A method for predicting the remaining life of mechanical structures based on Wiener process and P-EMD

Abstract

The present invention provides a method for predicting the remaining life of a mechanical structure based on a Wiener process and P‑EMD, and belongs to the technical field of the remaining life estimation of mechanical products. The method comprises: using P‑EMD to decompose the collected vibration signal of the mechanical structure to obtain a plurality of IMFs, wherein P‑EMD represents the empirical mode decomposition based on particle swarm optimization and based on Hermite interpolation polynomials, and IMF represents the intrinsic mode function; calculating the approximate entropy of the decomposed IMF signal, and discriminating the degradation trend of the approximate entropy; based on the change trajectory of the approximate entropy, using the remaining life estimation model based on the Wiener process to predict the remaining life of the mechanical structure. The present invention can improve the prediction accuracy of the remaining life of the mechanical structure.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical product remaining life prediction, and in particular to a mechanical structure remaining life prediction method based on Wiener process and P-EMD. Background Art

[0002] The remaining life estimation and evaluation of complex mechanical structural parts is crucial to the safety and reliability of equipment use. This technology has become a widely studied issue in industries such as high-speed rail, automobiles, and aerospace.

[0003] Common equipment failures include improper installation, improper storage, improper lubrication, etc. The coupling and superposition of multiple failure mechanisms lead to the aliasing of equipment failure modes. When the equipment has a complex structure, a changeable working environment, and a variety of failure modes, the commonly used remaining life estimation method based on mechanism modeling and analysis cannot give a good analysis result due to model uncertainty and environmental uncertainty.

[0004] The existing remaining life estimation methods can be roughly divided into three types, including experience-based, model-based and data-driven methods. Among them, the experience-based and model-based solutions, on the one hand, rely on a thorough analysis of the failure mechanism of the structure, and often require the establishment of a high-precision simulation model for the structure, which is a huge workload, complicated calculations, and it is difficult to simulate the performance degradation process of the equipment before failure. On the other hand, some methods rely heavily on failure interval time data. For mechanical products, it is impossible to obtain sufficient failure samples, or even failure data under test conditions. Therefore, for mechanical structures, it is more appropriate to extract the state degradation characteristics of the mechanical structure based on non-destructive signal acquisition methods and analyze the soft failure problems of the structure, that is, when the performance degradation accumulates over time and eventually exceeds an acceptable threshold, the components and systems fail. Therefore, it is of great significance to explore data-driven mechanical structure state assessment methods. Summary of the invention

[0005] The embodiment of the present invention provides a method for predicting the remaining life of a mechanical structure based on the Wiener process and P-EMD, which can improve the prediction accuracy of the remaining life of the mechanical structure. The technical solution is as follows:

[0006] The embodiment of the present invention provides a method for predicting the remaining life of a mechanical structure based on a Wiener process and P-EMD, comprising:

[0007] P-EMD is used to decompose the vibration signal of the collected mechanical structure to obtain multiple IMFs, where P-EMD represents empirical mode decomposition based on particle swarm optimization and Hermite interpolation polynomials, and IMF represents intrinsic mode function;

[0008] Calculating the approximate entropy of the IMF signal obtained by decomposition, and determining the degradation trend of the approximate entropy;

[0009] Based on the changing trajectory of approximate entropy, the remaining life of mechanical structure is predicted by using the remaining life prediction model based on Wiener process.

[0010] Further, the decomposing the collected vibration signal of the mechanical structure by using P-EMD includes:

[0011] A1, taking the collected vibration signal of the mechanical structure as the input signal x(t);

[0012] A2, using particle swarm optimization algorithm to optimize the shape control parameters, and obtain the optimal shape control parameters δ1 and δ2;

[0013] A3, extract the best first-order IMF with optimal δ1 and δ2 for the input signal x(t);

[0014] A4, denote the best first-order IMF as h, and calculate the difference between the input signal and h, which is used to determine whether the stopping criterion is met;

[0015] A5, judging whether the stopping criterion is satisfied, that is, whether the difference obtained in step A4 becomes a monotonic function and no longer components satisfying the IMF condition can be extracted from it; if not, returning to step A2 to continue execution; otherwise, the P-EMD process is completed.

[0016] Furthermore, the approximate entropy of the IMF signal obtained by calculating the decomposition includes:

[0017] B1, assuming that the obtained IMF signal series is: {x(1), x(2), ...x(N)}, N is the length of the obtained IMF signal series, determine the vibration dimension m, extract the series elements in turn, and obtain the m-dimensional vectors X(i) and X(j) to reconstruct the phase space:

[0018] X(i)=[x(i), x(i+1),…x(i+m-1)], i=1, 2,…N-m+1

[0019] X(j)=[x(j),x(j+1),…x(j+m-1)], j=1,2,…N-m+1

[0020] B2, define the distance between vectors X(i) and X(j) as d[X(i), X(j)], which is the maximum difference between corresponding elements:

[0021]

[0022] B3, preset the similarity tolerance threshold r, calculate the number of d[X(i), X(j)] less than r, divide the number of vectors Num{d[X(i), X(j)]<r} by N-m+1, and the result is expressed as

[0023]

[0024] in, Represents the correlation between vectors X(i) and X(j), which refers to the probability that d[X(i), X(j)] is less than r when vector X(i) is at the center. The autocorrelation of vector {X(i)} is φ m (r) is expressed as:

[0025]

[0026] B4, increase the dimension of the vibration mode to form an m+1 dimensional vector, repeat steps B1-B3 to obtain φ m+1 (r), by calculating φ m (r) and φ m+1 The difference between (r) gives the approximate entropy of the IMF data series:

[0027] Ap=ApEn(m,r,N)=φ m (r)-φ m+1 (r)

[0028] Among them, Ap and ApEn both represent the approximate entropy of the IMF data series.

[0029] Further, the determining the degradation trend of the approximate entropy includes:

[0030] The least square method is used to fit the approximate entropy of the collected vibration signal within the time period to determine the degradation trend:

[0031] If the slope of the fitted curve is greater than zero, the degradation trend becomes larger;

[0032] If the slope of the fitted curve is less than zero, the degradation trend becomes smaller.

[0033] Furthermore, the prediction of the remaining life of the mechanical structure based on the change trajectory of the approximate entropy and the remaining life prediction model based on the Wiener process includes:

[0034] When the approximate entropy Ap degrades and drifts over time, the degradation amount of the approximate entropy is expressed as:

[0035]

[0036] in, express The degradation amount at the moment, the degradation amount matrix of the approximate entropy has l parameters on the column vector, 1≤l≤n, n=N, N is the length of the obtained IMF signal series, and m parameters on the row vector k parameters, 1≤k≤n, the corresponding time is Indicates that each set of vibration signals can calculate m k Ap value; the increment of approximate entropy is expressed as:

[0037]

[0038] in, is the complexity degradation increment of the signal;

[0039] According to the degradation of the obtained approximate entropy, the approximate entropy threshold D when the mechanical structure fails is determined f :

[0040]

[0041] Among them, k γ is a constant coefficient, Ap l It represents the approximate entropy degradation of the lth signal point in the IMF signal series;

[0042] According to the obtained approximate entropy threshold D when the mechanical structure fails f , determine the remaining life estimation model of the mechanical structure:

[0043] R(t)=1-F(t)

[0044]

[0045]

[0046] Where t is time, which refers to the moment when the equipment life is reached; R(t) is the reliability function, which describes the probability of the equipment life reaching the moment t; F(t) is the intermediate expression, f(t) is the probability distribution function of the life of a single device; the remaining life T τ It is the difference between the time t when the equipment life is reached and the current time.

[0047] Furthermore, the maximum likelihood estimation method is used to solve the drift coefficient μ and the diffusion coefficient σ.

[0048] Further, the method of solving the drift coefficient μ and the diffusion coefficient by using the maximum likelihood estimation method includes:

[0049] In time The complexity degradation increment of the signal Obeying the normal distribution, the probability distribution function f(t) of the life of a single device is expressed as:

[0050]

[0051] The maximum likelihood function L(μ, σ 2 ) is defined as:

[0052]

[0053] Using the maximum likelihood method, we can get the estimated values ​​of drift coefficient μ and diffusion coefficient σ and

[0054]

[0055]

[0056] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0057] In the embodiment of the present invention, based on the lossless vibration signal, P-EMD is used to decompose the vibration signal, which effectively suppresses the shortcomings of the signal such as overshoot, mode mixing, false mode and end effect; the approximate entropy of the IMF signal obtained by decomposition is calculated to obtain the signal characteristics that characterize the degradation performance of the mechanical structure (i.e., the degradation characteristics of the vibration signal), and the degradation trend of the approximate entropy is determined; based on the change trajectory of the approximate entropy, the remaining life of the mechanical structure is predicted using the remaining life prediction model based on the Wiener process. Compared with the traditional model-based and experience-based remaining life assessment methods, the prediction method described in this embodiment has better adaptability and prediction accuracy and stronger robustness, avoiding the shortcomings of the traditional scheme of difficult and inaccurate mechanism modeling and small test data samples. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0059] Figure 1 A schematic flow chart of a method for predicting the remaining life of a mechanical structure based on the Wiener process and P-EMD provided in an embodiment of the present invention;

[0060] Figure 2 A schematic diagram of a P-EMD process provided by an embodiment of the present invention;

[0061] Figure 3 A schematic diagram of a process for predicting the remaining life of a steam turbine lubricating oil pump structure provided by an embodiment of the present invention;

[0062] Figure 4 A schematic diagram of working condition data of a steam turbine lubricating oil pump provided by an embodiment of the present invention;

[0063] Figure 5 A schematic diagram of the vibration signal waveform at point 1 and point 2 in period 1, period 17 and period 35 provided in an embodiment of the present invention;

[0064] FIG6( a ) is a schematic diagram of a P-EMD decomposition result of a vibration signal at point 1 provided by an embodiment of the present invention (IMFi (i=1, ..., 6) represents the i-th level component);

[0065] FIG6( b ) is a schematic diagram of a P-EMD decomposition result of a vibration signal at point 2 provided by an embodiment of the present invention (IMFi (i=1, ..., 6) represents the i-th level component);

[0066] FIG7( a ) is a schematic diagram of the approximate entropy value calculated based on IMFi of the vibration signal collected at point 1 of each test cycle provided by an embodiment of the present invention (IMFi (i=1, ..., 6) represents the i-th level component);

[0067] FIG7( b ) is a schematic diagram of the approximate entropy value calculated based on IMFi of the vibration signal collected at point 2 of each test cycle provided by an embodiment of the present invention (IMFi (i=1, ..., 6) represents the i-th level component);

[0068] Figure 8 A schematic diagram of the wear fluctuation trend of the axial thrust bearing of the lubricating oil pump reducer provided in an embodiment of the present invention;

[0069] Fig. 9 A schematic diagram of a reliability curve of a lubricating oil pump reducer based on wear provided in an embodiment of the present invention;

[0070] Fig.10 The relative error result provided for the embodiment of the present invention corresponds to k i Schematic diagram;

[0071] Fig.11 The constant coefficient k provided in the embodiment of the present invention is γ Schematic diagram of the reliability curve when taking different values. DETAILED DESCRIPTION

[0072] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0073] like Figure 1 As shown, an embodiment of the present invention provides a method for predicting the remaining life of a mechanical structure based on a Wiener process and P-EMD, comprising:

[0074] S101, using P-EMD to decompose the collected vibration signal of the mechanical structure to obtain multiple intrinsic mode functions (IMF), where P-EMD represents empirical mode decomposition based on particle swarm optimization and Hermite interpolation polynomials, such as Figure 2 As shown, the following steps may be specifically included:

[0075] A1, the vibration signal of the collected mechanical structure is used as the input signal x(t), and initialized (setting parameters and assigning values): r = x(t), n = 1;

[0076] A2, using particle swarm optimization algorithm to optimize the shape control parameters, and obtain the optimal shape control parameters δ1 and δ2;

[0077] A3, extract the best first-order IMF with optimal δ1 and δ2 for the input signal x(t);

[0078] A4, denote the best first-order IMF as h, and calculate the difference between the input signal and h, which is used to determine whether the stopping criterion is met;

[0079] A5, judging whether the stopping criterion is satisfied, that is, whether the difference obtained in step A4 becomes a monotonic function and no longer components satisfying the IMF condition can be extracted from it; if not, returning to step A2 to continue execution; otherwise, the P-EMD process is completed.

[0080] Figure 2 In the figure, r and n are variables involved in the algorithm loop. r represents the value of the input signal x(t) when initialized, and represents the remaining signal component after separating the IMF value in the subsequent loop. n represents the number of algorithm loops, c(n) represents the IMF value obtained in the nth loop, and Maxenv and Minenv represent the maximum envelope and minimum envelope, respectively.

[0081] S102, calculating the approximate entropy of the IMF signal obtained by decomposition, and determining the degradation trend of the approximate entropy;

[0082] In this embodiment, an approximate entropy algorithm is used to extract degradation features of the vibration signal after P-EMD processing, and a signal feature characterizing the degradation performance of the mechanical structure is extracted, namely, the approximate entropy, specifically referring to the approximate entropy of the IMF signal obtained by calculation and decomposition.

[0083] In this embodiment, calculating the approximate entropy of the IMF signal obtained by decomposition may specifically include the following steps:

[0084] B1, assuming that the obtained IMF signal series is: {x(1), x(2), ...x(N)}, N is the length of the obtained IMF signal series, determine the vibration dimension m, extract the series elements in turn, and obtain the m-dimensional vectors X(i) and X(j) to reconstruct the phase space:

[0085] X(i)=[x(i), x(i+1),…x(i+m-1)], i=1, 2,…N-m+1

[0086] X(j)=[x(j),x(j+1),…x(j+m-1)], j=1,2,…N-m+1

[0087] B2, define the distance between vectors X(i) and X(j) as d[X(i), X(j)], which is the maximum difference between corresponding elements:

[0088]

[0089] B3, preset the similarity tolerance threshold r, calculate the number of d[X(i), X(j)] less than r, divide the number of vectors Num{d[X(i), X(j)]<r} by N-m+1, and the result is expressed as

[0090]

[0091] in, Represents the correlation between vectors X(i) and X(j), which refers to the probability that d[X(i), X(j)] is less than r when vector X(i) is at the center. The autocorrelation of vector {X(i)} is φ m (r) is expressed as:

[0092]

[0093] B4, increase the dimension of the vibration mode to form an m+1 dimensional vector, repeat steps B1-B3 to obtain φ m+1 (r), by calculating φ m (r) and φ m+1 The difference between (r) gives the approximate entropy of the IMF data series:

[0094] Ap=ApEn(m,r,N)=φ m (r)-φ m+1 (r)

[0095] Among them, Ap and ApEn both represent the approximate entropy of the IMF data series.

[0096] It should be noted that the value of the approximate entropy will be affected by the length N of the IMF signal series, the vibration mode dimension m and the similarity tolerance threshold r. Therefore, in order to make the data description more accurate and have good statistical characteristics, N is usually between 100 and 5000, m is 1 or 2, and r is set to 0.1 to 0.25 times the standard deviation of the IMF signal series.

[0097] In this embodiment, the least square method can be used to fit the approximate entropy of the collected vibration signal within the time period to determine the degradation trend:

[0098] If the slope of the fitted curve is greater than zero, the degradation trend becomes larger;

[0099] If the slope of the fitted curve is less than zero, the degradation trend becomes smaller.

[0100] S103, based on the change trajectory of the approximate entropy, the remaining life of the mechanical structure is predicted using a remaining life prediction model based on the Wiener process.

[0101] In order to better understand the remaining life estimation model based on the Wiener process in this embodiment, the traditional Weiner process model framework is first explained. The traditional Weiner process model can be expressed as:

[0102] X(t)=λt+σB(t)

[0103] Where X(t) is the degradation at time t, λ is the drift coefficient used to characterize the degradation rate, σ is the diffusion coefficient, and B(t) is the standard Brownian motion. The Weiner process is used to describe the process of non-monotonic performance degradation and can be expressed as

[0104]

[0105] in, express The degradation amount at the moment, the column vector of the above matrix has l (1≤l≤n) parameters, and the row vector has m k parameters (1≤k≤n) (degradation at different time points), the corresponding moments are In addition, the degradation variable between each two consecutive measurements is

[0106]

[0107] in, Since the approximate entropy of the IMF signal is considered to be a degradation feature, it can be used to quantify the complexity of the system. When the approximate entropy Ap degrades and drifts over time, the degradation amount of the approximate entropy can be expressed as:

[0108]

[0109] in, express The degradation amount at the moment, the degradation amount matrix of the approximate entropy has l parameters on the column vector, 1≤l≤n, n=N, N is the length of the obtained IMF signal series, and m parameters on the row vector k parameters, 1≤k≤n, the corresponding time is Indicates that each set of vibration signals can calculate m k Ap value; the increment of approximate entropy is expressed as:

[0110]

[0111] in, is the complexity degradation increment of the signal.

[0112] The increment of the above approximate entropy is compared with the remaining life T of the mechanical structure. τ Connection refers to the time from the current moment when Ap(t) exceeds the approximate entropy threshold Df when the mechanical structure fails, that is:

[0113] T τ = inf{t:Ap(t+τ)≥D f , t>0}

[0114] Where t is time, inf represents the infimum of the set, τ is the time of approximate entropy degradation, and the Ap value here only represents the approximate entropy degradation amount, which can also be understood as the sum of the initial degradation amount Ap(0) and the subsequent degradation amount increments ΔAp;

[0115] According to the degradation of the obtained approximate entropy, the approximate entropy threshold D when the mechanical structure fails is determined f :

[0116]

[0117] Among them, k γ is a constant coefficient, Ap l It represents the approximate entropy degradation of the lth signal point in the IMF signal series, with a total of n signal points;

[0118] The mean and variance of the approximate entropy in the degradation process are expressed as:

[0119] E[Ap(t)]=μt

[0120] Var[Ap(t)]=σ 2 t

[0121] Where t is time, μ is drift coefficient, and σ is diffusion coefficient;

[0122] According to the obtained approximate entropy threshold D when the mechanical structure fails f, determine the remaining life estimation model of the mechanical structure:

[0123] R(t)=1-F(t)

[0124]

[0125]

[0126] Where t is time, specifically the time when the equipment life is reached; R(t) is the reliability function, which describes the probability of the equipment life reaching time t; F(t) is the intermediate expression, f(t) is the probability distribution function of the life of a single device; the remaining life T τ It is the difference between the time t when the equipment life is reached and the current time.

[0127] Remaining life T τ The expected value and variance of can be expressed as:

[0128]

[0129]

[0130] Among them, the drift coefficient μ and the diffusion coefficient σ need to be estimated using the maximum likelihood estimation method; The complexity degradation increment of the signal It obeys the normal distribution, so the probability density function f(t) can be expressed as:

[0131]

[0132] The maximum likelihood function L(μ, σ 2 ) is defined as:

[0133]

[0134] Using the maximum likelihood method, we can get the estimated values ​​of drift coefficient μ and diffusion coefficient σ and The calculation is as follows:

[0135]

[0136]

[0137] In order to better understand the present invention, the remaining life prediction method of the mechanical structure based on the Wiener process and P-EMD provided in the embodiment of the present invention is used to predict the remaining life of the steam turbine lubricating oil pump structure. Figure 3 As shown, the prediction process is as follows:

[0138] (1) Collect the vibration signal of the lubricating oil pump;

[0139] In this embodiment, the vibration signal of the lubricating oil pump is collected from the accelerometer: two accelerometers are respectively installed on the upper bearing (i.e., point 1) and the lower bearing (i.e., point 2) of the lubricating oil pump reducer, and the accelerometer is used to collect the vibration signals of different parts of the lubricating oil pump reducer.

[0140] In this embodiment, before collecting the vibration signal of the lubricating oil pump, a reliability test of the lubricating oil pump is also performed:

[0141] The lubricating oil pump structure of the steam turbine is taken as the research object, and the vibration signals of different parts of the lubricating oil pump reducer are collected. The reliability test of the lubricating oil pump takes 770 hours, which is divided into 35 cycles, and each cycle takes 22 hours. Figure 4 As shown. In order to reflect the actual engineering, the experiment was carried out at three speeds of 9600rpm, 8400rpm and 7200rpm of the turbine main shaft. According to the operating conditions, the lubricating oil pump operated at different speeds and steam pressures at different times of the test cycle. During the reliability test, a vibration signal with a sampling frequency of 5120Hz was obtained, and 36 sets of data were used for feature extraction, where each set of data contained a 72-second vibration signal.

[0142] (2) Vibration signal preprocessing

[0143] In this embodiment, for the steam turbine lubricating oil pump, P-EMD is used to decompose the vibration signal; the approximate entropy of the IMF signal obtained by decomposition is calculated, and its degradation trend is determined;

[0144] (3) Based on the change trajectory of approximate entropy, the remaining life of the mechanical structure is predicted using the remaining life prediction model based on the Wiener process;

[0145] In this embodiment, the approximate entropy is used to measure the degree of disorder of the vibration signal over a period of time, and further quantify the complexity change of the signal. Determine the approximate entropy threshold D when the mechanical structure fails f , based on the Weiner process, a remaining life estimation model is established and its parameters are estimated.

[0146] Figure 5 A time domain waveform obtained from different channels (i.e., 1, 17, and 35 cycles) at the beginning, middle, and end of the test is shown. Figure 6(a) and (b) show the decomposition results, the first six IMFs, and the residuals of the vibration signals collected at points 1 and 2 of the lubricating oil pump reducer, respectively. Figure 7(a) and (b) show the values ​​of the approximate entropy calculated by the IMFi of the vibration signals collected at points 1 and 2, respectively.

[0147] (4) Comparison and verification

[0148] After every 5 test cycles, the bearing clearance, bearing clearance and corresponding wear data of the thrust bearing of the lubricating oil pump reducer shaft are measured. At the same time, the fluctuation trend of the data is as follows: Figure 8 As shown, it can be found that the wear degradation of the bearing shows a fluctuating upward trend, which is a typical random degradation. The approximate entropy threshold for determining mechanical structure failure is 1mm, and the drift parameter and diffusion parameter are estimated based on the maximum likelihood parameter estimation method.

[0149] Finally, the reliability curve of the lubricating oil pump reducer is obtained, such as Fig. 9 In this embodiment, the relative error ε i The result corresponds to k i , i = 1, 2, ..., 250, where k i The coefficient k representing the i-th reliability curve γ , k γ is the constant coefficient in the above approximate entropy threshold calculation formula, where k γ The value of k i When it is 1.41, the relative error is the smallest. Fig.10 and Fig.11 shown.

[0150] In order to verify the effectiveness of the method described in the embodiment of the present invention, it is compared with the life prediction value calculated by the traditional stochastic process (SP) method, and it can be obtained that the life prediction value of the method described in the embodiment of the present invention is more accurate.

[0151] The method for predicting the remaining life of a mechanical structure based on the Wiener process and P-EMD provided in the embodiment of the present invention uses P-EMD to decompose the vibration signal based on the lossless vibration signal, effectively suppressing the overshoot phenomenon, mode mixing, false mode and end effect of the signal; the approximate entropy of the IMF signal obtained by decomposition is calculated to obtain the signal characteristics that characterize the degradation performance of the mechanical structure (i.e., the degradation characteristics of the vibration signal), and the degradation trend of the approximate entropy is determined; based on the change trajectory of the approximate entropy, the remaining life of the mechanical structure is predicted using the remaining life prediction model based on the Wiener process. Compared with the traditional model-based and experience-based remaining life assessment methods, it has better adaptability and prediction accuracy and stronger robustness, avoiding the shortcomings of the traditional scheme of difficult and inaccurate mechanism modeling and small test data samples.

[0152] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the remaining life of a mechanical structure based on Wiener process and P-EMD, characterized in that: include: P-EMD is used to decompose the vibration signal of the collected mechanical structure to obtain multiple IMFs, where P-EMD represents empirical mode decomposition based on particle swarm optimization and Hermite interpolation polynomials, and IMF represents intrinsic mode function; Calculating the approximate entropy of the IMF signal obtained by decomposition, and determining the degradation trend of the approximate entropy; Based on the change trajectory of approximate entropy, the remaining life of the mechanical structure is predicted using the remaining life prediction model based on the Wiener process; Wherein, the step of using P-EMD to decompose the collected vibration signal of the mechanical structure includes: A1, taking the collected vibration signal of the mechanical structure as the input signal x(t); A2, using particle swarm optimization algorithm to optimize the shape control parameters, and obtain the optimal shape control parameters δ1 and δ2; A3, extract the best first-order IMF with optimal δ1 and δ2 for the input signal x(t); A4, denote the best first-order IMF as h, and calculate the difference between the input signal and h, which is used to determine whether the stopping criterion is met; A5, judging whether the stopping criterion is satisfied, that is, the difference obtained in step A4 becomes a monotonic function and no longer can extract components satisfying the IMF condition from it. If not, returning to step A2 to continue execution, otherwise, the P-EMD process is completed; The approximate entropy of the IMF signal obtained by calculating the decomposition includes: B1, assume that the obtained IMF signal series is: {x(1), x(2), … x(N)}, N is the length of the obtained IMF signal series, determine the vibration dimension m, extract the series elements in turn, and obtain the m-dimensional vectors X(i) and X(j) to reconstruct the phase space: X(i)=[x(i),x(i+1),…x(i+m-1)],i=1,2,…N-m+1 X(j)=[x(j),x(j+1),…x(j+m-1)],j=1,2,…N-m+1 B2, define the distance between vectors X(i) and X(j) as d[X(i),X(j)], which is the maximum difference between corresponding elements: B3. Preset a similarity tolerance threshold r, calculate the number of d[X(i), X(j)] that is less than r, divide the number of vectors Num{d[X(i), X(j)] < r} by N - m + 1, and the result is expressed as in, Represents the correlation between vectors X(i) and X(j), which refers to the probability that d[X(i),X(j)] is less than r when vector X(i) is at the center. The autocorrelation of vector {X(i)} is φ m (r) is expressed as: B4, increase the dimension of the vibration mode to form an m+1 dimensional vector, repeat steps B1-B3 to obtain φ m+1 (r), by calculating φ m (r) and φ m+1 The difference between (r) gives the approximate entropy of the IMF data series: Ap=ApEn(m,r,N)=φ m (r)-φ m+1 (r) Among them, Ap and ApEn both represent the approximate entropy of the IMF data series; Wherein, the determining the degradation trend of the approximate entropy includes: The least square method is used to fit the approximate entropy of the collected vibration signal within the time period to determine the degradation trend: If the slope of the fitted curve is greater than zero, the degradation trend becomes larger; If the slope of the fitted curve is less than zero, the degradation trend becomes smaller; The method of predicting the remaining life of a mechanical structure based on the change trajectory of approximate entropy and using a remaining life prediction model based on a Wiener process includes: When the approximate entropy Ap degrades and drifts over time, the degradation amount of the approximate entropy is expressed as: in, express The degradation amount at the moment, the degradation amount matrix of the approximate entropy has l parameters on the column vector, 1≤l≤n, n=N, N is the length of the obtained IMF signal series, and m parameters on the row vector k parameters, 1≤k≤n, and the corresponding time is tl1,…, Indicates that each set of vibration signals can calculate m k Ap value; the increment of approximate entropy is expressed as: in, is the complexity degradation increment of the signal; According to the degradation of the obtained approximate entropy, the approximate entropy threshold D when the mechanical structure fails is determined f : Among them, k γ is a constant coefficient, Ap l It represents the approximate entropy degradation of the lth signal point in the IMF signal series; According to the obtained approximate entropy threshold D when the mechanical structure fails f , determine the remaining life estimation model of the mechanical structure: R(t)=1-F(t) Where t is time, which refers to the moment when the equipment life is reached; R(t) is the reliability function, which describes the probability of the equipment life reaching the moment t; F(t) is the intermediate expression, f(t) is the probability distribution function of the life of a single device; the remaining life T τ The difference between the time t when the equipment life is reached and the current time; Among them, the maximum likelihood estimation method is used to solve the drift coefficient μ and the diffusion coefficient σ; Wherein, the method of using the maximum likelihood estimation method to solve the drift coefficient μ and the diffusion coefficient includes: In time The complexity degradation increment of the signal Obeying the normal distribution, the probability distribution function f(t) of the life of a single device is expressed as: The maximum likelihood function L(μ,σ 2 ) is defined as: Using the maximum likelihood method, we can get the estimated values ​​of drift coefficient μ and diffusion coefficient σ and

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