Optimization design method for foundation structure of assembly type box-type substation

Abstract

An optimization design method for a foundation structure of an assembly type box-type substation is characterized by comprising the following steps that an initial finite element model of the box-type substation is established according to a design drawing of the assembly type box-type substation, optimization parameters are determined, an optimization target is formulated, and a final finite element model of the box-type substation is established; the method comprises the following steps: selecting box transformer substation variable parameters needing optimization design, determining an optimization design range according to actual engineering conditions, determining structural responses of the box transformer substation and constraint conditions of an optimization process, randomly generating N groups of variable parameters within the optimization design range, substituting the N groups of variable parameters into an initial finite element model of the box transformer substation, and carrying out operation to obtain N groups of corresponding structural responses; and calculating fitness values of all solutions in the initial population and the reverse population by using the constructed Kriging model. The method is reasonable in algorithm, the calculation amount is obviously reduced, the calculation time is short, the optimal solution can be quickly and accurately obtained, and the solving efficiency and precision are obviously improved.

Description

Technical Field

[0001] The present invention relates to an optimization design method for a substation foundation structure, and particularly to an optimization design method for a prefabricated box-type substation foundation structure, belonging to the field of engineering technology. Background Art

[0002] A box-type substation is also known as a prefabricated substation or a prefabricated substation. With the continuous popularization of electric vehicles, the box-type substation has obvious advantages over the traditional on-site casting construction method due to its factory production and rapid on-site assembly characteristics. Taking a medium- and low-voltage cable network system using a pipe laying method as an example, it mainly includes a prefabricated cable pipe part, a prefabricated cable manhole part, a prefabricated foundation part for a ring main unit, a prefabricated foundation part for a box-type substation, and a connection part. In actual engineering, design parameters such as the wall thickness and hole positions of different parts of the box substation foundation structure determine the structural strength, stress, assembly accuracy, construction cost, etc. of the box substation foundation structure, and also affect the stability, reliability, and service life of the box-type substation. How to balance various factors to make the physical performance and construction cost of the box substation foundation structure reach the best balance point is a technical problem that has not been solved for a long time.

[0003] The existing design methods for substation foundation structures are either relatively simple and primitive, or have complex algorithms, large amounts of calculations, and low accuracy, and cannot well meet the actual requirements. With the continuous expansion of the scale and complexity of the optimization design problem, traditional methods such as the optimality criterion method and the gradient descent method are often difficult to find high-quality solutions in a short time due to their sensitivity to problem forms and dimensions, especially showing limitations when dealing with multi-modal, high-dimensional, or non-linear constraint problems. Therefore, meta-heuristic algorithms with excellent global search capabilities have gradually become important tools for solving such complex optimization problems. Meta-heuristic algorithms can flexibly apply to various complex optimization scenarios with fewer assumptions by simulating physical phenomena, biological behaviors, or evolutionary processes in nature, and achieve a balance between global exploration and local development, thereby improving the solution efficiency and effect. Although meta-heuristic algorithms have shown superior performance, they still face a major challenge in actual engineering optimization, mainly manifested in: the computational cost of finite element analysis evaluation in the optimization process is relatively high, and complex mathematical models and high-precision solution processes usually require a large amount of computing resources, resulting in a long time-consuming for a single evaluation, especially in optimization algorithms that repeatedly call the finite element model for fitness calculation, this cost increases significantly. Based on the above technical problems, the present invention is proposed. Summary of the Invention

[0004] The object of the present invention is to address the deficiencies of the existing foundation structure of prefabricated box-type substations, where traditional design methods have complex algorithms, large computational amounts, long calculation times, low precision, difficulty in obtaining optimal parameters, and inability to well meet the needs of actual engineering. The present invention provides an optimization design method for the foundation structure of prefabricated box-type substations, with a reasonable algorithm, significantly reduced computational amount, short calculation time, capable of quickly and accurately obtaining the optimal solution, and significantly improved solution efficiency and precision, providing an important guarantee for the performance of the foundation structure of box-type substations.

[0005] To achieve the above object of the invention, the technical solution of the present invention is: an optimization design method for the foundation structure of prefabricated box-type substations, characterized by including the following steps:

[0006] Step 1: Establish an initial finite element model of the box-type substation foundation based on the design drawings;

[0007] Step 2: Define the optimization objective, select the optimization parameters and their optimization ranges, and determine the structural response variables and constraint conditions of the box-type substation foundation;

[0008] Step 3: Randomly generate N sets of optimization parameter sets within the optimization design range, and calculate the corresponding box-type substation foundation structure response sets through the finite element model;

[0009] Step 4: Use the two data sets in Step 3 to construct a Kriging model between the optimization parameters and the structural response;

[0010] Step 5: Randomly generate M sets of optimization parameters within the optimization design range, substitute them into the initial finite element model of the box-type substation foundation for calculation, and obtain M sets of corresponding structural responses as the test sample set; subsequently, use the constructed Kriging model to predict the optimization parameters of the test samples, obtain the corresponding box-type substation foundation structure responses, and compare the prediction results with the structural responses obtained by calculating with the initial finite element model, and evaluate the accuracy of the constructed Kriging model through error calculation;

[0011] Step 6: If the calculation result meets the preset accuracy requirement, it indicates that the constructed Kriging model can effectively replace the finite element model of the box-type substation foundation for structural response calculation and is applicable to the iterative optimization process; if the accuracy does not meet the requirement, it is necessary to increase the number of modeling samples and reconstruct the Kriging model, and repeat Steps 4 and 5 until the constructed Kriging model reaches the required accuracy standard;

[0012] Step 7: Configure the parameters of the ICSA algorithm, including the maximum number of iterations, the dimension of the variable parameters, and the population size, and randomly generate an initial population within the optimization design range with a size equal to the preset population quantity;

[0013] Step 8: Use the constructed Kriging model to calculate the fitness values of all individuals in the initial population and its reverse population respectively, and select the first half of the individuals with the optimal fitness from them to form an iterative population for subsequent optimization;

[0014] Step 9: Select the corresponding position update strategy according to the current iteration number, update the positions of all individuals in the initial population, and detect whether the new solutions after update exceed the design boundary. If they exceed, correct them to within the boundary range;

[0015] Step 10: Use the Kriging model to calculate the fitness values of all individuals in the updated population, and update the current optimal solution that satisfies the constraint conditions and its corresponding optimal fitness value;

[0016] Step 11: Loop through Steps 8 to 10 until the maximum iteration number is reached, terminate the calculation, and output the optimized basic parameters of the box-type substation and their corresponding optimal fitness values.

[0017] Furthermore, the Kriging prediction model in Step 4 is specifically as follows:

[0018] The Kriging model assumes the problem function to be solved as a Gaussian stationary random process, as shown in Equation (1).

[0019] Y(x) = F(β, x) + z(x) (1)

[0020]

[0021] In Equations (1) and (2), F(β, x) is the global approximation term of the model, β is the regression coefficient, k is the number of polynomials, and z(x) is a random process with a mean of 0 and a variance of σ 2 that provides local approximation for the model; within the design space, the covariance matrix of each z(x) is as shown in Equation (3):

[0022]

[0023] In the formula: R(θ, x1, x2) is the correlation function of any two points x1 and x2, and the value of R is greater than 0 and less than 1.

[0024] When obtaining n sample point sets S = [s1, s2,..., s n T and the corresponding response set Y = [y1, y2,..., y n T After that, the prediction of the Kriging model for any point x can be described by Equation (4):

[0025] ​​

[0026] Where: Y K is the predicted value of the Kriging model at point x, and ω is the weight coefficient;

[0027] To find the weight coefficient ω, the Kriging model needs to satisfy the unbiasedness constraint and the principle of minimizing the mean square error MSE of the deviation, as shown in Equations (5) and (6) respectively:

[0028]

[0029] F T ω - f = 0

[0030]

[0031] Where: r is a vector composed of the correlation function values of all known points and any point x;

[0032] To satisfy the minimum mean square error of the deviation, the Lagrange multiplier λ is introduced for calculation, as shown in Equation (7):

[0033] L(ω, λ) = σ 2 (1 + ω T Rω - 2ω T r) - λ T (F T ω - f) (7)

[0034] Finally, the Kriging prediction model is obtained as shown in Equation (8):

[0035] Y K = f T β + r T R -1 (Y - Fβ) (8).

[0036] Furthermore, the algorithm in the fifth step is specifically as follows:

[0037] The accuracy evaluation indicators are calculated using the relative root mean square error (RRMSE), relative maximum absolute error (RMAE), and R-squared value (R 2 ). The smaller the RRMSE value and the RMAE value, and the closer the R 2 value is to 1, the higher the accuracy of the model, and vice versa. The calculation formulas for the three are as shown in Equation (9):

[0038]

[0039] Where: n is the number of test samples, y i is the true value at the i-th point to be measured, Y i is the predicted value at the i-th point to be measured, MYi is the mean of all true values.

[0040] Further, the algorithm in Step 8 is specifically as follows:

[0041] A reverse learning strategy is adopted. In the population initialization stage, an initial population is first generated, and then a reverse population corresponding to the initial population is generated through Equation (10):

[0042] X io = L i + U i - X i (10)

[0043] In the formula, X io is the i-th solution of the reverse population, L i is the lower boundary of the search domain of the i-th solution, U i is the upper boundary of the search domain of the i-th solution, and X i is the i-th solution of the initial population; Calculate the fitness values of all solutions in the initial population and the reverse population, and select the first half of the solutions with the best fitness to form the iterative population finally used for optimization.

[0044] Further, the algorithm in Step 9 is specifically as follows:

[0045] The value of parameter c is set using the linearly decreasing mode of Equation (17), specifically as follows:

[0046]

[0047] In the formula, c max and c min represent the maximum and minimum values of c, c max = 0.8, c min = 0.2.

[0048] The beneficial effects of the present invention are as follows:

[0049] 1. The present invention adopts three strategies on the basis of the standard circle search algorithm to improve its search performance: (1) Reverse learning strategy. By generating the reverse population of the current population, the algorithm can start iteration from a better initial solution, which helps to accelerate the convergence speed and improve the global search ability; (2) Adaptive update parameter strategy. Dynamically adjust the parameters according to the feedback information during the operation of the algorithm, avoiding the limitations brought by the fixed parameters in the standard circle search algorithm, so that it can maintain high performance in different types of problems; (3) New population individual update method selection strategy. By introducing a more effective individual update mechanism, the selection and update process of individuals in the population is optimized to balance the exploration and development capabilities of the algorithm, and the overall efficiency and accuracy of the algorithm are improved.

[0050] 2. Compared with the traditional design method, the optimized design using the method of the present invention enables the foundation structure of the prefabricated box-type substation to achieve the best assembly accuracy, structural strength, overall stability and economy. It provides an important guarantee for the performance of the box-type substation foundation structure and reliable technical support for the optimized design of similar engineering structures.

[0051] 3. The algorithm of the present invention is reasonable, the amount of calculation is significantly reduced, the calculation time is short, the optimal solution can be obtained quickly and accurately, and the solution efficiency and accuracy are significantly improved, providing an important guarantee for the performance of the box-type substation foundation structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is the flow chart of the optimized design method of the present invention.

[0053] Figure 2 is the information table of the CEC2019 benchmark test function in the embodiment of the present invention.

[0054] Figure 3 is the comparison table of the optimization results of the improved circle search algorithm (ICSA) and the standard circle search algorithm (CSA) in the embodiment of the present invention.

[0055] Figure 4 is the initial finite element model of the box-type substation foundation in the embodiment of the present invention.

[0056] Figure 5 is the Kriging prediction curve and the true curve of the side wall thickness and the most unfavorable stress response in the embodiment of the present invention.

[0057] Figure 6 is the curve of the average result of the optimization iteration of the two methods before and after the improvement of the present invention.

[0058] Figure 7 is the comparison table of the optimization cost and the optimized weight of the two methods before and after the improvement of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0059] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments.

[0060] See Figures 1 to 7 , an optimized design method for the foundation structure of a prefabricated box-type substation according to the present invention, characterized by comprising the following steps:

[0061] Step 1: Establish an initial finite element model of the box-type substation foundation based on the design drawings;

[0062] Step 2: Define the optimization objectives, select the optimization parameters and their optimization ranges, and determine the structural response variables and constraint conditions of the box-type substation foundation;

[0063] Step 3: Randomly generate N sets of optimized parameter sets within the optimized design range, and calculate the corresponding structural response sets of the box-type substation foundation through the finite element model;

[0064] Step 4: Use the two data sets in Step 3 to construct a Kriging model between the optimized parameters and the structural response;

[0065] Step 5: Randomly generate M sets of optimized parameters within the optimized design range, substitute them into the initial finite element model of the box-type substation foundation for calculation, and obtain M sets of corresponding structural responses as the test sample set; Subsequently, use the constructed Kriging model to predict the optimized parameters of the test samples, obtain the corresponding structural responses of the box-type substation foundation, and compare the prediction results with the structural responses obtained by the initial finite element model calculation, and evaluate the accuracy of the constructed Kriging model through error calculation;

[0066] Step 6: If the calculation result meets the preset accuracy requirements, it indicates that the constructed Kriging model can effectively replace the finite element model of the box-type substation foundation for structural response calculation and is applicable to the iterative optimization process; If the accuracy does not meet the requirements, it is necessary to increase the number of modeling samples and reconstruct the Kriging model, and repeat Steps 4 and 5 until the constructed Kriging model reaches the required accuracy standard;

[0067] Step 7: Configure the parameters of the ICSA algorithm, including the maximum number of iterations, the dimension of the variable parameters, and the population size, and randomly generate an initial population with the same size as the preset population number within the optimized design range;

[0068] Step 8: Use the constructed Kriging model to calculate the fitness values of all individuals in the initial population and its reverse population respectively, and select the first half of the individuals with the best fitness from them to form an iterative population for subsequent optimization;

[0069] Step 9: Select the corresponding position update strategy according to the current iteration number, update the positions of all individuals in the initial population, and detect whether the new solutions after update exceed the design boundary. If they exceed, correct them to within the boundary range;

[0070] Step 10: Use the Kriging model to calculate the fitness values of all individuals in the updated population, and update the current optimal solution that meets the constraint conditions and its corresponding optimal fitness value;

[0071] Step 11: Loop and execute Steps 8 to 10 until the maximum number of iterations is reached, terminate the calculation, and output the optimized box-type substation foundation parameters and their corresponding optimal fitness values.

[0072] In step 4, the Kriging prediction model is specifically as follows:

[0073] The Kriging model assumes the problem function to be solved as a Gaussian stationary random process, as shown in Equation (1).

[0074] Y(x)=F(β,x)+z(x) (1)

[0075]

[0076] In Equations (1) and (2), F(β,x) is the global approximation term of the model, β is the regression coefficient, k is the number of polynomials, and z(x) is a random process with a mean of 0 and a variance of σ 2 , providing local approximation for the model; within the design space, the covariance matrix of each z(x) is as shown in Equation (3):

[0077]

[0078] In the formula: R(θ,x1,x2) is the correlation function of any two points x1 and x2, and the value of R is greater than 0 and less than 1.

[0079] When obtaining n sample point sets S = [s1, s2,..., s n T and the corresponding response set Y = [y1, y2,..., y n T After that, the prediction of the Kriging model for any point x can be described by Equation (4):

[0080]

[0081] In the formula: Y K is the predicted value of the Kriging model for point x, and ω is the weight coefficient;

[0082] To find the weight coefficient ω, the Kriging model needs to satisfy the unbiasedness constraint and the principle of minimizing the mean square error MSE of the deviation, as shown in Equations (5) and (6) respectively:

[0083]

[0084] F T ω - f = 0

[0085]

[0086] In the formula: r is a vector composed of the correlation function values of all known points and any point x;

[0087] To satisfy the minimum mean square error of the deviation, the Lagrange multiplier λ is introduced for calculation, as shown in Equation (7):​​

[0088] L(ω,λ) = σ 2 (1 + ω T Rω - 2ω T r) - λ T (F T ω - f)(7)

[0089] Finally, the Kriging prediction model is as shown in Equation (8):

[0090] Y K = f T β + r T R -1 (Y - Fβ)(8).

[0091] The algorithm in Step 5 is specifically as follows:

[0092] The accuracy evaluation indicators use the relative root mean square error (RRMSE), relative maximum absolute error (RMAE), and R-squared value (R 2 ) for calculation. The smaller the RRMSE value and RMAE value, and the closer the R 2 value is to 1, the higher the accuracy of the model. Conversely, the lower the accuracy. The calculation formulas for the three are as shown in Equation (9):

[0093]

[0094] In the formula: n is the number of test samples, y i is the true value at the i-th point to be measured, Y i is the predicted value at the i-th point to be measured, MY i is the mean of all true values.

[0095] The algorithm in Step 8 is specifically as follows:

[0096] A reverse learning strategy is adopted. In the population initialization stage, an initial population is first generated, and then the corresponding reverse population is generated through Equation (10):

[0097] X io = L i + U i - X i (10)

[0098] In the formula, X io is the i-th solution of the reverse population, L i is the lower boundary of the search domain of the i-th solution, U i is the upper boundary of the search domain of the i-th solution, X iis the i-th solution of the initial population; calculate the fitness values of all solutions in the initial population and the reverse population, and select the first half of the solutions with the best fitness to form the iterative population finally used for optimization.

[0099] The algorithm in the ninth step is specifically as follows:

[0100] The value of parameter c is set using the linearly decreasing mode of Equation (17), specifically as follows:

[0101]

[0102] In the formula, c max and c min represent the maximum and minimum values of c, c max = 0.8, c min = 0.2. The selection method of the solution position update strategy is set to generate a random number rand between 0 and 1 each iteration. When rand is greater than and less than 1 - c, specific calculation methods are selected to update the solution position respectively.

[0103] The present invention aims at the optimal design of the prefabricated box-type substation foundation structure for the medium and low voltage cable network foundation. The main structure mainly includes the box substation foundation coping, straight side plates, C-shaped side plates, bottom plates, grit chambers and moisture-proof partitions. Using the optimal design method of the present invention can not only greatly reduce the design calculation amount, find high-quality solutions in a short time, significantly reduce the finite element calculation time compared with the traditional design method, save the calculation cost, but also effectively solve the technical problem that it is difficult to optimize the design of the prefabricated box-type substation foundation structure, and meet the requirements of high precision and fast convergence. The specific principle and method are as follows:

[0104] The present invention adopts the Improved Circle Search Algorithm—Kriging (ICSA—Kriging) method. As an improvement of the standard Circle Search Algorithm (CSA), the ICSA method adopted by the present invention introduces a reverse learning strategy. The basic idea of the reverse learning strategy is to first generate an initial population in the population initialization stage, and then through the formula: X io = L i + U i - X i generate a reverse population corresponding to the initial population. In the formula, X io is the i-th solution of the reverse population, L i is the lower boundary of the search domain of the i-th solution, U i is the upper boundary of the search domain of the i-th solution, X iis the \(i\)-th solution of the initial population. Calculate the fitness values of all solutions in the initial population and the reverse population, and select the first half of the solutions with the best fitness to form the initial population finally used for optimization iteration.

[0105] In step nine of the present invention, the positions of all initial solutions are updated according to the iteration times by selecting a calculation method, specifically as follows: In CSA, the calculation method for updating the population solutions is shown in formulas (12) to (17). When the iteration times Iter is greater than the product of the preset parameter \(c\) between 0 and 1 and the maximum iteration times Maxter, the \(\theta\) value is calculated using formula (13); otherwise, the \(\theta\) value is calculated using formula (14).

[0106]

[0107] \(\theta=\omega\times rand\) (13)

[0108] \(\theta=\omega\times p\) (14)

[0109] \(\omega = a\times rand - a\) (15)

[0110]

[0111] In the formula, \(X\) t i+1 is the new solution generated in the \((i + 1)\)-th iteration, \(X\) c i is the optimal solution generated in the \(i\)-th iteration, \(X\) t i is a solution in the population generated in the \(i\)-th iteration, and rand is a random number between 0 and 1.

[0112] As an improvement of CSA, the value of the parameter \(c\) in ICSA is set using the linear decreasing mode of the following formula, specifically as follows:

[0113]

[0114] In the formula, \(c\) max and \(c\) min represent the maximum value and the minimum value of \(c\), \(c\) max \( = 0.8\), \(c\) min \( = 0.2\).

[0115] The selection method of \(\theta\) is set to generate a random number rand between 0 and 1 each iteration. When rand is greater than \(1 - c\), \(\theta\) is calculated using formula (13); otherwise, it is calculated using formula (14).

[0116] The pseudocode of the ICSA algorithm of the present invention is:

[0117]

[0118] In order to more clearly illustrate the present invention, two specific embodiments are further described below:

[0119] Embodiment 1: Mainly targeting 10 CEC2019 benchmark test functions, used to prove the superiority of the improved optimization algorithm (ICSA) of the present invention over the original optimization algorithm (CSA).

[0120] The operating system used in the experiments of this embodiment is Windows 10 operating system, the CPU is Intel (R) Core (TM) i5-7300HQ, the main frequency is 2.50GHz, the machine has 8GB of RAM, and the programming software is MATLAB R2020a.

[0121] This embodiment is tested based on 10 CEC2019 benchmark test functions, which have been verified in many documents. Figure 2 As shown in the table, the dimension represents the dimension of the set function, and the search domain is the boundary of the function search space. The population size of the two algorithms is uniformly set to 30, the maximum number of iterations is 500, and each algorithm is run independently 30 times. The minimum value, average value and standard deviation obtained from 30 optimizations are used as statistical results. The optimization result analysis is shown in the attached Figure 3 Comparison of optimization results shown in the table.

[0122] The results show that ICSA performs better than CSA in F2 to F10 functions. By comparison, it is found that, except for F1 function, ICSA has achieved a good balance between global exploration and local development stages. The minimum and mean of the optimal solution obtained by ICSA optimization are much better than those of CSA, and the standard deviation of most test functions is not much different. This shows that ICSA can obtain better optimal solutions in most optimization problems without losing much robustness, and is more suitable for application scenarios that require high-precision optimization.

[0123] Embodiment 2: It mainly aims at the wall thickness optimization design problem of the foundation structure of the assembled box-type substation, and is also used to prove the feasibility and advancement of the optimization design method of the present invention in engineering design.

[0124] The side wall thickness of the box-type transformer foundation is taken as the design variable, the minimization of the side wall weight of the box-type transformer foundation is taken as the objective function, and the optimization is performed with the maximum stress of the box-type transformer foundation being less than the standard value of the concrete tensile strength as the constraint condition. The mathematical model of this optimization problem is: the design variable is X = [x bh ]; The objective function is to minimize the weight of the side wall of the box transformer min(f(x bh )).f(x bh )=(1.95+3.59)×2×x bh ; The constraint condition is that the maximum stress of the box-type transformer foundation σ≤w×σmax , where w is the safety factor. To ensure the safety margin of the design, w is set to 0.8, and σ max is the standard value of the tensile strength of concrete, which is 2.39 MPa. The search domain is [8 cm, 15 cm]. The number of algorithm iterations is set to 100, and the population size is 4. The improved circle search algorithm based on Kriging (ICSA-Kriging) method of the present invention and the standard circle search algorithm based on traditional finite element (CSA-FEA) method both run independently 30 times to eliminate the contingency of the optimization results.

[0125] First, an initial finite element model of the box substation foundation is established, as shown in the appendix Figure 4 . To construct a surrogate model for the relationship between the side wall thickness of the box substation foundation and the most unfavorable stress, a side wall thickness sample point is taken every 0.5 cm between 8 cm and 15 cm, and the most unfavorable stress response is obtained by bringing it into the finite element for calculation. These sample points and responses are used to form a sample set to construct a Kriging model and predict the most unfavorable stress response of the test points with a side wall thickness taken every 0.0001 cm between 8 cm and 15 cm. The results are compared as shown in the appendix Figure 5 . It can be seen that the constructed Kriging model has a very high accuracy and meets the calculation accuracy requirements for replacing the finite element model.

[0126] Appendix Figure 6 is the average result curve graph of the optimization iterations of the two optimization methods obtained after 30 optimizations. It can be seen from the figure that both ICSA-Kriging (black line) and CSA-FEA (red line) show a trend that the objective function value gradually decreases with the increase of the number of iterations, indicating that both methods can effectively optimize the objective function.

[0127] In the initial stage, about 0 - 30 iterations, the decreasing trends of the objective function values of the two methods are relatively close, indicating that the initial search efficiencies are similar. However, due to the introduction of the reverse learning strategy in the present invention, its initial iterative population is better than that of CSA-FEA, providing convenience for subsequent iterations. In the middle and late stages, about 30 - 60 iterations, the objective function values of the two methods are very close, indicating that both methods have found the neighborhood of the optimal solution at this time. In the later stage, that is, after 60 iterations, the objective function values of the two methods tend to be stable, but the objective function value reached by the method of the present invention is lower than that of CSA-FEA, indicating that the improved method also has a better performance in the exploitation ability.

[0128] From the later stage curve of the figure, it can be seen that the method of the present invention can reach a stable state earlier, indicating that its search path is more stable and may reduce unnecessary searches or oscillations.

[0129] Summary: The present invention is superior to the existing CSA-FEA in terms of overall convergence speed, exploration and development capabilities, and algorithm stability. This indicates that the method of the present invention has better performance in the balance between exploration and development, and is a more efficient optimization method, especially suitable for applications in scenarios with high requirements for high precision and fast convergence.

[0130] In addition, the running time of the optimization method based on the Kriging model proposed by the present invention and the time of the optimization method based on finite element analysis are compared as shown in the appendix Figure 7 As shown. It can be seen from the table that the iterative optimization times of ICSA-Kriging and CSA-FEA are both 0.3 seconds, which indicates that the time cost of using the iterative optimization of the present invention is basically the same in these two methods. However, there are significant differences in the finite element calculation times. The finite element calculation time of the present invention is 282.2 seconds, while the finite element calculation time of CSA-FEA is 1663.4 seconds, and the latter is nearly 5.9 times that of the former.

[0131] The total time is the sum of the iterative optimization time and the finite element calculation time. Therefore, the total time of the present invention is 282.5 seconds, while that of CSA-FEA is 1663.7 seconds. ICSA-Kriging significantly reduces the total calculation cost, saving approximately 83% of the total time compared with CSA-FEA.

[0132] The significant advantage of the present invention is that it effectively reduces the finite element calculation time. This benefits from the improvement of the ICSA–Kriging method in the way of evaluating the objective function value and constraints in iterative search, enabling the optimization process to use the Kriging model instead of finite element calculation to reduce the calculation cost without performing finite element calculation.

[0133] In addition, after constructing the Kriging surrogate model for the relationship between the wall thickness and stress of the component, the Kriging surrogate model does not need to be constructed again for subsequent optimization, that is, if optimization calculation is required later, the optimization time will be less, only the iterative optimization time, about 0.3s.

[0134] The above content is a further detailed description of the present invention in combination with specific embodiments. It cannot be considered that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, the present invention will have various simple substitutions, improvements and changes. All the simple substitutions, improvements and changes made should be regarded as belonging to the protection scope of the present invention.

Claims

1. An optimized design method for the foundation structure of an assembled box-type substation, characterized in that It includes the following steps: Step 1: Establish an initial finite element model of the box-type substation foundation based on the design drawings; Step 2: Define the optimization objectives, select the optimization parameters and their optimization ranges, and determine the structural response variables and constraint conditions of the box-type substation foundation; Step 3: Randomly generate N sets of optimization parameter sets within the optimization design range, and calculate the corresponding box-type substation foundation structure response sets through the finite element model; Step 4: Use the two data sets in Step 3 to construct a Kriging model between the optimization parameters and the structural response; Step 5: Randomly generate M sets of optimization parameters within the optimization design range, and substitute them into the initial finite element model of the box-type substation foundation for calculation to obtain M sets of corresponding structural responses as the test sample set; Subsequently, use the constructed Kriging model to predict the optimization parameters of the test samples, obtain the corresponding box-type substation foundation structure response, and compare the prediction results with the structural response obtained by the initial finite element model calculation, and evaluate the accuracy of the constructed Kriging model through error calculation; Step 6: If the calculation result meets the preset accuracy requirements, it indicates that the constructed Kriging model can effectively replace the finite element model of the box-type substation foundation for structural response calculation and is applicable to the iterative optimization process; If the accuracy does not meet the requirements, it is necessary to increase the number of modeling samples and reconstruct the Kriging model, and repeat Steps 4 and 5 until the constructed Kriging model reaches the required accuracy standard; Step 7: Configure the parameters of the ICSA algorithm, including the maximum number of iterations, the dimension of the variable parameters, and the population size, and randomly generate an initial population with the same size as the preset population number within the optimization design range; Step 8: Use the constructed Kriging model to calculate the fitness values of all individuals in the initial population and its reverse population respectively, and select the first half of the individuals with the best fitness from them to form an iterative population for subsequent optimization; Step 9: Select the corresponding position update strategy according to the current iteration number, update the positions of all individuals in the initial population, and detect whether the new solutions after update exceed the design boundary. If they exceed, correct them to within the boundary range; Step 10: Use the Kriging model to calculate the fitness values of all individuals in the updated population, and update the current optimal solution that meets the constraint conditions and its corresponding optimal fitness value; Step 11: Loop through Steps 8 to 10 until the maximum number of iterations is reached, terminate the calculation, and output the optimized box-type substation foundation parameters and their corresponding optimal fitness values.

2. The optimized design method for the foundation structure of an assembled box-type substation according to claim 1, characterized in that: The Kriging prediction model in Step 4 is specifically as follows: The Kriging model assumes the problem function to be solved as a Gaussian stationary random process, as shown in Equation (1): Y(x) = F(β,x) + z(x) (1) In equations (1) and (2), F(β,x) is the global approximation term of the model, β is the regression coefficient, k is the number of polynomials, and z(x) is a random process with a mean of 0 and a variance of σ 2 that provides a local approximation to the model; within the design space, the covariance matrix of each z(x) is shown in equation (3): In the formula: R(θ,x1,x2) is the correlation function of any two points x1 and x2, and the value of R is greater than 0 and less than 1; When obtaining n sample point sets S = [s1, s2, …, s n T and the corresponding response set Y = [y1, y2, …, y n T After that, the prediction of the Kriging model for any point x can be described by Equation (4):​​ where: Y K is the predicted value of the Kriging model at point x, and ω is the weight coefficient; To obtain the weight coefficient ω, the Kriging model needs to satisfy the unbiasedness constraint and the principle of minimizing the mean squared error MSE of the deviation, as shown in Eqs. (5) and (6) respectively: where: r is a vector composed of the correlation function values of all known points and any point x; To satisfy the minimization of the mean squared error of the deviation, the Lagrange multiplier λ is introduced for calculation, as shown in Eq. (7): Finally, the Kriging prediction model is obtained as shown in Eq. (8): Y K = f T β + r T R -1 (Y - Fβ) (8).

3. An optimized design method for the foundation structure of an assembled box-type substation, characterized in that: The algorithm in Step 5 is specifically as follows: The accuracy evaluation indicators use the relative root mean square error (RRMSE), relative maximum absolute error (RMAE), and R-squared value (R 2 ) for calculation. The smaller the RRMSE value and RMAE value, and the closer the R 2 value is to 1, the higher the accuracy of the model, and vice versa, the lower the accuracy. The calculation formulas for the three are shown in Equation (9): where: n is the number of test samples, y i is the true value at the i-th point to be measured, Y i is the predicted value at the i-th point to be measured, MY i is the mean of all true values.

4. An optimized design method for the foundation structure of an assembled box-type substation, characterized in that: The algorithm in Step 8 is specifically as follows: A reverse learning strategy is adopted. In the population initialization stage, an initial population is first generated, and then a reverse population corresponding to the initial population is generated through Eq. (10): X io = L i + U i - X i (10) where X io is the i-th solution of the reverse population, L i is the lower boundary of the search domain of the i-th solution, U i is the upper boundary of the search domain of the i-th solution, and X i is the i-th solution of the initial population; calculate the fitness values of all solutions in the initial population and the reverse population, and select the first half of the solutions with the best fitness to form the iterative population finally used for optimization.

5. An optimized design method for the foundation structure of an assembled box-type substation, characterized in that: The algorithm in Step 9 is specifically as follows: The value of parameter c is set using the linearly decreasing pattern of Eq. (17), specifically as follows: where c max and c min represent the maximum and minimum values of c, c max = 0.8, c min = 0.2.

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