , ,therefore, ;

[0041] in, It is a feature and The covariance of the measurement noise between , the state space model is expressed as:

[0042] , .

[0043] Step 3: Estimate the unknown parameters in the nonlinear state space prediction model using MLE and least squares method;

[0044] The specific operations of step 3 are:

[0045] In the observation equation, let The sensor extracts Different features, each feature shows a different degradation path, under the interference of the same external environment, there is correlation between different features, so it is necessary to estimate the parameters of the observation equation. , the correlation between different features is given by the covariance matrix Determine, the parameters of the measurement function are estimated in two steps;

[0046] The first step is to analyze each feature separately and estimate the model parameters , and ;

[0047] The second step is to jointly analyze all features and estimate the covariance matrix ;

[0048] First, the sensor data is smoothed by the local regression method to reduce noise. The filtered data is: ;

[0049] According to the degradation state and observation equation, the objective optimization function is constructed as follows:

[0050] ;

[0051] Estimate the parameters of the observation equation by least squares fitting , and thus calculate the measurement matrix ;

[0052] Next, we calculate the covariance matrix containing the correlation information of different measurement points , the variance matrix ;set up Features in A data set consisting of multiple measurement points at any given moment Obey multivariate normal distribution ;

[0053] Covariance The log-likelihood of is:

[0054] ;

[0055] Get the variance The maximum likelihood estimate of is:

[0056] ;Depend on , , calculate , and .

[0057] Step 4: Use the constructed nonlinear state space prediction model to perform RUL prediction on the wind turbine slewing bearing; the specific operations of step 4 are:

[0058] Assume that there is The monitoring data of samples, for the unit The sensor collects data and the fused state is recorded in the same time series ,in, is the total number of samples, is the last sampling time, i.e. the unit The failure time of The state sequence is represented as ,in, Indicates the Unit No. The sensors in The state after the moment is integrated;

[0059] When the drift coefficient is given , and the drift coefficient Is a random change, assuming that the degradation state obtained in different degradation processes is: , calculate the PDF of RUL, because and are independent random variables, ,get Approximate expression:

[0060] ,

[0061] Where, , , , .

[0062] Compared with the prior art, the present invention has the following advantages:

[0063] In the field of remaining useful life prediction, we first proposed a method to comprehensively evaluate the importance of features by integrating multiple evaluation indicators such as correlation, monotonicity, and robustness. Feature selection is achieved based on the continuous trend of the incremental sum of mutual information between features. Secondly, based on the random correlation between different features and the interaction between different degradation states under external environmental interference, we established a nonlinear state space model that considers the interaction of multiple degradation states and the random correlation of multiple features to achieve online RUL prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 Flowchart of the RUL prediction method;

[0065] Figure 2 Schematic diagram of RUL PDFs of four models;

[0066] Figure 3 The RUL prediction results of the four models are Comparison chart;

[0067] Figure 4 The RUL prediction results of the four models are Comparison chart;

[0068] Figure 5 For four models and Comparison chart. DETAILED DESCRIPTION

[0069] To gain a deeper understanding of the present invention, we will provide a comprehensive and detailed description thereof. However, the present invention has various implementations and is not limited to the specific examples listed herein. These examples are presented to enhance a comprehensive understanding of the present disclosure.

[0070] The method for predicting remaining useful life based on the interaction of multiple evaluation indicators and multiple features is characterized in that the method comprises the following steps:

[0071] Step 1: Randomly select different features of different sensor data from multiple dimensions, and use three evaluation indicators: correlation, monotonicity, and robustness to comprehensively analyze the importance of the features;

[0072] The Spearman correlation coefficient is calculated in step 1, and the formula is: ,

[0073] Where, is the total feature quantity, is the corresponding monitoring time series.

[0074] The monotonicity index describes the consistency of data performance degradation, which depends on the overall strength of the monotonic non-decreasing or monotonic non-increasing trend. The closer the monotonicity index is to 1, the better the monotonicity trend of this type of feature. Its formula is: ,

[0075] Where, is a unit step function;

[0076] The robustness index is defined as: .

[0077] Step 2: The CRITIC method is used to calculate the weight of each evaluation index to obtain the comprehensive optimization function value of the feature. The random correlation between different features of different sensor data and the interaction between different degradation states are considered to establish a nonlinear state space prediction model.

[0078] The specific operations of step 2 are:

[0079] The CRITIC method is based on the volatility and correlation of data to comprehensively measure the objective weight of indicators, which is better than the entropy weight method and standard deviation method. The CRITIC method is used to calculate the weight of each indicator. Assuming that Features, evaluation indicators to form an indicator data matrix: , where Represents a sample Middle evaluation index value.

[0080] (1) Dimensionless processing

[0081] In order to eliminate the influence of different dimensions on the evaluation results, it is necessary to perform dimensionless processing on each indicator. The CRITIC weight method does not recommend the use of standardization because if standardization is used, the standard deviations of all indicators are basically the same, which makes the subsequent variability indicators meaningless. The formula is: ;

[0082] (2) Indicator variability

[0083] The level of fluctuation in the values ​​of each indicator is measured by the standard deviation. The larger the standard deviation, the more obvious the fluctuation in the indicator value, which better reflects the diversity of information, indicating that the indicator is more important in the evaluation and should be given a greater weight. The formula is:

[0084] , ;

[0085] Where, Indicates the The standard deviation of an indicator.

[0086] (3) Conflicting indicators

[0087] The Spearman correlation coefficient is used to measure indicator conflict. A high correlation between an indicator and other indicators indicates that the conflict between the indicators is small, and more identical information can be obtained, which may reduce the importance of the indicator in the overall evaluation. Therefore, a relatively small weight should be given to the indicator to avoid information duplication. The formula is: , where Indicates evaluation indicators and The correlation coefficient between .

[0088] (4) The formula for information volume is:

[0089] , The larger the The more important an evaluation indicator is in the entire evaluation indicator system, the greater the weight it needs to be assigned.

[0090] (5) Objective weight

[0091] No. Objective weights assigned to evaluation indicators for:

[0092] ;

[0093] The comprehensive evaluation equation constructed will Substitute into the comprehensive evaluation equation to calculate the comprehensive evaluation function value , the formula is as follows:

[0094] ,

[0095] Calculate the weight of each indicator according to Sort the values ​​in descending order to obtain the features with the largest comprehensive evaluation function value. The order is: ;

[0096] Comprehensive evaluation function value The largest feature is the benchmark feature, and the comprehensive evaluation function value , calculate the mutual information between the benchmark features and other features in turn, and calculate the sum of the mutual information increments in turn to obtain its changing trend. The sum of the mutual information increments starts, and when the continuous change trend is less than the set value, it is considered that the Feature pair The combination of the features has little effect, so the first Features form a feature combination.

[0097] The mutual information equation is: , where yes and The joint probability distribution function of and They are and The marginal probability distribution function of

[0098] In the state space model, the state transition function is used to describe the degradation process of the state, and the measurement function analyzes the relationship between multiple features and the state. The formula is: , where is the measurement function; is the state transition function, 、 Represent the degenerate state and The characteristics of the moment, and represent state transition noise and measurement noise respectively, , , Drift coefficient, is the diffusion coefficient, It is a standard Brownian motion. is the measurement matrix, ;

[0099] exist Introducing hidden correlations between multiple degenerate states Matrix, the state transfer equation is: , where Features in Degraded state ,Right now , Extract the total number of features from the data collected by a single sensor, , , express The corresponding drift coefficient, the drift coefficient changes randomly, . , , , different Expressing different diffusion processes, ;

[0100] In the observation equation, the correlation is introduced Matrix, where , , therefore, the established observation equation is:

[0101] ;

[0102] Assume that the observation error , are independent of each other, and their observation functions are fused to construct the following multi-source observation function:

[0103] , where To monitor the time, , for the The feature vector of the group observation data; , ,therefore, ;

[0104] in, It is a feature and The covariance of the measurement noise between , the state space model is expressed as:

[0105] , .

[0106] Step 3: Estimate the unknown parameters in the nonlinear state space prediction model using MLE and least squares method;

[0107] The specific operations of step 3 are:

[0108] In the observation equation, let The sensor extracts Different features, each feature shows a different degradation path, under the interference of the same external environment, there is correlation between different features, so it is necessary to estimate the parameters of the observation equation. , the correlation between different features is given by the covariance matrix Determine, the parameters of the measurement function are estimated in two steps;

[0109] The first step is to analyze each feature separately and estimate the model parameters , and ;

[0110] The second step is to jointly analyze all features and estimate the covariance matrix ;

[0111] First, the sensor data is smoothed by the local regression method to reduce noise. The filtered data is: ;

[0112] According to the degradation state and observation equation, the objective optimization function is constructed as follows:

[0113] ;

[0114] Estimate the parameters of the observation equation by least squares fitting , and thus calculate the measurement matrix ;

[0115] Next, we calculate the covariance matrix containing the correlation information of different measurement points , the variance matrix ;set up Features in A data set consisting of multiple measurement points at any given moment Obey multivariate normal distribution ;

[0116] Covariance The log-likelihood of is:

[0117] ;

[0118] Get the variance The maximum likelihood estimate of is:

[0119] ;Depend on , , calculate , and .

[0120] Step 4: Use the constructed nonlinear state space prediction model to perform RUL prediction on the wind turbine slewing bearing; the specific operations of step 4 are:

[0121] Assume that there is The monitoring data of samples, for the unit The sensor collects data and the fused state is recorded in the same time series ,in, is the total number of samples, is the last sampling time, i.e. the unit The failure time of The state sequence is represented as ,in, Indicates the Unit No. The sensors in The state after the moment is integrated;

[0122] When the drift coefficient is given , and the drift coefficient Is a random change, assuming that the degradation state obtained in different degradation processes is: , calculate the PDF of RUL, because and are independent random variables, ,get Approximate expression:

[0123] ,

[0124] Where, , , , .

[0125] In order to verify the adaptability of the RUL prediction method, in addition to the proposed method, three representative modeling methods are also used for comparison. The method proposed in this paper considers the interaction between different degradation states in constructing the degradation model and also introduces the correlation between different features, which are recorded as Model, and the model of the present invention. The degradation process modeling method that does not consider the correlation between different features is recorded as model. The RUL prediction does not take into account the interaction between different degradation states in the diffusion coefficient matrix, and this model is recorded as Model. The principal component analysis method is used to integrate multiple features and build a nonlinear Wiener process model to achieve RUL prediction, which is recorded as Model.

[0126] Figure 2 The RUL distributions predicted by the four models at different times were compared. In the early stages of monitoring, when data was scarce, the prediction errors of the four models were large. As monitoring time increased, the predicted RUL errors gradually decreased. Compared with the other three models, the RUL PDF of the proposed method better covered the actual RUL. Furthermore, as more monitoring data was collected, the PDF shape gradually narrowed and grew taller, and the prediction results became more convergent. This demonstrates that the proposed model can improve the RUL prediction accuracy of wind turbine slewing bearings.

[0127] Finally, in order to further verify the effectiveness of the method proposed in this invention, we calculated 、 , Accuracy (A), and Prediction Interval Coverage Probability (PICP) are used to evaluate the performance of the four prediction models, as shown in Table 1. Figure 3 、 Figure 4 and Figure 5 In addition, at the same monitoring moment, the present invention proposes The RUL prediction of the model is smaller than the prediction results of the other three models. The model can more accurately predict the RUL of the slewing bearing.

[0128] Table 1 Quantitative comparison of accuracy and uncertainty of four methods

[0129]

[0130] Any matters not described in detail in this specification are prior art known to those skilled in the art. Although the above description of the present invention is based on specific embodiments to facilitate understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the specific embodiments. As long as various modifications are within the spirit and scope of the present invention as defined and determined by the appended claims, such modifications will be obvious to those skilled in the art, and all inventions and creations utilizing the concepts of the present invention are protected.

Claims

1. A remaining life prediction method based on the interaction of multiple evaluation indicators and multiple features, characterized by: The method comprises the following steps: Step 1: Randomly select different features of different sensor data from multiple dimensions, and use three evaluation indicators: correlation, monotonicity, and robustness to comprehensively analyze the importance of the features; Step 2: The CRITIC method is used to calculate the weight of each evaluation index to obtain the comprehensive optimization function value of the feature. The random correlation between different features of different sensor data and the interaction between different degradation states are considered to establish a nonlinear state space prediction model. Step 3: Estimate the unknown parameters in the nonlinear state space prediction model using MLE and least squares method; Step 4: Use the constructed nonlinear state space prediction model to predict the RUL of the wind turbine slewing bearing.

2. The method for predicting remaining useful life based on the interaction of multiple evaluation indicators and multiple features according to claim 1, characterized in that: The Spearman correlation coefficient is calculated in step 1, and the formula is: , Where, is the total feature quantity, is the corresponding monitoring time series; The monotonicity index describes the consistency of data performance degradation and its formula is: , Where, is a unit step function; The robustness index is defined as: .

3. The method for predicting remaining useful life based on the interaction of multiple evaluation indicators and multiple features according to claim 2, characterized in that: The specific operations of step 2 are: The CRITIC method is used to calculate the weight of each indicator. Assuming that Features, evaluation indicators to form an indicator data matrix: , where Represents a sample Middle Evaluation index value; In order to eliminate the influence of different dimensions on the evaluation results, each indicator is dimensionless, and the formula is as follows: ; The level of fluctuation of the values ​​within each indicator is measured by standard deviation, and the formula is: ， ； Where, Indicates the The standard deviation of each indicator; The Spearman correlation coefficient is used to measure the conflict of indicators. The formula is: , where Indicates evaluation indicators and The correlation coefficient between Calculate the indicator information volume, the formula is: ； No. Objective weights assigned to evaluation indicators for: ； The comprehensive evaluation equation constructed will Substitute into the comprehensive evaluation equation to calculate the comprehensive evaluation function value , the formula is as follows: ， Calculate the weight of each indicator according to Sort the values ​​in descending order to obtain the features with the largest comprehensive evaluation function value. The order is: ; Comprehensive evaluation function value The largest feature is the benchmark feature, and the comprehensive evaluation function value , calculate the mutual information between the benchmark feature and other features in turn, and calculate the sum of the mutual information increments in turn to obtain its changing trend; The mutual information equation is: , where yes and The joint probability distribution function of and They are and The marginal probability distribution function of In the state space model, the state transition function is used to describe the degradation process of the state, and the measurement function analyzes the relationship between multiple features and the state. The formula is: , where is the measurement function; is the state transition function, 、 Represent the degenerate state and The characteristics of the moment, and represent state transition noise and measurement noise respectively, , , Drift coefficient, is the diffusion coefficient, It is a standard Brownian motion. is the measurement matrix, ; exist Introducing hidden correlations between multiple degenerate states Matrix, the state transfer equation is: , where Features in Degraded state ,Right now , Extract the total number of features from the data collected by a single sensor, , , express The corresponding drift coefficient, the drift coefficient changes randomly, ; , , , different Expressing different diffusion processes, ; In the observation equation, the correlation is introduced Matrix, where , , therefore, the established observation equation is: ； Assume that the observation error , are independent of each other, and their observation functions are fused to construct the following multi-source observation function: , where To monitor the time, , for the The feature vector of the group observation data; , ,therefore, ; in, It is a feature and The covariance of the measurement noise between , the state space model is expressed as: ， 。 4. The method for predicting remaining useful life based on the interaction of multiple evaluation indicators and multiple features according to claim 3, characterized in that: The specific operations of step 3 are: In the observation equation, let The sensor extracts Different features, each feature shows a different degradation path, under the interference of the same external environment, there is correlation between different features, so it is necessary to estimate the parameters of the observation equation. , the correlation between different features is given by the covariance matrix Determine, the parameters of the measurement function are estimated in two steps; The first step is to analyze each feature separately and estimate the model parameters , and ; The second step is to jointly analyze all features and estimate the covariance matrix ; First, the sensor data is smoothed by the local regression method to reduce noise. The filtered data is: ; According to the degradation state and observation equation, the objective optimization function is constructed as follows: ； Estimate the parameters of the observation equation by least squares fitting , and thus calculate the measurement matrix ; set up Features in A data set consisting of multiple measurement points at any given moment Obey multivariate normal distribution ; Covariance The log-likelihood of is: ； Get the variance The maximum likelihood estimate of is: ;Depend on , , calculate , and .

5. The method for predicting remaining useful life based on the interaction of multiple evaluation indicators and multiple features according to claim 4, characterized in that: The specific operations of step 4 are: Assume that there is The monitoring data of samples, for the unit The sensor collects data and the fused state is recorded in the same time series ,in, is the total number of samples, is the last sampling time, i.e. the unit The failure time of The state sequence is represented as ,in, Indicates the Unit No. The sensors in The state after the moment is integrated; When the drift coefficient is given , and the drift coefficient Is a random change, assuming that the degradation state obtained in different degradation processes is: , calculate the PDF of RUL, because and are independent random variables, ,get Approximate expression: ， Where, , , , .

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