An interval-based uncertainty optimization method

Abstract

The present application provides an interval-based uncertainty optimization method, comprising the following steps: obtaining a plurality of design vector data using a PSO optimization algorithm, and establishing a data proxy model; importing the design vector data into the data proxy model to obtain an interval of an uncertain objective function; calculating the objective function of the uncertainty optimization problem based on the interval of the uncertain objective function; converting the objective function using a multi-objective evaluation function to obtain a multi-objective evaluation function value; performing the above calculation process on the plurality of design vector data to obtain corresponding fitness values, and selecting an optimal solution. The present application has the beneficial effect that the interval-based uncertainty optimization method does not require accurate probability distribution of uncertain parameters, uses interval numbers to represent uncertain parameters, and greatly reduces the requirements for original data.

Description

Technical Field

[0001] This invention belongs to the field of electrical equipment optimization, and in particular relates to an interval-based uncertainty optimization method. Background Technology

[0002] Optimization is a method of selecting the best decision from multiple options, and it plays a significant role in improving system performance, reducing energy consumption, rationally utilizing resources, and increasing economic benefits. Currently, the optimization design of electrical equipment is mostly based on determined system parameters and optimization models, and solved using classic deterministic optimization methods.

[0003] In the optimization process of electrical equipment, uncertainties always exist regarding loads, material properties, geometric characteristics, and boundary conditions. Currently, interval uncertainty optimization methods have achieved considerable success and good results in problems where explicit expressions can be established. However, the mapping relationship between design parameters and performance data of modern electrical equipment is complex, making it impossible to establish precise calculation formulas. Instead, surrogate models based on machine learning are used. Therefore, it is urgent to develop interval uncertainty optimization methods based on surrogate models to achieve reliable design of modern electrical equipment that considers uncertainties. Summary of the Invention

[0004] In view of this, the present invention aims to propose an interval-based uncertainty optimization method in order to solve at least one of the above-mentioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0006] In a first aspect, the present invention provides an interval-based uncertainty optimization method, comprising the following steps:

[0007] S1: Use the PSO optimization algorithm to obtain multiple design vector data and establish a data proxy model;

[0008] S2: Import the design vector data into the data proxy model to obtain the interval of the uncertain objective function;

[0009] S3: Obtain the objective function of the uncertain optimization problem based on the interval of the uncertain objective function;

[0010] S4: Use the multi-objective evaluation function to transform the objective function in step S3 to obtain the multi-objective evaluation function value;

[0011] S5: For multiple design vector data, perform the calculation process of steps S2-S4 to obtain the corresponding fitness values, and determine whether the fitness values ​​have converged.

[0012] If convergence occurs, the optimal solution is selected based on the fitness value.

[0013] If convergence is not achieved, recursive calculations are performed until the fitness value converges.

[0014] Furthermore, the data proxy model is a two-layer proxy model optimization structure, using the outer proxy model to perform optimization calculations on the design variables and the inner proxy model to perform optimization calculations on the uncertain variables.

[0015] The design variables and uncertain variables of electrical equipment are collected as data samples. The data samples are input into the inner surrogate model and two inner optimizations are performed to calculate the upper and lower bounds of the objective function.

[0016] The upper and lower bounds of the objective function are used as input data for the outer proxy model, and the uncertain objective function interval is obtained through the outer proxy model.

[0017] Furthermore, the inner proxy model takes the design vector and the uncertainty vector as input data, and takes the uncertain objective function value corresponding to the design vector and the uncertainty vector as the output data of the inner proxy model.

[0018] Furthermore, the outer proxy model takes the design vector as input data and the upper and lower bounds of the uncertain objective function as output data to obtain a nonlinear mapping relationship between the input data and the output data.

[0019] Furthermore, the design space is formed by using the design vector and its corresponding trust region radius. In the mixed space composed of the design space and the uncertainty region, multiple data samples composed of design variables and uncertainty variables are selected.

[0020] The data samples are imported into the finite element simulation model to calculate the uncertain objective function corresponding to the data samples, which is then used as training samples.

[0021] Multiple training samples are combined to form an inner agent model sample set, and the inner agent model is trained using the inner agent model sample set.

[0022] Furthermore, uncertain optimization problems include:

[0023] Load problem: The loads acting on the structure are uncertain;

[0024] Material property issues: The elastic modulus and density of the material are uncertain.

[0025] Geometric characteristic issues: Manufacturing and installation errors lead to uncertainties in geometric dimensions.

[0026] Boundary condition problem: the connections between structures and between components are uncertain.

[0027] In a second aspect, the present invention provides an electronic device including a processor and a memory communicatively connected to the processor and used to store processor-executable instructions, characterized in that: the processor is used to execute an interval-based uncertainty optimization method as described in any of the first aspects above.

[0028] In a third aspect, the present invention provides a server, characterized in that it includes at least one processor and a memory communicatively connected to the processor, the memory storing instructions executable by the at least one processor, the instructions being executed by the processor to cause the at least one processor to perform an interval-based uncertainty optimization method as described in any of the first aspects.

[0029] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, characterized in that: when the computer program is executed by a processor, it implements an interval-based uncertainty optimization method as described in any one of the first aspects.

[0030] Compared with existing technologies, the interval-based uncertainty optimization method described in this invention has the following advantages:

[0031] The present invention discloses an interval-based uncertainty optimization method. This method does not require a precise probability distribution of uncertain parameters, but uses the number of intervals to represent uncertain parameters, which greatly reduces the requirements for the original data. Attached Figure Description

[0032] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0033] Figure 1 This is a flowchart illustrating an interval-based uncertainty optimization method according to an embodiment of the present invention.

[0034] Figure 2 This is a schematic diagram of the two-dimensional simulation structure of the motor described in an embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram of the objective function variation curve according to an embodiment of the present invention;

[0036] Figure 4 This is a schematic diagram illustrating the distribution of the optimal solution under different weight coefficients as described in an embodiment of the present invention;

[0037] Figure 5 This is a schematic diagram of the optimization results under different multi-objective weight coefficients as described in the embodiments of the present invention;

[0038] Figure 6 This is a schematic diagram showing the comparison results of the solutions of the two optimization methods described in the embodiments of the present invention;

[0039] Figure 7 This is a schematic diagram of Pareto solution sets with different iteration numbers as described in the embodiments of the present invention;

[0040] Figure 8 This is a schematic diagram of the distribution of non-dominated solution sets obtained by the two methods described in the embodiments of the present invention. Detailed Implementation

[0041] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0042] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0043] Example 1:

[0044] like Figure 1 As shown: An interval-based uncertainty optimization method includes the following steps:

[0045] S1: Use the PSO optimization algorithm to obtain multiple design vector data and establish a data proxy model;

[0046] S2: Import the design vector data into the data proxy model to obtain the interval of the uncertain objective function;

[0047] S3: Calculate the objective function of the uncertain optimization problem based on the interval of the uncertain objective function;

[0048] S4: Use the multi-objective evaluation function to transform the objective function in step S3 to obtain the multi-objective evaluation function value, i.e., the PSO fitness value;

[0049] S5: For multiple design vector data, perform the calculation process of steps S2-S4 to obtain the corresponding fitness values, and determine whether the fitness values ​​have converged.

[0050] If convergence occurs, the optimal solution is selected based on the fitness value.

[0051] If convergence is not achieved, recursive calculations are performed until the fitness value converges.

[0052] Design vector: An n-dimensional input vector consisting of the design parameter variables that need to be optimized is called an n-dimensional design vector.

[0053] Step S3 involves calculating the interval for the uncertain objective function as follows: Obtain the midpoint and radius values ​​of the design vector data; calculate the linearly weighted evaluation function for objective optimization; and calculate the probability degree of the uncertain constraints based on the constraint interval. Finally, based on the aforementioned evaluation function and constraint probability degree, calculate the corresponding penalty function value.

[0054] The data proxy model is an optimized two-layer proxy model structure. The outer proxy model is used to perform optimization calculations on the design variables, and the inner proxy model is used to perform optimization calculations on the uncertain variables.

[0055] The design variables and uncertain variables of electrical equipment are collected as data samples. The data samples are input into the inner surrogate model and two inner optimizations are performed to calculate the upper and lower bounds of the objective function.

[0056] The upper and lower bounds of the objective function are used as input data for the outer proxy model, and the uncertain objective function interval is obtained through the outer proxy model.

[0057] The inner proxy model takes the design vector and uncertainty vector as input data, and the uncertain objective function value corresponding to the design vector and uncertainty vector as the output data of the inner proxy model.

[0058] The outer surrogate model takes the design vector as input data and the upper and lower bounds of the uncertain objective function as output data, thus obtaining a nonlinear mapping relationship between the input and output data, that is, the relationship between the input design vector and the corresponding range of values ​​of the uncertain objective function output by the surrogate model.

[0059] In a mixed space consisting of design space and uncertainty domain, multiple data samples composed of design variables and uncertainty variables are selected;

[0060] The data samples are imported into the finite element simulation model to calculate the uncertain objective function corresponding to the data samples, which is then used as training samples.

[0061] Multiple training samples are combined to form an inner agent model sample set, and the inner agent model is trained using the inner agent model sample set.

[0062] Work process:

[0063] Single-objective optimization example for intervals:

[0064] like Figure 2 As shown: The Prius 2010 permanent magnet synchronous motor was selected as the research object, and a single-objective optimization was performed in the interval under the condition of uncertain parameter variables. The sub-slot width x1, stator slot width x2, stator slot height x3, permanent magnet thickness x4, and permanent magnet width x5 were selected as design variables X. The optimization objective was to minimize torque ripple f. Uneven air gap of the motor will result in uneven magnetic field distribution, which will have a great impact on its performance and operational reliability.

[0065] Considering actual service conditions, uneven stress leading to shaft deformation, bearing wear, and installation errors can all cause misalignment between the motor's stator and rotor, resulting in uneven air gap and thus changes in the air gap length. Therefore, the air gap length is treated as an uncertain variable U to better reflect actual operating conditions. Thus, the following uncertain optimization problem can be established:

[0066]

[0067] st1.28≤x1≤2.28,4.2≤x2≤7.2

[0068] 29≤x3≤32, 4.8≤x4≤8

[0069] 33.5≤x5≤36.5, 0.67≤U≤0.82

[0070] Applying a multi-objective evaluation function to the above equation, some parameters are set as follows during optimization: β = 0.5, ξ = 0, φ and ψ = 1.0. This optimization problem can then be transformed into:

[0071]

[0072] st1.28≤x1≤2.28,4.2≤x2≤7.2

[0073] 29≤x3≤32, 4.8≤x4≤8

[0074] 33.5≤x5≤36.5, 0.67≤U≤0.82

[0075] like Figure 3 As shown: For this single-objective optimization problem, the inner and outer surrogate models adopt the DBN-DNN model, and the inner and outer optimization algorithms both adopt the single-objective PSO algorithm. The number of iterations is set to 100. The curve of the objective function value changing with the number of iterations is shown. After 100 iterations of optimization, the optimization process converges. At this time, the corresponding design variables X are: stator slot width x1 is 1.56302mm, stator slot width x2 is 7.16710mm, stator slot height x3 is 29.75526mm, permanent magnet thickness x4 is 7.99915mm and permanent magnet width x5 is 34.737125mm. The torque ripple variation range of this design variable within the uncertainty parameter range is [0.04133, 0.04373].

[0076] like Figure 4As shown: By changing the size of the multi-objective weight coefficient β, nonlinear interval number optimization is performed, and the distribution of the optimal solution under different β values ​​is observed. As the value of β increases, the midpoint value of the optimal solution of the objective function shows an upward trend, while the radius value shows a downward trend. This is because a larger β value increases the preference for the radius of the objective function and decreases the preference for the midpoint. Therefore, a smaller radius value and a larger midpoint value are obtained. That is, the motor obtains a smaller torque ripple fluctuation range while having a larger average torque ripple value.

[0077] like Figure 5 The results show the optimization results under six different multi-objective weight coefficients. Different optimal design vectors and objective function intervals were obtained under different β values. When β = 1.0, the objective function has the largest midpoint value of 0.05102 and the smallest radius value of 0.00016. At this time, the design reliability can be well guaranteed, that is, the sensitivity of torque ripple to uncertain variables is the smallest. However, the average value of torque ripple under the influence of uncertain factors is large, and the average design performance is poor. When β = 0.0, the objective function has the smallest midpoint value of 0.03751 and the largest radius value of 0.00206. At this time, the average design performance is good, that is, the average value of motor torque ripple is the smallest. However, the sensitivity of torque ripple to uncertain variables is the greatest, and the reliability is the worst.

[0078] When facing real-world engineering problems, it is necessary to appropriately select the β value based on the problem itself and the decision-maker's preferences in order to better achieve a balance between average design performance and design reliability. If reliability has little impact on the system and large performance fluctuations caused by uncertainties are acceptable, then a smaller β value can be selected to increase the preference for the midpoint of the objective function, thereby obtaining better average design performance to some extent.

[0079] If reliability has a significant impact on the system, such as when the system needs to operate very stably and it is desirable to have small performance fluctuations under the influence of uncertain factors, then a larger β value is selected to increase the preference for the radius of the objective function, thereby obtaining smaller performance fluctuations to a certain extent and ensuring the design reliability of the system.

[0080] like Figure 6 As shown: For this optimization problem, the traditional optimization method is used to perform deterministic optimization without considering the influence of uncertain parameters; then the method proposed in this paper is used to optimize the design considering the uncertainty of parameters, resulting in two optimization solutions.

[0081] Although some solutions obtained through interval uncertainty optimization are inferior to those obtained through traditional deterministic optimization, this approach considers the uncertainties in the optimization process and yields solutions that are interval-based rather than deterministic, thus better describing the performance fluctuations of permanent magnet synchronous motors under actual operating conditions caused by uncertainties. Furthermore, in practical engineering problems, interval uncertainty optimization can obtain different midpoint and radius values ​​with different weighting coefficients, providing designers with more options. This is something deterministic optimization methods cannot achieve; therefore, the method presented in this paper has certain advantages.

[0082] Interval multi-objective optimization example:

[0083] Taking an electromagnetic rail launcher as the research object, the armature is optimized under uncertain parameters. Variations in armature dimensions significantly affect its characteristic distribution. The armature head width (x1), armature length (x2), armature tail height (x3), and armature tail depth (x4) are selected as design variables X. The armature electromagnetic thrust (f1) and the maximum current density at the contact surface (f2) are used as optimization objectives. The uncertain optimization problem can be established as follows:

[0084]

[0085]

[0086] st7≤x1≤10,9≤x2≤12

[0087] 5≤x³≤8, 6≤x⁴≤8, 4≤U≤5.5

[0088] During the optimization process, some parameters are set as follows: β is 0.5, ξ is 0, and φ and ψ are 1.0. Therefore, this optimization problem can be transformed into:

[0089]

[0090]

[0091] st1.28≤x1≤2.28,4.2≤x2≤7.2

[0092] 29≤x3≤32, 4.8≤x4≤8

[0093] 33.5≤x5≤36.5, 0.67≤U≤0.82

[0094] For this multi-objective optimization problem, both the inner and outer surrogate models employ the DBN-DNN model. The inner optimization uses the single-objective PSO algorithm, while the outer optimization uses the MOPSO algorithm, with 200 iterations. Since multi-objective optimization rarely yields a single global optimum, a series of non-dominated better solutions are typically obtained.

[0095] The calculation results for iterations of 50, 100, 150, and 200 are as follows: Figure 7 As shown, the optimized values ​​at iterations of 150 and 200 are very similar to those at iteration 100, and the optimized values ​​at iterations of 150 and 200 are almost identical. Therefore, the optimization result can be considered convergent, indicating good convergence performance of the algorithm. It can be seen that the solution set points are relatively evenly distributed, and the multi-objective evaluation function f... 1d (X) is minimized to -1.71869, at which point the multi-objective evaluation function f 2d (X) is the maximum value of 0.70619; f 1d (X) is at its maximum of -1.54101, at which point f 2d (X) is the minimum value of 0.66790.

[0096] like Figure 8 As shown in the figure, for this optimization problem, a traditional optimization method is used, which does not consider the influence of uncertain parameters, and a deterministic optimization is performed. Then, the method proposed in this paper is used to consider the uncertainty of parameters and perform an optimization design. The non-dominated solution sets obtained by the two methods are shown in the figure. It can be seen that the deterministic optimization method does not consider the uncertainties of the electromagnetic rail launcher under actual operating conditions. The decision is based on the specific values ​​of the objective function and constraints at each design vector. Therefore, the non-dominated solution set obtained by the two methods is a series of Pareto points. The method proposed in this paper considers that the armature tail width is not a fixed value due to friction and wear. It uses interval numbers to represent the uncertainty of the armature tail width and introduces it into the optimization design process.

[0097] Therefore, for any given set of design vectors, the possible values ​​of the objective function will form an interval. The upper and lower bounds of the function are the upper and lower critical values ​​obtained by considering the uncertainty of the parameters. The resulting non-dominated solution set will also be a series of interval solution sets.

[0098] The method presented in this paper is better able to describe the performance fluctuations of electromagnetic rail launchers caused by uncertainties. This is important for reliability analysis of electromagnetic rail launchers and provides a reference for designers in solving practical engineering problems.

[0099] Example 2: An electronic device includes a processor and a memory communicatively connected to the processor and used to store executable instructions of the processor, characterized in that: the processor is used to execute an interval-based uncertainty optimization method as described in any of Examples 1 above.

[0100] Example 3: A server, characterized in that it includes at least one processor and a memory communicatively connected to the processor, the memory storing instructions executable by the at least one processor, the instructions being executed by the processor to cause the at least one processor to perform an interval-based uncertainty optimization method as described in any of Examples 1.

[0101] Example 4: A computer-readable storage medium storing a computer program, characterized in that: when the computer program is executed by a processor, it implements an interval-based uncertainty optimization method as described in any one of Examples 1.

[0102] Those skilled in the art will recognize that the units and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0103] In the several embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. For example, the division of units described above is merely a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. The aforementioned units may or may not be physically separated. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments of the present invention according to actual needs.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or some or all of the technical features can be replaced. Such modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

[0105] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, substitutions, or improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An interval-based uncertainty optimization method, characterized by, Includes the following steps: S1: Use the PSO optimization algorithm to obtain multiple design vector data, use the design vectors and their corresponding trust region radii to form the design space, and select multiple data samples composed of design variables and uncertain variables in the mixed space composed of the design space and the uncertainty region. The data samples are imported into the finite element simulation model to calculate the uncertain objective function corresponding to the data samples, which is used as training samples. Multiple training samples are combined to form an inner layer proxy model sample set. The inner layer proxy model is trained using the inner layer proxy model sample set to establish the data proxy model. S2: Import the design vector data into the data proxy model to obtain the interval of the uncertain objective function. The data proxy model is a two-layer proxy model optimization structure. The outer proxy model is used to perform optimization calculations on the design variables, and the inner proxy model is used to perform optimization calculations on the uncertain variables. The data samples are input into the inner proxy model to perform two inner-layer optimizations to calculate the upper and lower bounds of the objective function. The upper and lower bounds of the objective function are used as the input data of the outer proxy model to obtain the interval of the uncertain objective function. S3: Based on the interval of the uncertain objective function, obtain the objective function of the uncertain optimization problem, where the uncertain optimization problem includes: Load problem: The loads acting on the structure are uncertain; Material property issues: The elastic modulus and density of the material are uncertain. Geometric characteristic issues: Manufacturing and installation errors lead to uncertainties in geometric dimensions. Boundary condition problem: the connections between structures and between components are uncertain; S4: Use the multi-objective evaluation function to transform the objective function in step S3 to obtain the multi-objective evaluation function value; S5: For multiple design vector data, perform the calculation process of steps S2-S4 to obtain the corresponding fitness values, and determine whether the fitness values ​​have converged. If convergence occurs, the optimal solution is selected based on the fitness value. If convergence is not achieved, recursive calculations are performed until the fitness value converges.

2. The interval-based uncertainty optimization method according to claim 1, characterized in that: The inner proxy model takes the design vector and the uncertainty vector as input data, and takes the uncertain objective function value corresponding to the design vector and the uncertainty vector as the output data of the inner proxy model.

3. The interval-based uncertainty optimization method according to claim 1, characterized in that: The outer proxy model takes the design vector as input data and the upper and lower bounds of the uncertain objective function as output data, thus obtaining a nonlinear mapping relationship between the input data and the output data.

4. An electronic device, comprising a processor and a memory connected to the processor in communication, and configured to store executable instructions of the processor, characterized in that: The processor is used to execute an interval-based uncertainty optimization method as described in any one of claims 1-3.

5. A server, characterized by: The system includes at least one processor and a memory communicatively connected to the processor, the memory storing instructions executable by the at least one processor, the instructions being executed by the processor to cause the at least one processor to perform an interval-based uncertainty optimization method as described in any one of claims 1-3.

6. A computer readable storage medium storing a computer program, characterized in that: The computer program, when executed by a processor, implements the interval-based uncertainty optimization method according to any one of claims 1-3.

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