A method, apparatus, and medium for weld beam design optimization based on a variable selection bayesian optimization algorithm
By employing Bayesian optimization and roulette wheel variable selection strategies, the problem of genetic algorithms getting stuck in local optima in welded beam design was solved, enabling the search for the global optimal solution and improving design efficiency and flexibility.
Patent Information
- Application Number
- CN202411473575.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-22
- Publication Date
- 2025-11-28
- Estimated Expiration
- 2044-10-22
AI Technical Summary
In existing technologies, genetic algorithms are prone to getting stuck in local optima in welded beam design, especially when the design space is complex or there are many variables, making it difficult to find the globally optimal design solution.
A Bayesian optimization algorithm based on variable selection is adopted. By constructing a Gaussian process model and a roulette wheel variable selection strategy, the design of the welded beam is optimized. Combined with the expectation improvement criterion, the optimal solution is searched in the global scope to avoid local optima.
It effectively avoids local optima, saves computing resources, improves computing efficiency, adapts to various engineering constraints, and enables more flexible design optimization.
Smart Images

Figure CN119475685B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of architecture and engineering, and particularly to a welded beam design optimization method, device and medium based on variable selection Bayesian optimization algorithm. BACKGROUND
[0002] In modern industrial production, the design and manufacture of welded beams are critical links that directly affect the stability and safety of structures. In the field of architecture and engineering, welded beams are common structural components, and their design needs to meet various mechanical and geometric constraints, such as strength, stiffness, stability, and deflection limits.
[0003] In the prior art, genetic algorithms are probability-based optimization methods that may fall into local optimal solutions during the search process, especially in the design of welded beams. If the design space is complex or there are many local minimum points, the algorithm may not find the globally optimal design solution. SUMMARY
[0004] To solve the problem of local optimal solution in the prior art, the present application provides a welded beam design optimization method, device and medium based on variable selection Bayesian optimization algorithm.
[0005] The technical solution adopted by the present application is:
[0006] A welded beam design optimization method based on variable selection Bayesian optimization algorithm (RW-EGO for short), characterized by the following steps:
[0007] Step S1: Collect data of the welded beam, establish a welded beam design problem model with the problem of minimizing manufacturing cost as the design problem, and then determine a set of m-dimensional variables affecting manufacturing cost as the search space of the manufacturing cost minimization problem At the same time, determine the engineering constraint vector composed of n-dimensional engineering constraints .
[0008] Among them, , .
[0009] m-dimensional variables affecting manufacturing cost.
[0010] n-dimensional engineering constraints.
[0011] Step S2: According to the search space , construct a Gaussian process model in the Bayesian optimization algorithm, and calculate a new hyperparameter vector .
[0012] Step S3: According to the new hyperparameter vector computing a low-dimensional search subspace .
[0013] Step S4: performing acquisition function maximization in the Bayesian optimization algorithm on the low-dimensional search subspace to obtain an update point and substituting the update point into the objective function of the Gaussian process model as a new optimal solution to obtain an optimal value , i.e., an optimal value of minimum manufacturing cost.
[0014] Step S5: repeating the steps S2 to S4 to obtain a new optimal solution and an optimal value , and adding the new optimal solution and the optimal value obtained in each iteration to the sample set of the Gaussian process model constructed in the step S2 to train and update the Gaussian process model constructed in the step S2 until a preset number of iterations is reached, and then outputting a final optimal value ; wherein, in the iterative optimization process, the hyperparameter vector is the current hyperparameter vector.
[0015] Further, the sample points of the data of the welded beam collected in the step S1 are obtained by Latin hypercube sampling.
[0016] Further, when the step S2 computes a new hyperparameter vector * , the following steps are specifically performed:
[0017] Step S21: calculating the mean of each variable in the search space , and then initializing the hyperparameter vector , selecting a kernel function, and calculating a covariance matrix in sequence.
[0018] Step S22: constructing a Gaussian process model in the Bayesian optimization algorithm according to the calculated mean of each variable and the covariance matrix; wherein, the Gaussian process model is expressed as:
[0019] .
[0020] In the formula, is an objective function.
[0021] is a mean function.
[0022] is a Gaussian kernel function, which is specifically expressed as:
[0023] .
[0024] wherein,
[0025]
[0026] is the covariance matrix.
[0027] is the variance of the variable in each dimension of the search space X.
[0028] and is the variable in any two dimensions of the search space X.
[0029] n is the dimension of the variable in the search space X.
[0030] is the sub-hyperparameter corresponding to the i-th dimension of the variable in the search space X, which describes the weight of the i-th dimension of the search space X, and the greater the sub-hyperparameter, the greater the influence on the covariance matrix.
[0031] is the smoothness of the i-th dimension of the design space of the sub-hyperparameter, which is between [1, 2];
[0032] The hyperparameter vector includes the sub-hyperparameter corresponding to each dimension of the variable in the search space X, and is respectively expressed as .
[0033] When initializing the hyperparameter vector , all are assigned to 0.
[0034] Step S23: Calculate the hyperparameter vector by maximizing the likelihood function, to obtain a new hyperparameter vector , and the variables of the new hyperparameter vector are respectively expressed as ; wherein is the i-th dimension element of the new hyperparameter vector .
[0035] Further, the calculation expression of the new hyperparameter vector is:
[0036] ;
[0037] ;
[0038] wherein, are corresponding sub-hyperparameters.
[0039] is the likelihood function.
[0040] is the value of when the function reaches its maximum.
[0041] Further, the step S3 calculates a low-dimensional search subspace according to the new hyperparameter vector , and the step S4 performs the acquisition function maximization in the Bayesian optimization algorithm in the low-dimensional search subspace .
[0042] Step S31: using the new hyperparameter vector as the importance evaluation of each dimension variable, the search space is calculated, and the variables selected in each optimization are calculated, respectively, and the calculation expression is .
[0043] .
[0044] Step S32: the is composed into a probability vector , and the expression is:
[0045] ;
[0046] Then, according to the roulette variable selection strategy, the q-dimensional variables in the search space are selected, respectively, and the calculation expression is .
[0047] Step S33: the variables selected by the roulette are composed into the low-dimensional search subspace .
[0048] Further, the step S4 performs the acquisition function maximization in the low-dimensional search subspace to obtain the update point , and the step S4 performs the acquisition function maximization in the low-dimensional search subspace .
[0049] Step S41: the acquisition function is constructed and optimized, and the calculation expression is:
[0050]
[0051] wherein,
[0052] is the expected improvement function without considering constraints.
[0053] is the probability that the optimal solution satisfies the jth constraint.
[0054] is the probability that the optimal solution satisfies all constraints.
[0055] is the standard cumulative distribution function and probability density function.
[0056] and respectively represent the predicted value of the objective function and the variance of the predicted value.
[0057] and respectively represent the predicted value of the jth constraint and the variance of the predicted value.
[0058] is the optimal value.
[0059] Step S42: First, the low-dimensional search subspace obtained in step S3 is introduced into the vector , ,
[0060] .
[0061] Then, the vector is substituted into the optimization acquisition function constructed in step S41 ;
[0062] Finally, the vector is substituted into the expression
[0063]
[0064] to perform optimization, and the vector is obtained.
[0065] wherein , is a variable of .
[0066] is the value of when takes the maximum value.
[0067] Step S43: The vector obtained in step S42 is introduced into the search space , , , and the variable The rest of the variables are supplemented by the corresponding variable values of the current optimal solution, to obtain the update point , that is, the new optimal solution.
[0068] Wherein, ; then the target function described in step S22 And the constraint function described in step S1 Calculate the current optimal value .
[0069] Further, the target function described in step S2 The expression is:
[0070] .
[0071] Wherein,
[0072] The length of the welded beam strip;
[0073] The height of the welded beam strip;
[0074] The thickness of the welded beam strip;
[0075] The weld thickness;
[0076] The length of the clamp strip;
[0077] The production batch;
[0078] The welding current;
[0079] The labor cost.
[0080] Further, characterized in that, the step S1 determined engineering constraint conditions have 6 dimensions, respectively , the expressions are respectively:
[0081] ;
[0082] ;
[0083] ;
[0084] ;
[0085] ;
[0086] ;
[0087] wherein,
[0088] is a length of the welded beam;
[0089] is a height of the welded beam;
[0090] is a thickness of the welded beam;
[0091] is a weld thickness,
[0092] ,
[0093]
[0094]
[0095] .
[0096] Based on the same inventive concept, the present application also provides a computer device comprising a memory and a processor, which are in communication connection with each other, and the memory stores computer instructions, and the processor executes the computer instructions to perform the aforementioned welding beam design optimization method based on variable selection of a Bayesian optimization algorithm.
[0097] Based on the same inventive concept, the present application also provides a computer readable storage medium, which stores computer instructions for causing a computer to perform the aforementioned welding beam design optimization method based on variable selection of a Bayesian optimization algorithm.
[0098] The present application has the following beneficial effects:
[0099] Solve the local optimization problem: genetic algorithm and particle swarm algorithm may fall into local optimum in the process of searching for the optimal solution, especially when there are many welding beam design variables and the design space is complex. However, the Bayesian optimization can more effectively search for the global optimal solution in the global range by establishing a Gaussian process model of the objective function and combining the expected improvement criterion. Moreover, the variable selection strategy adopted by the present application not only focuses on selecting the best variable, because the best variable may not lead to the best solution. Instead, it also considers some "less" possible selection of "advantageous" variables to prevent the algorithm from falling into a local optimal solution.
[0100] 2. Save computing resources and improve computing efficiency: In actual welded beam design, the fitness value evaluation required by genetic algorithm optimization may result in high computing cost. The method of the present application intelligently selects the next most potential point for fitness value calculation through variable selection and acquisition function optimization, not only reducing the evaluation times in the design process, saving the computing cost, but also reducing the iteration times, thereby improving the computing efficiency.
[0101] 3. Stronger design flexibility: First, the Bayesian optimization algorithm allows designers to flexibly adjust design parameters and constraints to adapt to different engineering needs and goals. Because the parameter update of the Bayesian optimization algorithm is based on the probability model, i.e., the Gaussian process model, it has a strong theoretical basis. The setting of parameters of other design methods is more empirical, and multiple tests are required in welded beam design to determine them. Second, welded beam design usually needs to meet multiple constraints. The Bayesian optimization algorithm can naturally integrate constraints into the optimization process by defining appropriate acquisition functions and models to ensure that the solution meets all engineering constraints without additional processing mechanisms. BRIEF DESCRIPTION OF DRAWINGS
[0102] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.
[0103] Figure 1 A flowchart of a welded beam design optimization method based on variable selection of a Bayesian optimization algorithm.
[0104] Figure 2 A schematic diagram of a roulette wheel selection strategy.
[0105] Figure 3 A welded beam design optimization result iteration curve diagram. DETAILED DESCRIPTION
[0106] The present application provides a welded beam design optimization method, device and medium based on variable selection of a Bayesian optimization algorithm to solve the problem of local optimal solution in the prior art.
[0107] The embodiments provided in the following disclosure are not intended to limit the present application.
[0108] The embodiments of the present application will be described in detail below with reference to the accompanying drawings:
[0109] A welded beam design optimization method based on variable selection of a Bayesian optimization algorithm (RW-EGO for short), combined withFigure 1 The flow chart of the present application comprises the following steps, and each step is explained as follows:
[0110] A welding beam design optimization method based on a variable selection Bayesian optimization algorithm, comprising the following steps:
[0111] Step S1: Collect the data of the welding beam by using the Latin hypercube sampling method, prepare for subsequent construction of the Gaussian process model in the Bayesian optimization algorithm, establish a welding beam design problem model taking the minimum manufacturing cost problem as the design problem, and then determine the set of m-dimensional variables affecting the manufacturing cost as the search space of the minimum manufacturing cost problem At the same time, determine the engineering constraint vector composed of n-dimensional engineering constraint conditions In the embodiment, m is set to 8 and n is set to 6. The welding beam design problem model is established as the solution of the welding beam design cost minimization problem in the search space under the condition of satisfying .
[0112] Wherein, ,
[0113] .
[0114] are 8-dimensional variables affecting the manufacturing cost, in the embodiment, is the length of the welding beam strip, is the height of the welding beam strip, is the thickness of the welding beam strip, is the weld thickness, is the clamping strip length, is the production batch, is the welding current, is the labor cost. In the embodiment, are 6-dimensional engineering constraint conditions, wherein,
[0115] is that the shear stress borne by the welding beam must not be greater than the maximum limit value,
[0116] is that the bending stress borne by the welding beam must not be greater than the maximum limit value,
[0117] is that the weld thickness must not exceed the beam width,
[0118] is that the side constraint of the design variable must not exceed the set value,
[0119] The deviation of the end of the welded beam shall not be greater than 0.25mm,
[0120] The buckling load of the rod of the welded beam shall not be greater than the maximum limit value.
[0121] In this embodiment, The calculation expressions of the above are respectively:
[0122] ;
[0123] ;
[0124] ;
[0125] ;
[0126] ;
[0127] ;
[0128] Wherein, L is the length of the welded beam strip, H is the height of the welded beam strip, T is the thickness of the welded beam strip, S is the weld thickness.
[0129] ;
[0130]
[0131]
[0132] .
[0133] Step S2: constructing a Gaussian process model in the Bayesian optimization algorithm according to the search space , and calculating a new hyperparameter vector . The following steps are specifically implemented:
[0134] Step S21: calculating the mean of each variable in the search space , and then initializing the hyperparameter vector θ, selecting the kernel function, and calculating the covariance matrix in turn.
[0135] Step S22: constructing a Gaussian process model in the Bayesian optimization algorithm according to the calculated mean of each variable and the covariance matrix; wherein the Gaussian process model expression is:
[0136] ;
[0137] In the formula, is the objective function, in the embodiment The expression of
[0138] ;
[0139] is the mean function; is the Gaussian kernel function, and the specific expression is
[0140] .
[0141] wherein
[0142]
[0143] is the covariance matrix.
[0144] is the variance of each variable in the search space X.
[0145] and are any two-dimensional variables in the search space .
[0146] n is the variable dimension in the search space .
[0147] is the sub-hyperparameter corresponding to the i-th variable in the search space X, and the sub-hyperparameter describes the weight of the i-th variable in the search space X. The greater the sub-hyperparameter, the greater the influence on the covariance matrix.
[0148] is the smoothness of the sub-hyperparameter in the i-th design space, and is between 1 and 2.
[0149] The hyperparameter vector includes the sub-hyperparameters corresponding to each variable in the search space X, and is expressed as ; when initializing the hyperparameter vector , all are assigned to 0.
[0150] Step S23: Calculate the hyperparameter vector by maximizing the likelihood function, to obtain a new hyperparameter vector , and the variables of the new hyperparameter vector are expressed as ; wherein is the i-th element of the new hyperparameter vector . In the embodiment, the calculation expression is
[0151] ;
[0152] .
[0153] wherein, are corresponding sub-hyperparameters. are likelihood function, is the value of that maximizes .
[0154] Step S3: According to the new hyperparameter vector , the low-dimensional search subspace is calculated. The following steps are specifically implemented:
[0155] Step S31: Using the new hyperparameter vector as the importance evaluation of each dimension variable, the search space is calculated. The variables selected in each optimization are optimized with a probability of , and the calculation expression is:
[0156] .
[0157] Step S32: The is composed into a probability vector , which is expressed as:
[0158] ;
[0159] Then, according to the roulette variable selection strategy, q-dimensional variables in the search space are selected, and in the embodiment, q is set to 4, which are . The reason for this operation: in the design of the welded beam, there are many factors that affect the final manufacturing cost, that is, the problem variables will increase, and if all the variables are optimized, the calculation time cost will be large, so the roulette variable selection strategy is used, and each iteration selects the variable that is more likely to improve for optimization. The present application adopts the roulette strategy to select variables, and the probability of selecting a sector on the roulette wheel is proportional to the size of the sector center angle. In a similar way, the roulette is divided into several dimensional parts, and each dimensional part represents a one-dimensional variable. Then selecting a one-dimensional variable is equivalent to randomly selecting a one-dimensional point on the wheel and positioning the corresponding sector, as shown in the accompanying drawings. Figure 2 The roulette selection strategy is shown in the accompanying drawings. The selection strategy selects variables in proportion to the fitness value of the dimension body, which helps to preserve excellent dimension bodies in the optimization process.
[0160] Step S33: The variables selected by the roulette selection strategy Forming a low-dimensional search subspace .
[0161] Step S4: Search the low-dimensional subspace Maximize the acquisition function in the Bayesian optimization algorithm to obtain the update point. and update points Substituting the objective function of the Gaussian process model as the new optimal solution The optimal value is obtained through calculation. That is, the optimal value that minimizes manufacturing costs.
[0162] Step S4 performs a low-dimensional search of the subspace. Maximize the acquisition function in the Bayesian optimization algorithm to obtain the update point. At that time, the following steps shall be performed:
[0163] Step S41: Construct and optimize the acquisition function The expression is:
[0164] .
[0165] in, This is the expected improvement function without considering constraints.
[0166] This is the probability that the optimized solution satisfies the j-th dimension constraint.
[0167] This is the probability that the optimization scheme satisfies all constraints.
[0168] It is the standard cumulative distribution function and probability density function.
[0169] The two numbers represent the predicted value and the variance of the predicted value of the objective function, respectively.
[0170] Let represent the predicted value and the variance of the predicted value for the j-th dimension constraint, respectively.
[0171] This is the optimal value.
[0172] The reason for choosing this acquisition function is that commonly used types include UCB (Upper Confidence Limit), PI (Probability of Improvement), and EI (Expected Improvement). Among them, the EI standard is the most widely used. The expected improvement criterion provides a good one-dimensional balance between global and local search. This invention chooses the expected improvement criterion as the acquisition function for optimization in the subspace. Since there are engineering constraints in the design optimization of welded beams, these constraints can be directly considered when maximizing the EI function, thus transforming the problem of selecting update points from unconstrained optimization of the EI function to constrained optimization of the EI function. Acquisition Function The first term of the expression tends to select points where the expected improvement value is high, while the second term tends to select points where the constraints are likely to be satisfied. By multiplying these two terms, the expected improvement criterion selects points that are both highly likely to satisfy the constraints and offer a significant improvement as update points.
[0173] Step S42: First, the low-dimensional search subspace obtained in step S3... Import vector ,
[0174] Then, the vector Substitute the optimized acquisition function constructed in step S41 Finally, Substitute expression Optimize the vector to obtain the vector. .
[0175] in, , for Variables.
[0176] In order to find When the maximum value is obtained The value of .
[0177] Step S43: Convert the vector obtained in step S42 into... Import search space , Medium variables Replace the original variables with their respective values, and supplement the remaining variables with the corresponding variable values of the current optimal solution to obtain the update point. This is the new optimal solution.
[0178] in, .
[0179] Then to Perform step S22 objective function and the constraint function of step S1 Calculate to obtain the current optimal value. .
[0180] Step S5: repeating steps S2 to S4 to obtain a new optimal solution and the optimal value and the optimal value and the optimal value and the optimal value ; wherein, in the iterative optimization process, the hyperparameter vector is the current hyperparameter vector.
[0181] In order to reduce the Latin hypercube sampling is randomly generated initial vector or initial population, the end of each run results are not the same, the present application carried out 5 sets of repeated trials to improve the reliability of the final results. The minimum target value (i.e. the minimum manufacturing cost of the welding beam design) obtained by each iteration is saved, and finally the f min is averaged and plotted. The optimization effect of the method of the present application is shown in the form of an iteration curve, the abscissa is the number of target function calculations (evaluation times), the ordinate is the minimum manufacturing cost obtained by each iteration, the black solid line represents the average value of the optimization result of the method of the present application (referred to as RW-EGO), and the upper and lower dotted lines are the upper and lower boundaries of the optimization result according to the standard deviation. As shown in the attached Figure 3 The welding beam design optimization result iteration curve graph shows that the optimization algorithm has a certain degree of optimization for the initial value of the target function. It can be found that under the conditions of multi-dimensional design variables and multi-dimensional engineering constraints, the RW-EGO algorithm still has good optimization results for welding beam design optimization.
[0182] Based on the same inventive concept, the present application also provides a computer device, comprising: a memory and a processor, the memory and the processor are in communication connection with each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the welding beam design optimization method based on the variable selection Bayesian optimization algorithm.
[0183] Based on the same inventive concept, the present application also provides a computer readable storage medium, the computer readable storage medium stores computer instructions, and the computer instructions are used to make the computer execute the welding beam design optimization method based on the variable selection Bayesian optimization algorithm.
Claims
1. A method for designing and optimizing welded beams based on a Bayesian optimization algorithm with variable selection, characterized in that, Includes the following steps: Step S1: Collect data on the welded beams, establish a welded beam design problem model with the manufacturing cost minimization problem as the design problem, and then determine the set of m-dimensional variables affecting manufacturing cost as the search space for the manufacturing cost minimization problem. Simultaneously determine the engineering constraint vector composed of n-dimensional engineering constraints. ; in, , ; Let m be the m-dimensional variables affecting manufacturing costs; For n-dimensional engineering constraints; Step S2: Based on the search space Construct a Gaussian process model in the Bayesian optimization algorithm and calculate a new hyperparameter vector. ; Step S3: Based on the new hyperparameter vector The low-dimensional search subspace is calculated. ; Step S4: Search the low-dimensional subspace Maximize the acquisition function in the Bayesian optimization algorithm to obtain the update point. and the update point Substituting the new optimal solution into the objective function of the Gaussian process model The optimal value is obtained through calculation. That is, the optimal value that minimizes manufacturing costs; Step S5: Repeat steps S2 to S4 to obtain a new optimal solution. and optimal value And the new optimal solution obtained in each iteration and optimal value The Gaussian process model constructed in step S2 is added to the sample set, and the model is trained and updated until a preset number of iterations is reached. Then, the final optimal value is output. Among them, during the iterative optimization process, the hyperparameter vector This is the current hyperparameter vector; The sample points for collecting data on the welded beam in step S1 are obtained through Latin hypercube sampling. Step S2 calculates the new hyperparameter vector θ. * At that time, the following steps shall be performed: Step S21: Calculate the search space The mean of each dimension of the variable is calculated, and then the hyperparameter vector θ is initialized sequentially, the kernel function is selected, and the covariance matrix is calculated. Step S22: Construct a Gaussian process model in the Bayesian optimization algorithm based on the calculated mean of each variable and the covariance matrix; wherein, the expression of the Gaussian process model is: ; In the formula, It is the objective function; It is the mean function; It is the Gaussian kernel function, specifically expressed as: ; in, Let be the covariance matrix; Let X be the variance of the variable in each dimension of the search space X; and For the search space The variables described in any two dimensions; n is the search space Dimension of variables; Let X be the sub-hyperparameter corresponding to the i-th dimension of the variable in the search space X. The sub-hyperparameter describes the weight of the i-th dimension of the search space X. The larger the sub-hyperparameter is, the greater its influence on the covariance matrix. Let the smoothness of the sub-hyperparameter in the i-th dimension of the design space be denoted as . It takes values between [1, 2]. The hyperparameter vector Including the sub-hyperparameters corresponding to each dimension of the variable in the search space X, respectively expressed as: ; Initialize the hyperparameter vector Time All are assigned the value 0; Step S23: Maximize the likelihood function on the hyperparameter vector Calculations are performed to obtain a new hyperparameter vector. The new hyperparameter vector The variables are expressed as follows: ;in For the new hyperparameter vector The i-th element; The new hyperparameter vector The calculation expression is: ; ; in, They are respectively The corresponding sub-hyperparameters; for The likelihood function, In order to find When the maximum value is obtained The value; Step S3 is based on the new hyperparameter vector The low-dimensional search subspace is calculated. At that time, the following steps shall be performed: Step S31: Utilize the new hyperparameter vector The search space is calculated as an assessment of the importance of each dimension variable. variables The probabilities of being selected for optimization in each optimization are respectively The calculation expression is: ; Step S32: Composition of probability vectors , expressed as: ; Then, the search space is selected based on the roulette wheel variable selection strategy. The q-dimensional variables in the data are respectively ; Step S33: Select the variables from the roulette wheel. The low-dimensional search subspace is composed of ; Step S4 executes the low-dimensional search subspace. Maximize the acquisition function in the Bayesian optimization algorithm to obtain the update point. At that time, the following steps shall be performed: Step S41: Construct and optimize the acquisition function The expression is: ; in, For the expectation improvement function without considering constraints, To optimize the probability that the solution satisfies the j-th dimension constraint, To optimize the probability that the solution satisfies all constraints, These are the standard cumulative distribution function and probability density function. The two numbers represent the predicted value and the variance of the predicted value, respectively, of the objective function. Let represent the predicted value and the variance of the predicted value under the j-th dimension constraint, respectively; This is the optimal value; Step S42: First, the low-dimensional search subspace obtained in step S3... Import vector , ; Then, the vector Substitute the optimized acquisition function constructed in step S41 ; Finally Substitute expression Optimize the vector to obtain the vector. ; in, , for Variables; In order to find When the maximum value is obtained The value; Step S43: Convert the vector obtained in step S42 into... Import the search space , Medium variables Replace the original variables with their respective values, and supplement the remaining variables with the corresponding variable values of the current optimal solution to obtain the update point. That is, the new optimal solution; in, Then on Perform the objective function described in step S22. and the constraint function in step S1 Calculate to obtain the current optimal value. ; The objective function in step S2 The expression is: ; in, The length of the welded beam bar, The height of the welded beam bar, For the thickness of the welded beam bars, For weld thickness, The length of the clamping strip, For production batches, For welding current, For labor costs.
2. The welded beam design optimization method based on Bayesian optimization algorithm with variable selection according to claim 1, characterized in that: The engineering constraints determined in step S1 have six dimensions, namely: The expressions are as follows: ; ; ; ; ; ; in, This refers to the length of the welded beam strip; The height of the welded beam bar; The thickness of the welded beam strip; This refers to the weld thickness. , , , 。 3. A computer device, characterized in that, include: The system includes a memory and a processor, which are interconnected. The memory stores computer instructions, and the processor executes these computer instructions to perform a welded beam design optimization method based on a Bayesian optimization algorithm for variable selection, as described in claim 1 or 2.
4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute a welded beam design optimization method based on a Bayesian optimization algorithm for variable selection as described in claim 1 or 2.
Citation Information
Patent Citations
Method for learning optimal Bayesian network by using Dijkstra algorithm
CN113033810A
Bayesian optimization algorithm based on cooperative computing
CN116702450A