A multi-stage degradation evolution prediction method, device, and storage medium for devices based on statistical models and deep learning

Abstract

The present invention belongs to the technical field of equipment degradation evolution prediction, and discloses a multi-stage degradation evolution prediction method, equipment and storage medium for equipment based on a statistical model and deep learning. The present invention establishes an AR model to divide the degradation process of mechanical equipment into multiple degradation stages, and at the same time constructs a multi-stage degradation evolution prediction model by using LSTM optimized by GA, reduces the uncertainty of degradation evolution prediction, improves the prediction accuracy, and at the same time the multi-stage prediction results can estimate the state of each stage, which can better support the prediction of the remaining life of mechanical equipment, so it has practical application significance.

Description

Technical Field

[0001] The present invention belongs to the technical field of equipment degradation evolution prediction, and particularly relates to a multi-stage degradation evolution prediction method, equipment and storage medium for equipment based on a statistical model and deep learning. Background Art

[0002] With the development of industry, the structure and function of mechanical equipment are becoming increasingly complex, and the degree of automation is constantly improving. However, in actual engineering applications, due to the harsh and changeable working environment of mechanical equipment and complex working conditions, mechanical equipment is prone to degradation, affecting the normal operation and reliability of mechanical equipment. In order to ensure the safe and efficient operation of mechanical equipment, degradation evolution prediction has always been a hot issue in industrial research. Conducting degradation evolution prediction on equipment can effectively identify abnormal components, help prevent potential system failures, and improve the safety of mechanical equipment. Therefore, the degradation evolution prediction of mechanical equipment is of great significance for both its reliability and safety.

[0003] In most cases, the degradation trend of equipment presents different characteristics with different working conditions. It is very difficult for the prediction method based on a single-stage model to effectively capture the degradation characteristics of different stages, bringing great challenges to the reliable operation and maintenance of equipment. Deep learning has powerful computing capabilities in processing complex degradation data and is very suitable for processing multi-feature degradation sequences. The method based on statistics has clear mathematical expressions and analysis processes, can effectively describe the degradation trend of equipment, and provide repeatable degradation fitting results. Therefore, aiming at different degradation characteristics, effectively combining the advantages of statistical methods and deep learning methods can, to a certain extent, establish a clearer degradation analysis process and obtain high-precision prediction results.

[0004] Based on this, the present invention conducts multi-stage degradation evolution prediction based on a statistical model and deep learning for different degradation characteristics of mechanical equipment in different service stages, which can effectively reduce prediction errors and has practical application significance. Summary of the Invention

[0005] Aiming at the problems and deficiencies existing in the prior art, the purpose of the present invention is to provide a multi-stage degradation evolution prediction method, equipment and storage medium for equipment based on a statistical model and deep learning.

[0006] Based on the above purpose, the present invention adopts the following technical solutions:

[0007] The first aspect of the present invention provides a multi-stage degradation evolution prediction method for equipment based on a statistical model and deep learning, including the following steps:

[0008] S1: Extract the total set of degradation index time series data: Collect the time series data of the device degradation signal, use the root mean square as the degradation index, and extract the root mean square value of the time series data of the degradation signal according to the unit time period to obtain the total set of degradation index time series data;

[0009] S2: Identify the degradation mutation points: Segment the total set of degradation index time series data obtained in step S1, establish an AR model for each segment at the same time, and then obtain the one-step prediction error of the AR model according to the fitting result of the AR model, and identify the degradation mutation points with the goal of minimizing the multi-segment error;

[0010] S3: Obtain the optimal parameter combination of the LSTM model: Construct an LSTM model, and use the genetic algorithm GA to optimize the parameters involved in the LSTM model to obtain the optimal parameter combination;

[0011] S4: Divide the total set of degradation index time series data into multiple subsets of degradation index time series data with the degradation mutation points obtained in step S2 as the boundaries; Substitute the optimal parameter combination obtained in step S3 into the constructed LSTM model to construct a degradation prediction model, and train and test the degradation prediction model with each subset of degradation index time series data respectively, and obtain multiple segments of degradation prediction curves at the same time; Concatenate the multiple segments of degradation prediction curves in time series to obtain the multi-stage degradation prediction curve.

[0012] Preferably, the device degradation signal in step S1 can be a vibration signal, a temperature signal, a stress signal, etc. that can represent the device state.

[0013] More preferably, the mathematical expression of the root mean square value of the degradation index in step S1 is:

[0014]

[0015] where x

[0016] ,

[0015] , ,

[0020] , ,

[0019] ,

[0018] ,

[0017] , , , , i , ,

[0014] , ,

[0013] , represents the i-th data, and n represents the number of data within a single sampling time interval.

[0016] Preferably, the specific steps for identifying the degradation mutation points in step S2 are:

[0017] S21. Identify the first degradation mutation point:

[0018] S211. According to the change trend of the total set of degradation index time series data, delimit the interval where the first degradation mutation point is located;

[0019] S212. Select any point within the interval where the degradation mutation point is located to divide the total set of degradation index time series data into a first subset and a second subset;

[0020] S213. Based on the AR model, establish the first AR model and the second AR model using the first subset and the second subset respectively; then use the first AR model and the second AR model to fit the data in the first subset and the second subset respectively, and calculate the sum RSS of the sum of the squared one-step prediction errors of the first AR model and the sum of the squared one-step prediction errors of the second AR model;

[0021] S214. Traverse all the points in the interval where the degenerate mutation point described in step S211 is located, and repeat the calculation process of step S212 and step S213 to obtain the RSS of all the points in the interval where the degenerate mutation point is located; select the point corresponding to the minimum RSS as the first degenerate mutation point;

[0022] S22. Identify other degenerate mutation points: According to the data change trend after the first degenerate mutation point in the total set of degenerate index time series data, delimit the interval where the second degenerate mutation point is located again; select any point in the interval where the degenerate mutation point is located to divide the data after the first degenerate mutation point in the total set of degenerate index time series data into a first subset and a second subset; repeat step S213 and step S214 to obtain the second degenerate mutation point; and so on to obtain all the degenerate mutation points in the total set of degenerate index time series data.

[0023] More preferably, the specific steps of establishing the first AR model or the second AR model using the first subset or the second subset respectively in step S213 are as follows:

[0024] (1) Construct an AR model, and its mathematical expression is as follows:

[0025]

[0026] In the formula, p ∈ N is the order of the AR model, ε n is an independent and identically distributed white noise sequence that follows the normal distribution N(0, σ 2 ), is the autocorrelation coefficient matrix, Y n is the value corresponding to the time series, and n is the length of the sequence;

[0027] (2) Use the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) to determine the order p of the AR model, and select the p that makes both AIC and BIC reach the minimum value as the order of the AR model; its mathematical expression is as follows:

[0028]

[0029]

[0030] p = 0, 1,..., p0, p0 = 10lg n

[0031] Where p is the order of the model, is the maximum likelihood estimate of the variance of ε n under the condition of order p, and n is the length of the sequence;

[0032] (3) Estimate the parameters of . The least squares estimation is selected for the parameter estimation of the AR model. The specific steps are as follows:

[0033] For the sequence X = [x1, x2, …, x n , its corresponding values are Y = [y1, y2, …, y n . When j ≥ p + 1,

[0034] Denote

[0035] Then the AR model of order p can be expressed as

[0036] According to the least squares principle, the least squares estimate of the parameter is:

[0037] (4) Substitute the p value obtained in step (2) and the value obtained in step (3) into the mathematical expression of the AR model in step (1), and the specific expressions of the first AR model or the second AR model can be obtained.

[0038] More preferably, the specific steps for calculating the sum RSS of the one-step prediction error square sum of the first AR model and the one-step prediction error square sum of the second AR model in step S213 are as follows:

[0039] i) Obtain the one-step prediction errors ξ ione and ξ itwo of the first AR model and the second AR model respectively. Their mathematical expressions are as follows:

[0040]

[0041]

[0042] In the formula, A is the possible position for selecting the mutation point, are the true values of point A in the first subset and the second subset respectively, are the fitted values of point A in the first subset and the second subset after passing through the AR model respectively;

[0043] ii) Calculate the sum RSS of the one-step prediction error square sum of the first AR model and the one-step prediction error square sum of the second AR model. Its mathematical expression is as follows:

[0044]

[0045] Furthermore, the LSTM model stores all the information before each time step in the neural unit at the current time step. Each neural unit is controlled by an input gate, a forget gate, and an output gate. The input gate is used to control the input information of the neural unit at the current moment, the forget gate is used to control the historical information stored in the neural unit at the previous moment, and the output gate is used to control the output information of the neural unit at the current moment. The purpose of this design is to enable the LSTM model to selectively remember the more important part of the historical information.

[0046] Preferably, the specific steps for constructing the LSTM model in step S3 are as follows: The forget gate passes the hidden layer state h t-1 at the previous moment and the current input state x t to the sigmoid function to obtain the forgetting probability f t ;

[0047] f t = σ(w f [h t-1 , x t + b f )

[0048] In the formula, w f is the forget gate weight, and b f is the forget gate bias;

[0049] The input gate determines the information to be stored according to the current input state x t and the hidden layer state h t-1 to realize the update of the state C; The input gate determines the information to be stored according to the current input state x

[0050] i t = σ(w i [h t-1 , x t + b i )

[0051]

[0052] In the formula, w i , b i are the weight and bias of the input gate respectively, and w t , b t are the weight and bias of the memory cell state respectively;

[0053] The current cell state is updated according to the forget gate, the input gate, and the hidden layer state at the previous moment. The current cell state through the forget gate and the output gate is as follows:

[0054]

[0055] In the formula, i is the probability that new information is updated to the cell state;

[0056] The output gate represents the output of the hidden layer, as shown in the following formula:

[0057] o t = σ(w0[h t-1 , x t +b0)

[0058] h t = o t ·tanh(C t )

[0059] In the formula, w0 and b0 are the weights and biases of the output gate, tanh is the activation function, h t is the hidden layer state of the next layer, and o t is the output content.

[0060] Preferably, when the genetic algorithm GA is used to optimize the parameters involved in the LSTM model in step S3, with the minimum prediction error as the objective function, the optimal solution of the parameter search space is obtained to get the optimal parameter combination. The specific steps are as follows:

[0061] S31. Set the candidate solutions of the problem and perform chromosome coding, specifically:

[0062] After taking the values of the four parameters of the learning rate, number of training times, sequence length, and number of hidden layer neurons involved in the LSTM model, they form a group of candidate solutions;

[0063] In the genetic algorithm GA, the individual is the value of the parameter, and the value of the parameter in the present invention is a real number. The real number can be encoded as a vector representation. Therefore, after encoding the individual into a chromosome, each chromosome has 4 genes, corresponding to 4 parameters respectively. Each chromosome can be expressed as X = (learning rate, number of training times, sequence length, number of hidden layer neurons); its mathematical expression is as follows:

[0064] x(j) = a(j) + y(j)(b(j) - a(j)), j = 1, 2,... p

[0065] In the formula, p is the number of optimization parameters. In the present invention, p = 4, x(j) is the jth optimization parameter, [a(j), b(j)] is the change interval of x(j), and y(j) is the real number corresponding to the parameter encoding;

[0066] S32. Population initialization: Set the initial parameter values, generate the population by a random method, and set the value range of the 4 parameters that need to be optimized for the prediction model according to the prediction data;

[0067] S33. Construct the fitness function: Take the reciprocal of the root mean square error of the LSTM neural network as the fitness function, and its mathematical expression is:

[0068]

[0069] In the formula, n is the length of the data sequence, Y i is the true value, is the predicted value;

[0070] S34. Perform selection, crossover, and mutation operations on the individual solutions:

[0071] For the crossover operation, use the simulated binary crossover operator to complete the crossover operation, and the mathematical expression of the new individual after crossover is:

[0072]

[0073]

[0074]

[0075] In the formula, η is a user-defined factor, generally set to 1, and x is the possible values of the four parameters corresponding to the learning rate, number of training times, sequence length, and number of neurons in the hidden layer for the four parent individuals respectively, and random is the mutation probability;

[0076] For the mutation operation, the present invention selects the polynomial mutation operator for mutation operation, and its mathematical expression is as follows:

[0077] ν k =ν k +δ(μ k -l k )

[0078]

[0079]

[0080]

[0081] In the formula, ν k is a parent individual, and η is a user-defined factor, generally set to 1;

[0082] S35. Use the offspring individuals obtained from the previous crossover and mutation as the new generation of population, and obtain the target value of the fitness function. If the target value of the fitness function reaches the maximum, proceed to the next step; otherwise, return to step S33;

[0083] S36. Obtain the optimal parameter combination.

[0084] Preferably, the specific steps of training and testing the degradation prediction model with each subset of degradation index time series data in step S4 are as follows:

[0085] S41. Divide each subset of degradation index time series data into a training set and a test set;

[0086] S42. Use the training sets of different subsets of degradation index time series data to train the degradation prediction model respectively, and obtain multiple trained degradation prediction models;

[0087] S43. Input the test sets of each subset of degradation index time series data into the corresponding trained degradation prediction models for testing respectively, analyze the error between the prediction results and the expected results, and obtain multiple degradation prediction curves at the same time.

[0088] Preferably, the division ratio of the training set and the test set is 9:1.

[0089] More preferably, the evaluation index of the error analysis in step S43 is the root mean square error, and its mathematical expression is:

[0090]

[0091] In the formula, n is the length of the data sequence, Y i is the true value, is the predicted value.

[0092] In the second aspect of the present invention, an electronic device is provided, including a memory and a processor. A computer program is stored on the memory, and when the processor executes the computer program, any step in the multi-stage degradation evolution prediction method described in the first aspect above is implemented.

[0093] In the third aspect of the present invention, a computer-readable storage medium is provided. A computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, any step in the multi-stage degradation evolution prediction method described in the first aspect above is implemented.

[0094] Compared with the prior art, the present invention has the following beneficial effects:

[0095] The present invention takes into account that different service stages of the device have different degradation characteristics, establishes an AR model to divide the degradation process of mechanical equipment into multiple degradation stages, and at the same time uses an optimized LSTM to construct a multi-stage degradation evolution prediction model, reducing the uncertainty of degradation evolution prediction and improving the prediction accuracy; the multi-stage prediction results can estimate the state of each stage, and can better support the prediction of the remaining life of mechanical equipment. Description of the Drawings

[0096] Figure 1 This is the overall flowchart of the present invention;

[0097] Figure 2 This is the flowchart of the degradation evolution prediction based on the GA-LSTM model of the present invention;

[0098] Figure 3 This is the position of the first mutation point in the range interval [1400, 1800] in the embodiment of the present invention;

[0099] Figure 4 This is the position of the second mutation point in the range interval [2100, 2350] in the embodiment of the present invention;

[0100] Figure 5 This is the schematic diagram of the multi-stage division result of the true degradation curve in the embodiment of the present invention;

[0101] Figure 6 This is the first-stage degradation evolution prediction result of the multi-stage degradation evolution prediction model in the embodiment of the present invention;

[0102] Figure 7 This is the second-stage degradation evolution prediction result of the multi-stage degradation evolution prediction model in the embodiment of the present invention;

[0103] Figure 8 This is the third-stage degradation evolution prediction result of the multi-stage degradation evolution prediction model in the embodiment of the present invention;

[0104] Figure 9 This is the comparison of the degradation evolution prediction results between the multi-stage degradation evolution prediction model and the traditional single-stage model in the embodiment of the present invention. Detailed implementation manners

[0105] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below through embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0106] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0107] Embodiment 1

[0108] This embodiment provides a method for predicting the multi-stage degradation evolution of equipment based on a statistical model and deep learning, as Figure 1 shown. The method includes the following steps:

[0109] S1: Extract the total set of degradation index time series data: Collect the time series data of the device degradation signal (such as vibration signal, temperature signal, stress signal, etc. that can represent the device state), use the root mean square as the degradation index, and extract the root mean square value of the time series data of the degradation signal according to the unit time period to obtain the total set of degradation index time series data; the mathematical expression of the root mean square value of the degradation index is:

[0110]

[0111] where x i represents the i-th data, and n represents the number of data within the unit time period.

[0112] S2: Identify the degradation mutation points: Segment the total set of degradation index time series data obtained in step S1, and simultaneously establish AR models for each segment. Then, obtain the one-step prediction error of the AR model according to the fitting results of the AR model, and identify the degradation mutation points with the goal of minimizing the multi-segment error. The specific steps are as follows:

[0113] S21. Identify the first degradation mutation point:

[0114] S211. According to the change trend of the total set of degradation index time series data, delimit the interval where the first degradation mutation point A is located, that is, the inflection point area where the trend slope changes; denote X Aj ∈[X A1 ,X Ak , 0 ≤ A1 ≤ A k ≤ n, 1 ≤ j ≤ k, where A1 is the first point in the interval where the first degradation mutation point A is located, and Ak is the last point in the interval where the first degradation mutation point A is located.

[0115] S212. For the time series X = [x1, x2,..., x n , its corresponding degradation index time series data values are Y = [y1, y2,..., y n . Select any point such as X A1 within the interval where the first degradation mutation point A is located, and divide the time series into X one and X two two parts. Divide the total set of degradation index time series data into a first subset and a second subset, and denote them as

[0116] S213. Based on the AR model, establish the first AR model and the second AR model for the first subset and the second subset respectively; then, use the first AR model and the second AR model to fit the data in the first subset and the second subset respectively, and calculate the sum RSS of the one-step prediction error square sum of the first AR model and the one-step prediction error square sum of the second AR model.

[0117] Among them, the specific steps of establishing the first AR model or the second AR model with the first subset or the second subset respectively are as follows:

[0118] (1) Construct an AR model, and its mathematical expression is as follows:

[0119]

[0120] In the formula, p ∈ N is the order of the AR model, and ε n is an independent and identically distributed white noise sequence that follows the normal distribution N(0, σ 2 ), is the autocorrelation coefficient matrix, Y n is the value corresponding to the time series, and n is the length of the sequence;

[0121] (2) Use the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) to determine the order p of the AR model, and select the p that minimizes both AIC and BIC simultaneously as the order of the AR model; its mathematical expression is as follows:

[0122]

[0123]

[0124] p = 0, 1,..., p0, p0 = 10lg n

[0125] In the formula, p is the order of the model, is the maximum likelihood estimate of the variance of ε n under the condition of p order, and n is the length of the sequence;

[0126] (3) Perform parameter estimation on , and the least squares estimation is selected for the parameter estimation of the AR model. The specific steps are as follows:

[0127] For the sequence X = [x1, x2,..., x n , its corresponding values are Y = [y1, y2,..., y n . When j ≥ p + 1,

[0128] Denote

[0129] Then the p-order AR model can be expressed as

[0130] According to the least squares principle, the least squares estimate of the parameter is:

[0131] (4) Substitute the p value obtained in step (2) and the Substitute the value into the mathematical expression of the AR model in step (1), and the specific expressions of the first AR model or the second AR model can be obtained.

[0132] The specific steps for calculating the sum RSS of the one-step prediction error sum of squares of the first AR model and the one-step prediction error sum of squares of the second AR model are as follows:

[0133] i) Obtain the one-step prediction errors ξ ione and ξ itwo of the first AR model and the second AR model respectively. Their mathematical expressions are as follows:

[0134]

[0135]

[0136] In the formula, A is the possible position of the selected mutation point, are the true values of point A in the first subset and the second subset respectively, are the fitted values of point A in the first subset and the second subset after passing through the AR model respectively;

[0137] ii) Calculate the sum RSS of the one-step prediction error sum of squares of the first AR model and the one-step prediction error sum of squares of the second AR model. Its mathematical expression is as follows:

[0138]

[0139] S214. Traverse all points in the interval where the degenerate mutation point described in step S211 is located, and repeat the calculation processes of step S212 and step S213 to obtain the RSS of all points in the interval where the degenerate mutation point is located i , i = 1…k; Screen the minimum value RSS of RSS s = min(RSS i ), and the point A s corresponding to 1≤s≤k is the first degenerate mutation point.

[0140] S22. Identify other degenerate mutation points: Remove the data before the first degenerate mutation point and the data corresponding to the first degenerate mutation point itself. According to the data change trend after the first degenerate mutation point in the total set of degenerate index time series data, delimit the interval where the second degenerate mutation point is located again; Select any point in the interval where the degenerate mutation point is located to divide the data after the first mutation point in the total set of degenerate index time series data into a first subset and a second subset; Repeat step S213 and step S214 to obtain the second degenerate mutation point; And so on to obtain all degenerate mutation points in the total set of degenerate index time series data.

[0141] S3: Obtain the optimal parameter combination of the LSTM model: Construct an LSTM model and use the genetic algorithm GA to optimize the parameters involved in the LSTM model to obtain the optimal parameter combination.

[0142] The LSTM model stores all the information before each time step in the neuron at the current time step. Each neuron is controlled by an input gate, a forget gate, and an output gate. The input gate is used to control the input information of the neuron at the current moment, the forget gate is used to control the historical information stored in the neuron at the previous moment, and the output gate is used to control the output information of the neuron at the current moment. The purpose of this design is to enable the LSTM model to selectively remember the more important part of the historical information.

[0143] Therefore, the specific steps to construct an LSTM model are as follows: The forget gate passes the hidden layer state h at the previous moment t-1 and the current input state x t to the sigmoid function to obtain the forgetting probability f t ;

[0144] f t = σ(w f [h t-1 , x t + b f )

[0145] where w f is the forget gate weight and b f is the forget gate bias;

[0146] The input gate determines the information to be stored according to the current input state x t and the hidden layer state h t-1 to realize the update of the state C; i

[0147] = σ(w t [h i , x t-1 , x t + b i )

[0148]

[0149] where w i , b i [[ID=Z4]]are the weights and biases of the input gate respectively, and w t , b t are the weights and biases of the memory cell state respectively;

[0150] The current cell state is updated according to the forget gate, the input gate, and the hidden layer state at the previous moment. The current cell state through the forget gate and the output gate is as follows:

[0151]

[0152] Wherein, i is the probability that new information is updated to the cell state;

[0153] The output gate represents the output of the hidden layer, as shown in the following formula:

[0154] o t = σ(w0[h t-1 , x t +b0)

[0155] h t = o t ·tanh(C t )

[0156] Wherein, w0 and b0 are the weights and biases of the output gate, tanh is the activation function, h t is the hidden layer state of the next layer, and o t is the output content.

[0157] It should be noted that in the present invention, the open-source framework Keras in Python is selected to build the model, and the Sequential model is selected to construct the LSTM model. The LSTM in the present invention is set to be single-layer. For the learning rate, the number of training times, the sequence length, and the number of neurons in the hidden layer, there is no stable relationship between its parameters and the training results, and it is necessary to continuously try to adjust the parameters. Therefore, the present invention introduces GA to find the optimal parameters. In the modeling, the present invention selects the sigmoid function and the tanh function as the activation functions.

[0158] Furthermore, when using the genetic algorithm GA to optimize the parameters involved in the LSTM model, with the minimum prediction error as the objective function, the optimal solution of the parameter search space is obtained to get the optimal parameter combination. The process is as Figure 2 shown, and the specific steps are as follows:

[0159] S31. Set the candidate solutions of the problem and perform chromosome encoding, specifically:

[0160] After taking the values of the 4 parameters of the learning rate, the number of training times, the sequence length, and the number of neurons in the hidden layer involved in the LSTM model, they form a group of candidate solutions;

[0161] In the genetic algorithm GA, the individual is the value of the parameter, and the value of the parameter in the present invention is a real number. The real number can be encoded as a vector representation. Therefore, after encoding the individual as a chromosome, the number of genes in each chromosome is 4, corresponding to 4 parameters respectively. Each chromosome can be expressed as X = (learning rate, number of training times, sequence length, number of neurons in the hidden layer); its mathematical expression is as follows:

[0162] x(j) = a(j) + y(j)(b(j) - a(j)), j = 1, 2, … p

[0163] Where p is the number of optimization parameters, and in the present invention p = 4. x(j) is the j-th optimization parameter, [a(j), b(j)] is the variation range of x(j), and y(j) is the real number corresponding to the parameter coding;

[0164] S32. Population initialization: Set the initial parameter values, generate the population by a random method, and set the value ranges of the 4 parameters to be optimized by the prediction model according to the prediction data;

[0165] S33. Construct the fitness function: Take the reciprocal of the root mean square error of the LSTM neural network as the fitness function, and its mathematical expression is:

[0166]

[0167] Where n is the length of the data sequence, Y i is the true value, is the predicted value;

[0168] S34. Perform selection, crossover, and mutation operations on the individuals of the solution:

[0169] For the crossover operation, use the simulated binary crossover operator to complete the crossover operation, and the mathematical expression of the new individual after crossover is:

[0170]

[0171]

[0172]

[0173] Where η is a user-defined factor, generally set to 1, x is the possible values of the 4 parent individuals corresponding to the learning rate, the number of training times, the sequence length, and the number of neurons in the hidden layer respectively, and random is the mutation probability;

[0174] For the mutation operation, the present invention selects the polynomial mutation operator to perform the mutation operation, and its mathematical expression is as follows:

[0175] ν k = ν k + δ(μ k - l k )

[0176]

[0177]

[0178]

[0179] where ν k is a parental individual, η is a user-defined factor, usually set to 1;

[0180] S35. The offspring individuals obtained from the previous crossover and mutation are used as a new generation of population, and the target value of the fitness function is obtained. If the target value of the fitness function reaches the maximum, proceed to the next step; otherwise, return to step S33;

[0181] S36. Obtain the optimal parameter combination.

[0182] S4: Divide the total set of degradation index time series data into multiple subsets of degradation index time series data with the degradation mutation points obtained in step S2 as the boundaries; substitute the optimal parameter combination obtained in step S3 into the constructed LSTM model to construct a degradation prediction model, and train and test the degradation prediction model with each subset of degradation index time series data respectively, and at the same time obtain multiple segments of degradation prediction curves; concatenate the multiple segments of degradation prediction curves in time series to obtain a multi-stage degradation prediction curve.

[0183] Among them, the specific steps of training and testing the degradation prediction model with each subset of degradation index time series data respectively are as follows:

[0184] S41. Divide each subset of degradation index time series data into a training set and a test set according to 9:1;

[0185] S42. Use the training sets of different subsets of degradation index time series data to train the degradation prediction model respectively to obtain multiple trained degradation prediction models;

[0186] S43. Input the test sets of each subset of degradation index time series data into the corresponding trained degradation prediction models for testing respectively, and perform error analysis on the prediction results and the expected results, and at the same time obtain multiple segments of degradation prediction curves. The evaluation index of the error analysis is the root mean square error, and its mathematical expression is:

[0187]

[0188] where n is the length of the data sequence, Y i is the true value, is the predicted value.

[0189] Actual measurement and analysis:

[0190] Case analysis is carried out using bearings. The full-life bearing data comes from the bearing data provided by the FEMTO-ST Institute. The test bench consists of a rotating part, a degradation generation part, and a measurement part. To accelerate the degradation process of the bearing and shorten its life cycle, the radial load of the rolling bearing is continuously increased until it reaches the maximum rated value of the bearing. Under three different working conditions, 17 bearings are used for degradation experiments, and 17 complete vibration data are obtained. The three working conditions are: rotational speed of 1800 revolutions per minute and radial load of 4000 N; rotational speed of 1650 revolutions per minute and radial load of 4200 N; rotational speed of 1500 revolutions per minute and radial load of 5000 N. Among them, 7 bearings are tested under the first working condition, and their numbers are 1_1 to 1_7. In this method, bearing 1_3 is randomly selected as the object for predicting degradation evolution. The working condition of the selected bearing 1_3 is a rotational speed of 1800 revolutions per minute, a radial load of 4000 N, and a vibration sensor sampling frequency of 25.6 kHZ. The monitoring data of bearing 1_3 from 8:33 on November 17, 2010 to 15:08 on November 17, 2010 is selected. The specific steps of the multi-stage degradation evolution prediction method for bearings are as follows:

[0191] 1) Data processing

[0192] The vibration signal of the bearing is selected as the state monitoring information of the equipment. The root mean square describes the effective value of the vibration signal and can reflect the energy and change trend of the vibration signal. Due to the good stability and trend of the root mean square of the vibration signal and its ability to change with degradation evolution, the root mean square has become a widely used degradation index to reflect its state. However, since the monitoring data of the bearing vibration signal has reached the microsecond level, the root mean square of the bearing vibration signal is extracted at a unit time interval of every 10 s as the degradation index, with a total of 2375 sampling points.

[0193] 2) Multi-stage degradation division

[0194] 2.1) Establish an AR model to fit the degradation index data of the bearing. The specific steps are as follows:

[0195] First, since the degradation process of the bearing is usually divided into three stages with different characteristics: a stable operation period, a decline period, and a failure period, the bearing degradation index data is divided into three stages in this invention. According to the trend characteristics of the degradation index data, it is found that the trend of the degradation index data changes its slope for the first time at the 1400-1800th points. Therefore, the range interval of the first mutation point is selected as the 1400-1800th points.

[0196] Then, traverse all the points within the mutation point range in sequence, divide the degradation index data into two segments, and establish an AR model for data fitting. Specifically: take the p corresponding to the minimum values of AIC and BIC as the order of the AR model, and use the least squares method to estimate its parameters to obtain the parameters of the AR model.

[0197] 2.2) Obtain the one-step prediction error of the AR model, and establish a mutation point recognition mechanism with the goal of minimizing the multi-stage error. Specifically: calculate the RSS of the AR model, and select the point with the minimum RSS value as the degradation mutation point. As Figure 3 shown, Table 1 shows the 10 sampling points with the minimum RSS within the interval [1400, 1800].

[0198] Table 1. RSS values of the 10 sampling points with the minimum within the first mutation point interval [1400, 1800]

[0199] Sampling point 1768 1763 1744 1799 1794 1795 1800 1786 1798 1769 RSS 5.3799 5.3946 5.4013 5.4018 5.4021 5.4022 5.4022 5.4027 5.4027 5.4028

[0200] From Figure 3 and Table 1, it can be obtained that the RSS of the 1768th point within the interval [1400, 1800] reaches the minimum value. Therefore, the first mutation point is selected as the 1768th point.

[0201] 2.3) Remove the data of the first 1768 points of the degradation index data, and then repeat step 2.1) to determine the range of the second mutation point as the 2100th - 2330th points.

[0202] 2.4) Repeat step 2.2) to select the mutation points. As Figure 4 shown, Table 2 shows the 10 sampling points with the minimum RSS within the interval [2100, 2330].

[0203] Table 2. RSS values of the 10 sampling points with the minimum within the second mutation point interval [2100, 2330]

[0204] Sampling point 2258 2257 2239 2238 2237 2231 2235 2132 2232 2233 RSS 4.7575 4.7603 4.7711 4.7741 4.7754 4.7827 4.7848 4.8101 4.8355 4.8359

[0205] From Figure 4 and Table 2, it can be obtained that the RSS of the 2258th point within the interval [2100, 2330] reaches the minimum value. Therefore, the second mutation point is selected as the 2258th point.

[0206] 2.5) Based on the above steps, divide the bearing degradation index into three stages. The segmentation result is as Figure 5 shown. In the figure, the 1st - 1768th points are the first stage, the 1769th - 2258th points are the second stage, and the 2259th - 2375th points are the third stage.

[0207] 3) Construct a multi-stage degradation evolution prediction model

[0208] Select the open-source framework Keras in Python to build the model. Select the Sequential model to construct the LSTM model. Set the LSTM to a single layer. There is only one feature variable as the input variable, which is the degradation index data. Therefore, the sequence dimension is 1. Use the GA to find the optimal parameter values for the learning rate, number of training times, sequence length, and number of neurons in the hidden layer. The specific process is as follows:

[0209] First, set the candidate solutions to the problem. The parameters to be adjusted include the learning rate, number of training times, sequence length, and number of neurons in the hidden layer. Therefore, the possible solutions of this algorithm are the possible values of a set of four parameters.

[0210] Second, chromosome encoding. The individual is the value of the parameter, which is four real numbers. So encode the real numbers into vector representation. The individual encoding becomes a chromosome. The number of genes in each chromosome of this method is set to 4, corresponding to the four parameters respectively. Therefore, each chromosome can be represented as X = (learning rate, number of training times, sequence length, number of hidden neurons).

[0211] Third, set the initial values of the four parameters to be optimized. The learning rate is set in the range of [0.002, 0.008], the number of training times is set as an integer between [500, 2000], the sequence length is set as an integer between [10, 100], and the number of neurons in the hidden layer is set in the range of [30, 200].

[0212] Next, construct the fitness function. Its mathematical expression is as follows:

[0213]

[0214] In the formula, n is the length of the data sequence, Y i is the true value, is the predicted value.

[0215] Finally, perform the crossover and mutation operations. The crossover probability is set to 0.5, and the mutation probability is set to 0.04.

[0216] After the above genetic algorithm operations, generate the latest population. After calculating the fitness values, iterate the population repeatedly, and select the parameters that make the fitness optimal as the optimal parameters obtained by the genetic algorithm. The optimal parameters are as follows: learning rate 0.006, number of training times 1000, sequence length 10, and number of neurons in the hidden layer 100.

[0217] 4) Model training and multi-stage degradation evolution prediction

[0218] Set the parameters of the LSTM according to the above steps, and use 90% of the degradation index data of each stage as the training set to input the prediction model for training.

[0219] The multi-stage degradation index data is input into the model for prediction. The prediction results of the three degradation stages of bearing data 1_3 are respectively as Figure 6 , Figure 7 , Figure 8 shown. It can be seen from the figure that the multi-stage model prediction curve fits well with the real degradation curve in the first two stages and is relatively well-fitted in the third stage. The comparison of the prediction results between the multi-stage model and the single-stage model is as Figure 9 shown. It can be seen from Figure 9 that the prediction result curve of the multi-stage model is closer to the real degradation curve than that of the single-stage model. Especially when the degradation index rises sharply, its error is shown in Table 3.

[0220] Table 3 Comparison of degradation prediction errors between the multi-stage model and the single-stage model

[0221]

[0222] It can be seen from Table 3 that the model proposed by the present invention performs better in the prediction process. Among them, the root mean square error of each stage of the multi-stage model is 25%, 38.5%, and 17.9% lower than that of the single-stage model respectively, and the overall data average root mean square error of the multi-stage model is 24.5% lower than that of the single-stage model. Therefore, the model proposed by the present invention predicts the degradation process of the bearing more accurately and has important theoretical and application values for the health assessment of the bearing.

[0223] The model involved in the present invention can divide the entire degradation process of mechanical equipment into multiple stages, and thus can perform multi-stage degradation evolution prediction on the degradation process of the bearing, improving the accuracy of prediction.

[0224] Example 2

[0225] An electronic device includes a memory and a processor. A computer program is stored on the memory. When the processor executes the computer program, any step in the multi-stage degradation evolution prediction method described in Example 1 is implemented.

[0226] Furthermore, the process of the multi-stage degradation evolution prediction method described in Example 1 can be implemented as a computer software program. For example, this embodiment includes a computer program product, which includes a computer program carried on a computer-readable medium. The computer program contains program codes for executing the method. In such an embodiment, the computer program can be downloaded and installed from the network and / or installed from a removable medium. When the computer program is executed by the processor, the above functions defined in the method of the present application are executed.

[0227] Example 3

[0228] A computer-readable storage medium stores a computer program thereon, and when the computer program is executed by a processor, any step in the multi-stage degradation evolution prediction method described in Embodiment 1 is implemented.

[0229] The computer-readable medium described in this application can be a computer-readable signal medium, a computer-readable storage medium, or any combination of the two above. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this application, a computer-readable storage medium can be any tangible medium that contains or stores a program, and this program can be used by or combined with an instruction execution system, apparatus, or device. And in this application, a computer-readable signal medium can include a data signal propagated in a baseband or as part of a carrier wave, in which the computer-readable program code is carried. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, and this computer-readable medium can send, propagate, or transmit a program for use by or combined with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium can be transmitted by any suitable medium, including but not limited to: wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0230] The computer program code for performing the operations of this application can be written in one or more programming languages or combinations thereof. The programming languages include object-oriented programming languages - such as Java, Smalltalk, C++, and also include conventional procedural programming languages - such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network - including a local area network (LAN) or a wide area network (WAN) - or can be connected to an external computer (for example, by using an Internet service provider to connect through the Internet).

[0231] In summary, the present invention effectively overcomes the deficiencies in the prior art and has high industrial utilization value. The role of the above embodiments is to illustrate the substantial content of the present invention, but does not limit the protection scope of the present invention. Those of ordinary skill in the art should understand that the technical solution of the present invention can be modified or equivalently replaced without departing from the essence and protection scope of the technical solution of the present invention.

Claims

1. A multi-stage degradation evolution prediction method for devices based on statistical models and deep learning, characterized in that, The steps include: S1: extracting a total set of degradation indicator time series data: collecting time series data of device degradation signals, taking the root mean square as the degradation indicator, extracting the root mean square value of the time series data of the degradation signal per unit time period, and obtaining a total set of degradation indicator time series data; S2: Identify degradation mutation points: The total set of degradation index time series data obtained in step S1 is segmented and an AR model is established segment by segment. Then, the one-step prediction error of the AR model is obtained based on the AR model fitting results. The degradation mutation points are identified with the goal of minimizing the multi-segment error. S3: Obtain the optimal parameter combination of the LSTM model: Build an LSTM model and use the genetic algorithm (GA) to optimize the parameters involved in the LSTM model to obtain the optimal parameter combination; S4: Divide the total set of degradation indicator time series data into multiple degradation indicator time series data subsets based on the degradation mutation point obtained in step S2; substitute the optimal parameter combination obtained in step S3 into the constructed LSTM model to construct a degradation prediction model, and train and test the degradation prediction model with each degradation indicator time series data subset respectively, and simultaneously obtain multiple degradation prediction curves; after splicing the multiple degradation prediction curves in time sequence, a multi-stage degradation prediction curve is obtained; The specific steps of identifying the degradation mutation point in step S2 are: S21. Identify the first degradation mutation point: S211, delineating an interval where a first degradation mutation point is located according to a change trend of the total set of degradation indicator time series data; S212, selecting any point within the interval where the degradation mutation point is located to divide the total set of degradation indicator time series data into a first subset and a second subset; S213. Based on the AR model, establish a first AR model and a second AR model using the first subset and the second subset, respectively; then use the first AR model and the second AR model to fit the data in the first subset and the second subset, respectively, and calculate the sum of the squares of the one-step prediction error of the first AR model and the sum of the squares of the one-step prediction error of the second AR model (RSS); S214, traverse all points in the interval where the degradation mutation point is located in step S211, repeat the calculation process of step S212 and step S213 to obtain the RSS of all points in the interval where the degradation mutation point is located; select the point corresponding to the minimum RSS as the first degradation mutation point; S22. Identify other degradation mutation points: Based on the data change trend after the first degradation mutation point in the degradation indicator time series data set, re-delineate the interval where the second degradation mutation point is located; select any point within the interval where the degradation mutation point is located to divide the data after the first degradation mutation point in the degradation indicator time series data set into a first subset and a second subset; repeat steps S213 and S214 to obtain a second degradation mutation point; and so on to obtain all degradation mutation points in the degradation indicator time series data set.

2. The multi-stage degradation evolution prediction method according to claim 1, wherein In step S3, when the genetic algorithm GA is used to optimize the parameters involved in the LSTM model, the objective function is to minimize the prediction error, obtain the optimal solution of the parameter search space, and obtain the optimal parameter combination. The specific steps are as follows: S31. Set candidate solutions to the problem and perform chromosome encoding, specifically: After taking the values of the four parameters of the learning rate, number of training times, sequence length, and number of neurons in the hidden layer involved in the LSTM model, a group of candidate solutions is formed; In the genetic algorithm GA, the individual is the value of the parameter, and the value of the parameter is a real number. The real number is encoded as a vector representation. Therefore, after encoding the individual into a chromosome, the number of genes in each chromosome is 4, corresponding to the 4 parameters respectively. Each chromosome is represented as X = (learning rate, number of training times, sequence length, number of neurons in the hidden layer); its mathematical expression is as follows: x(j) = a(j) + y(j)(b(j) - a(j)), j = 1, 2, … p In the formula, p is the number of optimization parameters, p = 4, x(j) is the jth optimization parameter, [a(j), b(j)] is the change interval of x(j), and y(j) is the real number corresponding to the parameter encoding; S32. Population initialization: Set the initial parameter values, use a random method to generate the population, and set the value range of the 4 parameters that need to be optimized by the prediction model according to the prediction data; S33. Construct the fitness function: Take the reciprocal of the root mean square error of the LSTM neural network as the fitness function, and its mathematical expression is: where n is the length of the data sequence, Y i is the true value, is the predicted value; S34. Perform selection, crossover, and mutation operations on the individuals of the solution: For the crossover operation, use the simulated binary crossover operator to complete the crossover operation, and the mathematical expression of the new individual after crossover is: In the formula, η is a user-defined factor, generally set to 1, and x is the 4 parent individuals Corresponding to the values of four parameters: learning rate, number of training times, sequence length, and number of neurons in the hidden layer, respectively, where random is the mutation probability; For the mutation operation, select the polynomial mutation operator to perform the mutation operation, and its mathematical expression is as follows: ν k = ν k + δ(μ k - l k ) where ν k is a parental individual, η is a user-defined factor, which is generally set to 1; S35. Use the offspring individuals obtained from the previous crossover and mutation as the new generation of population, obtain the target value of the fitness function. If the target value of the fitness function reaches the maximum, proceed to the next step; otherwise, return to step S33; S36. Obtain the optimal parameter combination.

3. The multi-stage degradation evolution prediction method according to claim 1, wherein The specific steps of training and testing the degradation prediction model with each subset of the time series data of the degradation index in step S4 are as follows: S41. Divide each subset of the time series data of the degradation index into a training set and a test set; S42. Use the training sets of different subsets of the time series data of the degradation index to train the degradation prediction model respectively, and obtain multiple trained degradation prediction models; S43. Input the test sets of each subset of the time series data of the degradation index into the corresponding trained degradation prediction models for testing respectively, and perform error analysis on the prediction results and the expected results, and obtain multiple segments of degradation prediction curves at the same time.

4. The multi-stage degradation evolution prediction method according to claim 1, characterized in that The device degradation signal in step S1 is a vibration signal, a temperature signal, and a stress signal that can represent the device state.

5. The multi-stage degradation evolution prediction method according to claim 3, characterized in that The division ratio of the training set and the test set is 9∶1.

6. The multi-stage degradation evolution prediction method according to claim 3, wherein The evaluation index of the error analysis described in step S43 is the root mean square error, and its mathematical expression is: where n is the length of the data sequence, Y i is the true value, is the predicted value.

7. The multi-stage degradation evolution prediction method according to claim 1, wherein The specific steps of establishing the first AR model or the second AR model with the first subset or the second subset in step S213 are as follows: (1) Construct the AR model, and its mathematical expression is as follows: where \(p\in N\) is the order of the AR model, \(\varepsilon\) n is an independent and identically distributed white noise sequence that follows the normal distribution \(N(0,\sigma\) 2 ), is the autocorrelation coefficient matrix, \(Y\) n is the value corresponding to the time series, and \(n\) is the length of the sequence; (2) Use the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) to determine the order p of the AR model, and select the p that makes AIC and BIC both obtain the minimum value as the order of the AR model; its mathematical expression is as follows: p = 0, 1,..., p0, p0 = 10lgn where p is the order of the model, is the maximum likelihood estimate of the variance of ε n under the condition of order p, and n is the length of the sequence; (3) For parameter estimation is carried out. The least squares estimation is selected for the parameter estimation of the AR model, and the specific steps are as follows: For the sequence X = [x1, x2, …, x n , its corresponding values are Y = [y1, y2, …, y n . When j ≥ p + 1, denote Then the p-order AR model is expressed as The parameters obtained by the least squares principle The least squares estimates are as follows: (4) Substitute the p value obtained in step (2) and the value obtained in step (3) into the mathematical expression of the AR model in step (1), and the specific expression of the first AR model or the second AR model can be obtained.

8. An electronic device, comprising a memory and a processor, wherein a computer program is stored on the memory, characterized in that, When the processor executes the computer program, it implements the multi-stage degradation evolution prediction method according to any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, it implements the multi-stage degradation evolution prediction method according to any one of claims 1-7.

Images