Optimization method of demand samples based on active learning Kriging model

Abstract

The present invention discloses a method for optimizing demand samples based on an active learning Kriging model. The reliability optimization method of the active learning Kriging model comprises: S1: performing a sampling operation in a sample database to obtain a small sample library; S2: establishing a new active learning Kriging model by using a learning function according to the small sample library and an initial active learning Kriging model; S3: improving the sampling accuracy of the modified active learning Kriging model by using an adaptive candidate region model, an influence function IF and a clustering method to obtain an active learning Kriging model with high accuracy; S4: obtaining an optimization result of the demand sample by using the active learning Kriging model with high accuracy and a sequence optimization and reliability evaluation method according to the demand sample.

Description

Technical Field

[0001] The present invention relates to the technical field of machine learning, and in particular to an optimization method for demand samples based on an active learning Kriging model. Background Art

[0002] Currently, reliability-based design optimization (RBDO) has become a commonly used design method in aerospace engineering. However, due to the high nonlinearity and uncertainty of its analysis process, this method is not practical in industrial applications. Although the active learning Kriging (ALK) method and the sequential optimization and reliability assessment (SORA) model have been used for many years to try to improve the practicality of RBDO, more effective methods are still needed to deal with complex problems and low precision problems. Summary of the invention

[0003] The object of the present invention is to provide an optimization method for demand samples based on an active learning Kriging model, so as to improve the accuracy of the active learning Kriging model and obtain the optimal optimization result of the demand samples.

[0004] If f(x) is the optimization objective function, G(x) or g(x) is the reliability function, G(x) = 0 or g(x) = 0 is the limit state equation. Generally, there may be n limit state equations in a system, that is, g i (x) = 0, i = 1, 2, ..., n, the reliability optimization problem can be defined as an optimization problem that satisfies the reliability function constraint, as follows:

[0005] Search for the deterministic design parameter d and the mean value μ of the uncertain design parameter X ;

[0006] Make the objective function f(d,μ X ,μ P ) smallest (big)

[0007] Satisfy the constraint condition P(g i (d,X,P)≥0)≥R i ,i=1,2,...,n

[0008] d∈[d L ,d U ],μ X ∈[μ X L ,μ X U ]

[0009] Where P(*) is the probability, R iThe reliability of the demand. Due to the uncertainty of probability, it is difficult to optimize the reliability. In view of this type of problem, the technical solution of the present invention to solve the above technical problem is as follows:

[0010] The present invention provides a method for optimizing demand samples based on an active learning Kriging model, wherein the reliability optimization method of the active learning Kriging model comprises:

[0011] S1: Perform sampling operations in the sample database to obtain a small sample database;

[0012] S2: Based on the small sample library and the initial active learning Kriging model, a new active learning Kriging model is established using a learning function;

[0013] S3: using an adaptive candidate region model, an influence function IF and a clustering method to improve the sampling accuracy of the modified active learning Kriging model, and obtaining an active learning Kriging model with high accuracy;

[0014] S4: According to the demand sample, the high-precision active learning Kriging model and the sequence optimization and reliability evaluation method are used to obtain the optimization result of the demand sample.

[0015] Optionally, the step S2 includes:

[0016] S21: using the Latin hypercube method, performing a sampling operation in the small sample library to obtain a sampling result;

[0017] S22: constructing an initial active learning Kriging model using the sampling results;

[0018] S23: predicting a large number of candidate points M using the current active learning Kriging model to obtain prediction results and true results of the large number of candidate points M;

[0019] S24: Calculate the learning function values ​​of all prediction results, and determine the current candidate point corresponding to the largest learning function value among all the learning function values;

[0020] S25: Determine whether the current candidate point meets the convergence condition. If so, output the current active learning Kriging model as the new active learning Kriging model; otherwise, add the current candidate point to the sampling result and return to step S22.

[0021] Optionally, in step S25, the convergence condition δ max for:

[0022] δ max=max(LF (p) )-max(LF (p-1) )≤ε

[0023] Among them, max(·) represents the maximum value, LF (·) represents the active learning value, p represents the number of iterations and is a positive integer, and ε represents the error.

[0024] Optionally, in step S2, the learning function is an exponential acceleration function EIE:

[0025]

[0026] Alternatively, the learning function is an improved exponential distance function EID:

[0027]

[0028] Among them, g min Represents the minimum value predicted by the performance function, that is represents the predicted value of g(x), σ represents the standard deviation, and the superscript ^ represents the predicted value. represents the predicted value of g(x) calculated at the kth iteration, represents the predicted value of σ(x) calculated at the kth iteration, x min Expressed so that the formula The value of x in the minimum case, EXP(·) represents the exponential function with the natural constant e as the base, η represents and η=max(||x min -x1|| k ,||x min -x2|| k ,...,||x min -x n || k ), φ(·) and ψ(·) are the probability cumulative function (CDF) and probability density function (PDF) under the standard normal distribution, respectively. EI represents the expected function. The expected function of the kth Kriging model can be expressed as:

[0029]

[0030] x1~x n represents n sampling points, represents the predicted value of f(x), f(x) represents the objective function of optimization, and g(x) represents the reliability function.

[0031] Optionally, step S3 includes:

[0032] S31: determining the adaptive candidate region according to the learning function and the 3σ criterion;

[0033] S32: dividing the adaptive candidate region into a plurality of parallel adaptive candidate sub-regions by a clustering method;

[0034] S33: Calculate the influence function values ​​and parallel learning function values ​​of all training points in the current parallel adaptive candidate area;

[0035] S34: taking the training point corresponding to the maximum value among all the parallel learning function values ​​as the target training point;

[0036] S35: Determine whether the calculation results of the influence function value and the parallel learning function value of the target training point meet the preset conditions. If so, proceed to step S36; otherwise, take the next parallel adaptive candidate region as the current parallel adaptive candidate region and return to step S33;

[0037] S36: marking the target training point as a model training point to train the new active learning Kriging model, so as to improve the accuracy of the new active learning Kriging model and obtain an active learning Kriging model with high accuracy.

[0038] Optionally, in step S35, the influence function value and the parallel learning function value of the target training point are calculated as follows:

[0039]

[0040] in, represents the maximum value of PLF(·) from 1 to np, PLF(·) represents the parallel training point determined by the product of the influence function value and the parallel learning function value, np is the number of parallel samples in one iteration, x Pa represents the training point, LF(x u ) represents the value of the learning function at the training point, x u represents the updated training point.

[0041] Optionally, the step S4 comprises:

[0042] S41: Obtain reliability constraints;

[0043] S42: According to the demand sample, using the high-precision active learning Kriging model, obtain the initial optimization result d of the demand sample (0) ;

[0044] S43: Obtain the most likely failure point in the current optimization result of the demand sample;

[0045] S44: Determine whether the most likely failure point meets the reliability constraint condition, if so, proceed to step S45, otherwise, proceed to step S46;

[0046] S45: Determine whether the current optimization result of the demand sample meets the preset conditions. If so, output the current optimization result of the demand sample as the optimization result of the demand sample. Otherwise, update the current optimization result of the demand sample using the incremental coefficient related to the optimization algorithm, and return to step S43.

[0047] S46: Use the optimization formula of the demand sample to update the current optimization result of the demand sample, and return to step S43.

[0048] Optionally, in step S41, the reliability constraint condition is:

[0049] G(X MPP )>0

[0050] Among them, X MPP represents the failure point, G(X MPP ) indicates that the failure point is safe.

[0051] Optionally, in step S45, the preset condition is:

[0052] ||d (k+1) -d (k) ||2<ε

[0053] The updating of the current optimization result of the demand sample by using the incremental coefficient related to the optimization algorithm includes:

[0054] Let d (k+1) =d (k+1) -λ (k+1) d (k)

[0055] Among them, d (k+1) represents the optimal design point obtained in the k+1th iteration step, d (k) represents the optimal design point obtained in the kth step, λ represents the incremental coefficient related to the optimization algorithm, and ε represents the optimization convergence parameter.

[0056] Optionally, in step S46, the optimization formula of the demand sample is:

[0057]

[0058] Among them, d (k+1) represents the optimal design point obtained in the k+1th iteration step, d (k) represents the optimal design point obtained in the kth step, d s represents the step size, |G min (X MPTP)| indicates that under the current design point, G(x) obtains the minimum value when the MPP point is reached, G(d (k) ) indicates that G(x) obtains the optimal design point d (k) When the size of G(x) is MPTP Indicates the maximum possible failure point.

[0059] The present invention has the following beneficial effects:

[0060] The method of the present invention is based on the active learning Kriging (ALK) method and makes full use of the return error analysis of Kriging modeling to form an adaptive change sample region, called the parallel adaptive candidate region (PACR). With the help of PACR technology, the accuracy of the active learning Kriging model is improved; in addition, the initial optimization results of the demand samples are iteratively judged using sequence optimization and reliability evaluation methods, and the optimal optimization results can be output. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of the optimization method of the demand sample based on the active learning Kriging model of the present invention;

[0062] Figure 2 The figure is a comparison chart of the optimization results of the optimization method of the present invention and the optimization results of the original optimization method. DETAILED DESCRIPTION

[0063] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0064] Example

[0065] The present invention provides an optimization method for demand samples based on active learning Kriging model, referring to Figure 1 As shown, the reliability optimization method of the active learning Kriging model includes:

[0066] S1: Perform sampling operations in the sample database to obtain a small sample database;

[0067] S2: Based on the small sample library and the initial active learning Kriging model, a new active learning Kriging model is established using a learning function;

[0068] Specifically, the present invention uses the learning function (LF) as the key technology of the active learning Kriging model (ALK), and provides a mathematical method for determining the most valuable samples for training an accurate ALK model. The present invention uses the following LF function (herein, the U function) to select the training point g(x) with the highest probability of wrong prediction, where

[0069] Here, σ is the standard deviation and the superscript ^ represents the predicted value. For the kth Kriging model, Using the expected function EI (that is, the efficiency global optimization algorithm), the kth EI is in φ(·) and ψ(·) are the standard normal cumulative function and standard normal probability density function respectively. In this way, the sample can gradually approach the optimal g min The expected feasibility function EFF is a general type of EI. The samples selected by EFF are located in the sensitive area of ​​g(x) = a, which can be expressed as:

[0070]

[0071] ; The expected risk function can improve the accuracy of the performance function prediction by learning the training points whose signs have the greatest risk of being mispredicted, where the larger the ERF value, the greater the possibility of misprediction from positive to negative or from negative to positive; The importance learning function can be used to consider the importance of the prediction point to improve sampling efficiency Where U is the learning function mentioned above, which can also be replaced by EFF, ERF, etc. η(x) is the reliability index value of the current point, which is:

[0072] The present invention improves the EIE acquisition function to make its performance more stable. where η = max(||x min -x1|| k ,||x min -x2|| k ,...,||x min -x n || k ), x min is the minimum point, and n is the number of all candidate elements, which is usually larger than the number of original sample points. Therefore, an improved exponential distance (EID) function is added, which adds a new term to represent the error when the selected point is too far away from the optimal point of the current prediction: Where p is a positive integer, indicating the number of iterations. The convergence condition is: max =max(LF (p) )-max(LF (p-1) )≤ε.

[0073] Therefore, step S2 of the present invention is specifically divided into the following steps:

[0074] If you want to get a global optimal solution with an error of ε, N is required to be greater than 10 2-log(ε). For example, ε = 0.01 requires 104 samples. The iteration of the ALK strategy is summarized as follows:

[0075] S21: Using the Latin hypercube method, in the small sample library D (0) Perform sampling operation in order to obtain sampling results;

[0076] S22: constructing an initial active learning Kriging model using the sampling results;

[0077] S23: Use the current active learning Kriging model to predict a large number of candidate points M, let i=i+1, and obtain the predicted results and the real results of the large number of candidate points M; here, i is a counter.

[0078] S24: Calculate the learning function values ​​(LF values) of all prediction results, and determine the current candidate point (i.e., LF (X)) corresponding to the largest learning function value among all the learning function values. U(i) ) The maximum value of X U(i) );

[0079] S25: Determine whether the current candidate point meets the convergence condition. If so, output the current active learning Kriging model as the new active learning Kriging model; otherwise, add the current candidate point to the sampling result and return to step S22.

[0080] Here, the convergence condition is:

[0081] δ max =max(LF (p) )-max(LF (p-1) )≤ε

[0082] Among them, max(·) represents the maximum value, LF (·) represents the active learning value, p represents the number of iterations and is a positive integer, and ε represents the error.

[0083] That is, if the convergence condition is met, a new active learning Kriging model is obtained; otherwise, 1 X U(i) Add to small sample library D (i) It is used to update the current active learning Kriging model.

[0084] In step S2, the learning function is an exponential acceleration function EIE:

[0085]

[0086] Alternatively, the learning function is an improved exponential distance function EID:

[0087]

[0088] Among them, g min Represents the minimum value predicted by the performance function, that is represents the predicted value of g(x), σ represents the standard deviation, and the superscript ^ represents the predicted value. represents the predicted value of g(x) calculated at the kth iteration, represents the predicted value of σ(x) calculated at the kth iteration, x min Expressed so that the formula The value of x in the minimum case, EXP(·) represents the exponential function with the natural constant e as the base, η represents and η=max(||x min -x1|| k ,||x min -x2|| k ,...,||x min -x n || k ), φ(·) and ψ(·) are the probability cumulative function (CDF) and probability density function (PDF) under the standard normal distribution, respectively. EI represents the expected function. The expected function EI of the kth Kriging model is k It can be expressed as:

[0089]

[0090] x1~x n represents n sampling points, represents the predicted value of f(x), f(x) represents the objective function of optimization, and g(x) represents the reliability function.

[0091] S3: using an adaptive candidate region model, an influence function IF and a clustering method to improve the sampling accuracy of the modified active learning Kriging model, and obtaining an active learning Kriging model with high accuracy;

[0092] Here, the adaptive candidate region (ACR) is applied. Every time the active learning Kriging function is updated, in order to prevent the actual case from obtaining more and more information as the active learning continues, the adaptive candidate region is used to actively modify its sampling core to a sensitive area or narrow its sampling range according to the prior information of the previous iteration.

[0093] Based on the above theory, the probability that the actual optimal point is located in the current ACR area is where x=[x1,x2,...,x n ] Tis a possible sample point, n is the dimension of the variable, P ACR is the desired probability value. f(x) is the joint probability density function. We can assume that the i-th ACR is a normally distributed region N(μ a (i) ,σ a (i) ). Therefore, according to the 3σ criterion, ACR is a core a (i) , with a radius of 3σ a (i) The calculation of the ACR sample core is of great significance. Define a point set The intersection ε of the candidate set M obtained by Latin hypercube (optimization) or random distribution (reliability) and the point whose LF value is greater than the threshold ACR ,have: where ε ACR is the global convergence criterion set to be greater than ε, so the core is the set The core of is expressed as: At the same time, a (i) is considered as the radius of the superellipse ACR, which is expressed as: in, The mean is 0 and the standard deviation is σ LF (i) / max(LF (i) ) Normal cumulative function. Because the accuracy increases as ALK iterations continue, the ACR is narrowed to the important area and eventually reaches the target.

[0094] When there are multiple local optimal points or multiple failure areas, the influence function and clustering method are used for parallel calculation. Different from the traditional parallel calculation, this method adds a judgment mechanism to determine whether parallel points are needed in the current iteration. When the value required for parallel calculation in the iteration is low, unnecessary parallel training points are deleted. If the difference is less than the threshold, the candidate point will not be selected to train the active Kriging model.

[0095] When there are multiple local optimal points or multiple failure areas, the IF parallel calculation method is used, which can be written as: in is the update point. d is the number of test points. θk and Pk can be set as needed (generally set to θk = 1, Pk = 2). Defined as PLF, it is the second parallel training point selected by multiplying LF and IF to reduce the level, where PLF is expressed as PLF(x) = IF(x,x u )·LF(x).

[0096] Different from the traditional intermediate frequency parallel computing, based on the assumption that the value required for parallel computing in the kth iteration is low, a judgment mechanism is added to determine whether parallel training points are needed in the current iteration to delete unnecessary parallel training points. The value of the parallel candidate function When the difference is small. If the difference is less than the threshold ε p , then no candidate point will be selected To train the ALK model. Then the parallel The set can be described as: in is the maximum value of the order of PLF from 1 to np. np is the number of parallel samples in the kth iteration. Based on the ε convergence criterion, the algorithm also has adaptive ability (np is the number of parallel samples in one iteration). However, when there is a local optimum or multiple local least squares, the efficiency is low. Therefore, the K-means clustering method is used to classify the parallel acr (PACR) into different clusters to improve the accuracy. K-means requires the minimum value of the Euclidean distance objective function to be Where m is the number of samples in ACR and nk is the number of clusters. Uj is the centroid of cluster j. Therefore, the core of pacr is modified to μ j (i) =u j ,

[0097] The number of clusters K-means needs to be defined in advance. Density-based Spatial Clustering of Noise Applications (DBSCAN) is a clustering method based on sample density. A cluster is defined as a point set when the number of points in an area with a radius R is greater than the minimum number of points NMinPts predefined by the designer. Therefore, the number of clusters cannot be known in advance. The classified noise points are extracted from DBSCAN and ignored for training, which is not important in ACR.

[0098] Therefore, optionally, the step S3 includes:

[0099] S31: determining the adaptive candidate region according to the learning function and the 3σ criterion;

[0100] S32: dividing the adaptive candidate region into a plurality of parallel adaptive candidate sub-regions by a clustering method;

[0101] S33: Calculate the influence function values ​​and parallel learning function values ​​of all training points in the current parallel adaptive candidate area;

[0102] S34: taking the training point corresponding to the maximum value among all the parallel learning function values ​​as the target training point;

[0103] S35: Determine whether the calculation results of the influence function value and the parallel learning function value of the target training point meet the preset conditions. If so, proceed to step S36; otherwise, take the next parallel adaptive candidate region as the current parallel adaptive candidate region and return to step S33;

[0104] Here, the calculation method of the influence function value and the parallel learning function value of the target training point is:

[0105]

[0106] in, represents the maximum value of PLF(·) from 1 to np, PLF(·) represents the parallel training point determined by the product of the influence function value and the parallel learning function value, np is the number of parallel samples in one iteration, x Pa represents the training point, LF(x u ) represents the value of the learning function at the training point, x u represents the updated training point.

[0107] S36: marking the target training point as a model training point to train the new active learning Kriging model, so as to improve the accuracy of the new active learning Kriging model and obtain a high-precision active learning Kriging model.

[0108] S4: According to the demand sample, the high-precision active learning Kriging model and the sequence optimization and reliability evaluation method are used to obtain the optimization result of the demand sample.

[0109] The main idea of ​​this step is to convert the uncertainty optimization into the deterministic optimization of the most likely failure design. MPP , defined as the input point where the functional function G(x) is the smallest among all samples that conform to the input uncertainty distribution.

[0110] Optionally, the step S4 includes:

[0111] S41: Obtain reliability constraints;

[0112] Based on "satisfying the most likely failure point X MPP Safety, that is, G(X MPP )>0, that is, 100% meets the reliability requirement" and modify the reliability constraint

[0113] Pr(G i (x)≥0)=Φ(β i )=R i

[0114] Where i is the failure state mode. When the target has only one failure mode, i=1. Pr represents the probability, and β is the value of the original reliability requirement R. i The converted reliability index in the standard normal distribution space. Finally, the reliability optimization problem of the original design goal is modified into a common deterministic optimization problem to reduce the optimization difficulty:

[0115] The reliability constraints are:

[0116] G(X MPP )>0

[0117] Among them, X MPP represents the failure point, G(X MPP ) indicates that the failure point is safe.

[0118] S42: According to the demand sample, using the high-precision active learning Kriging model, obtain the initial optimization result d of the demand sample (0) ;

[0119] Since it is not known whether the reliability constraints are actually met at this time, the following judgments need to be made:

[0120] Before that, find the most likely failure point X MPP

[0121] find x MPP

[0122]

[0123] st||U||=β

[0124] Where U is the point after x is mapped to the standard normal distribution space, ||*|| is the norm, generally the 2 norm, that is, the Euclidean distance;

[0125] S43: Obtain the most likely failure point in the current optimization result of the demand sample;

[0126] S44: Determine whether the most likely failure point meets the reliability constraint condition, if so, proceed to step S45, otherwise, proceed to step S46;

[0127] S45: Determine whether the current optimization result of the demand sample meets the preset conditions. If so, output the current optimization result of the demand sample as the optimization result of the demand sample. Otherwise, update the current optimization result of the demand sample using the incremental coefficient related to the optimization algorithm, and return to step S43.

[0128] Optionally, in step S45, the preset condition is:

[0129] ||d(k+1) -d (k) ||2<ε

[0130] The updating of the current optimization result of the demand sample by using the incremental coefficient related to the optimization algorithm includes:

[0131] Let d (k+1) =d (k+1) -λ (k+1) d (k)

[0132] Among them, d (k+1) represents the optimal design point obtained in the k+1th iteration step, d (k) represents the optimal design point obtained in the kth step, λ represents the incremental coefficient related to the optimization algorithm, and ε represents the optimization convergence parameter.

[0133] S46: Use the optimization formula of the demand sample to update the current optimization result of the demand sample, and return to step S43.

[0134] Optionally, in step S46, the optimization formula of the demand sample is:

[0135]

[0136] Among them, d (k+1) represents the optimal design point obtained in the k+1th iteration step, d (k) represents the optimal design point obtained in the kth step, d s represents the step size, |G min (X MPTP )|| indicates that under the current design point, G(x) obtains the minimum value when the MPP point is reached, G(d (k) ) indicates that G(x) obtains the optimal design point d (k) When the size of G(x) is MPTP Indicates the maximum possible failure point.

[0137] In the present invention, the required sample can be any sample, for example, it can be a planetary roller screw mechanism (PRSM). PRSM transmits motion and force through multi-point contact of rollers between the screw and the nut. In order to avoid contact fatigue damage of overloaded threads due to uneven load distribution at the screw-roller and nut-roller interfaces, the reliability of the PRSM structure needs to be optimized. Based on the stiffness model of force balance conditions and deformation coordination relationship, double-loop implicit iterative calculation is performed, which can better reflect the structural characteristics of PRSM and solve the nonlinear load distribution f=[F NR1 ,F NR2 ,…,F NRτ ,F SR1 ,F SR2 ,…,FSRτ ] T The subscripts SR and NR represent the contact surfaces of the screw roller and the nut roller, respectively. SRi and F NRi (i=1,2,…,τ) is the load of the i-th pair of threads, z SR and z NR is the number of unloaded threads. Solving the load distribution is obviously a strongly nonlinear problem, and the traditional method cannot meet the requirements in terms of accuracy and efficiency.

[0138] According to the method proposed in the present invention, reliability optimization design is performed. The design variables are the pitch P of the screw, roller and nut = (P S ,P R ,P N ). The maximum load common coefficient ψ of the optimization objective SR (P,μ x )=max i＝1,2，...，τ (zτF SRi / F) and ψ NR (P,μ x )=max i＝1,2，...，τ (zτF NRi / F), where μ x represents the mean vector of other random variables except P. Obviously, this is a multi-objective optimization problem. Here, we transform it into a single-objective optimization problem by assigning weight factors. The constraint is the reliability constraint P(σ SR <σ Hlim )>β SR and P(σ NR <σ Hlim )>β NR , and geometric size constraints. The mathematical expression of the PRSM load distribution multi-objective optimization model is:

[0139] find P=(P S ,P R ,P N )

[0140] min ψ=w SR ψ SR (P,μ x )+w NR ψ NR (P,μ x )

[0141]

[0142]

[0143]

[0144] β SR =β NR =0.999,P l =(4.995,4.995,4.995),P u =(5.005,5.005,5.005)

[0145] w SR =w NR =0.5

[0146] Where: SR ,∑ρ SR ,L(e SR ) and k eSR are the maximum contact stress, principal curvature, second-kind complete elliptic integral and the ratio of the semi-major axis to the semi-minor axis of the contact ellipse of the thread pair on the screw-roller contact surface. NR ,∑ρ NR ,L(e NR ) and k eNR are the parameters corresponding to the contact fatigue limit mentioned above, σ Hlim is the contact fatigue limit. l and P u is the upper and lower limit vector of P, λ=tan -1 (P R / πd R0 ) and θ=tan -1 (tanβ R cosλ) is the helix angle and contact angle of the roller. It can be easily found that solving this optimization problem has a strong nonlinear nature. In the clustering method, K-means clustering predefines 4 clusters, while DBSCAN is set to R = 0.5 and NMinPts = 4.

[0147] After optimizing the planetary roller screw mechanism using the present invention, the optimization results obtained show that:

[0148] The maximum load, von Mises stress and contact stress on both sides of the roller are reduced. The minimum load is no longer on the free end, but on the middle thread. Using the optimization method provided by the present invention, refer to Table 1 and Figure 2 As shown, under the condition of meeting the reliability requirements, the standard deviation of the load sharing coefficient is reduced from 0.5833 to 0.3259, a reduction of 44.12%. Finite element verification also shows that the average relative error of the optimized load distribution obtained by the present invention is less than 1%, which can meet the requirements of the optimized design.

[0149] Table 1 Comparison of the method of the present invention and the existing method in PRSM optimization

[0150]

[0151] The method of the present invention is based on the active learning Kriging (ALK) method and makes full use of the return error analysis of Kriging modeling to form an adaptive change sample region, called the parallel adaptive candidate region (PACR). With the help of PACR technology, the accuracy of the active learning Kriging model is improved; in addition, the initial optimization results of the demand samples are iteratively judged using sequence optimization and reliability evaluation methods, and the optimal optimization results can be output.

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

Claims

1. An optimization method for demand samples based on active learning Kriging model, characterized in that: The reliability optimization method of the active learning Kriging model includes: S1: Perform sampling operation in the sample database to obtain a small sample library of planetary roller screw mechanism; The design variables of the planetary roller screw mechanism are the pitch of the screw, roller and nut P = (P S ,P R ,P N ), the maximum load common coefficient ψ of the optimization target SR (P,μ x )=max i＝1,2，...，τ (zτF SRi / F) and ψ NR (P,μ x )=max i＝1,2，…，τ (zτF NRi / F); Among them, μ x represents the mean vector of other random variables except P, F SRi and F NRi is the load of the i-th pair of threads, i=1,2,…,τ; S2: establishing a new active learning Kriging model using a learning function based on a small sample library of the planetary roller screw mechanism and an initial active learning Kriging model; S3: using an adaptive candidate region model, an influence function and a clustering method to improve the sampling accuracy of the new active learning Kriging model, and obtaining an active learning Kriging model with high accuracy; S4: According to the demand sample, the demand sample is a planetary roller screw mechanism, and the optimization result of the planetary roller screw mechanism is obtained by using the high-precision active learning Kriging model and the sequence optimization and reliability evaluation method; The step S2 comprises: S21: using the Latin hypercube method, performing a sampling operation in the small sample library to obtain a sampling result; S22: constructing an initial active learning Kriging model using the sampling results; S23: predicting a large number of candidate points M using the current active learning Kriging model to obtain prediction results and true results of the large number of candidate points M; S24: Calculate the learning function values ​​of all prediction results, and determine the current candidate point corresponding to the largest learning function value among all the learning function values; S25: Determine whether the current candidate point meets the convergence condition. If so, output the current active learning Kriging model as the new active learning Kriging model; otherwise, add the current candidate point to the sampling result and return to step S22; In step S2, the learning function is an exponential acceleration function EIE: Alternatively, the learning function is an improved exponential distance function EID: Among them, g min Represents the minimum value predicted by the performance function, that is, represents the predicted value of g(x), σ represents the standard deviation, and the superscript ^ represents the predicted value. represents the predicted value of g(x) calculated at the kth iteration, represents the predicted value of σ(x) calculated at the kth iteration, x min Expressed so that the formula The value of x in the minimum case, EXP(·) represents the exponential function with the natural constant e as the base, η represents the sampling parameter and η=max(||x min -x1|| k ,||x min -x2|| k ,...,||x min -x n || k ), φ(·) and ψ(·) are the probability cumulative function and probability density function under the standard normal distribution, respectively. EI represents the expected function. The expected function EI of the kth Kriging model is k It is expressed as: x1~x n represents n sampling points, represents the predicted value of f(x), f(x) represents the objective function of optimization, and g(x) represents the functional function of reliability; The step S3 comprises: S31: determining the adaptive candidate region according to the learning function and the 3σ criterion; S32: dividing the adaptive candidate region into a plurality of parallel adaptive candidate sub-regions by a clustering method; S33: Calculate the influence function values ​​and parallel learning function values ​​of all training points in the current parallel sub-adaptive candidate area; S34: taking the training point corresponding to the maximum value among all the parallel learning function values ​​as the target training point; S35: Determine whether the calculation results of the influence function value and the parallel learning function value of the target training point meet the preset conditions. If so, proceed to step S36; otherwise, take the next parallel adaptive candidate region as the current parallel adaptive candidate region and return to step S33; S36: marking the target training point as a model training point to train the new active learning Kriging model, so as to improve the accuracy of the new active learning Kriging model and obtain an active learning Kriging model with high accuracy; In step S35, the influence function value and the parallel learning function value of the target training point are calculated as follows: in, Indicates that PLF(·) ranges from 1 to n p The maximum value of the order, PLF(·) represents the parallel training point determined by the product of the influence function value and the parallel learning function value, n p is the number of parallel samples in one iteration, x Pa represents the target training point, LF(x u ) represents the value of the learning function at the training point, x u represents the updated training point; The step S4 comprises: S41: Obtain reliability constraints; S42: According to the demand sample, using the high-precision active learning Kriging model, obtain the initial optimization result d of the demand sample (0) ; S43: Obtain the most likely failure point in the current optimization result of the demand sample; S44: Determine whether the most likely failure point meets the reliability constraint condition, if so, proceed to step S45, otherwise, proceed to step S46; S45: Determine whether the current optimization result of the demand sample meets the preset conditions. If so, output the current optimization result of the demand sample as the optimization result of the demand sample. Otherwise, update the current optimization result of the demand sample using the incremental coefficient related to the optimization algorithm, and return to step S43. S46: Use the optimization formula of the demand sample to update the current optimization result of the demand sample, and return to step S43.

2. The optimization method for demand samples based on active learning Kriging model according to claim 1 is characterized in that: In step S25, the convergence condition δ max for: δ max =max(LF (p) )-max(LF (p-1) )≤ε Among them, max(·) represents the maximum value, LF (·) represents the active learning value, p represents the number of iterations and is a positive integer, and ε represents the error.

3. The optimization method for demand samples based on active learning Kriging model according to claim 1 is characterized in that: In step S41, the reliability constraint condition is: G(X MPP )>0 Among them, X MPP represents the failure point, G(X MPP ) indicates that the failure point is safe.

4. The optimization method for demand samples based on active learning Kriging model according to claim 1 is characterized in that: In step S45, the preset condition is: ||d (k+1) -d (k) ||2<ε The updating of the current optimization result of the demand sample by using the incremental coefficient related to the optimization algorithm includes: Let d (k+1) = d (k+1) - λ (k+1) d (k) Among them, d (k+1) represents the optimal design point obtained in the k+1th iteration step, d (k) represents the optimal design point obtained in the kth step, λ represents the incremental coefficient related to the optimization algorithm, and ε represents the optimization convergence parameter.

5. The optimization method for demand samples based on active learning Kriging model according to any one of claims 3 to 4, characterized in that: In step S46, the optimization formula of the demand sample is: Among them, d (k+1) represents the optimal design point obtained in the k+1th iteration step, d (k) represents the optimal design point obtained in the kth step, d s represents the step size, |G min (X MPTP )| indicates that under the current design point, G(x) obtains the minimum value when the MPP point is reached, G(d (k) ) indicates that G(x) obtains the optimal design point d (k) When the size of G(x) is MPTP Indicates the maximum possible failure point.

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