CN114417534A - Mechanical structure residual life prediction method based on Wiener process and P-EMD - Google Patents

Mechanical structure residual life prediction method based on Wiener process and P-EMD Download PDF

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CN114417534A
CN114417534A CN202210158176.4A CN202210158176A CN114417534A CN 114417534 A CN114417534 A CN 114417534A CN 202210158176 A CN202210158176 A CN 202210158176A CN 114417534 A CN114417534 A CN 114417534A
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赵彦琳
尚锦奇
阳建宏
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University of Science and Technology Beijing USTB
Beihang University
Shunde Graduate School of USTB
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Abstract

The invention provides a method for predicting the residual life of a mechanical structure based on a Wiener process and P-EMD (P-empirical mode decomposition), and belongs to the technical field of residual life estimation of mechanical products. The method comprises the following steps: decomposing the acquired vibration signals of the mechanical structure by adopting P-EMD to obtain a plurality of IMFs, wherein the P-EMD represents empirical mode decomposition based on particle swarm optimization and Hermite interpolation polynomial, and the IMFs represent eigenmode functions; calculating approximate entropy of an IMF signal obtained by decomposition, and judging the degradation trend of the approximate entropy; and predicting the residual life of the mechanical structure by using a residual life prediction model based on a Wiener process based on the change track of the approximate entropy. By adopting the method and the device, the prediction precision of the residual service life of the mechanical structure can be improved.

Description

Mechanical structure residual life prediction method based on Wiener process and P-EMD
Technical Field
The invention relates to the technical field of residual life estimation of mechanical products, in particular to a method for predicting the residual life of a mechanical structure based on a Wiener process and P-EMD.
Background
The estimation and evaluation of the residual life of the complex mechanical structural part are very important for the safety and reliability of the equipment. The technology has become a problem of extensive research in the industries of high-speed rail, automobiles, aerospace and the like.
Common equipment faults include improper installation, improper storage, improper lubrication and the like, and a plurality of fault failure mechanisms are coupled and superposed to cause fault mode aliasing of the equipment. When the structure of the equipment is complex, the working environment is changeable, and the failure modes are diversified, the commonly used residual life estimation method based on mechanism modeling and analysis cannot provide a better analysis result due to the existence of model uncertainty, environment uncertainty and the like.
The existing residual life estimation methods can be roughly divided into three methods, including methods based on experience, models and data driving; on one hand, the scheme based on experience and models depends on thorough analysis of a structure failure mechanism, a high-precision simulation model is often required to be established for a structure, the workload is huge, the calculation is complicated, and the performance degradation process of equipment before failure is difficult to simulate; on the other hand, some methods rely heavily on time between failure data, and for mechanical products, fail to obtain sufficient samples, even under test conditions. Therefore, for mechanical structures, it is more appropriate to extract the state degradation characteristics of the mechanical structure based on a lossless signal acquisition mode, analyze the structure for soft failure problems, i.e., component and system failures when the performance degradation accumulates over time and eventually exceeds an acceptable threshold. Therefore, it is important to explore a mechanical structure state evaluation method based on data driving.
Disclosure of Invention
The embodiment of the invention provides a method for predicting the residual life of a mechanical structure based on a Wiener process and P-EMD (P-empirical mode decomposition), which can improve the prediction precision of the residual life of the mechanical structure. The technical scheme is as follows:
the embodiment of the invention provides a method for predicting the residual life of a mechanical structure based on a Wiener process and P-EMD (P-empirical mode decomposition), which comprises the following steps:
decomposing the acquired vibration signals of the mechanical structure by adopting P-EMD to obtain a plurality of IMFs, wherein the P-EMD represents empirical mode decomposition based on particle swarm optimization and Hermite interpolation polynomial, and the IMFs represent eigenmode functions;
calculating approximate entropy of an IMF signal obtained by decomposition, and judging the degradation trend of the approximate entropy;
and predicting the residual life of the mechanical structure by using a residual life prediction model based on a Wiener process based on the change track of the approximate entropy.
Further, the decomposing the acquired vibration signal of the mechanical structure by using the P-EMD includes:
a1, using the collected vibration signal of the mechanical structure as an input signal x (t);
a2, optimizing the shape control parameter by particle swarm optimization to obtain the optimal shape control parameter delta1And delta2；
A3, extracting the input signal x (t) with optimal delta1And delta2The best first order IMF of (a);
a4, representing the best first-order IMF as h, and calculating the difference between the input signal and h, wherein the difference is used for judging whether the stop criterion is met;
a5, judging whether the stopping criterion is satisfied, namely the difference value obtained in the step A4 becomes a monotonous function from which the components satisfying the IMF condition can not be extracted, if not, returning to the step A2 to continue execution, otherwise, completing the P-EMD process.
Further, the calculating the approximate entropy of the decomposed IMF signal includes:
b1, setting the obtained IMF signal series as: { x (1), x (2),.. x (N) }, N is the length of the obtained IMF signal series, the mode shape dimension m is determined, and the series elements are sequentially extracted to obtain 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, defining the distance between vectors x (i) and x (j) as d [ x (i), x (j) ], i.e. the maximum difference between the corresponding elements:
Figure BDA0003513088950000021
b3, presetting a similar tolerance threshold r, and calculating d [ X (i), X (j) less than r]Number of vectors Num { d [ X (i), X (j)]< r } divided by N-m +1, the result is expressed as
Figure BDA0003513088950000022
Figure BDA0003513088950000023
Wherein the content of the first and second substances,
Figure BDA0003513088950000024
representing the degree of association between vectors X (i) and X (j), and is d [ X (i), X (j) ] when vector X (i) is located at the center]Probability less than r, autocorrelation of the vector { X (i) }, phim(r) is expressed as:
Figure BDA0003513088950000031
b4, increasing the vibration mode dimension to form an m + 1-dimensional vector, and repeating the steps B1-B3 to obtain phim+1(r) by calculating phim(r) and phim+1(r) obtaining approximate entropy of the IMF data series:
Ap＝ApEn(m，r，N)＝φm(r)-φm+1(r)
where Ap and ApEn both represent approximate entropies of the IMF data series.
Further, the judging the degradation trend of the approximate entropy comprises:
fitting the approximate entropy in the acquired vibration signal time by adopting a least square method, and judging the degradation trend:
if the slope of the fitted curve is greater than zero, the degradation trend is increased;
if the slope of the fitted curve is less than zero, the degradation tendency becomes smaller.
Further, the predicting the residual life of the mechanical structure by using a residual life estimation model based on a Wiener process based on the change track of the approximate entropy comprises the following steps:
when the approximate entropy Ap degenerates and drifts over time, the degradation amount of the approximate entropy is expressed as:
Figure BDA0003513088950000032
wherein the content of the first and second substances,
Figure BDA0003513088950000033
to represent
Figure BDA0003513088950000034
The time degradation quantity is a matrix of the approximate entropy degradation quantity with l parameters on a column vector, l is more than or equal to 1 and less than or equal to N, N is equal to N, N is the length of the obtained IMF signal series, and m is on a row vectorkA parameter, k is more than or equal to 1 and less than or equal to n, corresponding to a time
Figure BDA0003513088950000035
Representing the ability to calculate m for each set of vibration signalskAn Ap value; wherein the increment of approximate entropy is expressed as:
Figure BDA0003513088950000036
wherein the content of the first and second substances,
Figure BDA0003513088950000037
is the incremental complexity degradation of the signal;
determining an approximate entropy threshold D when the mechanical structure fails according to the obtained approximate entropy degradation quantityf：
Figure BDA0003513088950000038
Wherein k isγIs a constant coefficient, AplRepresenting the approximate entropy degradation amount of the ith signal point in the IMF signal series;
according to the obtained approximate entropy threshold D when the mechanical structure failsfDetermining a residual life prediction model of the mechanical structure:
R(t)＝1-F(t)
Figure BDA0003513088950000041
Figure BDA0003513088950000042
wherein t is time and refers to the time when the service life of the equipment reaches; r (t) is reliabilityA function representing a description of the probability that the lifetime of the device reaches time t; f (t) is an intermediate expression, f (t) is a probability distribution function of the service life of a single device; residual life TτThe difference between the time t when the service life of the equipment reaches and the current time is obtained.
Further, a maximum likelihood estimation method is adopted to solve the drift coefficient mu and the diffusion coefficient sigma.
Further, the solving of the drift coefficient μ and the diffusion coefficient by using the maximum likelihood estimation method includes:
at the time of
Figure BDA0003513088950000043
Of the signal of
Figure BDA0003513088950000044
Following a normal distribution, the probability distribution function f (t) for a single device lifetime is expressed as:
Figure BDA0003513088950000045
will maximum likelihood function L (mu, sigma)2) Is defined as:
Figure BDA0003513088950000046
obtaining estimated values of drift coefficient mu and diffusion coefficient sigma by using maximum likelihood method
Figure BDA0003513088950000049
And
Figure BDA00035130889500000410
Figure BDA0003513088950000047
Figure BDA0003513088950000048
the technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
in the embodiment of the invention, on the basis of a lossless vibration signal, the P-EMD is adopted to decompose the vibration signal, so that the defects of the overshoot phenomenon, the mode mixing, the false mode, the end effect and the like of the signal are effectively inhibited; calculating the approximate entropy of the IMF signal obtained by decomposition to obtain signal characteristics (namely, the degradation characteristics of the vibration signal) representing the degradation performance of the mechanical structure, and judging the degradation trend of the approximate entropy; and predicting the residual life of the mechanical structure by using a residual life prediction model based on a Wiener process based on the change track of the approximate entropy. Compared with the traditional model-based and experience-based residual life assessment method, the prediction method has better adaptability, prediction accuracy and stronger robustness, and avoids the defects of difficult and inaccurate mechanism modeling and smaller test data subsample of the traditional scheme.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for predicting the remaining life of a mechanical structure based on a Wiener process and P-EMD according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a P-EMD process according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart illustrating a residual life prediction of a turbine lubricating oil pump structure according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of turbine lubricant pump operating condition data provided in accordance with an embodiment of the present invention;
fig. 5 is a schematic waveform diagram of vibration signals at points 1 and 2 in periods 1, 17 and 35 according to an embodiment of the present invention;
fig. 6(a) is a schematic diagram of a P-EMD decomposition result of a vibration signal at a point 1 (IMFi (i ═ 1, …, 6) indicates an i-th component) provided by an embodiment of the present invention;
fig. 6(b) is a schematic diagram of a P-EMD decomposition result of a vibration signal at a point 2 (IMFi (i ═ 1, …, 6) indicates the ith component) provided by an embodiment of the present invention;
fig. 7(a) is a schematic diagram of values of approximate entropy calculated based on the IMFi of the vibration signal collected at point 1 of each test cycle (IMFi (i ═ 1, …, 6) denotes the ith-level component) provided by the embodiment of the present invention;
fig. 7(b) is a schematic diagram of values of approximate entropy calculated based on the IMFi of the vibration signal acquired at each test cycle point 2 (IMFi (i ═ 1, …, 6) denotes the ith-level component) provided by the embodiment of the present invention;
FIG. 8 is a schematic diagram illustrating a trend of wear fluctuation of an axial thrust bearing of a speed reducer of a lubricating oil pump according to an embodiment of the present invention;
FIG. 9 is a graphical illustration of wear-based lubrication pump retarder reliability curves provided by embodiments of the present invention;
FIG. 10 shows the relative error result corresponding to k according to the embodiment of the present inventioniA schematic diagram;
FIG. 11 shows a constant coefficient k according to an embodiment of the present inventionγAnd (5) taking a schematic diagram of a reliability curve at different values.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
As shown in fig. 1, an embodiment of the present invention provides a method for predicting remaining life of a mechanical structure based on a Wiener process and P-EMD, including:
s101, decomposing the acquired vibration signal of the mechanical structure by using P-EMD to obtain a plurality of eigenmode functions (IMFs), where the P-EMD represents empirical Mode decomposition based on particle swarm optimization and Hermite interpolation polynomial, and as shown in fig. 2, may specifically include the following steps:
a1, taking the collected vibration signal of the mechanical structure as an input signal x (t), and performing initialization processing (setting parameters and assigning values): r ═ x (t), n ═ 1;
a2, optimizing the shape control parameter by particle swarm optimization to obtain the optimal shape control parameter delta1And delta2；
A3, extracting the input signal x (t) with optimal delta1And delta2The best first order IMF of (a);
a4, representing the best first-order IMF as h, and calculating the difference between the input signal and h, wherein the difference is used for judging whether the stop criterion is met;
a5, judging whether the stopping criterion is satisfied, namely the difference value obtained in the step A4 becomes a monotonous function from which the components satisfying the IMF condition can not be extracted, if not, returning to the step A2 to continue execution, otherwise, completing the P-EMD process.
In fig. 2, r and n are variables participating in algorithm cycle, r represents a value of an input signal x (t) when initialized, a residual signal component after an IMF value is separated is represented in a subsequent cycle process, n represents an algorithm cycle number, c (n) represents an IMF value obtained in an nth cycle, and Maxenv and Minenv represent a maximum envelope and a minimum envelope respectively.
S102, calculating approximate entropy of the IMF signal obtained by decomposition, and judging the degradation trend of the approximate entropy;
in this embodiment, an approximate entropy algorithm is used to extract degradation features of the vibration signal after the P-EMD processing, and signal features representing the degradation performance of the mechanical structure, that is, an approximate entropy, specifically, an approximate entropy of the IMF signal obtained by computational decomposition, is extracted.
In this embodiment, calculating the approximate entropy of the decomposed IMF signal may specifically include the following steps:
b1, setting the obtained IMF signal series as: { x (1), x (2),.. x (N) }, N is the length of the obtained IMF signal series, the mode shape dimension m is determined, and the series elements are sequentially extracted to obtain 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, defining the distance between vectors x (i) and x (j) as d [ x (i), x (j) ], i.e. the maximum difference between the corresponding elements:
Figure BDA0003513088950000071
b3, presetting a similar tolerance threshold r, and calculating d [ X (i), X (j) less than r]Number of vectors Num { d [ X (i), X (j)]< r } divided by N-m +1, the result is expressed as
Figure BDA0003513088950000072
Figure BDA0003513088950000073
Wherein the content of the first and second substances,
Figure BDA0003513088950000074
representing the degree of association between vectors X (i) and X (j), and is d [ X (i), X (j) ] when vector X (i) is located at the center]Probability less than r, autocorrelation of the vector { X (i) }, phim(r) is expressed as:
Figure BDA0003513088950000075
b4, increasing the vibration mode dimension to form an m + 1-dimensional vector, and repeating the steps B1-B3 to obtain phim+1(r) by calculating phim(r) and phim+1(r) obtaining approximate entropy of the IMF data series:
Ap＝ApEn(m，r，N)＝φm(r)-φm+1(r)
where Ap and ApEn both represent approximate entropies of the IMF data series.
It should be noted that the value of the approximate entropy is influenced by the length N, the mode-shape dimension m and the similar tolerance threshold r of the IMF signal series, so 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 be 0.1 to 0.25 times of the standard deviation of the IMF signal series.
In this embodiment, the least square method may be adopted to fit the approximate entropy within the time of the collected vibration signal, and the degradation trend is determined:
if the slope of the fitted curve is greater than zero, the degradation trend is increased;
if the slope of the fitted curve is less than zero, the degradation tendency becomes smaller.
And S103, predicting the residual life of the mechanical structure by using a residual life prediction model based on a Wiener (Wiener) process based on the change track of the approximate entropy.
To better understand the remaining life prediction model based on Wiener process in this embodiment, a description is first made of a conventional Weiner process model framework, which can be expressed as:
X(t)＝λt+σB(t)
where X (t) is the amount of degradation at time t, λ represents the drift coefficient used to characterize the rate of degradation, σ is the diffusion coefficient, and B (t) is the standard Brownian motion. The Weiner process is used to describe a process that is not monotonic of performance degradation and can be expressed as
Figure BDA0003513088950000081
Wherein the content of the first and second substances,
Figure BDA0003513088950000082
to represent
Figure BDA0003513088950000083
The time degradation amount is that the column vector of the matrix has l (1 ≦ l ≦ n) parameters, and the row vector has mkA parameter (1. ltoreq. k. ltoreq. n) (amount of degradation at different points in time) corresponding to the instant
Figure BDA0003513088950000084
In addition, every twoThe degradation variable between successive measurements is
Figure BDA0003513088950000085
Wherein the content of the first and second substances,
Figure BDA0003513088950000086
since the approximate entropy of the IMF signal is considered a degradation feature, it can be used to quantify the complexity of the system. When the approximate entropy Ap degenerates and drifts over time, the amount of degradation of the approximate entropy can be expressed as:
Figure BDA0003513088950000087
wherein the content of the first and second substances,
Figure BDA0003513088950000088
to represent
Figure BDA0003513088950000089
The time degradation quantity is a matrix of the approximate entropy degradation quantity with l parameters on a column vector, l is more than or equal to 1 and less than or equal to N, N is equal to N, N is the length of the obtained IMF signal series, and m is on a row vectorkA parameter, k is more than or equal to 1 and less than or equal to n, corresponding to a time
Figure BDA00035130889500000810
Representing the ability to calculate m for each set of vibration signalskAn Ap value; wherein the increment of approximate entropy is expressed as:
Figure BDA00035130889500000811
wherein the content of the first and second substances,
Figure BDA00035130889500000812
is the incremental complexity degradation of the signal.
The increment of the approximate entropy is compared with the residual life T of the mechanical structureτContact, i.e. meanFrom the present moment ap (t) the time when the approximate entropy threshold Df at the time of the mechanical structure failure is exceeded, i.e.:
Tτ＝inf{t：Ap(t+τ)≥Df，t＞0}
where t is time, inf represents the infimum bound of the set, τ is time of approximate entropy degradation, and the Ap value here represents only the approximate entropy degradation amount, which can also be understood as the sum of the initial degradation amount Ap (0) and a plurality of degradation amount increments Δ Ap thereafter;
determining an approximate entropy threshold D when the mechanical structure fails according to the obtained approximate entropy degradation quantityf：
Figure BDA00035130889500000813
Wherein k isγIs a constant coefficient, AplRepresenting approximate entropy degradation of the ith signal point in the IMF signal series, wherein the total number of the signal points is n;
the mean and variance of the approximate entropy during degradation are expressed as:
E[Ap(t)]＝μt
Var[Ap(t)]＝σ2t
wherein t is time, μ is a drift coefficient, and σ is a diffusion coefficient;
according to the obtained approximate entropy threshold D when the mechanical structure failsfDetermining a residual life prediction model of the mechanical structure:
R(t)＝1-F(t)
Figure BDA0003513088950000091
Figure BDA0003513088950000092
wherein t is time, in particular the time when the service life of the equipment reaches; r (t) is a reliability function and represents the description of the probability that the service life of the equipment reaches t moment; f (t) is an intermediate expression, f (t) is a single equipment lifeA probability distribution function of hits; residual life TτI.e. the difference between the time t at which the service life of the device has reached and the current time.
Residual life TτThe expected value and variance of (c) can be expressed as:
Figure BDA0003513088950000093
Figure BDA0003513088950000094
wherein, the drift coefficient mu and the diffusion coefficient sigma need to adopt a maximum likelihood estimation method to carry out parameter estimation; due to the time
Figure BDA0003513088950000095
Of the signal of
Figure BDA0003513088950000096
Obey a normal distribution, so the probability density function, f (t), can be expressed as:
Figure BDA0003513088950000097
will maximum likelihood function L (mu, sigma)2) Is defined as:
Figure BDA0003513088950000098
obtaining estimated values of drift coefficient mu and diffusion coefficient sigma by using maximum likelihood method
Figure BDA0003513088950000099
And
Figure BDA00035130889500000910
the calculation method is as follows:
Figure BDA00035130889500000911
Figure BDA0003513088950000101
in order to better understand the method, the method for predicting the residual life of the mechanical structure based on the Wiener process and the P-EMD provided by the embodiment of the invention is used for predicting the residual life of the lubricating oil pump structure of the steam turbine, as shown in fig. 3, the prediction process is as follows:
(1) collecting a vibration signal of the lubricating oil pump;
in this embodiment, the vibration signal of the lubricant pump is collected from the accelerometer: two accelerometers are respectively arranged on an upper bearing (namely, a point 1) and a lower bearing (namely, a point 2) of the lubricating oil pump reducer, and vibration signals of different parts of the lubricating oil pump reducer are collected by the accelerometers.
In this embodiment, before gathering the vibration signal of lubrication oil pump, still carry out the lubrication oil pump reliability test:
the method comprises the steps of taking a lubricating oil pump structure of a steam turbine as a research object, and collecting vibration signals of different parts of a speed reducer of the lubricating oil pump. The reliability test of the lubricating oil pump takes 770 hours and is divided into 35 cycles, each of which takes 22 hours, as shown in fig. 4. In order to reflect the practical situation of the project, the experiment was carried out at three rotational speeds of 9600rpm, 8400rpm and 7200rpm of the main shaft of the steam turbine. The lubrication pump is operated at different speeds and vapor pressures during different periods of the test cycle, depending on the operating conditions. In the reliability test process, a vibration signal with the sampling frequency of 5120Hz is obtained, and 36 groups of data are adopted for feature extraction, wherein each group of data comprises a vibration signal of 72 seconds.
(2) Vibration signal preprocessing
In the embodiment, a P-EMD is adopted to decompose a vibration signal for a turbine lubricating oil pump; calculating the approximate entropy of the IMF signal obtained by decomposition, and judging the degradation trend of the IMF signal;
(3) predicting the residual life of the mechanical structure by utilizing a residual life prediction model based on a Wiener process based on the change track of the approximate entropy;
in this embodiment, the degree of disorder of the vibration signal over a period of time is measured using approximate entropy to further quantify the complexity change of the signal. Determining an approximate entropy threshold D at mechanical structure failurefAnd establishing a residual life estimation model based on the Weiner process, and estimating parameters in the residual life estimation model.
Fig. 5 shows a segment of the time domain waveform obtained from different channels (i.e., 1, 17, and 35 cycles) at the beginning, middle, and end of the test. Fig. 6(a), (b) show the decomposition results of the vibration signals collected at the lube pump reducer point 1 and point 2, the first six IMFs and the residual, respectively. Fig. 7(a), (b) show values of approximate entropy calculated from IMFi of vibration signals acquired at point 1 and point 2, respectively.
(4) Comparison and verification
After every 5 test periods, the bearing play and the corresponding wear data of the thrust bearing of the lubricating oil pump reducer are measured, and meanwhile, the data have fluctuation trends as shown in fig. 8, and the wear degradation of the bearing is found to have a trend of rising fluctuation, which is typical random degradation. And determining that the approximate entropy threshold value is 1mm when the mechanical structure fails, and estimating the drift parameter and the diffusion parameter based on a maximum likelihood parameter estimation method.
Finally, a reliability curve of the lubricating oil pump speed reducer is obtained, as shown in fig. 9. In this embodiment, the relative error εiResult of (1) corresponds to ki1, 2, 250, where kiCoefficient k representing the i-th reliability curveγ，kγIs a constant coefficient in the above approximate entropy threshold calculation formula, where kγValue of (a) kiThe relative error is smallest at 1.41, as shown in fig. 10 and 11.
In order to verify the effectiveness of the method provided by the embodiment of the invention, the life prediction value of the method provided by the embodiment of the invention can be obtained more accurately by comparing the life prediction value with a life prediction value calculated by a traditional random Process (SP) method.
According to the method for predicting the residual life of the mechanical structure based on the Wiener process and the P-EMD, provided by the embodiment of the invention, on the basis of a lossless vibration signal, the P-EMD is adopted to decompose the vibration signal, so that the defects of the overshoot phenomenon, the mode mixing, the false mode, the end effect and the like of the signal are effectively inhibited; calculating the approximate entropy of the IMF signal obtained by decomposition to obtain signal characteristics (namely, the degradation characteristics of the vibration signal) representing the degradation performance of the mechanical structure, and judging the degradation trend of the approximate entropy; and predicting the residual life of the mechanical structure by using a residual life prediction model based on a Wiener process based on the change track of the approximate entropy. Compared with the traditional model-based and experience-based residual life evaluation method, the method has better adaptability, prediction accuracy and stronger robustness, and avoids the defects of difficult and inaccurate mechanism modeling and smaller test data subsample of the traditional scheme.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (7)

1. A method for predicting the residual life of a mechanical structure based on a Wiener process and P-EMD is characterized by comprising the following steps:
decomposing the acquired vibration signals of the mechanical structure by adopting P-EMD to obtain a plurality of IMFs, wherein the P-EMD represents empirical mode decomposition based on particle swarm optimization and Hermite interpolation polynomial, and the IMFs represent eigenmode functions;
calculating approximate entropy of an IMF signal obtained by decomposition, and judging the degradation trend of the approximate entropy;
and predicting the residual life of the mechanical structure by using a residual life prediction model based on a Wiener process based on the change track of the approximate entropy.
2. The method for predicting the residual life of a mechanical structure based on a Wiener process and P-EMD as claimed in claim 1, wherein the decomposing the collected vibration signal of the mechanical structure by using the P-EMD comprises:
a1, using the collected vibration signal of the mechanical structure as an input signal x (t);
a2, optimizing the shape control parameter by particle swarm optimization to obtain the optimal shape control parameter delta1And delta2；
A3, extracting the input signal x (t) with optimal delta1And delta2The best first order IMF of (a);
a4, representing the best first-order IMF as h, and calculating the difference between the input signal and h, wherein the difference is used for judging whether the stop criterion is met;
a5, judging whether the stopping criterion is satisfied, namely the difference value obtained in the step A4 becomes a monotonous function from which the components satisfying the IMF condition can not be extracted, if not, returning to the step A2 to continue execution, otherwise, completing the P-EMD process.
3. The method for predicting the residual life of a mechanical structure based on a Wiener process and P-EMD as claimed in claim 1, wherein the calculating the approximate entropy of the decomposed IMF signal comprises:
b1, setting the obtained IMF signal series as: { x (1), x (2),.. x (N) }, N is the length of the obtained IMF signal series, the mode shape dimension m is determined, and the series elements are sequentially extracted to obtain 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, defining the distance between vectors x (i) and x (j) as d [ x (i), x (j) ], i.e. the maximum difference between the corresponding elements:
Figure FDA0003513088940000021
b3, presetting a similar tolerance threshold r, and calculating d [ X (i), X (j) less than r]Number of vectors Num { d [ X (i), X (j)]< r } divided by N-m +1, the result is expressed as
Figure FDA0003513088940000022
Figure FDA0003513088940000023
Wherein the content of the first and second substances,
Figure FDA0003513088940000024
representing the degree of association between vectors X (i) and X (j), and is d [ X (i), X (j) ] when vector X (i) is located at the center]Probability less than r, autocorrelation φ of vector { x (i) }m(r) is expressed as:
Figure FDA0003513088940000025
b4, increasing the vibration mode dimension to form an m + 1-dimensional vector, and repeating the steps B1-B3 to obtain phim+1(r) by calculating phim(r) and phim+1(r) obtaining approximate entropy of the IMF data series:
Ap＝ApEn(m，r，N)＝φm(r)-φm+1(r)
where Ap and ApEn both represent approximate entropies of the IMF data series.
4. The method for predicting the residual life of a mechanical structure based on a Wiener process and P-EMD as claimed in claim 1, wherein the discriminating the degradation trend of the approximate entropy comprises:
fitting the approximate entropy in the acquired vibration signal time by adopting a least square method, and judging the degradation trend:
if the slope of the fitted curve is greater than zero, the degradation trend is increased;
if the slope of the fitted curve is less than zero, the degradation tendency becomes smaller.
5. The method for predicting the residual life of the mechanical structure based on the Wiener process and the P-EMD as claimed in claim 1, wherein the predicting the residual life of the mechanical structure by using the residual life prediction model based on the Wiener process based on the change track of the approximate entropy comprises:
when the approximate entropy Ap degenerates and drifts over time, the degradation amount of the approximate entropy is expressed as:
Figure FDA0003513088940000026
wherein the content of the first and second substances,
Figure FDA0003513088940000027
to represent
Figure FDA0003513088940000028
The time degradation quantity is a matrix of the approximate entropy degradation quantity with l parameters on a column vector, l is more than or equal to 1 and less than or equal to N, N is equal to N, N is the length of the obtained IMF signal series, and m is on a row vectorkA parameter, k is more than or equal to 1 and less than or equal to n, the corresponding time is tl1，…，
Figure FDA0003513088940000031
Representing the ability to calculate m for each set of vibration signalskAn Ap value; wherein the increment of approximate entropy is expressed as:
Figure FDA0003513088940000032
wherein the content of the first and second substances,
Figure FDA0003513088940000033
is the incremental complexity degradation of the signal;
determining an approximate entropy threshold D when the mechanical structure fails according to the obtained approximate entropy degradation quantityf：
Figure FDA0003513088940000034
Wherein k isγIs a constant coefficient, AplRepresenting the approximate entropy degradation amount of the ith signal point in the IMF signal series;
according to the obtained approximate entropy threshold D when the mechanical structure failsfDetermining a residual life prediction model of the mechanical structure:
R(t)＝1-F(t)
Figure FDA0003513088940000035
Figure FDA0003513088940000036
wherein t is time and refers to the time when the service life of the equipment reaches; r (t) is a reliability function and represents the description of the probability that the service life of the equipment reaches t moment; f (t) is an intermediate expression, f (t) is a probability distribution function of the service life of a single device; residual life TτThe difference between the time t when the service life of the equipment reaches and the current time is obtained.
6. The method for predicting the residual life of the mechanical structure based on the Wiener process and the P-EMD as claimed in claim 5, wherein the maximum likelihood estimation method is adopted to solve the drift coefficient μ and the diffusion coefficient σ.
7. The method for predicting the residual life of the mechanical structure based on the Wiener process and the P-EMD as claimed in claim 6, wherein the solving of the drift coefficient μ and the diffusion coefficient by the maximum likelihood estimation method comprises:
at the time of
Figure FDA0003513088940000037
Of the signal of
Figure FDA0003513088940000038
Subject to normal distribution, the individual devicesThe probability distribution function f (t) of the reserve life is expressed as:
Figure FDA0003513088940000041
will maximum likelihood function L (mu, sigma)2) Is defined as:
Figure FDA0003513088940000042
obtaining estimated values of drift coefficient mu and diffusion coefficient sigma by using maximum likelihood method
Figure FDA0003513088940000043
And
Figure FDA0003513088940000044
Figure FDA0003513088940000045
Figure FDA0003513088940000046
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115438556A (en) * 2022-11-10 2022-12-06 北京理工大学 Method, device and equipment for predicting structural rigidity degradation rate of flexible inflatable aircraft
CN117630649A (en) * 2024-01-26 2024-03-01 深圳维盛半导体科技有限公司 PCBA testing method, device, equipment and storage medium

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115438556A (en) * 2022-11-10 2022-12-06 北京理工大学 Method, device and equipment for predicting structural rigidity degradation rate of flexible inflatable aircraft
CN115438556B (en) * 2022-11-10 2022-12-30 北京理工大学 Method, device and equipment for predicting structural rigidity degradation rate of flexible inflatable aircraft
CN117630649A (en) * 2024-01-26 2024-03-01 深圳维盛半导体科技有限公司 PCBA testing method, device, equipment and storage medium
CN117630649B (en) * 2024-01-26 2024-03-26 深圳维盛半导体科技有限公司 PCBA testing method, device, equipment and storage medium

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