Parallel constraint Bayesian optimization method and system for solving time-consuming optimization problem of variable-thickness and variable-strength thin-wall structure

Abstract

The invention discloses a parallel constraint Bayesian optimization method and system for solving the time-consuming optimization problem of a variable-thickness and variable-strength thin-wall structure, and the method comprises the steps: S1, determining an optimization equation and the trust region side length of a variable according to the structure optimization problem; s2, if the iteration is not the first iteration, executing S3, otherwise, selecting an expensive sample point from the variables, and calculating an objective function value and an implicit constraint function value; s3, performing bilog transformation on the implicit constraint function, and constructing / updating a Gaussian process regression model of the objective function and the implicit constraint function; s4, updating a trust region; s5, by taking the three acquisition functions as objective functions and the explicit constraint function as a constraint, constructing a multi-objective optimization equation, solving a Pareto frontier, screening out a plurality of expensive sample points from the Pareto frontier, and parallelizing objective function values and implicit constraint function values of the expensive sample points to obtain an optimal solution of current iteration; and S6, if the global convergence condition is not met, combining all the'expensive 'sample points, and returning to S3, otherwise, outputting an optimal solution.

Description

Technical Field

[0001] The invention belongs to the technical field of optimization, and in particular relates to a parallel constrained Bayesian optimization method for solving time-consuming optimization problems of thin-walled structures with variable thickness and strength. Background Art

[0002] In recent years, computer technology has developed rapidly in the fields of ships, automobiles, aircraft, etc. Especially in the automotive field, computer-based virtual simulation analysis and optimization design have taken a dominant position. Under the influence of the future market, the vehicle design process has become more complicated, and optimization methods have become the main means to solve this problem.

[0003] At present, the more classic methods for thin-walled structure optimization problems include gradient optimization methods, evolutionary algorithms (such as genetic algorithms), etc. However, using gradient optimization methods to solve thin-walled structure optimization problems is prone to falling into local optimal solutions; using evolutionary algorithms to solve thin-walled structure optimization problems usually requires thousands of numerical simulation iterative calculations, resulting in a very long optimization time.

[0004] Bayesian optimization algorithm is a global optimization algorithm currently widely used to solve time-consuming optimization problems. The more classic Bayesian optimization algorithms include the standard EGO algorithm based on the CEI criterion and the standard EGO algorithm based on the PI criterion. As the constraint functions of thin-walled structure optimization problems become more and more complex and the number of design variables continues to increase, the optimization difficulty increases greatly. Solving with traditional Bayesian optimization algorithms often encounters the following problems:

[0005] (1) The proxy model is less sensitive to sample points near the boundary of the constraint function, and often ignores some valid sample points that meet the constraints when using the acquisition function to update the sample points;

[0006] (2) Due to the existence of the "curse of dimensionality", the size of the design space grows exponentially with the increase in the number of design variables. The surrogate model constructed with a small number of sample points is often difficult to accurately fit high-dimensional problems (dimension greater than 10);

[0007] (3) When optimizing non-convex problems, a single acquisition function cannot take into account all valid sample points in the global or local range, resulting in decreased convergence efficiency. Summary of the invention

[0008] In view of the deficiencies in the prior art, the present invention provides a parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength.

[0009] The present invention achieves the above technical objectives through the following technical means.

[0010] A parallel constrained Bayesian optimization method for solving a time-consuming optimization problem of a thin-walled structure with variable thickness and strength comprises the following steps:

[0011] S1, in the computer, according to the actual variable thickness and variable strength thin-wall structure optimization problem, determine the mathematical optimization equation and the trust region length of the design variables;

[0012] The mathematical optimization equation includes an objective function, an explicit constraint function and an implicit constraint function of design variables; the design variables include a transition zone position variable, a thickness variable and a strength variable;

[0013] S2, determine whether it is the first iteration of the Bayesian optimization algorithm. If not, execute S3; if it is the first iteration, select the initial sample from the design variables of the mathematical optimization equation, calculate the objective function value f(x) and the implicit constraint function value, and call the initial sample point an "expensive" sample point, and jump to S8;

[0014] S3, performs bilog transformation of implicit constraint function;

[0015] S4, using the objective function value f(x) and the transformed i-th implicit constraint function value g′ i (x), build / update the Gaussian process regression model of the objective function And the Gaussian process regression model with implicit constraint function

[0016] S5, update the trust region of the design variables;

[0017] S6, taking the acquisition functions KSEI, CEI, and CLCB as the objective functions and the explicit constraint functions as the constraint functions, constructs the multi-objective optimization equation and uses the multi-objective genetic algorithm to solve the Pareto frontier of the design variables;

[0018] S7, select multiple high-quality sample points, i.e., “expensive” sample points, from the Pareto front of the design variables, calculate the objective function values ​​and implicit constraint function values ​​of the high-quality sample points in parallel, and obtain the optimal solution of the current iteration;

[0019] S8, if the global convergence condition of the Bayesian optimization algorithm is not met, all "expensive" sample points are merged and returned to S3; if the global convergence condition is met, the algorithm converges and outputs the optimal solution, that is, a set of optimal design variables, which are used in the actual design and manufacturing of thin-walled structures.

[0020] Further, the design variables include continuous variables and discrete variables, the continuous variables are transition zone position variables, and the discrete variables include thickness variables and strength variables;

[0021] The trust region length for each continuous variable is:

[0022]

[0023] Where: L z is the trust region length of the zth continuous variable, λ z is the characteristic length of the zth continuous variable in the surrogate model kernel, SF z is the scaling factor of the trust region length of the zth continuous variable, d is the total number of continuous variables, and h is the total number of discrete variables;

[0024] The trust region length for each discrete variable is:

[0025]

[0026]

[0027] Among them, q c is the adjustment coefficient of the cth discrete variable, S c is the variable set of the c-th discrete variable, o is the variable subscript of the c-th discrete variable, is the maximum side length of the trust region of the cth discrete variable, is the minimum trust region length of the cth discrete variable, λ c is the characteristic length of the cth discrete variable in the surrogate model kernel, SF c is the scaling factor of the trust region length of the cth discrete variable, index is the variable set subscript corresponding to the maximum or minimum value of the trust region length of the cth discrete variable, x c * The current optimal value sample point, e is the number of variables L of the cth discrete variable c , is the length of the trust region of the cth discrete variable.

[0028] Furthermore, the bilog transformation of the implicit constraint function is:

[0029] g′ i (x) = sgn(g i (x))·ln(1+|g i (x)|), i=1,2,3…n

[0030] Where: g i (x) is the value of the ith implicit constraint function, g′ i (x) is the value of the i-th implicit constraint function after transformation.

[0031] Furthermore, the specific process of updating the trust region of the design variables is:

[0032] Count the number of successful improvements and failed improvements within the trust region, and adjust the size of the trust region of the design variable based on the number of successful improvements and failed improvements: If the number of successful improvements reaches 3 times, change the length of each side of the trust region of the continuous variable to L z ←min{L z max,2L z}, change the length of each side of the trust region of the discrete variable to L c →min{L c max,2L c}; If the number of improvement failures reaches max{D / 4,1} times, the side length of the trust region of the design variable is reduced to half of the original, where L z max represents the maximum length of the trust region of the zth continuous variable, L c max represents the maximum side length of the trust region of the cth discrete variable, and D is the dimension of the objective function. When the trust region changes, the number of successful improvements and the number of failed improvements are reset.

[0033] Furthermore, if the maximum value of the trust region side length exceeds the maximum boundary of the parameter space, the maximum boundary of the parameter space is set to the maximum value of the trust region side length; conversely, if the minimum value of the trust region side length exceeds the minimum boundary of the parameter space, the maximum boundary of the parameter space is set to the minimum value of the trust region side length.

[0034] Furthermore, the acquisition function KSEI is:

[0035]

[0036] Among them: J min is the minimum value of the loss function among all current sample points, is the predicted value of the Gaussian process regression model of the loss function, σ J (x) is the standard deviation of the Gaussian process regression model of the loss function, Φ is the cumulative distribution function of the standard normal distribution, φ is the probability density function of the standard normal distribution, and the Gaussian process regression model of the loss function is:

[0037]

[0038] Among them, μ J (x) is the loss function of the Gaussian process regression model The mean function, k(x,x * ) is the loss function of the Gaussian process regression model Covariance function, the According to the variable x and the loss function value J i (x) constructs the loss function value J i (x) is:

[0039]

[0040] Among them, ρ is a positive real number, y i is the value of the ith explicit constraint function, J i (x) is the loss function value of the i-th explicit constraint function.

[0041] Furthermore, the acquisition function CEI is:

[0042]

[0043] Among them, f min is the optimal value among all current sample points, is the predicted value of the objective function model, Φ is the cumulative distribution function of the standard normal distribution, φ is the probability density function of the standard normal distribution, σ f (x) is the standard deviation of the objective function model, and tpof(x) is the constraint judgment function of the trend feasibility probability, specifically:

[0044]

[0045] in, is the predicted value of the ith implicit constraint function model, is the standard deviation of the ith implicit constraint function model, g i · (x d ) is the true value of the point closest to the predicted point, x d is the point closest to the predicted point, and erf(x) is the error function.

[0046] Furthermore, the acquisition function CLCB is:

[0047]

[0048] Among them, μ f (x) is the mean of the objective function model, σ f (x) is the standard deviation of the objective function model, the parameter k balances the expectation and standard deviation, Φ is the cumulative distribution function of the standard normal distribution, is the probability of satisfying all constraint functions.

[0049] Furthermore, the method of selecting multiple high-quality sample points from the Pareto front of the design variables selects one of the following three parallel screening strategies:

[0050] (1) Add 1 to 2 points in parallel

[0051] Extract the point with the smallest mean and the largest variance among all candidate points in the Pareto front of the design variables;

[0052] (2) Add 3 to 5 points in parallel

[0053] Based on (1), three points with the largest acquisition function values ​​are selected from the Pareto frontier of the design variables;

[0054] (3) Add 6 or more points in parallel

[0055] Take the three points p0, p1, and p2 with the largest values ​​of the three acquisition functions as the center points, and use the Euclidean distance method to calculate the distances from the remaining points except the above three points to these three points respectively, select the shortest distance as the overall distance from the point to p0, p1, and p2, and finally select the farthest and second farthest points among the remaining points according to the number of added points.

[0056] A parallel constrained Bayesian optimization system for solving time-consuming optimization problems of thin-walled structures with variable thickness and strength, comprising:

[0057] The algorithm initialization module defines the design variables and output responses according to the actual variable thickness and variable strength thin-walled structure optimization problem, and divides the constraints into explicit constraints and implicit constraints; according to the variable type, the trust region edge length is automatically calculated;

[0058] The initial sampling module selects the initial sample points and calculates the objective function value and the implicit constraint function value;

[0059] Feature enhancement module, which performs bilog transformation of implicit constraint functions;

[0060] Model building module, building / updating Gaussian process regression model of objective function and Gaussian process regression model of implicit constraint function;

[0061] Trust region update module, adjusts the size of the trust region of the design variables;

[0062] The acquisition function optimization module uses the acquisition functions KSEI, CEI, and CLCB as objective functions and explicit constraint functions as constraint functions to construct multi-objective optimization equations and use multi-objective genetic algorithms to solve the Pareto frontier of design variables;

[0063] The candidate point update module selects multiple high-quality sample points, i.e., "expensive" sample points, from the Pareto frontier, and calculates the objective function values ​​and implicit constraint function values ​​of the high-quality sample points in parallel to obtain the optimal solution for the current iteration;

[0064] Convergence judgment module, used for global convergence condition judgment.

[0065] The beneficial effects of the present invention are:

[0066] (1) The present invention proposes a bilog transformation of the implicit constraint function of the design variables of the variable thickness and variable strength thin-walled structure optimization problem, transforms the implicit constraint function, increases the sampling probability of the acquisition function in the feasible domain near the implicit constraint boundary, and improves the search efficiency and convergence.

[0067] (2) The constraint judgment function of trend feasibility probability proposed in the present invention makes up for the shortcoming of the original feasibility probability function that lacks trend optimization and increases the probability of the algorithm searching for feasible solutions.

[0068] (3) The present invention designs three parallel screening point strategies. According to the needs of the thin-walled structure optimization problem with variable thickness and strength, one of the strategies is selected to screen out multiple high-quality sample points from the Pareto front of the design variables, thereby obtaining the optimal solution for the current iteration. This not only increases the diversity of optimization solutions, but also realizes multi-task parallel computing in the optimization process, thereby improving search efficiency.

[0069] (4) The variable trust region method of the design variables proposed in the present invention dynamically updates the parameter space and balances the exploration and development of the search process, thereby effectively solving the problem of low accuracy of the surrogate model fitting high-dimensional optimization problems.

[0070] (5) The parallel constrained Bayesian optimization method of the present invention for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength can efficiently handle the multi-constrained feasible domain problem of the system and can be widely used in the automotive field. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 A parallel constrained Bayesian optimization flow chart for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to the present invention;

[0072] Figure 2 Schematic diagram of a variable thickness and variable strength front anti-collision beam system in an embodiment of the present invention;

[0073] FIG3( a ) is a thickness distribution diagram of a variable thickness and variable strength anti-collision beam structure in an embodiment of the present invention;

[0074] FIG3( b ) is a strength distribution diagram of a variable thickness and variable strength anti-collision beam structure in an embodiment of the present invention;

[0075] FIG4( a ) is a thickness distribution diagram of a variable thickness and variable strength energy absorption box structure in an embodiment of the present invention;

[0076] FIG4( b ) is a strength distribution diagram of the energy absorption box structure with variable thickness and strength according to an embodiment of the present invention;

[0077] FIG5( a ) is a thickness distribution diagram of a variable thickness and variable strength front longitudinal beam structure in an embodiment of the present invention;

[0078] FIG5( b ) is a strength distribution diagram of a front longitudinal beam structure with variable thickness and strength in an embodiment of the present invention;

[0079] Figure 6 It is a comparison diagram of iteration curves of PCBO and PCEGO algorithms in an embodiment of the present invention;

[0080] FIG. 7( a ) is a comparison diagram of the thickness distribution of the front and rear anti-collision beams optimized in an embodiment of the present invention;

[0081] FIG. 7( b ) is a comparison diagram of the strength distribution of the front and rear anti-collision beams optimized in an embodiment of the present invention;

[0082] FIG8( a ) is a comparison diagram of the thickness distribution of the energy absorption box before and after optimization in an embodiment of the present invention;

[0083] FIG8( b ) is a comparison diagram of the strength distribution of the energy absorption box before and after optimization in an embodiment of the present invention;

[0084] FIG9( a ) is a comparison diagram of the thickness distribution of the front longitudinal beam before and after optimization in an embodiment of the present invention;

[0085] FIG9( b ) is a comparison diagram of the strength distribution of the front longitudinal beam before and after optimization in an embodiment of the present invention. DETAILED DESCRIPTION

[0086] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0087] like Figure 1 As shown, the present invention provides a parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength, which specifically includes the following steps:

[0088] S1, according to the actual variable thickness and variable strength thin-walled structure optimization problem, determine the mathematical optimization equation and the trust region length of the design variables.

[0089] S1.1. In a computer, according to the actual variable thickness and variable strength thin-walled structure optimization problem, design variables and output responses are defined. The design variables include transition zone position variables, thickness variables, and strength variables. The specific output response is determined by the thin-walled structure optimization problem. Taking the anti-collision beam as an example, the output response includes component intrusion amount or intrusion velocity or overall acceleration or component collision force difference, etc. The constraint function with explicit expression between design variables is defined as explicit constraint (that is, the function value directly calculated by variables or numerical values ​​is defined as explicit constraint), and the constraint function without explicit expression between design variables is defined as implicit constraint (that is, the response value is obtained through time-consuming finite element analysis), thereby defining the mathematical optimization equation for the actual frame-type thin-walled structure optimization problem as shown in formula (1):

[0090]

[0091] Among them, f(x) is the objective function value, p represents the transition zone position variable (continuous variable), t represents the thickness variable (discrete variable), mat represents the strength variable (discrete variable), g i (x) is the value of the ith implicit constraint function, c j (x) is the value of the jth explicit constraint function, n is the number of implicit constraint functions, and m is the number of explicit constraint functions.

[0092] S1.2, initialize the trust region of the design variables. When the trust region is first enabled, select the optimal point among the sample points obtained by initial sampling (specifically the finite element model) as the center of the trust region. The side length of the trust region is L init Initialized to 0.8, the maximum trust region length L max Set to 1.6; In the objective function f(x) of different dimensions, the minimum trust region length is different: In the objective function f(x) below 10 dimensions, the minimum trust region length L min Set to 0.025, in the objective function f(x) above 10 dimensions, the minimum trust region length L min Set to 2 -7 .

[0093] According to the characteristic length λ of each dimension in the surrogate model kernel i or c To scale;

[0094] The actual side length of each transition zone position variable is obtained as:

[0095]

[0096] Where: z is the characteristic length of the zth transition zone position variable in the surrogate model kernel, L z is the trust region side length of the zth transition zone position variable, d is the total amount of transition zone position variables, h is the total amount of thickness and strength variables, SF z is the scaling factor for the side length of the trust region of the zth transition region position variable.

[0097] The actual side lengths for each thickness and strength variable are:

[0098]

[0099] Among them, λ c is the characteristic length of the cth thickness and strength variable in the surrogate model kernel, SF c is the scaling factor for the length of the trust region for the cth thickness and strength variable, q c is the adjustment coefficient of the cth thickness and strength variable, S cis the variable set of the cth thickness and strength variable, o is the variable subscript of the cth thickness and strength variable, is the maximum side length of the trust region for the cth thickness and strength variable, is the minimum trust region length of the cth thickness and strength variable, L c is the trust region side length of the cth thickness and strength variable, index is the variable set subscript corresponding to the maximum or minimum value of the trust region side length of the cth thickness and strength variable, x c * is the current optimal value sample point (i.e., the sample point corresponding to the optimal objective function value), and e is the number of variables of the cth thickness and strength variable.

[0100] Among them, the characteristic length λ i or c It is an adjustable and optimizable hyperparameter in the surrogate model that controls the stationarity or volatility of the Gaussian process. The smaller the characteristic length, the more sensitive the Gaussian process regression model is and the more sensitive it is to small changes in the input data (i.e., the design variable), resulting in a more unstable prediction curve. On the contrary, the larger the characteristic length, the smoother the Gaussian process regression model is and the less sensitive it is to small changes in the input data, resulting in a smoother prediction curve. The optimal characteristic length is determined by maximizing the marginal log-likelihood using Newton's method, thereby determining the actual side length of the variable.

[0101] S2, determine whether it is the first iteration of the Bayesian optimization algorithm. If not, execute S3; if it is the first iteration, use a sampling algorithm (such as random sampling, Latin square sampling, etc.) to select an initial sample (denoted as Ns) from the design variable x, and calculate the objective function value and the implicit constraint function value through finite element simulation analysis; and the sample points for performing finite element simulation analysis (i.e., initial sample points) are called "expensive" sample points.

[0102] S3, performs the bilog transformation of the implicit constraint function.

[0103] In order to better fit the surrogate model, the implicit constraints are transformed as follows:

[0104] g′ i (x) = sgn(g i (x))·ln(1+|g i (x)|), i=1,2,3…n (4)

[0105] Where: g i (x) is the value of the ith implicit constraint function, g′ i (x) is the value of the i-th implicit constraint function after transformation.

[0106] This transformation amplifies the range around zero, emphasizing that the change in sign is decisive for feasibility, while also scaling larger values ​​to a smaller range.

[0107] S4, using the objective function value f(x) and the transformed i-th implicit constraint function value g′ i (x) Construct (or update) the Gaussian process regression model of the objective function And the Gaussian process regression model with implicit constraint function

[0108]

[0109] Where: μ f (x) and They are the mean function of the objective function, the mean function of the i-th implicit constraint function after transformation, and k f (x,x * )and is the covariance function of the objective function and the transformed i-th implicit constraint function.

[0110] S5, automatically adjusts the size of the trust region of the design variables according to the optimization of the sample points.

[0111] In the iterative process, the current optimal value sample point (i.e., the sample point corresponding to the optimal objective function value) is used as the center point to divide the parameter space (i.e., the design variable) into a trust region; then the number of successful improvements and failed improvements of the current optimal value sample point in the trust region is counted, and the size of the trust region of the design variable is adjusted based on the number of successful improvements and failed improvements. Specifically, if the number of successful improvements reaches 3 times, the length of each side of the trust region of the transition zone position variable is changed to L z ←min{L z max,2L z}, change the length of each side of the trust region of thickness and strength variables to L c ←min{L c max,2L c}, L z max represents the maximum trust region length of the zth transition zone position variable, L c max represents the maximum side length of the trust region for the cth thickness and strength variable; if the number of improvement failures reaches max{D / 4,1} times, the side length of the trust region is reduced to half of the original, where D is the dimension of the objective function. When the trust region changes, the number of improvement successes and improvement failures are reset. In addition, if the maximum side length of the trust region L max If the maximum boundary of the parameter space is exceeded, the maximum boundary of the parameter space is set to the maximum value of the trust region side length; otherwise, if the minimum trust region side length L minIf the minimum boundary of the parameter space is exceeded, the maximum boundary of the parameter space is set to the minimum value of the trust region side length.

[0112] S6, taking the acquisition functions KSEI, CEI, and CLCB as objective functions and the explicit constraint functions as constraint functions, constructs a multi-objective optimization equation and uses a multi-objective genetic algorithm to solve the Pareto frontier of the design variables.

[0113] S6.1, construct a loss function J through Kreisselmeier-Steinhauser (KS function) i (x) as follows:

[0114]

[0115] Where: ρ is a positive real number, y i is the value of the ith explicit constraint function, J i (x) is the loss function value of the i-th explicit constraint function.

[0116] At the same time, according to the sample point (design variable x) and the loss function value J i (x) Constructing Gaussian process regression model The details are as follows:

[0117]

[0118] Among them, μ J (x) is the loss function of the Gaussian process regression model The mean function, k(x,x * ) is the loss function of the Gaussian process regression model Covariance function.

[0119] S6.2, construct the constraint judgment function of trend probability of feasibility, as follows:

[0120]

[0121] Among them, g i · (x d ) is the true value of the point closest to the predicted point, x d is the point closest to the predicted point, is the predicted value of the ith implicit constraint function model, is the standard deviation of the ith implicit constraint function model, erf(x) is the error function, and its expression is:

[0122]

[0123] S6.3, three acquisition functions are introduced, namely: KSEI (Kreisselmeier-Steinhauser Expected Improvement) improved according to the feasible domain boundary function, CEI (Constrained Expected Improvement) and CLCB (Constrained Lower Confidence Bound) that extends the lower bound of the confidence interval to the constraint; among them, the KSEI function tends to search for sample points at the boundary of the feasible domain to increase the search efficiency of the optimal solution, the CEI function tends to search for sample points that are better than the current point and meet the constraints to ensure the stability of the acquisition function, and the CLCB with a constrained confidence interval lower bound comprehensively considers the points with the smallest lower bound of the confidence interval in the global range and that meet the constraints, thereby avoiding the optimizer from falling into the local optimal solution, as shown in equations (10) to (12):

[0124]

[0125] Among them, J min is the minimum value of the loss function among all current sample points, is the predicted value of the Gaussian process regression model of the loss function, σ J (x) is the standard deviation of the Gaussian process regression model of the loss function, f min is the optimal value among all current sample points, is the predicted value of the objective function model, Φ is the cumulative distribution function of the standard normal distribution, φ is the probability density function of the standard normal distribution, σ f (x) is the standard deviation of the objective function model, μ f (x) is the mean of the objective function model, and the parameter k balances the expectation and standard deviation. is the probability of satisfying all constraint functions.

[0126] S6.4, taking the above three acquisition functions as optimization objectives and the explicit constraint function as the constraint function, the multi-objective genetic algorithm NSGA-Ⅱ is used to solve the optimization problem and obtain the Pareto frontier of the design variables; the details are as follows:

[0127]

[0128] S7, selects multiple high-quality sample points ("expensive" sample points) from the Pareto front of the design variables, calculates the objective function value and implicit constraint function value of the high-quality sample points in parallel, and obtains the optimal solution of the current iteration.

[0129] To screen out multiple high-quality sample points from the Pareto front of the design variables, the present invention designs three parallel screening strategies:

[0130] (1) Add 1 to 2 points in parallel

[0131] In order to further balance the game between exploration and exploitation, the points with the smallest mean and the largest variance of all candidate points in the Pareto front of the design variables are extracted; in Bayesian optimization, the point with the smallest mean is usually considered to be the current optimal solution or close to the optimal solution sampled in the known area; the point with the largest variance is usually considered to be the point with the least exploration in the area near it, and global exploration can be performed.

[0132] (2) Add 3 to 5 points in parallel

[0133] On the basis of (1), in order to make full use of the advantages of multiple acquisition functions, three points with the largest acquisition function values ​​are selected from the Pareto front of the design variables so that deeper sampling and optimization can be carried out near these points, thereby exploring more potential solutions in the parameter space; this strategy can accelerate the convergence speed of the algorithm and improve the quality of the optimization results.

[0134] (3) Add 6 or more points in parallel

[0135] In order to meet the needs of complex optimization problems, the present invention designs FPS (Farthest Point Sampling). This sampling method takes the three points (p0, p1, p2) with the largest acquisition function values ​​as the center points, and uses the Euclidean distance method to calculate the distances from the remaining points except the above three points to these three points, and selects the shortest distance as the overall distance from this point to p0, p1, p2. Finally, the farthest and second farthest points among the remaining points are selected according to the number of added points.

[0136] According to the needs of the optimization problem of thin-walled structures with variable thickness and strength, one of the three parallel screening strategies is selected to screen out multiple high-quality sample points from the Pareto front of the design variables.

[0137] S8, global convergence condition judgment of the Bayesian optimization algorithm: If the global convergence condition is not met, all "expensive" sample points are merged and returned to S3; if the global convergence condition is met, the algorithm converges and outputs the optimal solution, that is, a set of optimal design variables, which are used in the actual thin-walled structure design and manufacturing; the details are as follows:

[0138] For different optimization problems, the present invention designs two convergence conditions:

[0139] (1) Maximum number of iterations convergence condition: Determine whether the preset number of iterations has been reached. When this set value is reached, it is determined that convergence has been achieved;

[0140] (2) Convergence condition of posterior probability: Determine whether the change of posterior probability is less than a predefined threshold, expressed as:

[0141] |P(y|x t )-P(y|x t*-1 )|≤δ (14)

[0142] Among them, P(y|x t ) represents the posterior probability of the tth iteration, and δ is the predefined posterior probability convergence threshold.

[0143] When the change in the posterior probability is less than the threshold, it is judged to have converged.

[0144] Since the true optimal feasible solution (or approximate optimal feasible solution) of the test function is known, the optimization efficiency of the algorithm can be measured by comparing the number of iterations required for different algorithms to find the true optimal feasible solution of the test function. For all compared algorithms, when the difference between the optimal feasible solution found by the algorithm and the target value of the true optimal feasible solution of the original problem is equal to or less than 1%, the algorithm is considered to have successfully found the optimal feasible solution and terminated, and the number of iterations for the algorithm to find the optimal feasible solution is recorded. If the algorithm does not find the optimal feasible solution of the original problem within the maximum number of iterations allowed, the number of iterations for the algorithm to find the optimal solution is considered to be the maximum number of iterations.

[0145] The variable thickness and variable strength front anti-collision beam system under four test conditions is selected as a test case to verify the effectiveness of the present invention. The main components of the system are the front anti-collision beam, the energy absorption box, the front longitudinal beam and its connecting plate, such as Figure 2 The four test conditions are RCAR low-speed collision condition, 25km / h frontal collision, 32km / h frontal pole collision and 50km / h frontal collision.

[0146] In this system, the variable thickness and variable strength anti-collision beam adopts a five-segment symmetrical thickness distribution form, including three equal thickness zones with different thickness variables (t 1,1 , t 1,2 , t 1,3 ), 2 transition zone position variables (p 1,1 , p 1,2 ), as shown in Figure 3(a). The thickness distribution function is shown in formula (15), where p s is the position of the symmetry line. The mathematical expression of the process constraint that needs to be satisfied is shown in formula (16). The strength distribution of the variable thickness and variable strength anti-collision beam adopts a nine-segment symmetrical strength distribution form, including five strength variables of equal strength zones (s 1,1 ,s 1,2 ,s 1,3 ,s 1,4 ,s 1,5 ), as shown in Figure 3(b).

[0147]

[0148] Among them, x min is the minimum value of the coordinates of each component, l 1,1 , l 1,2 is the width of the transition zone of the anti-collision beam.

[0149] In this system, the variable thickness and variable strength energy absorption box adopts a two-stage thickness distribution form, including two equal thickness zones with thickness variables (t 2,1 , t 2,2 ) and a transition zone position variable (p 2,1 ), as shown in Figure 4(a). The thickness distribution function is shown in formula (17), and the mathematical expression of the process constraints that need to be met is shown in formula (18). The strength distribution of the variable thickness and variable strength energy absorption box adopts a three-segment asymmetric strength distribution form, including three equal strength zones of strength variables (s 2,1 ,s 2,2 ,s 2,3 ), as shown in Figure 4(b).

[0150]

[0151] Among them, x max is the maximum value of the coordinates of each component, l 2,1 is the width of the transition zone of the energy absorption box.

[0152] In this system, the variable thickness and variable strength front longitudinal beam adopts a two-stage thickness distribution form, including two thickness variables (t 3,1 , t 3,2 ) and a transition zone position variable (p 3,1 ), as shown in Figure 5(a). The thickness distribution function is shown in formula (19), and the mathematical expression of the process constraints that need to be met is shown in formula (20). The strength distribution adopts a three-segment asymmetric strength distribution form, including three equal-intensity zones of strength variables (s 3,1 ,s 3,2 ,s 3,3 ), as shown in Figure 5(b).

[0153]

[0154] Among them, l 3,1 is the width of the transition zone of the front longitudinal beam.

[0155] In summary, a total of 26 design variables are defined for the variable thickness and variable strength front anti-collision beam system, including 13 variable thickness variables, 2 thickness variables and 11 variable strength variables. The variable descriptions and upper and lower limits are detailed in Table 1.

[0156] Table 1 Variable settings for structural optimization design of variable thickness and variable strength front anti-collision beam system

[0157]

[0158] It is crucial to consider the structural design under different collision scenarios to ensure that the vehicle can protect the safety of occupants in various situations. In a 40% offset collision, only the front-end components on one side of the vehicle are involved in the collision, which requires the structure on that side to be strong enough to withstand the huge collision force and protect the occupants. Therefore, the system is required to fully absorb energy, the total energy absorption is required to be greater than or equal to 3200J, the difference in collision force between the energy absorption box and the front longitudinal beam is less than or equal to 0, the maximum intrusion of the front longitudinal beam in the X direction is less than or equal to 5mm, and the maximum acceleration of the vehicle body within the first 20ms is less than or equal to 5g.

[0159] Under the 25km / h frontal collision condition, if the anti-collision beam and energy absorption box are not strong enough, the acceleration during the collision will be difficult to reach the airbag detonation requirement and cannot meet the design standard. Therefore, the total energy absorption of the system is required to be greater than or equal to 9600J, the difference in collision force between the energy absorption box and the front longitudinal beam is less than or equal to 0, and the maximum X-direction intrusion of the anti-collision beam and energy absorption box is greater than or equal to 65mm and 110mm.

[0160] The 32km / h pole impact test simulates the collision between the vehicle and a narrow object (such as a pedestrian's leg or a tree). It requires that the front anti-collision beam and other structures must not only have sufficient strength, but also have good energy absorption characteristics to prevent excessive bending of the structure. Therefore, the maximum bending force in the X direction of the midpoint of the anti-collision beam is required to be greater than or equal to 8.5kN, and the maximum intrusion amount of the anti-collision beam in the X direction is less than or equal to 390mm.

[0161] In a 50km / h frontal collision, the energy box and the front longitudinal beam need to have sufficient energy absorption capacity to ensure the safety of the passenger compartment. Although the same vehicle front-end structure is competent under the design requirements of 100% frontal collision or frontal column collision, it may not meet the requirements of low-speed frontal collision or offset collision. Therefore, the system is required to fully absorb energy, the total energy absorption is required to be greater than or equal to 37000J, the difference in collision force between the energy box and the front longitudinal beam is less than or equal to 0mm, the maximum X-direction intrusion of the anti-collision beam, energy box and front longitudinal beam is greater than or equal to 85mm, 110mm and 140mm, and the maximum acceleration of the vehicle body in the first 20ms is between 20g and 50g.

[0162] The mathematical equation for the above optimization problem is:

[0163]

[0164] In order to compare the superiority of the parallel constrained Bayesian optimization method (PCBO) proposed in the present invention, the currently more advanced PCEGO algorithm is introduced for comparison. The initial sample number of the two is 15, the maximum number of iterations is 40, and 4 sample points are added in each iteration. When the change amplitude of the posterior probability is less than 0.01, the algorithm is judged to converge. If the two algorithms converge but not at the same time, the algorithm that converges earlier will continue to operate until the other algorithm also reaches a convergence state. Figure 6 Comparison of iteration curves of PCBO and PCEGO algorithms.

[0165] From above Figure 6 It can be seen that the PCBO algorithm found the global optimal solution in the 15th iteration, the minimum mass of the VRB anti-collision beam system was 6.10kg, and a total of 67 finite element models were calculated; while the PCEGO algorithm found the optimal solution in the 14th iteration, the minimum mass of the VRB anti-collision beam system was 6.41kg, and a total of 65 finite element models were calculated. PCBO showed high efficiency in finding the initial solution, and was able to jump out of local convergence and finally find an effective lightweight solution, which once again verified the efficiency of the PCBO algorithm.

[0166] To further demonstrate the optimization effect of the PCBO algorithm, Table 2 lists the design variable values ​​of the initial design and the optimal solution.

[0167] Table 2 Optimal solution variables for multi-condition optimization

[0168]

[0169]

[0170] The thickness and strength distribution of the variable thickness and variable strength structure anti-collision beam after optimization are shown in Figure 7 (a) and (b), the thickness and strength distribution of the variable thickness and variable strength structure energy absorption box after optimization are shown in Figure 8 (a) and (b), and the thickness and strength distribution of the variable thickness and variable strength structure front longitudinal beam after optimization are shown in Figure 9 (a) and (b). Table 3 compares the output responses before and after optimization of each working condition. Before optimization, all components were designed with uniform thickness and strength, and the design had a certain material redundancy. After optimization, the non-uniform distribution of thickness and strength was achieved based on performance requirements. In each working condition, the front anti-collision beam system can fully absorb energy, so that the acceleration of the vehicle body is controlled within a reasonable range. At the same time, the intrusion amount of each component is also effectively controlled, and the difference in collision force between the energy absorption box and the front longitudinal beam is always less than 0. The objective function value of the optimal feasible solution is finally obtained to be 6.10kg, and the weight reduction ratio is 33.0%.

[0171] Table 3 Optimal solution variable values ​​for multi-condition optimization

[0172]

[0173]

[0174] The present invention also provides a parallel constrained Bayesian optimization system for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength, comprising:

[0175] The algorithm initialization module defines the design variables and output responses according to the actual frame-type thin-walled structure optimization problem, and divides the constraints into explicit constraints and implicit constraints; according to the variable type, the trust region edge length is automatically calculated;

[0176] The initial sampling module selects the initial sample points and calculates the objective function value and the implicit constraint function value;

[0177] Feature enhancement module, which performs bilog transformation of implicit constraint functions;

[0178] A model building module, which builds (or updates) a Gaussian process regression model of an objective function and a Gaussian process regression model of an implicit constraint function;

[0179] Trust region update module, adjusts the size of the trust region;

[0180] The acquisition function optimization module uses the acquisition functions KSEI, CEI, and CLCB as objective functions and explicit constraint functions as constraint functions to construct multi-objective optimization equations and solve the Pareto frontier using a multi-objective genetic algorithm;

[0181] The candidate point update module selects multiple high-quality sample points ("expensive" sample points) from the Pareto frontier, calculates the objective function value and implicit constraint function value of the high-quality sample points in parallel, and obtains the optimal solution of the current iteration;

[0182] Convergence judgment module, used for global convergence condition judgment.

[0183] Based on the same inventive concept as a parallel constrained Bayesian optimization method for solving time-consuming optimization problems of thin-walled structures of frame type, the present application also provides an electronic device, which includes one or more processors and one or more memories, wherein a computer-readable code is stored in the memory, wherein the computer-readable code, when executed by one or more processors, implements a parallel constrained Bayesian optimization method for solving time-consuming optimization problems of thin-walled structures of frame type. Among them, the memory may include a non-volatile storage medium and an internal memory; the non-volatile storage medium may store an operating system and a computer-readable code. The computer-readable code includes program instructions, which, when executed, may enable the processor to execute any parallel constrained Bayesian optimization method for solving time-consuming optimization problems of thin-walled structures of frame type. The processor is used to provide computing and control capabilities to support the operation of the entire electronic device. The memory provides an environment for the operation of the computer-readable code in the non-volatile storage medium, and when the computer-readable code is executed by the processor, the processor may execute any parallel constrained Bayesian optimization method for solving time-consuming optimization problems of thin-walled structures of frame type.

[0184] It should be understood that the processor may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Among them, the general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0185] The computer-readable storage medium may be an internal storage unit of the electronic device described in the aforementioned embodiment, such as a hard disk or memory of the computer device. The computer-readable storage medium may also be an external storage device of the electronic device, such as a plug-in hard disk, a smart memory card (SmartMedia Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the electronic device.

[0186] The embodiments are preferred implementations of the present invention, but the present invention is not limited to the above-mentioned implementations. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essential content of the present invention belong to the protection scope of the present invention.

Claims

1. A parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength, characterized in that: The following steps are involved: S1, in the computer, according to the actual variable thickness and variable strength thin-wall structure optimization problem, determine the mathematical optimization equation and the trust region length of the design variables; The mathematical optimization equation includes an objective function, an explicit constraint function and an implicit constraint function of design variables; the design variables include a transition zone position variable, a thickness variable and a strength variable; S2, determine whether it is the first iteration of the Bayesian optimization algorithm. If it is not the first iteration, execute S3; If it is the first iteration, select the initial sample from the design variables of the mathematical optimization equation, calculate the objective function value f(x) and the implicit constraint function value, and call the initial sample point the "expensive" sample point, and jump to S8; S3, performs bilog transformation of implicit constraint function; S4, using the objective function value f(x) and the transformed i-th implicit constraint function value g i ′(x), build / update the Gaussian process regression model of the objective function And the Gaussian process regression model with implicit constraint function S5, update the trust region of the design variables; S6, taking the acquisition functions KSEI, CEI, and CLCB as the objective functions and the explicit constraint functions as the constraint functions, constructs the multi-objective optimization equation and uses the multi-objective genetic algorithm to solve the Pareto frontier of the design variables; S7, select multiple high-quality sample points, i.e., "expensive" sample points, from the Pareto front of the design variables, calculate the objective function values ​​and implicit constraint function values ​​of the high-quality sample points in parallel, and obtain the optimal solution of the current iteration; S8, if the global convergence condition of the Bayesian optimization algorithm is not met, all "expensive" sample points are merged and returned to S3; if the global convergence condition is met, the algorithm converges and outputs the optimal solution, that is, a set of optimal design variables, which are used in the actual design and manufacturing of thin-walled structures.

2. The parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to claim 1 is characterized in that: The design variables include continuous variables and discrete variables, the continuous variables are transition zone position variables, and the discrete variables include thickness variables and strength variables; The trust region length for each continuous variable is: Where: L z is the trust region length of the zth continuous variable, λ z is the characteristic length of the zth continuous variable in the surrogate model kernel, SF z is the scaling factor of the trust region length of the zth continuous variable, d is the total number of continuous variables, and h is the total number of discrete variables; The trust region length for each discrete variable is: Among them, q c is the adjustment coefficient of the cth discrete variable, S c is the variable set of the c-th discrete variable, o is the variable subscript of the c-th discrete variable, is the maximum side length of the trust region of the cth discrete variable, is the minimum trust region length of the cth discrete variable, λ c is the characteristic length of the cth discrete variable in the surrogate model kernel, SF c is the scaling factor of the trust region length of the cth discrete variable, index is the variable set subscript corresponding to the maximum or minimum value of the trust region length of the cth discrete variable, x c * is the current optimal value sample point, e is the number of variables L of the cth discrete variable c , L c is the length of the trust region of the cth discrete variable.

3. The parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to claim 1 is characterized in that: The bilog transform of the implicit constraint function is: g′ i (x)=sgn(g i (x))·ln(1+|g i (x)|),i=1,2,3…n Where: g i (x) is the value of the ith implicit constraint function, g i ′(x) is the value of the i-th implicit constraint function after transformation.

4. The parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to claim 2 is characterized in that: The specific process of updating the trust region of the design variables is: Count the number of successful improvements and failed improvements within the trust region, and adjust the size of the trust region of the design variable based on the number of successful improvements and failed improvements: If the number of successful improvements reaches 3 times, change the length of each side of the trust region of the continuous variable to L z ←min{L z max,2L z }, change the length of each side of the trust region of the discrete variable to L c →min{L c max,2L c }; If the number of improvement failures reaches max{D / 4,1} times, the side length of the trust region of the design variable is reduced to half of the original, where L z max represents the maximum length of the trust region of the zth continuous variable, L c max represents the maximum side length of the trust region of the cth discrete variable, and D is the dimension of the objective function. When the trust region changes, the number of successful improvements and the number of failed improvements are reset.

5. The parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to claim 4 is characterized in that: If the maximum value of the trust region side length exceeds the maximum boundary of the parameter space, the maximum boundary of the parameter space is set to the maximum value of the trust region side length; conversely, if the minimum value of the trust region side length exceeds the minimum boundary of the parameter space, the maximum boundary of the parameter space is set to the minimum value of the trust region side length.

6. The parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to claim 1 is characterized in that: The acquisition function KSEI is: Among them: J min is the minimum value of the loss function among all current sample points, is the predicted value of the Gaussian process regression model of the loss function, σ J (x) is the standard deviation of the Gaussian process regression model of the loss function, Φ is the cumulative distribution function of the standard normal distribution, φ is the probability density function of the standard normal distribution, and the Gaussian process regression model of the loss function is: Among them, μ J (x) is the loss function of the Gaussian process regression model The mean function, k(x,x * ) is the loss function of the Gaussian process regression model Covariance function, the According to the variable x and the loss function value J i (x) constructs the loss function value J i (x) is: Among them, ρ is a positive real number, y i is the value of the ith explicit constraint function, J i (x) is the loss function value of the i-th explicit constraint function.

7. The parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to claim 1 is characterized in that: The acquisition function CEI is: Among them, f min is the optimal value among all current sample points, is the predicted value of the objective function model, Φ is the cumulative distribution function of the standard normal distribution, φ is the probability density function of the standard normal distribution, σ f (x) is the standard deviation of the objective function model, and tpof(x) is the constraint judgment function of the trend feasibility probability, specifically: in, is the predicted value of the ith implicit constraint function model, is the standard deviation of the ith implicit constraint function model, g i · (x d ) is the true value of the point closest to the predicted point, x d is the point closest to the predicted point, and erf(x) is the error function.

8. The parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to claim 1 is characterized in that: The acquisition function CLCB is: Among them, μ f (x) is the mean of the objective function model, σ f (x) is the standard deviation of the objective function model, the parameter k balances the expectation and standard deviation, Φ is the cumulative distribution function of the standard normal distribution, is the probability of satisfying all constraint functions.

9. The parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength according to claim 1, characterized in that: The method of selecting multiple high-quality sample points from the Pareto front of the design variables is to select one of the following three parallel screening strategies: (1) Add 1 to 2 points in parallel Extract the point with the smallest mean and the largest variance among all candidate points in the Pareto front of the design variables; (2) Add 3 to 5 points in parallel Based on (1), three points with the largest acquisition function values ​​are selected from the Pareto front of the design variables; (3) Add 6 or more points in parallel Take the three points p0, p1, and p2 with the largest values ​​of the three acquisition functions as the center points, and use the Euclidean distance method to calculate the distances from the remaining points except the above three points to these three points respectively, select the shortest distance as the overall distance from the point to p0, p1, and p2, and finally select the farthest and second farthest points among the remaining points according to the number of added points.

10. A system for implementing the parallel constrained Bayesian optimization method for solving the time-consuming optimization problem of thin-walled structures with variable thickness and strength as described in any one of claims 1 to 9, characterized in that: include: The algorithm initialization module defines the design variables and output responses according to the actual variable thickness and variable strength thin-walled structure optimization problem, and divides the constraints into explicit constraints and implicit constraints; Automatically calculate the trust region length according to the variable type; The initial sampling module selects the initial sample points and calculates the objective function value and the implicit constraint function value; Feature enhancement module, which performs bilog transformation of implicit constraint functions; Model building module, building / updating Gaussian process regression model of objective function and Gaussian process regression model of implicit constraint function; Trust region update module, adjusts the size of the trust region of the design variables; The acquisition function optimization module uses the acquisition functions KSEI, CEI, and CLCB as objective functions and explicit constraint functions as constraint functions to construct multi-objective optimization equations and use multi-objective genetic algorithms to solve the Pareto frontier of design variables; The candidate point update module selects multiple high-quality sample points, i.e. "expensive" sample points, from the Pareto frontier, and calculates the objective function value and implicit constraint function value of the high-quality sample points in parallel to obtain the optimal solution for the current iteration; Convergence judgment module, used for global convergence condition judgment.

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