Mechanism strength time-varying reliability analysis method

Abstract

The embodiment of the invention provides a mechanism strength time-varying reliability analysis method, and relates to the technical field of mechanism reliability analysis, and the method comprises the steps: obtaining basic parameters of a mechanism; according to the basic parameters, obtaining a probability density function of stress by using an improved rotation quasi-symmetric point method and a maximum entropy method; according to the basic parameters, an improved orthogonal series expansion method is combined with a gamma process to establish a strength degradation model; calculating the time-varying reliability of the mechanism strength based on the probability density function of the stress and the degradation model of the strength; on the premise of considering strength degradation, the time-varying reliability of the strength of the mechanism is efficiently and precisely estimated.

Description

Technical Field

[0001] The present application relates to the technical field of time-varying reliability analysis of mechanisms, and in particular to a method for analyzing the time-varying reliability of mechanism strength. Background Art

[0002] With the continuous advancement of science and technology in the fields of aerospace, machinery, etc. and the increasing sophistication of engineering design, the requirements for mechanism reliability are gradually increasing. In terms of mechanism precision design, many scholars have conducted a lot of research and formed a relatively complete system. However, with the changes of the times, the designed mechanism should not only focus on motion accuracy, but also meet the requirements of strength, wear, and stagnation. Compared with the research on the reliability of mechanism motion accuracy, the research on the reliability of mechanism strength is relatively small.

[0003] In fact, there are already a lot of studies on strength reliability, but the objects of related research are mostly structures. However, unlike structures, the motion characteristics of mechanisms are often time-varying and dynamic. Therefore, the strength reliability of mechanisms is also time-varying, which is different from the reliability assessment method of structures. In addition, most of the current strength reliability studies regard strength as a constant. However, in actual engineering, mechanisms are subject to repeated loads, and complex environmental factors such as high temperature, low temperature, humidity, and salt spray will affect the performance of the mechanism, accelerate the process of strength degradation, and affect the strength reliability of the mechanism. Therefore, considering the impact of mechanism strength degradation on mechanism strength reliability is more in line with engineering practice.

[0004] At present, the research progress of non-Gaussian expansion methods is relatively slow, and the application of related methods in strength degradation modeling is relatively small. In addition, the existing time-varying reliability calculation methods are still inefficient. At present, for some complex structures and mechanisms, most of them still obtain response values ​​through finite element methods. There are common time-varying reliability calculation methods such as adaptive Kriging method, which sometimes have too many calls or even no convergence. Summary of the invention

[0005] The purpose of the embodiments of the present application is to provide a method for analyzing the time-varying reliability of the strength of a mechanism, so as to estimate the time-varying reliability of the strength of the mechanism efficiently and accurately under the premise of considering the strength degradation.

[0006] In a first aspect, an embodiment of the present application provides a method for analyzing time-varying reliability of mechanism strength, comprising:

[0007] Get the basic parameters of the organization;

[0008] According to the basic parameters, the probability density function of stress is obtained by using the improved rotational quasi-symmetric point method and the maximum entropy method.

[0009] According to basic parameters, the strength degradation model is established by using the improved orthogonal series expansion method combined with the gamma process.

[0010] Based on the probability density function of stress and the strength degradation model, the time-varying reliability of the mechanism strength is calculated.

[0011] In the above implementation process, the basic parameters of the mechanism are obtained; based on the basic parameters, the probability density function of stress is obtained using the improved rotational quasi-symmetric point method and the maximum entropy method; based on the basic parameters, the strength degradation model is established using the improved orthogonal series expansion method combined with the gamma process; based on the probability density function of stress and the strength degradation model, the time-varying reliability of the mechanism strength is calculated; and under the premise of considering strength degradation, the time-varying reliability of the mechanism strength is estimated efficiently and accurately.

[0012] Furthermore, the probability density function of stress is obtained using the improved rotational quasi-symmetric point method and the maximum entropy method according to the basic parameters, including:

[0013] Determine the number of input variables and the corresponding mean, standard deviation, and distribution type;

[0014] Determine the quasi-symmetric points and corresponding weights according to the number of input variables;

[0015] The optimal rotation angle is determined by a particle swarm optimization algorithm, wherein the objective function of the optimization algorithm is constructed by the minimum error between the fractional moment of the random variable in the fractional order interval of the point estimate after rotation and the exact value;

[0016] The rotation matrix is ​​calculated, and the quasi-symmetric point is rotated to obtain the rotated quasi-symmetric point;

[0017] Calculate the stress response value corresponding to the quasi-symmetric point after rotation;

[0018] Obtain the optimal shape parameters and size parameters through optimization algorithms;

[0019] The probability density function of stress is obtained based on the maximum entropy method.

[0020] In the above implementation process, the probability density function of stress is calculated so as to calculate the time-varying reliability of the strength of the mechanism according to the probability density function of stress and the strength degradation model.

[0021] Furthermore, the intensity degradation model is established based on the basic parameters by using an improved orthogonal series expansion method combined with a gamma process, including:

[0022] The gamma process is used to simulate the intensity degradation process. The gamma process is expanded into an expression of superposition of orthogonal time functions with random coefficients through an improved orthogonal series expansion method.

[0023] Sampling is performed according to the probability density function of stress to obtain stress;

[0024] A Gaussian random variable is extracted and substituted into the expression of orthogonal time function superposition to obtain the intensity degradation amount. Given the initial value of the intensity, the formula is used to obtain the intensity value that changes with time.

[0025] In the above implementation process, the time-varying reliability of the strength of the mechanism is calculated based on the probability density function of stress and the strength degradation model; and the time-varying reliability of the strength of the mechanism is estimated efficiently and accurately under the premise of considering the strength degradation.

[0026] Furthermore, the process of simulating intensity degradation using the gamma process is to expand the gamma process into an expression of superposition of orthogonal time functions with random coefficients through an improved orthogonal series expansion method, including:

[0027] Select several orthogonal functions and calculate several Gauss-Legendre numerical integration weights and integration points;

[0028] Calculate relevant non-Gaussian variables based on orthogonal functions, integration weights and integration points;

[0029] Calculate the first four moments of the correlated non-Gaussian variables and calculate the correlation coefficient matrix based on the autocorrelation function;

[0030] The chaotic polynomial expansion method is introduced, independent Gaussian variables are used to represent the related non-Gaussian variables, and the coefficients of the chaotic polynomial are solved using the optimization algorithm.

[0031] Solve the correlation coefficient matrix and use the principal component analysis method to transform the correlated standard Gaussian variables into independent standard Gaussian variables;

[0032] Representing correlated non-Gaussian variables as functions of independent standard Gaussian variables;

[0033] By obtaining the expression of the target non-Gaussian random process with respect to independent Gaussian variables and time, we can obtain the expression of the superposition of orthogonal time functions with random coefficients.

[0034] In the above implementation process, expressions about independent Gaussian variables and time are calculated, so as to facilitate the subsequent acquisition of the intensity degradation model.

[0035] Furthermore, the determining of the quasi-symmetric points and corresponding weights according to the number of input variables includes:

[0036] Determine the quasi-symmetric points based on the number of input variables:

[0037]

[0038] Where h is equal to ±1; n is the number of input variables;

[0039] The corresponding weights are:

[0040]

[0041] Furthermore, the calculation obtains a rotation matrix, rotates the quasi-symmetric point, and obtains the rotated quasi-symmetric point, including:

[0042] The maximum error between the estimated value and the exact value of each moment is expressed by the following matrix:

[0043]

[0044] The error between the estimated value and the exact value is evaluated by the F norm of the matrix:

[0045]

[0046] The objective function of the optimization algorithm is:

[0047]

[0048] Calculate the rotation matrix:

[0049]

[0050] The calculation formula of the quasi-symmetric point after rotation is:

[0051]

[0052] Furthermore, the obtaining of the optimal shape parameters and size parameters by the optimization algorithm includes: obtaining the optimal shape parameters and size parameters by a simplex search method:

[0053]

[0054] Among them, z is the stress response value, α i (i=1,…,M) is the shape parameter, λ i (i=1,…,is the size parameter, M is a constant;

[0055] The probability density function of stress obtained based on the maximum entropy method includes:

[0056] The calculation formula of stress probability density function is:

[0057]

[0058] λ=[λ1,λ2,...,λ M ] is the Lagrange multiplier;

[0059]

[0060] Furthermore, the process of simulating intensity degradation using the gamma process is to expand the gamma process into an expression of superposition of orthogonal time functions with random coefficients through an improved orthogonal series expansion method, including:

[0061] The form of the improved orthogonal series expansion method is:

[0062]

[0063] Among them, μ(t) is the mean function; h(t) is a set of orthogonal time functions, which are constructed by Legendre polynomials;

[0064] χ i (θ) is the relevant non-Gaussian variable, calculated using the Gauss-Legendre integration method:

[0065]

[0066] Among them, w r and a r are the weight and integration point of the Gauss-Legendre formula, respectively, so that χ i (θ) can be expressed as:

[0067]

[0068] in:

[0069]

[0070] μ=(μ(a1),μ(a2),...,μ(a R )) T ;

[0071] F(θ)=(F(a1,θ),F(a2,θ),...,F(a R ,θ)) T .

[0072] Furthermore, the chaotic polynomial expansion method is introduced, independent Gaussian variables are used to represent related non-Gaussian variables, and the coefficients of the chaotic polynomial are solved by an optimization algorithm, including:

[0073] For any random variable F, we use the one-dimensional Hermitian polynomial ψ of the standard normal variable ξ i To approximate:

[0074]

[0075] Among them, the coefficient of the chaotic polynomial b0 = μ F ;μ F is the first moment of F;

[0076] Among them, b i (i=1,2,3) is obtained through the optimization algorithm:

[0077]

[0078] in:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] in, are the second, third and fourth moment of F respectively.

[0086] Furthermore, the solving of the correlation coefficient matrix, using the principal component analysis method to convert the related standard Gaussian variables into independent standard Gaussian variables, includes:

[0087] The obtained correlation coefficient matrix C γ Perform eigenvalue decomposition:

[0088] C γ ·Φ=Φ·λ;

[0089] Get R composed of eigenvalues ​​and eigenvectors respectively 2 dimensional matrices λ and Φ;

[0090] Sort λ ​​and Φ according to the eigenvalues, and only keep the first M principal components, that is, only use the first M eigenvalues ​​and eigenvectors. γ is approximately expressed as:

[0091]

[0092] Among them, λ M and Φ M Respectively represent M 2 dimensional truncated λ and Φ;

[0093] The related standard Gaussian variable:

[0094] γ=[γ1,γ2,...,γ R ] T ;

[0095] Transformed into independent standard Gaussian variables:

[0096] ξ=[ξ1,ξ2,...,ξ M ] T .

[0097] Furthermore, the time-varying reliability of the strength of the mechanism is calculated based on the probability density function of stress and the degradation model of strength, including:

[0098] The calculation formula for the intensity at different times is:

[0099]

[0100] Calculate the time-varying reliability of the intensity:

[0101]

[0102] Among them, N is the total number of samples, N g≤0 is the number of function functions less than or equal to 0;

[0103] The function is:

[0104] g = RS;

[0105] Among them, R is the strength value and S is the stress value.

[0106] In the above implementation process, the time-varying reliability of the mechanism is calculated and obtained.

[0107] In a second aspect, an embodiment of the present application provides a device for analyzing time-varying reliability of mechanical strength, comprising:

[0108] Parameter acquisition module, used to obtain basic parameters of the organization;

[0109] A stress acquisition module is used to obtain the probability density function of stress based on basic parameters using an improved rotational quasi-symmetric point method and a maximum entropy method;

[0110] A model acquisition module is used to establish a strength degradation model based on basic parameters using an improved orthogonal series expansion method combined with a gamma process;

[0111] The result calculation module is used to calculate the time-varying reliability of the mechanism strength based on the probability density function of stress and the degradation model of strength.

[0112] In a third aspect, an embodiment of the present application provides a mechanism strength time-varying reliability analysis system, comprising: a mechanism strength time-varying reliability analysis device and a locking mechanism as described above, wherein the mechanism strength time-varying reliability analysis device is connected to the locking mechanism.

[0113] In a fourth aspect, an embodiment of the present application provides an electronic device, including:

[0114] A processor, a memory and a bus, wherein the processor is connected to the memory via the bus, and the memory stores computer-readable instructions. When the computer-readable instructions are executed by the processor, they are used to implement the time-varying reliability analysis method of the mechanism strength as described above.

[0115] In a fifth aspect, an embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a server, the method for analyzing the time-varying reliability of the strength of a mechanism as described above is implemented. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0117] Figure 1 A schematic diagram of a flow chart of a method for analyzing time-varying reliability of a mechanism strength provided in an embodiment of the present application;

[0118] Figure 2 A flapping-wing mechanism structure diagram of a mechanism strength time-varying reliability analysis method provided in an embodiment of the present application;

[0119] Figure 3 A diagram of the dimensions and material variables of a flapping-wing mechanism of a flapping-wing mechanism in a method for analyzing the time-varying reliability of mechanism strength provided in an embodiment of the present application;

[0120] Figure 4 A probability density function diagram of flapping-wing mechanism stress in a method for analyzing the time-varying reliability of mechanism strength provided in an embodiment of the present application;

[0121] Figure 5 A comparison chart of time-varying failure probability results of a method for analyzing the time-varying reliability of a mechanism strength provided in an embodiment of the present application;

[0122] Figure 6 A comparison chart of 1-4 order moment results of a gamma process simulated by an improved orthogonal series expansion method for a method for analyzing time-varying reliability of mechanical strength provided in an embodiment of the present application;

[0123] Figure 7 A comparison diagram of the first-order moment of a gamma process simulated by an improved orthogonal series expansion method and the actual first-order moment of a gamma process in a method for analyzing time-varying reliability of mechanical strength provided in an embodiment of the present application;

[0124] Figure 8A comparison diagram of the second-order moment of a gamma process simulated by an improved orthogonal series expansion method and the actual second-order moment of a gamma process provided by an embodiment of the present application for a method for analyzing the time-varying reliability of a mechanism strength;

[0125] Fig. 9 A comparison diagram of the third-order moment of a gamma process simulated by an improved orthogonal series expansion method and the actual third-order moment of a gamma process provided by an embodiment of the present application in a method for analyzing the time-varying reliability of a mechanism strength;

[0126] Fig.10 A comparison diagram of the fourth-order moment of a gamma process simulated by an improved orthogonal series expansion method and the actual fourth-order moment of a gamma process provided by an embodiment of the present application for a method for analyzing the time-varying reliability of a mechanism strength;

[0127] Fig.11 A time-varying failure probability diagram of the strength of a flapping-wing mechanism according to a method for analyzing the time-varying reliability of the mechanism strength provided in an embodiment of the present application;

[0128] Fig.12 It is a structural schematic diagram of a device for analyzing time-varying reliability of mechanism strength provided in an embodiment of the present application;

[0129] Fig.13 It is a structural schematic diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0130] The technical solutions in the embodiments of the present application will be described below in conjunction with the drawings in the embodiments of the present application.

[0131] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of this application, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0132] Please see Figure 1 , Figure 1 A flow chart of a method for analyzing the time-varying reliability of a mechanism strength provided in an embodiment of the present application. The method for analyzing the time-varying reliability of a mechanism strength comprises:

[0133] 100. Obtain the basic parameters of the organization.

[0134] For example, taking a flapping wing mechanism as an example, Figure 2 This is a simplified schematic diagram of a flapping-wing mechanism, the core of which is a single-crank double-rocker mechanism. The characteristic of this mechanism is that the cranks of the two crank-rocker mechanisms are fixed together to achieve synchronous drive.

[0135] Figure 2 In the figure, component OA is the input crank of the mechanism, and the length of OA is set to l1. The lengths of the connecting rod AB / AB′ and the rocker BC / B′C′ in the flapping-wing mechanism are l2 and l3 respectively. The finite element parametric model of the flapping-wing mechanism is established using Ansys finite element analysis software, and the stress variation of the flapping-wing mechanism during the rotation [0,2π] is calculated.

[0136] Optionally, basic parameters of the mechanism include rod lengths l1, l2, l3 and Young's modulus Y and Poisson's ratio B of the material, and the basic parameters are used as input variables (random variables).

[0137] 200. According to the basic parameters, the probability density function of stress is obtained using the improved rotational quasi-symmetric point method and maximum entropy method.

[0138] 210. Determine the number of input variables and the corresponding mean, standard deviation and distribution type.

[0139] For example, the mean, standard deviation and distribution type of each input variable are as follows: Figure 3 shown.

[0140] 220. Determine the quasi-symmetric points uu0, uu1 and the corresponding weights w0, w1 according to the number of input variables.

[0141] Optionally, determine quasi-symmetric points based on the number of input variables:

[0142]

[0143] Among them, h is equal to ±1; n is the number of input variables; the number of points of uu0 is n1, the number of points of uu1 is n2, n1 and n2 are determined according to the number of random variables m, n1=2m, n2=N-n1, N is the number of quasi-symmetric points.

[0144] The corresponding weights are:

[0145]

[0146] The optimal rotation angle θ is determined by a particle swarm optimization algorithm, wherein the objective function of the optimization algorithm is constructed by the minimum error between the fractional moment of the random variable in the fractional order interval of the point estimate after rotation and the exact value.

[0147] Optionally, estimates of the first to fourth order moments of the ith random variable are calculated by rotating the multidimensional nodes and weights as follows:

[0148]

[0149] in, Indicates the i-th Points.

[0150] The exact values ​​of the first to fourth moments of the ith random variable are calculated as follows:

[0151]

[0152] 240. Calculate the rotation matrix W p,q (θ), the quasi-symmetric point u k Rotate to obtain the quasi-symmetrical point after rotation

[0153] Optionally, the maximum error between the estimated value and the exact value of each moment is expressed by the following matrix:

[0154]

[0155] The error between the estimated value and the exact value is evaluated by the F norm of the matrix:

[0156]

[0157] The objective function of the optimization algorithm is:

[0158]

[0159] That is, the objective function of the optimization algorithm is obtained by inputting parameters into the simulation software.

[0160] Calculate the rotation matrix:

[0161]

[0162] The calculation formula of the quasi-symmetric point after rotation is:

[0163]

[0164] 250. Calculate the stress response value corresponding to the quasi-symmetric point after rotation.

[0165] Exemplarily, a dynamic parameterized model of a flapping-wing mechanism is established in the Ansys finite element analysis software, five variables including three rod lengths, Young's modulus of the material, and Poisson's ratio are set as parameters, and the quasi-symmetric points after rotation are substituted to obtain the stress response values ​​of each group.

[0166] 260. The optimal shape parameters and size parameters are obtained through optimization algorithm.

[0167] The optimal shape parameter α and size parameter λ are obtained by the simplex search method:

[0168]

[0169] Among them, z is the stress response value, αi (i=1,…,M) is the shape parameter, λ i (i=1, ..., M) is a size parameter; M is a constant, which is generally a constant and is set to 4 here.

[0170] 270. Obtain the probability density function of stress based on the maximum entropy method.

[0171] Optionally, the stress probability density function is calculated as:

[0172]

[0173] λ=[λ1,λ2,...,λ M ] is the Lagrange multiplier;

[0174]

[0175] For example, the probability density function of stress is obtained as Figure 4 As shown by the lines in .

[0176] In the above implementation process, the probability density function of stress is calculated so as to calculate the time-varying reliability of the strength of the mechanism according to the probability density function of stress and the strength degradation model.

[0177] 300. According to the basic parameters, the intensity degradation model is established by using the improved orthogonal series expansion method combined with the gamma process.

[0178] 310. The gamma process is used to simulate the intensity degradation process. The gamma process is expanded into an expression of superposition of orthogonal time functions with random coefficients through an improved orthogonal series expansion method.

[0179] The parameters of the Gamma process are assumed to be: shape parameter α = 1, size parameter β = 0.5, the time of intensity degradation is given as t = [0, 1] (unit: ten years), and the time interval is divided into N t = 11 segments, N are extracted at each time point x =The number of samples is 106.

[0180] Optionally, the improved orthogonal series expansion method is in the form of:

[0181]

[0182] Among them, μ(t) is the mean function; h(t) is a set of orthogonal time functions, which are constructed by Legendre polynomials;

[0183] χ i (θ) is the relevant non-Gaussian variable, calculated using the Gauss-Legendre integration method:

[0184]

[0185] Among them, w r and a r are the weight and integration point of the Gauss-Legendre formula, respectively, so that χ i (θ) can be expressed as:

[0186]

[0187] in:

[0188]

[0189] μ=(μ(a1),μ(a2),...,μ(a R )) T ;

[0190] F(θ)=(F(a1,θ),F(a2,θ),...,F(a R ,θ)) T .

[0191] 311. Select several orthogonal functions and calculate several Gauss-Legendre numerical integration weights and integration points.

[0192] Among them, Legendre polynomials are used to construct N orthogonal basis functions (h1(t),h2(t),...,h N (t)) T , take N = 15, calculate R Gauss-Legendre numerical integration weights w r and integral point a r (r=1,2,…,R), take R=25, and transform it to the given time interval [0,1].

[0193] 312. Calculate the relevant non-Gaussian variables based on orthogonal functions, integration weights and integration points.

[0194] 313. Calculate the first four moments of the relevant non-Gaussian variable F(θ), and according to the autocorrelation function C(Δt) = exp(-|Δt| 2 ) to calculate the correlation coefficient matrix.

[0195] 314. Introduce the chaotic polynomial expansion method, expand the related gamma variable F(θ) using the chaotic polynomial method, use independent Gaussian variables to represent the related non-Gaussian variables, and use the optimization algorithm to solve the coefficient b of the chaotic polynomial i (i=0,1,2,3).

[0196] Optionally, for any random variable F, use the one-dimensional Hermitian polynomial ψ of the standard normal variable ξ i To approximate:

[0197]

[0198] Among them, the coefficient of the chaotic polynomial b0 = μ F ;μ F is the first moment of F;

[0199] Among them, b i (i=1,2,3) is obtained through the optimization algorithm:

[0200]

[0201] in:

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208] in, are the second, third and fourth moment of F respectively.

[0209] 315. Solve the γ correlation coefficient matrix C γ , the principal component analysis method is used to transform the relevant standard Gaussian variables γ=[γ1,γ2,...,γ R ] T are independent standard Gaussian variables ξ=[ξ1,ξ2,...,ξ M ] T .

[0210] Optionally, obtain the correlation coefficient matrix C γ Perform eigenvalue decomposition:

[0211] C γ ·Φ=Φ·λ;

[0212] Get R composed of eigenvalues ​​and eigenvectors respectively 2 dimensional matrices λ and Φ;

[0213] Sort λ ​​and Φ according to the eigenvalues, and only retain the first M principal components (here M = 15), that is, only use the first M eigenvalues ​​and eigenvectors, and γ is approximately expressed as:

[0214]

[0215] Among them, λ M and Φ M Respectively represent M 2 dimensional truncated λ and Φ;

[0216] The related standard Gaussian variable:

[0217] γ=[γ1,γ2,...,γ R ] T ;

[0218] Transformed into independent standard Gaussian variables:

[0219] ξ=[ξ1,ξ2,...,ξ M ] T .

[0220] Among them, γ i and γ j Correlation coefficient Obtained through the following optimization algorithm:

[0221]

[0222] Among them, Cov[F i ,F j ] is the covariance of any two variables in F, F is a series of gamma-distributed random variables, and all random variables can be approximated as:

[0223]

[0224] 316. Express the correlated non-Gaussian variables F(θ) as independent standard Gaussian variables ξ=[ξ1,ξ2,...,ξ M ] T function.

[0225] Optionally, by passing the obtained Substituting into the formula:

[0226]

[0227] 317. By obtaining the expression of the target non-Gaussian random process with respect to independent Gaussian variables and time, we can obtain the expression of the superposition of orthogonal time functions with random coefficients, that is, the process of expressing the non-Gaussian random process using independent Gaussian variables is realized.

[0228] Optionally, this is achieved by substituting the expression of F obtained in step 316 into the formula.

[0229] In the above implementation process, expressions about independent Gaussian variables and time are calculated, so as to facilitate the subsequent acquisition of the intensity degradation model.

[0230] For example, the exact values ​​and simulated values ​​of the 1st to 4th order moments of the gamma process are compared to verify the accuracy of the improved orthogonal series expansion method. The moment comparison results are as follows: Figure 6-Figure 10 As shown, according to the results, the maximum error of the moment is less than 5%.

[0231] 320. Sampling is performed according to the probability density function of stress to obtain stress.

[0232] 330. Extract Gaussian random variables and substitute them into the expression of superposition of orthogonal time functions F(t,θ)≈μ(t)+h(t) T ·Wh·(F(θ)-μ), the strength degradation amount is obtained, and the strength value that changes with time is obtained using the formula given the initial strength value R0.

[0233] Optionally, the initial strength value R0 is set to 164 MPa.

[0234] Optionally, the calculation formula for the intensity at different moments is:

[0235]

[0236] 400. Based on the probability density function of stress and the strength degradation model, the time-varying reliability of the structure strength is calculated.

[0237] Optionally, compute the time-varying failure probability of the strength:

[0238]

[0239] Calculate the time-varying reliability of the intensity:

[0240]

[0241] Among them, N is the total number of samples, N g≤0 is the number of function functions less than or equal to 0;

[0242] The function is:

[0243] g = RS;

[0244] Among them, R is the strength value and S is the stress value.

[0245] For example, according to Figure 4 and Fig.11 It can be seen that the failure probabilities obtained based on the proposed improved rotational quasi-symmetric point method all fall within the confidence interval. Figure 4The probability density function diagram of stress obtained by the proposed method is basically consistent with the probability density function diagram obtained by the Monte Carlo method, which verifies the accuracy of the proposed method. Compared with the Monte Carlo method, the proposed method only needs to call Ansys for 42 calculations; therefore, this embodiment fully proves the accuracy and efficiency of the proposed method.

[0246] The improved orthogonal series expansion method simulates the strength degradation process of the flapping-wing mechanism very well. Considering the time-varying failure probability of the flapping-wing mechanism under strength degradation is about 0.5 after ten years. Compared with the constant strength, reliability analysis considering strength degradation is more in line with the actual situation of the mechanism.

[0247] In the above implementation process, the time-varying reliability of the strength of the mechanism is calculated based on the probability density function of stress and the strength degradation model; and the time-varying reliability of the strength of the mechanism is estimated efficiently and accurately under the premise of considering the strength degradation.

[0248] Exemplarily, the Monte Carlo method is used to verify the calculation results of the proposed improved rotational quasi-symmetric point and the maximum entropy method. The Latin hypercube sampling method is used for sampling. Due to the long calculation time of the finite element simulation, 5000 groups of input points are extracted. The stress response results are calculated using Ansys. The calculation method of the strength degradation amount is the same as that in step 310-step 330. The failure probability is calculated by the Monte Carlo method and compared with the result of step 400. Since only 5000 groups of samples are extracted, a confidence interval with a confidence level of 98% is used here. The failure probability calculated by the Monte Carlo method is as follows: Figure 5 As shown in the second column of , the lower and upper bounds of the 98% confidence interval are Figure 5 As shown in the 3rd and 4th columns of , the stress probability density function diagram obtained by the proposed method and Monte Carlo is shown in Figure 3 shown.

[0249] The embodiment of the present application utilizes the gamma process to simulate the process of strength degradation of the mechanism, and applies the improved orthogonal technology expansion method to the expansion of the gamma process. The strength degradation model established based on the gamma process is more in line with engineering practice than the one with constant strength. At the same time, an improved rotational quasi-symmetric point is proposed, which is combined with the maximum entropy method to obtain the probability density function of stress. Compared with the Monte Carlo method, the number of finite element calls is reduced, which greatly improves the calculation efficiency of the time-varying reliability of the mechanism strength.

[0250] As described above, the embodiment of the present application obtains the basic parameters of the mechanism; based on the basic parameters, the probability density function of stress is obtained using the improved rotational quasi-symmetric point method and the maximum entropy method; based on the basic parameters, a strength degradation model is established using the improved orthogonal series expansion method combined with the gamma process; based on the probability density function of stress and the strength degradation model, the time-varying reliability of the mechanism strength is calculated; and under the premise of considering the strength degradation, the time-varying reliability of the mechanism strength is estimated efficiently and accurately.

[0251] The above steps are not to be performed in a strict order as described in the numbers, but should be understood as an overall solution.

[0252] In the second aspect, based on the above embodiments, Fig.12 This is a schematic diagram of the structure of a device for analyzing the time-varying reliability of a mechanism strength provided by an embodiment of the present application. Fig.12 The device for analyzing the time-varying reliability of mechanical strength provided in this embodiment specifically includes: a parameter acquisition module 1201 , a stress acquisition module 1202 , a model acquisition module 1203 and a result calculation module 1204 .

[0253] Among them, the parameter acquisition module 1201 is used to obtain the basic parameters of the mechanism; the stress acquisition module 1202 is used to obtain the probability density function of stress based on the basic parameters using the improved rotational quasi-symmetric point method and the maximum entropy method; the model acquisition module 1203 is used to establish a strength degradation model based on the basic parameters using the improved orthogonal series expansion method combined with the gamma process; the result calculation module 1204 is used to calculate the time-varying reliability of the mechanism strength based on the probability density function of stress and the strength degradation model.

[0254] As described above, the embodiment of the present application obtains the basic parameters of the mechanism; based on the basic parameters, the probability density function of stress is obtained using the improved rotational quasi-symmetric point method and the maximum entropy method; based on the basic parameters, a strength degradation model is established using the improved orthogonal series expansion method combined with the gamma process; based on the probability density function of stress and the strength degradation model, the time-varying reliability of the mechanism strength is calculated; and under the premise of considering the strength degradation, the time-varying reliability of the mechanism strength is estimated efficiently and accurately.

[0255] In the third aspect, based on the above embodiment, the embodiment of the present application also provides a mechanism strength time-varying reliability analysis system. The mechanism strength time-varying reliability analysis system provided in this embodiment specifically includes: the mechanism strength time-varying reliability analysis device and the mechanism as described above, wherein the mechanism strength time-varying reliability analysis device is connected to the mechanism.

[0256] In a fourth aspect, an embodiment of the present application further provides an electronic device that can integrate the mechanism strength time-varying reliability analysis device provided in an embodiment of the present application. Fig.13Schematic diagram of the structure of an electronic device provided by an embodiment of the present application. Fig.13 The electronic device includes: an input device 93, an output device 94, a memory 92 and one or more processors 91; the memory 92 is used to store one or more programs; when the one or more programs are executed by the one or more processors 91, the one or more processors 91 implement the time-varying reliability analysis method of the mechanism strength provided in the above embodiment. The input device 93, the output device 94, the memory 92 and the processor 91 can be connected by a bus or other means. Fig.13 The example of connecting through bus is taken in the following.

[0257] The processor 91 executes various functional applications and data processing of the device by running the software programs, instructions and modules stored in the memory 92, that is, realizes the above-mentioned mechanism strength time-varying reliability analysis method.

[0258] The electronic device provided above can be used to execute the time-varying reliability analysis method of mechanism strength provided in the above embodiment, and has corresponding functions and beneficial effects.

[0259] In the fifth aspect, an embodiment of the present application also provides a computer-readable storage medium, which includes a stored computer program; wherein, when the computer program is running, the device where the computer-readable storage medium is located is controlled to execute the time-varying reliability analysis method of the mechanism strength as described above, and can achieve the same beneficial effects.

[0260] Of course, the storage medium containing computer executable instructions provided in an embodiment of the present application is not limited to the mechanism strength time-varying reliability analysis method described above, and can also execute related operations in the mechanism strength time-varying reliability analysis method provided in any embodiment of the present application.

[0261] In a sixth aspect, the embodiments of the present application also provide a computer program product, and the methods described in the various embodiments of the present application can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instruction is loaded and executed on a computer, the process or function described in the various embodiments of the present application is executed in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, a network device, a user device, a core network device, an OAM (Open Application Model) or other programmable device.

[0262] The computer program or instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer program or instructions may be transmitted from one website, computer, server or data center to another website, computer, server or data center by wired or wireless means. The computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium may be a magnetic medium, such as a floppy disk, a hard disk, or a magnetic tape; it may also be an optical medium, such as a digital video disk; it may also be a semiconductor medium, such as a solid-state drive. The computer-readable storage medium may be a volatile or non-volatile storage medium, or may include both volatile and non-volatile types of storage media.

[0263] In several embodiments provided in the present application, it should be understood that the disclosed devices and methods can also be implemented in other ways. The device embodiments described above are merely schematic. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the devices, methods and computer program products according to multiple embodiments of the present application. In this regard, each box in the flowchart or block diagram can represent a module, a program segment or a part of a code, and the module, a program segment or a part of a code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart can be implemented with a dedicated hardware-based system that performs a specified function or action, or can be implemented with a combination of dedicated hardware and computer instructions.

[0264] In addition, the functional modules in the various embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.

[0265] If the function is implemented in the form of a software function module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions for an electronic device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0266] The above description is only an embodiment of the present application and is not intended to limit the scope of protection of the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the scope of protection of the present application. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0267] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0268] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or equipment including elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or equipment. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or equipment including the elements.

Claims

1. A method for analyzing time-varying reliability of mechanism strength, characterized in that: include: Get the basic parameters of the organization; According to the basic parameters, the probability density function of stress is obtained by using the improved rotational quasi-symmetric point method and the maximum entropy method. According to basic parameters, the strength degradation model is established by using the improved orthogonal series expansion method combined with the gamma process. Based on the probability density function of stress and the strength degradation model, the time-varying reliability of the mechanism strength is calculated.

2. The time-varying reliability analysis method of mechanism strength according to claim 1 is characterized in that: The method of obtaining the probability density function of stress using the improved rotational quasi-symmetric point method and the maximum entropy method according to the basic parameters includes: Determine the number of input variables and the corresponding mean, standard deviation, and distribution type; Determine the quasi-symmetric points and corresponding weights according to the number of input variables; The optimal rotation angle is determined by a particle swarm optimization algorithm, wherein the objective function of the optimization algorithm is constructed by the minimum error between the fractional moment of the random variable in the fractional order interval of the point estimate after rotation and the exact value; The rotation matrix is ​​calculated, and the quasi-symmetric point is rotated to obtain the rotated quasi-symmetric point; Calculate the stress response value corresponding to the quasi-symmetric point after rotation; Obtain the optimal shape parameters and size parameters through optimization algorithms; The probability density function of stress is obtained based on the maximum entropy method.

3. The time-varying reliability analysis method of mechanism strength according to claim 1 is characterized in that: The intensity degradation model is established based on the basic parameters by using an improved orthogonal series expansion method combined with a gamma process, including: The gamma process is used to simulate the intensity degradation process. The gamma process is expanded into an expression of superposition of orthogonal time functions with random coefficients through an improved orthogonal series expansion method. Sampling is performed according to the probability density function of stress to obtain stress; A Gaussian random variable is extracted and substituted into the expression of orthogonal time function superposition to obtain the intensity degradation amount. Given the initial value of the intensity, the formula is used to obtain the intensity value that changes with time.

4. The time-varying reliability analysis method of mechanism strength according to claim 3 is characterized in that: The process of simulating intensity degradation by using the gamma process, expanding the gamma process into an expression of superposition of orthogonal time functions with random coefficients through an improved orthogonal series expansion method, includes: Select several orthogonal functions and calculate several Gauss-Legendre numerical integration weights and integration points; Calculate relevant non-Gaussian variables based on orthogonal functions, integration weights and integration points; Calculate the first four moments of the correlated non-Gaussian variables and calculate the correlation coefficient matrix based on the autocorrelation function; The chaotic polynomial expansion method is introduced, independent Gaussian variables are used to represent the related non-Gaussian variables, and the coefficients of the chaotic polynomial are solved using the optimization algorithm. Solve the correlation coefficient matrix and use the principal component analysis method to transform the correlated standard Gaussian variables into independent standard Gaussian variables; Representing correlated non-Gaussian variables as functions of independent standard Gaussian variables; By obtaining the expression of the target non-Gaussian random process with respect to independent Gaussian variables and time, we can obtain the expression of the superposition of orthogonal time functions with random coefficients.

5. The time-varying reliability analysis method of mechanism strength according to claim 2 is characterized in that: Determining the quasi-symmetric points and corresponding weights according to the number of input variables includes: Determine the quasi-symmetric points based on the number of input variables: Where h is equal to ±1; n is the number of input variables; The corresponding weights are: The calculation to obtain a rotation matrix and to rotate the quasi-symmetric point to obtain the rotated quasi-symmetric point includes: The maximum error between the estimated value and the exact value of each moment is expressed by the following matrix: The error between the estimated value and the exact value is evaluated by the F norm of the matrix: The objective function of the optimization algorithm is: Calculate the rotation matrix: The calculation formula of the quasi-symmetric point after rotation is: The method of obtaining the optimal shape parameters and size parameters by using an optimization algorithm includes: The optimal shape and size parameters are obtained by simplex search: Among them, z is the stress response value, α i (i=1,…,M) is the shape parameter, λ i (i=1, ..., M) is a size parameter, M is a constant; Wherein, the probability density function of stress obtained based on the maximum entropy method includes: The calculation formula of stress probability density function is: λ=[λ1,λ2,…,λ M ] is the Lagrange multiplier; 6. The time-varying reliability analysis method of mechanism strength according to claim 3 is characterized in that: The process of simulating intensity degradation by using the gamma process, expanding the gamma process into an expression of superposition of orthogonal time functions with random coefficients through an improved orthogonal series expansion method, includes: The form of the improved orthogonal series expansion method is: Among them, μ(t) is the mean function; h(t) is a set of orthogonal time functions, which are constructed by Legendre polynomials; χ i (θ) is the relevant non-Gaussian variable, calculated using the Gauss-Legendre integration method: Among them, w r and a r are the weight and integration point of the Gauss-Legendre formula, respectively, so that χ i (θ) is shown as: in, μ=(μ(a1),μ(a2),...,μ(a R )) T ; F(θ)=(F(a1,θ),F(a2,θ),...,F(a R ,θ)) T 。 7. The time-varying reliability analysis method of mechanism strength according to claim 4 is characterized in that: The method of introducing a chaotic polynomial expansion, using independent Gaussian variables to represent related non-Gaussian variables, and using an optimization algorithm to solve the coefficients of the chaotic polynomial include: For any random variable F, we use the one-dimensional Hermitian polynomial ψ of the standard normal variable ξ i To approximate: Among them, the coefficient of the chaotic polynomial b0 = μ F ;μ F is the first moment of F; Among them, b i (i=1,2,3) is obtained through the optimization algorithm: in, in, They are the second, third and fourth order moments of F respectively; The method of solving the correlation coefficient matrix and converting the related standard Gaussian variables into independent standard Gaussian variables by principal component analysis includes: The obtained correlation coefficient matrix C γ Perform eigenvalue decomposition: C γ ·Φ=Φ·λ; Get R composed of eigenvalues ​​and eigenvectors respectively 2 dimensional matrices λ and Φ; Sort λ ​​and Φ according to the eigenvalues, and only keep the first M principal components, that is, only use the first M eigenvalues ​​and eigenvectors. γ is approximately expressed as: Among them, λ M and Φ M Respectively represent M 2 dimensional truncated λ and Φ; The related standard Gaussian variable: γ=[γ1,γ2,...,γ R ] T ; Transformed into independent standard Gaussian variables: ξ=[ξ1,ξ2,...,ξ M ] T 。 8. The method for analyzing time-varying reliability of mechanical strength according to any one of claims 1 to 7, characterized in that: The method of calculating the time-varying reliability of the strength of the mechanism based on the probability density function of stress and the degradation model of strength includes: The calculation formula for the intensity at different times is: Calculate the time-varying reliability of the intensity: Among them, N is the total number of samples, N g≤0 is the number of function functions less than or equal to 0; The function is: g = RS; Among them, R is the strength value and S is the stress value.

9. A device for analyzing time-varying reliability of mechanical strength, characterized in that: include: Parameter acquisition module, used to obtain basic parameters of the organization; A stress acquisition module is used to obtain the probability density function of stress based on basic parameters using an improved rotational quasi-symmetric point method and a maximum entropy method; A model acquisition module is used to establish a strength degradation model based on basic parameters using an improved orthogonal series expansion method combined with a gamma process; The result calculation module is used to calculate the time-varying reliability of the mechanism strength based on the probability density function of stress and the degradation model of strength.

10. A time-varying reliability analysis system for mechanism strength, characterized in that: include: The mechanism strength time-varying reliability analysis device and mechanism as described in claim 9, wherein the mechanism strength time-varying reliability analysis device is connected to the mechanism.

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