Torque sensor failure probability function estimation method

Abstract

The invention relates to a torque sensor failure probability function estimation method, which combines two stages of improved cross entropy important sampling ICE-IS and adaptive Kriging to carry out failure probability function estimation, in the first stage, a small number of Monte Carlo simulation MCS samples are generated in an augmented space, a performance function of a torque sensor is replaced by a Kriging model, an initial Kriging model is constructed, and the initial Kriging model is used as an initial Kriging model; an MCS sample is adopted to train the model, and an initial Kriging model after training is obtained; in the second stage, ICE-IS is executed on the Kriging model constructed in the first stage to generate candidate sample points, after sampling training, the initial Kriging model predicts the candidate sample points and calculates learning function values for training, and retraining of the Kriging model is completed; the trained Kriging model can replace a real performance function to estimate a torque sensor failure probability function. The calculation efficiency is effectively improved, and the method has important reference value and guiding significance for reliability design of the torque sensor.

Description

Technical Field

[0001] The invention relates to the field of torque sensor detection, and in particular to a method for estimating a failure probability function of a torque sensor. Background Art

[0002] In various engineering problems, uncertainties often lead to inaccurate torque sensor measurements and serious accidents, which are often small failure probability problems. Failure probability function is an effective method for reliability design. However, sampling Monte Carlo simulation (MCS) to obtain failure probability function requires a lot of calculations. Summary of the invention

[0003] Aiming at the problem of low computational efficiency of existing failure probability function estimation, a torque sensor failure probability function estimation method is proposed to quickly obtain the reliability analysis of the torque sensor failure probability function.

[0004] The technical solution of the present invention is: a method for estimating the failure probability function of a torque sensor, which combines improved cross entropy importance sampling ICE-IS and adaptive Kriging in two stages to estimate the failure probability function. In the first stage, a small number of Monte Carlo simulation MCS samples are generated in the augmented space. In order to realize the Kriging model replacing the functional function of the torque sensor, an initial Kriging model is constructed, and the model is trained using MCS samples. Then, Kriging is gradually updated until the stopping criterion is met, and the trained initial Kriging model is obtained; in the second stage, ICE-IS is executed on the Kriging model constructed in the first stage to generate candidate sample points, and the initial Kriging model after sampling training predicts the candidate sample points and calculates the learning function value, and Kriging is gradually updated through the learning function to complete the re-training of the Kriging model; when the Kriging of the second stage meets the stopping criterion, the constructed Kriging model can replace the real functional function to estimate the failure probability function of the torque sensor.

[0005] Further, the MCS sample acquisition method is as follows: first generate N samples that obey The sample {θ j ,j=1,2,L,N}, where θ is the design parameter, i.e. the standard deviation of the Young's modulus of the torque sensor, is the distribution obeyed by the design parameters, is uniformly distributed; then for each sample, generate a sample {x j, j = 1, 2, L, N}, x is a random variable. For the torque sensor, x is the flange radius, Young's modulus, Poisson's ratio, yield limit, tensile limit of the torque sensor, which are five random variables that obey the normal distribution. Each sample obeys f(xθ j ), the sample set is marked as S 1 .

[0006] Furthermore, the initial Kriging model construction method is: 1 Randomly select N 0 The experimental design DoE consists of a sample and a function to calculate the true response. 1 Lieutenant General N 0 After samples are selected, N 0 The samples are N 0 The matrix is ​​a 5-column matrix, where the first column represents the flange radius, the second column represents the Young's model, the third column represents the Poisson's ratio, the fourth column represents the yield strength, and the fifth column represents the tensile strength. Call ANSYS software and convert N 0 Sample input, the response is N 0 A matrix with 1 row and 1 column; constructs the initial Kriging model based on DoE.

[0007] The beneficial effects of the present invention are as follows: the torque sensor failure probability function estimation method of the present invention effectively improves the calculation efficiency, and the method has important reference value and guiding significance for the reliability design of the torque sensor. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 The overall technical framework of the method of the present invention;

[0009] Figure 2 A schematic diagram of a torque sensor according to an embodiment of the present invention;

[0010] Figure 3 A comparison diagram of the failure probability function obtained by MCS and the failure probability function obtained by ALK-ICE according to an embodiment of the present invention. DETAILED DESCRIPTION

[0011] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0012] The torque sensor failure probability function estimation method of the present invention combines improved cross-entropy importance sampling (ICE-IS) and adaptive Kriging (Active learning Kriging, ALK) in two stages to estimate the failure probability function. In the first stage, a small number of Monte Carlo simulation (MCS) samples are generated in the augmented space. In order to realize that the Kriging model replaces the function function of the torque sensor, an initial Kriging model is constructed, and the model is trained using Monte Carlo simulation samples. Then, Kriging is gradually updated until the stopping criterion is met to obtain the initial Kriging model after training; in the second stage, ICE-IS is executed on the Kriging model constructed in the first stage to generate candidate sample points, and the initial Kriging model after sampling training predicts the candidate sample points and calculates the learning function value, and Kriging is gradually updated through the learning function to complete the re-training of the Kriging model; when the Kriging of the second stage meets the stopping criterion, the constructed Kriging model can replace the real function to estimate the failure probability function of the torque sensor. The new method for estimating the failure probability function effectively improves the calculation efficiency.

[0013] like Figure 1 The overall technical framework of the method of the present invention is shown, and the specific implementation steps of the method are as follows:

[0014] Step 1: Generate N MCS samples that obey the marginal distribution f(x) in the augmented space. The generation method is as follows:

[0015] First generate N obedient The sample {θ j ,j=1,2,L,N}, where θ is the design parameter, i.e. the standard deviation of the Young's modulus of the torque sensor, is the distribution that the design parameters obey. In the present invention, is uniformly distributed. Then for each sample, generate a sample {x j , j = 1, 2, L, N}, x is a random variable. For the torque sensor, x is the flange radius, Young's modulus, Poisson's ratio, yield limit, tensile limit of the torque sensor, which are five random variables that obey the normal distribution. Each sample obeys f(xθ j ). Therefore, the sample set {(x j ,θ j ),j=1,2,L,N} obey f(x,θ). Ignore sample θ, so {x j ,j=1,2,L,N} obeys the distribution f(x).

[0016] Label the sample set as S 1 .

[0017] Step 2: In S 1 Randomly select N 0 The Design of Experiment (DoE) consists of taking samples and calling a function to calculate the true response.

[0018] Although the failure probability of the torque sensor will change with the change of design parameters, the failure mode (i.e., the function function) of the torque sensor is independent and does not change with the design parameters. The purpose of this invention is to use the Kriging model to replace the function function of the torque sensor. 1 Lieutenant General N 0 After samples are selected (N 0 The samples are N 0 The matrix is ​​composed of 5 rows and 5 columns, where the first column represents the flange radius, the second column represents the Young's model, the third column represents the Poisson's ratio, the fourth column represents the yield strength, and the fifth column represents the tensile strength). Call ANSYS software and convert N 0 Sample input, the response is N 0 A matrix with 1 row and 1 column.

[0019] Construct an initial Kriging model based on DoE.

[0020] Step 3: Sample Kriging model to predict candidate sample set S 1 And calculate the U learning function value. The formula of U learning function is:

[0021] The Kriging method is an effective alternative model method in reliability analysis. The expression of Kriging is: K (x) = β + z(x)

[0022] Where β is the global estimate and z(x) is the random process. In an experimental design with m samples, for a new sample x new , the predicted response and variance of Kriging are:

[0023]

[0024] Among them, 1 is the unit vector, r(Θ,x new ) is the correlation matrix, and R(Θ) is the correlation matrix between any two training samples. is the parameter of Kriging. g is the response of m samples, which is a matrix with m rows and 1 column. σ and Θ are the parameters of Kriging. Θ is solved by optimization. The optimization problem about Θ is

[0025] Where μ(x) is the mean of the Kriging prediction and σ(x) is the standard deviation of the Kriging prediction. If minU(x) is greater than or equal to 2, proceed to step 4. Otherwise, select the sample with the smallest U learning function value and add it to the DoE to retrain the Kriging model, and repeat step 3.

[0026] Step 4: Execute ICE-IS on the Kriging model constructed in step 3. The derivation process of the important sampling density function of the last layer of samples of ICE-IS is:

[0027] Theoretically, there is an optimal important sampling density function in the augmented space:

[0028]

[0029] where f(x) can be expressed as because Uniform distribution Therefore f(x) can be further expressed as in is the integral over the design region. F (x) is the failure indicator function. When the response of the sample is greater than 0, I F (x) is equal to 0. When the sample response is less than or equal to 0, I F (x) is equal to 1. P(F) is the augmented failure probability.

[0030] Therefore, a quasi-optimal importance sampling density function h(x; v) can be constructed, where the parameter v is estimated as:

[0031]

[0032] δ is a smooth indicator function, Φ is the cumulative probability function of the standard normal distribution. When δ is small enough and approaches 0, if g(x) is greater than 0, then Φ(-g(x) / δ) is approximately equal to 0. If g(x) is less than or equal to 0, then Φ(-g(x) / δ) is approximately equal to 1. Therefore, Φ(-g(x) / δ) can be used to replace I. F (x), by F (x) is replaced by Φ(-g(x) / δ), where δ is a smoothing parameter. Introducing an important sampling density function h(x; w) of the same family as h(x; v), the above formula can be rewritten as:

[0033]

[0034] Therefore, the optimal parameter estimate for the last layer of samples is v T , the quasi-optimal important sampling density function is h(x; vT Once h(x;v) is obtained T ), the last layer of important samples of ICE-IS can be obtained.

[0035] The important samples in the last layer of ICE-IS are marked as S 2 .

[0036] Step 5: Sample Kriging model to predict candidate sample set S 2 And calculate the U learning function value. If minU(x) is greater than or equal to 2, execute step 6. Otherwise, select the sample with the smallest U learning function value and add it to DoE to retrain the Kriging model, and repeat step 5.

[0037] Step 6: Evaluate the failure probability function. The formula for evaluating the failure probability function is derived as follows:

[0038] According to Bayesian theory, Expressed as

[0039]

[0040] Where E x|F [g] stands for Therefore, can be re-expressed as

[0041]

[0042] in can be rewritten as:

[0043]

[0044] In the augmented space, the failure probability function is expressed as:

[0045]

[0046] in Therefore, ALK-ICE evaluates the failure probability function using the following formula:

[0047]

[0048] The following is a specific example to illustrate the implementation process. Figure 2 The schematic diagram of the torque sensor is shown. For a torque sensor working at 200KN, the flange radius, Young's modulus, Poisson's ratio, yield strength and tensile strength of the torque sensor are taken as random variables considered. The information of the random variables is shown in Table 1.

[0049] Table 1

[0050]

[0051] Under the action of 200KN torque, the average strain in the strain measurement area is 2.3034×10-4, so the function corresponding to the reliability of measurement accuracy is:

[0052]

[0053] Where Δ is the average strain of the strain measurement area calculated by ANSYS. When g≤0, it is determined that the torque sensor is inaccurately measured, that is, it is failed.

[0054] The standard deviation of the torque sensor Young's modulus is taken as the design parameter, and its design range is θ∈[81.2-203]MPa. Ten nodes are selected within this range. MCS needs to perform 10 7 calculations, while ALK-ICE only needs 134 calculations. The failure probability functions obtained by both are as follows: Figure 3 As shown in Figure 2, it can be seen that the computational efficiency of ALK-ICE is much higher than that of MCS, and it is an effective method for estimating the failure probability function of torque sensors.

[0055] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached claims.

Claims

1. A method for estimating a torque sensor failure probability function, characterized in that: The failure probability function is estimated in two stages by combining improved cross entropy importance sampling ICE-IS and adaptive Kriging. In the first stage, a small number of Monte Carlo simulation MCS samples are generated in the augmented space. In order to realize the function of replacing the torque sensor with the Kriging model, an initial Kriging model is constructed and the model is trained using MCS samples. Then, Kriging is gradually updated until the stopping criterion is met to obtain the initial Kriging model after training. In the second stage, ICE-IS is executed on the Kriging model constructed in the first stage to generate candidate sample points. After sampling training, the initial Kriging model predicts the candidate sample points and calculates the learning function value. The Kriging is gradually updated through the learning function to complete the re-training of the Kriging model. When the Kriging of the second stage meets the stopping criterion, the constructed Kriging model can replace the real functional function to estimate the failure probability function of the torque sensor.

2. The torque sensor failure probability function estimation method according to claim 1, characterized in that: The MCS sample acquisition method is as follows: first generate N The sample {θ j ,j=1,2,L,N}, where θ is the design parameter, i.e. the standard deviation of the Young's modulus of the torque sensor, is the distribution obeyed by the design parameters, is uniformly distributed; then for each sample, generate a sample {x j , j = 1, 2, L, N}, x is a random variable. For the torque sensor, x is the flange radius, Young's modulus, Poisson's ratio, yield limit, tensile limit of the torque sensor, which are five random variables that obey the normal distribution. Each sample obeys f(xθ j ), the sample set is marked as S1.

3. The method for estimating the failure probability function of a torque sensor according to claim 2, characterized in that: The initial Kriging model construction method is as follows: N0 samples are randomly selected in S1 and a function is called to calculate the true response to form an experimental design DoE. Specifically, after N0 samples are selected in S1, the N0 samples are a matrix with N0 rows and 5 columns, wherein the first column represents the flange radius, the second column represents the Young's model, the third column represents the Poisson's ratio, the fourth column represents the yield strength, and the fifth column represents the tensile strength. The ANSYS software is called, the N0 samples are input, and the obtained response is a matrix with N0 rows and 1 column; the initial Kriging model is constructed according to the DoE.

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