CN115935813A - Equipment multi-stage degradation evolution prediction method and equipment based on statistical model and deep learning and storage medium - Google Patents
Equipment multi-stage degradation evolution prediction method and equipment based on statistical model and deep learning and storage medium Download PDFInfo
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Abstract
The invention belongs to the technical field of equipment degradation evolution prediction, and discloses a method, equipment and a storage medium for predicting equipment multi-stage degradation evolution based on a statistical model and deep learning. According to the invention, the AR model is established to divide the degradation process of the mechanical equipment into a plurality of degradation stages, meanwhile, the GA optimized LSTM is adopted to construct the multi-stage degradation evolution prediction model, the uncertainty of degradation evolution prediction is reduced, the prediction precision is improved, meanwhile, the state of each stage can be estimated through the multi-stage prediction result, and the prediction of the residual life of the mechanical equipment can be better supported, so that the method has practical application significance.
Description
Technical Field
The invention belongs to the technical field of equipment degradation evolution prediction, and particularly relates to a method and equipment for predicting equipment multi-stage degradation evolution based on a statistical model and deep learning, and a storage medium.
Background
With the development of industry, the structure and function of mechanical equipment become more and more complex, and the automation degree is continuously improved. However, in practical engineering application, because the working environment of mechanical equipment is severe and changeable and the working condition is complex, the mechanical equipment is easy to degrade, and the normal operation and reliability of the mechanical equipment are affected. In order to ensure the safe and efficient operation of mechanical equipment, the prediction of degradation evolution is always a hot problem for research in the industrial field. The equipment is subjected to degradation evolution prediction, so that abnormal parts can be effectively identified, potential system faults can be prevented, and the safety of mechanical equipment is improved. Therefore, the degradation evolution prediction of the mechanical equipment has important guarantee significance on the reliability and the safety of the mechanical equipment.
In most cases, the degradation trend of the equipment presents different characteristics along with different working conditions, and the single-stage model-based prediction method is difficult to effectively capture the degradation characteristics of different stages, so that great challenges are brought to the reliability, operation and maintenance of the equipment. The deep learning has strong computing power in the aspect of complex degradation data processing, and is very suitable for processing multi-feature degradation sequences. The method based on statistics has clear mathematical expression and analysis process, can effectively describe equipment degradation trend, and provides repeatable degradation fitting results. Therefore, aiming at different degradation characteristics, the advantages of a statistical method and a deep learning method are effectively combined, a clearer degradation analysis process can be established to a certain extent, and a high-precision prediction result can be obtained.
Based on the method, the multi-stage degradation evolution prediction based on the statistical model and the deep learning is carried out on different degradation characteristics of different service stages of the mechanical equipment, so that the prediction error can be effectively reduced, and the method has practical application significance.
Disclosure of Invention
In view of the problems and deficiencies in the prior art, the present invention aims to provide a device multi-stage degradation evolution prediction method, device and storage medium based on statistical model and deep learning.
Based on the purpose, the invention adopts the following technical scheme:
the invention provides a device multi-stage degradation evolution prediction method based on a statistical model and deep learning, which comprises the following steps:
s1: extracting a degradation index time series data aggregate: acquiring time series data of equipment degradation signals, taking root mean square as a degradation index, and extracting root mean square values of the time series data of the degradation signals according to unit time periods to obtain a degradation index time series data total set;
s2: identifying degenerated mutation points: the total set of the time series data of the degradation indexes obtained in the step S1 is processed in a segmented mode, meanwhile, an AR model is built in a segmented mode, then one-step prediction errors of the AR model are obtained according to fitting results of the AR model, and degradation mutation points are identified by taking the minimum multi-segment errors as targets;
s3: obtaining the optimal parameter combination of the LSTM model: constructing an LSTM model, and optimizing parameters related to the LSTM model by adopting a genetic algorithm GA to obtain an optimal parameter combination;
s4: dividing the total set of the time sequence data of the degradation indexes into a plurality of time sequence data subsets of the degradation indexes by taking the degradation mutation points obtained in the step S2 as boundaries; substituting the optimal parameter combination obtained in the step S3 into the constructed LSTM model to construct a degradation prediction model, training and testing the degradation prediction model by each degradation index time sequence data subset respectively, and obtaining a plurality of sections of degradation prediction curves at the same time; and splicing the multiple sections of degradation prediction curves according to time sequence to obtain the multi-stage degradation prediction curve.
Preferably, the device degradation signal in step S1 may be a vibration signal, a temperature signal, a stress signal, or the like, which may indicate the state of the device.
More preferably, the mathematical expression of the root mean square value of the degradation indicator in step S1 is:
in the formula, x i Representing the ith data and n representing the number of data in a single sampling interval.
Preferably, the specific steps of identifying the degenerate mutation point in step S2 are:
s21, identifying a first degeneration mutation point:
s211, according to the change trend of the time series data set of the degradation indexes, defining an interval where a first degradation mutation point is located;
s212, selecting any one point in an interval where a degeneration mutation point is located to divide the degeneration index time sequence data total set into a first subset and a second subset;
s213, establishing a first AR model and a second AR model by respectively using the first subset and the second subset on the basis of the AR models; fitting the data in the first subset and the second subset by respectively adopting a first AR model and a second AR model, and calculating to obtain 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;
s214, traversing all the points in the interval where the degeneration mutation points are located in the step S211, and repeating the calculation processes of the step S212 and the step S213 to obtain RSS of all the points in the interval where the degeneration mutation points are located; screening a point corresponding to the minimum RSS as a first degeneration mutation point;
s22, identifying other degeneration mutation points: according to the data change trend after the first degeneration mutation point in the degeneration index time series data aggregate, the section where the second degeneration mutation point is located is defined again; selecting any point in the interval where the degeneration mutation point is located to divide the data after the first degeneration mutation point in the degeneration index time sequence data total set into a first subset and a second subset; repeating the step S213 and the step S214 to obtain a second degeneration mutation point; and obtaining all degeneration mutation points in the degeneration index time sequence data collection by analogy.
More preferably, the specific steps of establishing the first AR model or the second AR model by using the first subset or the second subset in step S213 are:
(1) An AR model is constructed, and the mathematical expression of the model is as follows:
wherein p is the order of AR model, epsilon n Is subject to a normal distribution N (0, σ) 2 ) The independent white noise sequence of the same distribution,
is a matrix of autocorrelation coefficients, Y n Is the value corresponding to the time sequence, and n is the length of the sequence;
(2) Determining the order p of the AR model by using an Akaichi Information Criterion (AIC) and a Bayesian Information Criterion (BIC), and selecting the order p when the AIC and the BIC simultaneously obtain the minimum value as the order of the AR model; the mathematical expression is as follows:
p＝0,1,...,p 0 ,p 0 ＝10lg n
where p is the order of the model,
is epsilon under the p-order condition n N is the length of the sequence;
(3) To pair
And performing parameter estimation, wherein the parameter estimation of the AR model adopts least square estimation, and the specific steps are as follows:
for sequence X = [ X = 1 ,x 2 ,…,x n ]The corresponding value is Y = [ Y ] 1 ,y 2 ,…,y n ]When j is more than or equal to p +1,
note the book
The order p AR model can be expressed as
Obtaining parameters by the least-squares principle
The least squares estimate of (d) is: />
(4) The p value obtained in the step (2) and the p value obtained in the step (3) are compared
And (3) substituting the value into the mathematical expression of the AR model in the step (1) to obtain a specific expression of the first AR model or the second AR model.
More preferably, the specific step of calculating the RSS of the sum of the square sum of the one-step prediction error of the first AR model and the sum of the square sums of the one-step prediction errors of the second AR model in step S213 is:
i) Respectively obtaining one-step prediction errors xi of the first AR model and the second AR model ione And xi itwo The mathematical expression is as follows:
in the formula, A is a possible point position for selecting a mutation point,
the true values of A points in the first subset and the second subset, respectively>
Fitting values of the points A after passing through the AR model in the first subset and the second subset are respectively;
ii) calculating the sum RSS of the sum of the square of the one-step prediction error of the first AR model and the sum of the square of the one-step prediction error of the second AR model, the mathematical expression of which is as follows:
furthermore, the LSTM model stores all information before each time step in the neural unit of the current time step, each neural unit is controlled by an input gate, a forgetting gate and an output gate, the input gate is used for controlling the input information of the neural unit at the current time, the forgetting gate is used for controlling the historical information stored in the neural unit at the previous time, and the output gate is used for controlling the output information of the neural unit at the current time.
Preferably, the specific steps of constructing the LSTM model in step S3 are: forget the hidden layer state h of the door at the previous moment t-1 And the current input state x t Transmitting to sigmoid function to obtain forgetting probability f t ；
f t ＝σ(w f [h t-1 ,x t ]+b f )
In the formula, w f Is forgetting the weight of the door, b f Is a forgetting gate bias;
the input gate is based on the current input state x t And hidden layer state h t-1 To determine the information to be stored
Realizing the updating of the state C;
i t ＝σ(w i [h t-1 ,x t ]+b i )
in the formula, w i ,b i Weight and offset of the input gate, w t ,b t Weight and bias of memory cell state, respectively;
current cell state
Updating according to the states of the forgetting gate, the input gate and the previous-time hidden layer, wherein the cell states at the current time through the forgetting gate and the output gate are as follows:
wherein i is the probability of updating new information to a cellular state;
the output gate represents the output of the hidden layer as shown in the following equation:
o t ＝σ(w 0 [h t-1 ，x t ]+b 0 )
h t ＝o t ·tanh(C t )
in the formula, w 0 ,b 0 Is the weight and bias of the output gate, tanh is the activation function, h t Is the hidden state of the next layer, o t Is the output content.
Preferably, when the genetic algorithm GA is used to optimize the parameters related to the LSTM model in step S3, the optimal solution of the parameter search space is obtained with the minimum prediction error as the objective function, so as to obtain the optimal parameter combination, and the specific steps are as follows:
s31, setting a problem candidate solution and carrying out chromosome coding, specifically:
4 parameters of learning rate, training times, sequence length and the number of neurons in a hidden layer related to the LSTM model are evaluated to form a group of candidate solutions;
individuals in the genetic algorithm GA are taken as values of parameters, while the values of the parameters are real numbers, and the real numbers can be coded into vector representation, so that after the individuals are coded into chromosomes, the number of genes of each chromosome is 4, and the genes correspond to 4 parameters respectively, and each chromosome can be represented as X = (learning rate, training times, sequence length, number of neurons in a hidden layer); the 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 the optimized parameters, in the invention, p =4, x (j) is the jth optimized parameter, [ a (j), b (j) ] is the variation interval of x (j), and y (j) is the real number corresponding to the parameter coding;
s32, population initialization: setting initial parameter values, generating a population by adopting a random method, and setting the value ranges of 4 parameters needing to be optimized of a prediction model according to prediction data;
s33, constructing a fitness function: taking the reciprocal of the root mean square error of the LSTM neural network as a fitness function, wherein the mathematical expression is as follows:
wherein n is the data sequence length, Y i Is the true value of the,
is a predicted value;
s34, carrying out selection cross mutation operation on the solved individuals:
for the crossover operation, a simulation binary crossover operator is adopted to complete crossover operation, and the mathematical expression of a new individual after crossover is as follows:
where η is a custom factor, typically set to 1, x is the parent 4 individuals
Respectively corresponding to possible values of four parameters of learning rate, training times, sequence length and the number of neurons in a hidden layer, wherein random is variation probability;
for mutation operation, the invention selects a polynomial mutation operator to perform mutation operation, and the mathematical expression is as follows:
ν k ＝ν k +δ(μ k -l k )
in the formula, v k Is a parent individual, eta is a self-defined factor and is generally set to be 1;
s35, obtaining a target value of a fitness function by taking the filial generation individuals obtained by the previous cross variation as a new generation population, and carrying out the next step if the target value of the fitness function reaches the maximum; otherwise, returning to the step S33;
and S36, obtaining the optimal parameter combination.
Preferably, the specific steps of training and testing the degradation prediction model with each degradation indicator time series data subset in step S4 are:
s41, dividing each degradation index time sequence data subset into a training set and a test set;
s42, training the degradation prediction model by using training sets of different degradation index time sequence data subsets respectively to obtain a plurality of trained degradation prediction models;
and S43, inputting the test set of each degradation index time sequence data subset into a corresponding trained degradation prediction model for testing, carrying out error analysis on a prediction result and an expected result, and obtaining a multi-section degradation prediction curve.
Preferably, the division ratio of the training set and the test set is 9: 1.
More preferably, the evaluation index of the error analysis in step S43 is a root mean square error, and the mathematical expression thereof is:
wherein n is the data sequence length, Y i Is the true value of the,
is a predicted value. />
A second aspect of the invention provides an electronic device comprising a memory having a computer program stored thereon and a processor which, when executed, implements any of the steps of the multi-stage degradation evolution prediction method according to the first aspect.
A third aspect of the invention provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements any of the steps of the multi-stage degradation evolution prediction method according to the first aspect.
Compared with the prior art, the invention has the following beneficial effects:
in the invention, considering that different service stages of the equipment have different degradation characteristics, the AR model is established to divide the degradation process of the mechanical equipment into a plurality of degradation stages, and meanwhile, the optimized LSTM is adopted to construct a multi-stage degradation evolution prediction model, thereby reducing the uncertainty of degradation evolution prediction and improving the prediction precision; the multi-stage prediction result can estimate the state of each stage, and can better support the prediction of the residual life of the mechanical equipment.
Drawings
FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is a flowchart of the prediction of the degradation evolution based on the GA-LSTM model according to the present invention;
FIG. 3 shows the position of a first mutation point in a range interval [1400,1800] according to an embodiment of the present invention;
FIG. 4 shows the position of a second mutation point in the range interval [2100,2350] according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating the multi-stage partitioning result of the true degradation curve according to an embodiment of the present invention;
FIG. 6 is a first stage degenerate evolution prediction result of the multi-stage degenerate evolution prediction model according to an embodiment of the present invention;
FIG. 7 shows the second stage degradation evolution prediction result of the multi-stage degradation evolution prediction model in the embodiment of the present invention;
FIG. 8 is a third-stage degenerate evolution prediction result of the multi-stage degenerate evolution prediction model according to an embodiment of the present invention;
FIG. 9 is a comparison of the multi-stage model for predicting the degradation evolution and the conventional single-stage model for predicting the degradation evolution in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail by the following embodiments with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
Example 1
The embodiment provides a device multi-stage degradation evolution prediction method based on a statistical model and deep learning, as shown in fig. 1. The method comprises the following steps:
s1: extracting a degradation index time series data aggregate: acquiring time sequence data of equipment degradation signals (vibration signals, temperature signals, stress signals and the like capable of representing equipment states), taking root mean square as a degradation index, and extracting the root mean square value of the time sequence data of the degradation signals according to unit time period to obtain a degradation index time sequence data total set; the mathematical expression of the root mean square value of the degradation index is as follows:
in the formula, x i Indicates the ith data, and n indicates the number of data in a unit time period.
S2: identifying degenerated mutation points: the method comprises the following steps of (1) carrying out sectional processing on the total set of the time series data of the degradation indexes obtained in the step S1, establishing an AR model in a sectional manner, then obtaining one-step prediction errors of the AR model according to fitting results of the AR model, and identifying degradation mutation points by taking the minimum multi-section errors as a target, wherein the method comprises the following specific steps:
s21, identifying a first degeneration mutation point:
s211, according to the change trend of the degradation index time sequence data total set, defining an interval where a first degradation mutation point A is located, namely an inflection point area with a changed trend slope; note X Aj ∈[X A1 ,X Ak ],0≤A 1 ≤A k N is more than or equal to n, j is more than or equal to 1 and less than or equal to k, wherein A1 is the first point of the interval where the first degeneration mutation point A is located, and Ak is the last point of the interval where the first degeneration mutation point A is located.
S212, X = [ X ] for time series 1 ,x 2 ,…,x n ]The corresponding degradation indicator time series data value is Y = [ Y = [) 1 ,y 2 ,…,y n ]Selecting any point such as X in the interval of the first degeneration mutation point A A1 Dividing the time series into X one And X two Two parts, dividing the total time series data set of the degradation index into a first subset and a second subset, and respectively recording the first subset and the second subset as
S213, establishing a first AR model and a second AR model respectively according to the first subset and the second subset on the basis of the AR model; and then fitting the data in the first subset and the second subset by respectively adopting the first AR model and the second AR model, and calculating to obtain the sum RSS of the one-step prediction error sum of the first AR model and the one-step prediction error sum of the second AR model.
The specific steps of establishing the first AR model or the second AR model by using the first subset or the second subset respectively are as follows:
(1) An AR model is constructed, and the mathematical expression of the model is as follows:
wherein p is the order of AR model, epsilon n Is subject to a normal distribution N (0, σ) 2 ) The independent white noise sequence of the same distribution,
is a matrix of autocorrelation coefficients, Y n Is the value corresponding to the time sequence, and n is the length of the sequence;
(2) Determining the order p of the AR model by using an Akaichi Information Criterion (AIC) and a Bayesian Information Criterion (BIC), and selecting the order p when the AIC and the BIC simultaneously obtain the minimum value as the order of the AR model; the mathematical expression is as follows:
p＝0,1,...,p 0 ,p 0 ＝10lg n
where p is the order of the model,
is epsilon under the p-order condition n N is the length of the sequence;
(3) To pair
And performing parameter estimation, wherein the parameter estimation of the AR model adopts least square estimation, and the specific steps are as follows:
for sequence X = [ X = 1 ,x 2 ,…,x n ]The corresponding value is Y = [ Y ] 1 ,y 2 ,…,y n ]When j is not less than p +1,
note the book
/>
The order p AR model can be expressed as
Obtaining parameters by the least-squares principle
The least squares estimate of (d) is: />
(4) The p value obtained in the step (2) and the p value obtained in the step (3) are compared
And (3) substituting the value into the mathematical expression of the AR model in the step (1) to obtain a specific expression of the first AR model or the second AR model.
The specific steps of calculating the RSS of the sum of the square sum of the one-step prediction error of the first AR model and the square sum of the one-step prediction error of the second AR model are as follows:
i) Is divided intoObtaining one-step prediction errors xi of the first AR model and the second AR model respectively ione And xi itwo The mathematical expression is as follows:
in the formula, A is a possible point position for selecting a mutation point,
the true values of A points in the first subset and the second subset, respectively>
Respectively obtaining fitting values of points A after passing through the AR model in the first subset and the second subset;
ii) calculating the sum RSS of the sum of the square of the one-step prediction error of the first AR model and the sum of the square of the one-step prediction error of the second AR model, the mathematical expression of which is as follows:
s214, traversing all the points in the interval where the degeneration mutation point is located in the step S211, and repeating the calculation processes of the step S212 and the step S213 to obtain the RSS of all the points in the interval where the degeneration mutation point is located i I =1 \ 8230k; screening RSS minimum RSS s ＝min(RSS i ) S is more than or equal to 1 and less than or equal to k s Is the first degenerate mutation point.
S22, identifying other degeneration mutation points: removing data before the first degeneration mutation point and corresponding to the first degeneration mutation point, and re-defining the section where the second degeneration mutation point is located according to the data change trend after the first degeneration mutation point in the degeneration index time sequence data aggregation; selecting any point in the interval where the degeneration mutation point is located to divide the data behind the first mutation point in the degeneration index time sequence data total set into a first subset and a second subset; repeating the step S213 and the step S214 to obtain a second degeneration mutation point; and in this way, all degeneration mutation points in the degeneration index time sequence data collection are obtained.
S3: obtaining the optimal parameter combination of the LSTM model: and constructing an LSTM model, and optimizing parameters related to the LSTM model by adopting a genetic algorithm GA to obtain an optimal parameter combination.
The LSTM model stores all information before each time step in the neural unit of the current time step, each neural unit is controlled by an input gate, a forgetting gate and an output gate, the input gate is used for controlling the input information of the neural unit at the current time, the forgetting gate is used for controlling the historical information stored in the neural unit at the previous time, and the output gate is used for controlling the output information of the neural unit at the current time.
Therefore, the specific steps for constructing the LSTM model are as follows: forget the hidden layer state h of the door at the previous moment t-1 And the current input state x t Transmitting to sigmoid function to obtain forgetting probability f t ；
f t ＝σ(w f [h t-1 ,x t ]+b f )
In the formula, w f Is forgetting gate weight, b f Is a forgotten gate bias;
the input gate is based on the current input state x t And hidden layer state h t-1 To determine the information to be stored
Realizing the update of the state C;
i t ＝σ(w i [h t-1 ,x t ]+b i )
in the formula, w i ,b i Weight and offset of the input gate, w t ,b t Weight and bias of memory cell state, respectively;
current cell state
Updating according to the states of the forgetting gate, the input gate and the previous-time hidden layer, wherein the cell states at the current time through the forgetting gate and the output gate are as follows:
wherein i is the probability of updating the new information to the cellular state;
the output gate represents the output of the hidden layer as shown in the following equation:
o t ＝σ(w 0 [h t-1 ，x t ]+b 0 )
h t ＝o t ·tanh(C t )
in the formula, w 0 ,b 0 Is the weight and bias of the output gate, tanh is the activation function, h t Is the hidden state of the next layer o t Is the output content.
It should be noted that the invention selects an open source framework Keras building model in Python, and selects a Sequential model to construct an LSTM model. The invention sets LSTM as single layer, for learning rate, training times, sequence length and number of neurons in hidden layer, there is no stable relation between the parameters and training result, and it needs to try to adjust parameters continuously, so the invention introduces GA to search for optimal parameters. In modeling, the invention selects a sigmoid function and a tanh function as activation functions.
Further, when a genetic algorithm GA is used to optimize parameters related to the LSTM model, the optimal solution of the parameter search space is obtained with the minimum prediction error as a target function, and an optimal parameter combination is obtained, where the process is shown in fig. 2, and the specific steps are as follows:
s31, setting a problem candidate solution and carrying out chromosome coding, specifically:
4 parameters of learning rate, training times, sequence length and the number of neurons in a hidden layer related to the LSTM model are evaluated to form a group of candidate solutions;
individuals in the genetic algorithm GA are taken as the values of parameters, while the values of the parameters are real numbers, and the real numbers can be coded into vector representation, so that after the individuals are coded into chromosomes, the number of genes of each chromosome is 4, and the genes correspond to 4 parameters respectively, and each chromosome can be represented as X = (learning rate, training times, sequence length and number of neurons in a hidden layer); the 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 the optimized parameters, in the invention, p =4, x (j) is the jth optimized parameter, [ a (j), b (j) ] is the variation interval of x (j), and y (j) is the real number corresponding to the parameter coding;
s32, population initialization: setting initial parameter values, generating a population by adopting a random method, and setting the value ranges of 4 parameters needing to be optimized of a prediction model according to prediction data;
s33, constructing a fitness function: taking the reciprocal of the root mean square error of the LSTM neural network as a fitness function, wherein the mathematical expression is as follows:
wherein n is the length of the data sequence, Y i Is the true value of the,
is a predicted value;
s34, carrying out selection cross mutation operation on the solved individuals:
for the crossover operation, a simulated binary crossover operator is adopted to complete crossover operation, and the mathematical expression of a new individual after crossover is as follows:
where η is a custom factor, typically set to 1, x is the parent 4 individuals
Respectively corresponding to possible values of four parameters of learning rate, training times, sequence length and the number of neurons in a hidden layer, wherein random is variation probability;
for mutation operation, the invention selects a polynomial mutation operator to perform mutation operation, and the mathematical expression is as follows:
ν k ＝ν k +δ(μ k -l k )
in the formula, v k Is a parent individual, eta is a self-defined factor and is generally set to be 1;
s35, obtaining a target value of a fitness function by taking the filial generation individuals obtained by the cross mutation as a new generation population, and carrying out the next step if the target value of the fitness function reaches the maximum; otherwise, returning to the step S33;
and S36, obtaining the optimal parameter combination.
S4: dividing the total set of the time sequence data of the degradation indexes into a plurality of time sequence data subsets of the degradation indexes by taking the degradation mutation points obtained in the step S2 as boundaries; substituting the optimal parameter combination obtained in the step S3 into the constructed LSTM model to construct a degradation prediction model, training and testing the degradation prediction model by each degradation index time sequence data subset respectively, and obtaining a plurality of sections of degradation prediction curves at the same time; and splicing the multiple sections of degradation prediction curves according to time sequence to obtain the multi-stage degradation prediction curve.
The specific steps of training and testing the degradation prediction model by using each degradation index time sequence data subset are as follows:
s41, dividing each degradation index time sequence data subset into a training set and a test set according to the ratio of 9: 1;
s42, training the degradation prediction model by using training sets of different degradation index time sequence data subsets respectively to obtain a plurality of trained degradation prediction models;
and S43, inputting the test set of each degradation index time sequence data subset into a corresponding trained degradation prediction model for testing, carrying out error analysis on a prediction result and an expected result, and obtaining a multi-section degradation prediction curve. The evaluation index of the error analysis is root mean square error, and the mathematical expression of the error analysis is as follows:
wherein n is the data sequence length, Y i Is a true value of the number of pixels,
is a predicted value.
Actual measurement and analysis:
case analysis was performed using bearings. The life-cycle bearing data was derived from bearing data provided by the FEMTO-ST research institute. The test stand consists of a rotating part, a degradation generating part and a measuring part, and in order to accelerate the descending process of the bearing and shorten the service life of the bearing, the radial load of the rolling bearing is continuously increased until the maximum rated value of the bearing is reached. A degradation experiment was performed using 17 bearings under three different operating conditions and 17 complete vibration data were obtained. The three working conditions are respectively as follows: the rotating speed is 1800 revolutions per minute, and the radial load is 4000N; the rotating speed is 1650 revolutions per minute, and the radial load is 4200N; the speed of rotation is 1500 rpm, and the radial load is 5000N. In the first of these, 7 bearings were tested under the first operating conditions, numbered 1 to 1. According to the method, the bearing 1_3 is randomly selected as a degradation evolution prediction object, the selected working condition of the bearing 1 _u3 is the rotating speed of 1800 rpm, the radial load is 4000N, the sampling frequency of a vibration sensor is 25.6kHZ, and monitoring data of the bearing 1 _u3 from 33 minutes at 11/17/8 2010 to 8 minutes at 15 minutes at 11/17/2010 are selected. The method for predicting the multi-stage degradation evolution of the bearing comprises the following specific steps:
1) Data processing
The state monitoring information of the equipment selects a vibration signal of the bearing. The root mean square describes the effective value of the vibration signal, which can reflect the energy and the variation trend of the vibration signal. Because the stability and trend of the root mean square of the vibration signal are relatively good and can change along with the degradation evolution, the root mean square has become a degradation index widely used for reflecting the state of the vibration signal. However, since the monitoring data of the vibration signal of the bearing reaches the microsecond level, the root mean square of the vibration signal of the bearing is extracted as a degradation index every unit time interval of 10s, and 2375 sampling points are counted.
2) Multi-stage degeneration partitioning
2.1 Establishing an AR model to fit degradation index data of the bearing, and specifically comprising the following steps of:
firstly, the degradation process of the bearing is generally divided into three stages with different characteristics, namely a stable operation period, a degradation period and a failure period, so that the degradation index data of the bearing is divided into three stages. According to the trend characteristics of the degradation index data, the trend of the degradation index data is found to have a first slope change at 1400 th-1800 th points, and therefore the range interval of the first catastrophe point is selected as 1400 th-1800 th points.
And then, sequentially traversing all points in the range of the catastrophe points to divide the degradation index data into two sections, and establishing an AR model for data fitting. The method specifically comprises the following steps: and according to the order of the AR model, which is the corresponding p when the values of the AIC and the BIC are minimum, performing parameter estimation on the order by using a least square method to obtain the parameters of the AR model.
2.2 Obtaining a one-step prediction error of the AR model, and establishing a mutation point identification mechanism by taking the minimum multi-stage error as a target, wherein the method specifically comprises the following steps: the AR model RSS was calculated and the point with the smallest RSS value was selected as the degenerate catastrophe point, as shown in fig. 3, table 1 is the 10 sample points with the smallest RSS in the interval [1400,1800 ].
TABLE 1 RSS values of the smallest 10 samples in the first mutation point interval [1400,1800]
| 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 |
As can be seen from FIG. 3 and Table 1, the RSS at 1768 points in the interval [1400,1800] is the minimum, so the first mutation point is the 1768 point.
2.3 1768 points before removing the degeneration index data, and then repeating the step 2.1) to select a second mutation point with the range of 2100 th to 2330 th points.
2.4 ) the mutation points selected in step 2.2) are repeated as shown in fig. 4, and table 2 shows the 10 sampling points with the minimum RSS in the interval [2100,2330 ].
TABLE 2 RSS values for the smallest 10 sample points in the second transition interval [2100,2330] of RSS
| 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 |
As can be seen from FIG. 4 and Table 2, the RSS at 2258 points in the interval [2100,2330] takes a minimum value, so the second mutation point was chosen as 2258.
2.5 Based on the steps, the bearing degradation index is divided into three stages, the segmentation result is shown in fig. 5, in the figure, the 1 st to 1768 points are the first stage, the 1769 th to 2258 points are the second stage, and the 2259 th to 2375 points are the third stage.
3) Construction of a Multi-stage degenerate evolution prediction model
Selecting an open source framework Keras building model in Python, selecting a Sequential model to construct an LSTM model, setting the LSTM as a single layer, inputting only one characteristic variable which is degradation index data, and finding optimal parameter values by adopting GA for learning rate, training times, sequence length and hidden layer neuron number, wherein the sequence dimension is 1, and the specific process is as follows:
firstly, setting a problem candidate solution, wherein parameters needing to be adjusted comprise learning rate, training times, sequence length and the number of neurons in a hidden layer, so that the possible solution of the algorithm is a group of possible values of four parameters.
Secondly, in chromosome coding, an individual is a value of a parameter and is four real numbers, so the real numbers are coded into vector representation. The individual codes become chromosomes, the number of genes of each chromosome is set to be 4, and the genes correspond to four parameters respectively, so that each chromosome can be expressed as X = (learning rate, training times, sequence length and number of hidden neurons).
Thirdly, setting initial values of four parameters to be optimized, setting the learning rate to be within a range of [0.002,0.008], setting the training times to be an integer between [500,2000], setting the sequence length to be an integer between [10,100], and setting the number of neurons in the hidden layer to be an integer between [30,200 ].
From the second time, a fitness function is constructed, and the mathematical expression of the fitness function is as follows:
wherein n is the data sequence length, Y i Is a true value of the number of pixels,
is a predicted value.
And finally, carrying out cross mutation operation, wherein the cross probability is set to be 0.5, and the mutation probability is set to be 0.04.
After the above genetic algorithm operation, the newest population is generated, after the fitness value is calculated, the population is iterated repeatedly, the parameter which enables the fitness to be optimal is selected as the optimal parameter obtained by the genetic algorithm, and the optimal parameter is obtained as follows: the learning rate is 0.006, the training times are 1000, the sequence length is 10, and the number of neurons in a hidden layer is 100.
4) Model training and multi-stage degenerate evolution prediction
And setting parameters of the LSTM according to the steps, and inputting 90% of the degradation index data of each stage into the prediction model as a training set for training.
The multi-stage degradation index data is input into the model for prediction, the prediction results of three degradation stages of the bearing data 1 _3are respectively shown in fig. 6, 7 and 8, and it can be seen from the figure that the multi-stage model prediction curve is very fit with the real degradation curve in the first two stages and is more fit with the real degradation curve in the third stage. The ratio of the predicted results of the multi-stage model and the single-stage model is shown in fig. 9, and it can be seen from fig. 9 that the predicted result curve of the multi-stage model is closer to the true degradation curve than the predicted result curve of the single-stage model, and particularly when the degradation index sharply increases, the error is shown in table 3.
TABLE 3 comparison of Multi-stage model degradation prediction and Single-stage model degradation prediction errors
As can be seen from Table 3, the model provided by the invention performs better in the prediction process, wherein the root mean square error of each stage of the multi-stage model is respectively 25%,38.5% and 17.9% lower than that of the single-stage model, and the mean root mean square error of the overall data of the multi-stage model is 24.5% lower than that of the single-stage model. Therefore, the model provided by the invention can predict the degradation process of the bearing more accurately, and has important theoretical and application values for health evaluation of the bearing.
The model can divide the whole degradation process of mechanical equipment into a plurality of stages, and further can predict the degradation process of the bearing through multi-stage degradation evolution, so that the prediction accuracy is improved.
Example 2
An electronic device comprising a memory having stored thereon a computer program and a processor that when executed implements any of the steps of the multi-stage degradation evolution prediction method as described in embodiment 1.
Further, the multi-stage degradation evolution prediction method process described in embodiment 1 can be implemented as a computer software program. For example, the present embodiments include a computer program product comprising a computer program embodied on a computer readable medium, the computer program comprising program code for performing the method. In such an embodiment, the computer program may be downloaded and installed from a network, and/or installed from a removable medium. Which when executed by a processor performs the above-described functions defined in the method of the present application.
Example 3
A computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements any of the steps of the multi-stage degradation evolution prediction method as described in embodiment 1.
The computer readable medium described herein may be a computer readable signal medium or a computer readable storage medium or any combination of the two. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples of the computer readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, 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 disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this application, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In this application, however, a computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, fiber optic cable, RF, etc., or any suitable combination of the foregoing.
Computer program code for carrying out operations for aspects of the present application may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, smalltalk, C + + or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may 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 the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
In conclusion, the present invention effectively overcomes the disadvantages of the prior art and has high industrial utilization value. The above-described embodiments are intended to illustrate the substance of the present invention, but are not intended to limit the scope of the present invention. It will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the true spirit and scope of the invention.
Claims (10)
1. A device multi-stage degradation evolution prediction method based on a statistical model and deep learning is characterized by comprising the following steps:
s1: extracting a degradation index time series data aggregate: acquiring time series data of equipment degradation signals, taking root mean square as a degradation index, and extracting root mean square values of the time series data of the degradation signals according to unit time periods to obtain a degradation index time series data total set;
s2: identifying degenerated mutation points: the total set of the time series data of the degradation indexes obtained in the step S1 is processed in a segmented mode, meanwhile, an AR model is built in a segmented mode, then one-step prediction errors of the AR model are obtained according to fitting results of the AR model, and degradation mutation points are identified by taking the minimum multi-segment errors as targets;
s3: obtaining the optimal parameter combination of the LSTM model: constructing an LSTM model, and optimizing parameters related to the LSTM model by adopting a genetic algorithm GA to obtain an optimal parameter combination;
s4: dividing the total set of the time sequence data of the degradation indexes into a plurality of time sequence data subsets of the degradation indexes by taking the degradation mutation points obtained in the step S2 as boundaries; substituting the optimal parameter combination obtained in the step S3 into the constructed LSTM model to construct a degradation prediction model, training and testing the degradation prediction model by each degradation index time sequence data subset respectively, and obtaining a plurality of sections of degradation prediction curves at the same time; and splicing the multiple sections of degradation prediction curves according to time sequence to obtain the multi-stage degradation prediction curve.
2. The multi-stage degenerate evolution prediction method according to claim 1, characterized in that the specific steps of identifying the degenerate mutation points in step S2 are:
s21, identifying a first degeneration mutation point:
s211, according to the change trend of the total degradation index time sequence data set, defining an interval where a first degradation mutation point is located;
s212, selecting any one point in an interval where a degeneration mutation point is located to divide the degeneration index time sequence data total set into a first subset and a second subset;
s213, establishing a first AR model and a second AR model respectively according to the first subset and the second subset on the basis of the AR model; fitting the data in the first subset and the second subset by respectively adopting a first AR model and a second AR model, and calculating to obtain 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;
s214, traversing all the points in the interval where the degeneration mutation points are located in the step S211, and repeating the calculation processes of the step S212 and the step S213 to obtain RSS of all the points in the interval where the degeneration mutation points are located; screening a point corresponding to the minimum RSS as a first degeneration mutation point;
s22, identifying other degeneration mutation points: according to the data change trend after the first degeneration mutation point in the degeneration index time series data aggregate, the section where the second degeneration mutation point is located is defined again; selecting any point in the interval where the degeneration mutation point is located to divide the data behind the first degeneration mutation point in the degeneration index time sequence data total set into a first subset and a second subset; repeating the step S213 and the step S214 to obtain a second degenerate mutation point; and in this way, all degeneration mutation points in the degeneration index time sequence data collection are obtained.
3. The multi-stage degradation evolution prediction method according to claim 1, wherein when the genetic algorithm GA is adopted in step S3 to optimize the parameters related to the LSTM model, the prediction error minimum is taken as an objective function to obtain the optimal solution of the parameter search space, so as to obtain the optimal parameter combination, and the specific steps are as follows:
s31, setting a problem candidate solution and carrying out chromosome coding, specifically:
4 parameters of learning rate, training times, sequence length and the number of neurons in a hidden layer related to the LSTM model are evaluated to form a group of candidate solutions;
individuals in the genetic algorithm GA are taken as values of parameters, while the values of the parameters are real numbers, and the real numbers can be coded into vector representation, so that after the individuals are coded into chromosomes, the number of genes of each chromosome is 4, and the genes correspond to 4 parameters respectively, and each chromosome can be represented as X = (learning rate, training times, sequence length, number of neurons in a hidden layer); the 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 the optimized parameters, in the invention, p =4, x (j) is the jth optimized parameter, [ a (j), b (j) ] is the variation interval of x (j), and y (j) is the real number corresponding to the parameter coding;
s32, population initialization: setting initial parameter values, generating a population by adopting a random method, and setting the value ranges of 4 parameters needing to be optimized of a prediction model according to prediction data;
s33, constructing a fitness function: taking the reciprocal of the root mean square error of the LSTM neural network as a fitness function, wherein the mathematical expression is as follows:
wherein n is the data sequence length, Y i Is the true value of the,
is a predicted value;
s34, carrying out selection cross mutation operation on the solved individuals:
for the crossover operation, a simulated binary crossover operator is adopted to complete crossover operation, and the mathematical expression of a new individual after crossover is as follows:
where η is a custom factor, typically set to 1, x is the parent 4 individuals
Respectively corresponding to possible values of four parameters of learning rate, training times, sequence length and the number of neurons in a hidden layer, wherein random is variation probability;
for mutation operation, the invention selects a polynomial mutation operator to perform mutation operation, and the mathematical expression is as follows:
ν k ＝ν k +δ(μ k -l k )
in the formula, v k Is a parent individual, eta is a self-defined factor and is generally set to be 1;
s35, obtaining a target value of a fitness function by taking the filial generation individuals obtained by the previous cross variation as a new generation population, and carrying out the next step if the target value of the fitness function reaches the maximum; otherwise, returning to the step S33;
and S36, obtaining the optimal parameter combination.
4. 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 degradation indicator time series data subset in step S4 are as follows:
s41, dividing each degradation index time sequence data subset into a training set and a test set;
s42, training the degradation prediction model by using training sets of different degradation index time sequence data subsets respectively to obtain a plurality of trained degradation prediction models;
and S43, inputting the test set of each degradation index time sequence data subset into a corresponding trained degradation prediction model for testing, carrying out error analysis on a prediction result and an expected result, and obtaining a multi-section degradation prediction curve.
5. The multi-stage degradation evolution prediction method according to claim 1, wherein the device degradation signal in step S1 is a vibration signal, a temperature signal, a stress signal capable of representing the device state.
6. The multi-stage degenerate evolution prediction method according to claim 4, characterized in that the training set and the test set are divided in a ratio of 9: 1.
7. The multi-stage degradation evolution prediction method according to claim 4, characterized in that the evaluation index of the error analysis in step S43 is a root mean square error, and the mathematical expression thereof is:
wherein n is the data sequence length, Y i Is a true value of the number of pixels,
is a predicted value.
8. The multi-stage degradation evolution prediction method according to claim 2, wherein the steps of establishing the first AR model or the second AR model with the first subset or the second subset in step S213 are:
(1) Constructing an AR model, wherein the mathematical expression of the AR model is as follows:
wherein p ∈ N is the order of AR model, ε n Is subject to a normal distribution N (0, σ) 2 ) The independent white noise sequence of the same distribution,
is a matrix of autocorrelation coefficients, Y n Is the value corresponding to the time sequence, and n is the length of the sequence;
(2) Determining the order p of the AR model by using an Akaba Information Criterion (AIC) and a Bayesian Information Criterion (BIC), and selecting the order p when the AIC and the BIC simultaneously obtain the minimum value as the order of the AR model; the mathematical expression is as follows:
p＝0,1,...,p 0 ,p 0 ＝10lgn
where p is the order of the model,
is epsilon in the p-th order n N is the length of the sequence;
(3) To pair
And performing parameter estimation, wherein the parameter estimation of the AR model adopts least square estimation, and the specific steps are as follows:
for sequence X = [ X = 1 ,x 2 ,...,x n ]The corresponding value is Y = [ Y ] 1 ,y 2 ,...,y n ]When j is not less than p +1, note
/>
The order p AR model can be expressed as
Obtaining parameters by the principle of least squares
The least squares estimate of (d) is: />
(4) The p value obtained in the step (2) and the p value obtained in the step (3) are compared
And (3) substituting the value into the mathematical expression of the AR model in the step (1) to obtain a specific expression of the first AR model or the second AR model.
9. An electronic device comprising a memory and a processor, the memory having a computer program stored thereon, wherein the processor, when executing the computer program, implements a multi-stage degradation evolution prediction method according to any of claims 1-8.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored thereon a computer program which, when executed by a processor, implements the multi-stage degenerative evolution prediction method according to any one of claims 1-8.
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