Wireless charging coil multi-objective optimization method based on improved linmap
Patent Information
- Application Number
- CN202611400414.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-10
- Publication Date
- 2026-10-13
AI Technical Summary
[0003]目前无线充电线圈拓扑的主流优化方法多局限于单目标优化，普遍以传输效率为唯一优化准则，忽视了偏移效率损失率、制造成本、输出功率等同等重要的工程指标
1、突破传统单目标优化的局限，可同时对传输效率、抗偏移能力、制造成本与输出功率等多个相互制约的性能指标开展协同优化，通过多属性决策获得综合最优的线圈拓扑方案，避免单一指标优化导致的其他性能劣化，适配工程实际的多元需求。
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Figure CN122904553A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of wireless charging technology, and in particular to a multi-objective optimization method for wireless charging coils based on improved LINMAP. Background Technology
[0002] The coupling coil is the core electromagnetic carrier for energy exchange in a wireless power transmission system. Its geometry, physical dimensions, number of turns, spatial relative position, and core arrangement are all interconnected, jointly determining the system's mutual inductance level. This, in turn, profoundly affects power transmission capacity, energy conversion efficiency, and stable power supply under conditions of lateral offset and air gap fluctuations. Conducting scientific multi-objective design optimization of the coil topology is a key approach to improving the overall performance of wireless charging systems.
[0003] Currently, most mainstream optimization methods for wireless charging coil topologies are limited to single-objective optimization, generally using transmission efficiency as the sole optimization criterion, neglecting equally important engineering indicators such as offset efficiency loss rate, manufacturing cost, and output power. These indicators are inherently interdependent: excessively pursuing maximum transmission efficiency often leads to a significant decrease in the coil's anti-offset capability or a sharp increase in system material costs, making it difficult to adapt to industrial production and practical application requirements. Single-objective optimization can only obtain a locally optimal solution under a single indicator, failing to achieve global coordination and comprehensive trade-offs among multiple performance indicators.
[0004] Meanwhile, existing multi-objective decision-making methods still have significant shortcomings when applied to wireless charging coil optimization: on the one hand, traditional decision-making methods such as LINMAP are prone to extreme weights, leading to severely unbalanced optimization results and failing to balance various performance aspects; on the other hand, existing methods struggle to effectively incorporate engineering experience and scenario-based subjective preferences, failing to adaptively select the comprehensive optimal solution based on the performance requirements of different application scenarios such as electric vehicles and consumer electronics. Furthermore, coil optimization involves numerous design variables with a wide range of values; a full traversal solution leads to an exponential increase in computational space, resulting in high computational resource consumption, low optimization efficiency, and difficulty in balancing optimization accuracy and solution cost. Summary of the Invention
[0005] The purpose of this invention is to provide a multi-objective optimization method for wireless charging coils based on improved LINMAP, thereby solving the aforementioned technical problems.
[0006] To achieve the above objectives, this invention provides a multi-objective optimization method for wireless charging coils based on improved LINMAP, comprising the following steps: S1. Obtain the basic design structure of the wireless charging coil and determine multiple optimization objectives and multiple optimization variables; S2. Deconstruct and hierarchically divide the optimization variables into upper-level discrete variables and lower-level continuous variables, and reduce the solution space by using a hierarchical solution method. S3. Construct a basic solution set for the upper-level discrete variables, and obtain the optimization objective parameter values for each scheme through simulation calculation; S4. Normalize the optimization target parameter values of all schemes, and convert positive and negative indicators into positive evaluation indicators to construct an initial evaluation matrix. S5. Based on the application scenario, set the importance of subjective preferences for optimization objectives, construct an ordered set of preference pairs for pairwise comparison of solutions, and set regularization parameters, weight lower bound parameters, and consistency threshold parameters. S6. The improved LINMAP method, which introduces L2 regularization and subjective preference weights, is used to solve the initial evaluation matrix to obtain the comprehensive weights of each optimization objective and to select the optimal solution that is closest to the ideal solution. S7. Based on the optimal solution of the upper-level discrete variables, the same improved LINMAP method is used to optimize the lower-level continuous variables to obtain the comprehensive optimal combination of wireless charging coil topology parameters.
[0007] Preferably, the upper-level discrete variables include coil shape and number of winding turns; the lower-level continuous variables include coil outer radius, coil inner radius, additional core coverage, and transmission air gap spacing.
[0008] Preferably, for the upper-level discrete variables, an enumeration method is used to construct all design combinations as the basic solution set; for the lower-level continuous variables, the Taguchi method or uniform design method is used to construct experimental schemes, and representative solutions are selected to form the basic solution set; when the number of basic solution schemes is greater than the preset number of basic solution sets, non-dominated sorting is performed on the basic solution set, the Pareto optimal solution set is extracted as the input of the subsequent LINMAP method, and dominated inferior solutions are eliminated to reduce the amount of computation.
[0009] Preferably, in S4, the index is normalized using the Max-Min linear normalization method, specifically as follows: For positive metrics such as transmission efficiency and output power, a positive normalization formula is used: ; For negative indicators such as manufacturing cost and offset efficiency loss rate, an inverse normalization formula is used: ; In the formula, For the first The first scheme is in the The original evaluation values under each optimization objective For all schemes in the first The maximum value under each optimization objective For all schemes in the first Minimum value under each optimization objective This is the normalized evaluation value.
[0010] Preferably, the optimization objectives include at least transmission efficiency, offset resistance, manufacturing cost, and output power; wherein offset resistance is quantified using the offset efficiency loss rate, and the offset efficiency loss rate... The calculation formula is: ; In the formula, The transmission efficiency before coil offset, This represents the transmission efficiency after the coil is offset.
[0011] Preferably, in S6, a weighted squared Euclidean distance is used to measure the difference between each solution and the ideal positive solution. A subjective preference weight coefficient is introduced into the distance calculation. The specific calculation formula is as follows: ; In the formula, For the first The weighted squared Euclidean distance between each solution and the ideal solution. To optimize the number of targets, For the first An algorithm for solving weights with an optimization objective. For the first The importance coefficient of subjective preferences for each optimization objective. For the ideal correct solution, in the first... The ideal solution is set as a vector of all 1s where each normalized index takes the maximum value under the optimization objective.
[0012] Preferably, in S6, consistency and inconsistency indices are constructed based on the scheme preference set, and an improved LINMAP linear programming objective function is constructed by combining the L2 regularization penalty term, specifically as follows: Inconsistent Indicators for: ; Consistency Indicators for: ; The objective function of the optimization model with L2 regularization is: ; In the formula, For the plan and plan Comparison of ordered preferences for sets For the first The weighted squared Euclidean distance between each solution and the ideal solution. For preference weights, , The regularization intensity coefficient is . , This is the L2 regularization penalty term, which is the sum of squares of the weights of each optimization objective.
[0013] The preferred constraints for the optimization model with L2 regularization are: ; In the formula, This is the consistency threshold. These are the lower limits for the weights of each optimization objective; After obtaining the initial weights, a second normalization is performed by combining the subjective preference weight coefficients to obtain the final comprehensive weights.
[0014] Preferably, in S7, the optimization reuse of the normalization processing, parameter setting and improved LINMAP solution process of the upper layer is used for the optimization of the lower layer continuous variables; under the premise of fixing the optimal discrete parameters of the upper layer, orthogonal experimental design and optimization solution are carried out on the dimension of continuous variables to obtain the comprehensive optimal combination of coil topology parameters.
[0015] Preferably, in S3, the self-inductance and mutual inductance parameters of each coil topology are obtained through finite element simulation. The self-inductance and mutual inductance parameters are then substituted into the wireless charging system circuit model to calculate the transmission efficiency and output power optimization target parameter values corresponding to each scheme.
[0016] Therefore, the beneficial effects of the above-mentioned multi-objective optimization method for wireless charging coils based on improved LINMAP in this invention are as follows: 1. Breaking through the limitations of traditional single-objective optimization, it can simultaneously carry out collaborative optimization of multiple mutually restrictive performance indicators such as transmission efficiency, anti-offset capability, manufacturing cost and output power. Through multi-attribute decision-making, it obtains the comprehensive optimal coil topology scheme, avoids the performance degradation caused by single indicator optimization, and adapts to the diverse needs of actual engineering.
[0017] 2. By introducing an L2 regularization penalty term into the traditional LINMAP method, the generation of extreme weights is effectively suppressed, ensuring the rationality and stability of weight allocation. At the same time, a subjective preference weight mechanism is incorporated, which can combine expert experience and application scenario requirements to set the importance ranking of targets, realizing the combination of data-driven and engineering experience, so that the optimization results are more in line with the actual use needs of different scenarios.
[0018] 3. A variable deconstruction hierarchical strategy is adopted, which splits the optimization variables into discrete and continuous variables for hierarchical solution. Combined with non-dominated sorting to extract the Pareto optimal solution set, the solution space is greatly reduced and dominated inferior solutions are eliminated. While ensuring optimization accuracy, the consumption of computing resources is significantly reduced and the solution efficiency of multi-objective optimization is improved.
[0019] 4. The optimization process can be flexibly controlled by adjusting parameters such as regularization strength, consistency threshold and weight lower limit, which not only ensures the stability of the solution, but also allows for adjustment of the optimization bias according to needs, providing a fast and reliable technical path for multi-objective optimization of wireless charging coil topology.
[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0021] Figure 1 This is a flowchart of the multi-objective optimization method for wireless charging coils based on improved LINMAP of the present invention; Figure 2 This is a structural diagram of the WPT system according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a simulation model of a wireless charging system circuit according to an embodiment of the present invention. Detailed Implementation
[0022] To make the objectives, technical solutions, and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.
[0023] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.
[0024] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0025] The multi-objective optimization method for wireless charging coils based on improved LINMAP provided by this invention fully combines the core requirements of practical wireless charging applications. It introduces L2 regularization terms and subjective preference weights on the basis of the classic LINMAP method, thereby taking into account both data-driven and designer experience, and comprehensively optimizes multiple structural parameters such as coil shape, core coverage, number of turns, and air gap length.
[0026] In a specific embodiment, the outer radius, inner radius, core coverage, and charging interval are selected as optimization variables (which can also be flexibly adjusted according to the specific optimization direction). At the same time, transmission efficiency, anti-offset capability, coil manufacturing cost, and output power are selected as four key optimization objectives. This constructs a complete multi-objective optimization framework. Finally, considering subjective preference ranking and weight constraints, the coil topology parameter combination closest to the ideal solution is selected, effectively balancing performance, economy, and engineering feasibility.
[0027] like Figures 1-3 As shown, this invention provides a multi-objective optimization method for wireless charging coil topology based on an improved LINMAP method, employing the following technical solution: S1. Obtain the basic design structure of the wireless charging coil. Based on the structure type (such as planar disc type, spiral tube type, etc.) and specific application scenarios (such as power level, transmission distance requirements), reasonably determine multiple optimization objectives (such as transmission efficiency, coupling coefficient, temperature rise, volume, etc.) and multiple optimization variables (such as coil turns, wire diameter, spacing, magnetic core size, etc.). S2. When there are many optimization variables, the optimization variables are deconstructed and layered to reduce the solution space and save computational resources. The layering method can be discrete-continuous layering (the upper layer is discrete variables and the lower layer is continuous variables), or other layering strategies can be selected according to the properties of the variables (such as geometric dimensions, material parameters, etc.). S3. For the upper-level discrete variables, use the enumeration method to construct all design combinations as the basic solution set. For the lower-level continuous variables, use the Taguchi method or uniform design method to construct experimental schemes. Select representative solutions to form the basic solution set to obtain the initial scheme. Preset the number of basic solution sets as the standard for judging the number of basic solution schemes. When using methods such as Latin hypercube sampling, if the number of basic solution schemes is greater than the preset number of basic solution sets, it means that there are too many solutions. The schemes can be sorted by non-dominated order first. Based on the optimization objective parameter values obtained after simulation calculation, select the Pareto optimal solution and eliminate the dominated inferior solutions to reduce the amount of subsequent calculations. S4. Normalize the optimization target parameter values of all schemes, and unify the positive indicators (the larger the better) and negative indicators (the smaller the better) into positive evaluation indicators (that is, the larger the value of all indicators, the better the performance), construct the initial evaluation matrix, and lay the data foundation for subsequent multi-objective optimization. S5. Based on the application scenario, rank the subjective preferences of the optimization objectives according to their importance, and construct an ordered set of preference pairs for pairwise comparison of the solutions; assign initial weights to the subjective preferences based on their importance differences; and set regularization parameters (if the results depend more on the data and the preference pairs themselves, the regularization parameters can be appropriately reduced; if the goal is to prevent extreme weights or obtain a more even weight distribution, the regularization parameters can be appropriately increased), weight lower bound parameters, and consistency threshold parameters. Note that the consistency threshold parameter should be carefully selected: too small a value may lead to extreme solutions, while too large a value may result in no solution. A suitable initial value can be obtained through trial and error. S6. The improved LINMAP method, which introduces L2 regularization and subjective preference weights, is used to solve the normalized initial evaluation matrix to obtain the comprehensive weights of each optimization objective. The scheme closest to the ideal solution (i.e., the virtual solution composed of the optimal values of each objective) is selected as the optimal solution of the current layer. S7. Based on the optimal solution of the upper-level discrete variables, fix their values and use the same improved LINMAP method to further optimize the lower-level continuous variables, and finally obtain the comprehensive optimal combination of wireless charging coil topology parameters. The upper-level discrete variables include coil shape and number of winding turns; the lower-level continuous variables include coil outer radius, coil inner radius, magnetic core additional coverage and transmission air gap spacing.
[0028] Example 1: First, we obtain the basic model of the coil: This example uses the LCC-S compensated magnetic induction WPT system as an example, focusing on optimizing the topology of the transmitting and receiving coils. The structure of the WPT system is as follows: Figure 2 As shown, it mainly includes a DC power supply, an inverter circuit, a transmitting-side compensation network, a transmitting coil, a receiving coil, a receiving-side compensation network, a rectifier circuit, and a load. The basic model is set as follows: the outer radius of the coil is 100mm, the inner radius is 30mm, the number of coil turns is 10, the magnetic core only covers the area of the coil and is exactly equal to the area of the coil, that is, the extra coverage rate is 0%, the magnetic core thickness is 5mm, and the transmission air gap is 100mm.
[0029] Discrete variable optimization involves defining a basic solution set for the discrete variables while keeping the values of the continuous variables in the basic model fixed. Unprocessed solution ,in m For shape sequence number, n The number of turns is shown in Table 1.
[0030] Table 1: Parameter Settings
[0031] The simulation model of the wireless charging system circuit simulates these ten different coil structures, as shown in the simulation model below. Figure 3 As shown, the simulation can obtain the corresponding coil self-inductance and mutual inductance; by substituting the self-inductance and mutual inductance values into the circuit simulation model, various parameters such as the transmission efficiency and output power of the wireless charging system under this topology can be calculated, which can be used as the basic solution set.
[0032] The feasible solution set obtained after constraints is then optimized with efficiency, anti-offset capability, price, and output power as optimization objectives. If the number of solution sets is too large, the feasible solution set can be non-dominated sorted to extract the upper-level Pareto optimal solution set. For the lower-level continuous variables, this embodiment uses the Taguchi method to obtain representative solutions without non-dominated sorting. When calculating efficiency, actual simulation shows that the mutual resistance between the two coils is extremely low and negligible. The efficiency calculation formula is as follows: ; In the formula, For transmission efficiency, For output power, Input power; A value is defined to determine the offset efficiency loss rate of a wireless charging coil, in order to measure the offset resistance of the coil topology. In this embodiment, the offset resistance is quantified by the offset efficiency loss rate. The calculation formula is: ; In the formula, This indicates the efficiency before the offset. This indicates the efficiency after offset. This indicator is negative; the smaller the value, the better the operating condition.
[0033] The price fluctuates due to variations in the coil cross-sectional area resulting from different numbers of coil turns, as well as differences in the size and thickness of the magnetic core. In this example, the coil material is copper, and the magnetic core material is PC95. The price of copper is taken as 100 yuan / kg, and the price of PC95 is also taken as 100 yuan / kg. For simplicity, the density of copper is taken as 9 g / cm³. 3 The density of PC95 is taken as 5 g / cm³. 3 The final price of the circular topology structure for: ; In the formula, The outer radius of the coil, The inner radius of the coil, The number of coil turns. For the core thickness, Additional coverage for the magnetic core; Square topology price for: ; After calculating the specific values of each optimization objective of the above solutions, the final solution set is obtained. A Solution set A Each solution should be a non-inferior solution after comprehensive consideration, and will serve as the initial input for subsequent LINMAP multi-attribute decision-making.
[0034] During the optimization process, the following settings are provided: There are optimization objectives and solution sets. One solution, The solution is in The optimization objectives are normalized and all are unified into positive indicators. Since different indicators have different properties, the normalization methods differ slightly. Efficiency and output power are positive indicators, and the Max-Min linear normalization formula is used as follows: ; For price and offset efficiency loss rate, which are negative indicators, the normalization formula is: ; In the formula, For the first The first scheme is in the The original evaluation values under each optimization objective For all schemes in the first The maximum value under each optimization objective For all schemes in the first Minimum value under each optimization objective This is the normalized evaluation value. Optimization objectives include at least transmission efficiency, offset resistance, manufacturing cost, and output power.
[0035] Construct the initial evaluation matrix R=(r ij ) n×m ,in r ij Representation scheme In the j The evaluation values under each optimization objective are normalized according to the above formula, and the normalized matrix is shown in Table 2.
[0036] Table 2: Normalized Matrix Results
[0037] Based on expert experience or engineering practice, provide a set of ordered preference pairs for pairwise comparisons of solutions. Preference pairs do not need to be numerous; only groups with significant differences are required, but they should not be directly conflicting. Preference pairs should be selected from candidate solutions that are not mutually dominant, prioritizing combinations of solutions with significant differences on a few evaluation indicators and minor differences on others. This reduces confusion caused by simultaneous changes in different evaluation indicators and improves the identifiability of indicator weights. Absolutely dominant preferences should be prohibited. The most important weight will vary depending on the purpose of the coil optimization. For example, efficiency is paramount in electric vehicle scenarios, losses are paramount in confined space scenarios (excessive losses may lead to severe overheating), cost is paramount for mass-produced consumer products, and anti-displacement capability may be paramount for wireless charging of mobile phones. In this example, the selected preference pair is A. 15 Better than A 22 A 14 Better than A 24 A 15 Better than A 24 Then, assuming the existence of an ideal positive solution, in this embodiment, the ideal optimal solution is directly set as... Assuming the weighting index is Then each scheme With the ideal optimal solution X The weighted squared Euclidean distance is expressed as: ; In the formula, For the first The weighted squared Euclidean distance between each solution and the ideal solution. For the first The first scheme is in the Normalized evaluation value under each optimization objective For the ideal correct solution, in the first... The ideal solution is set as a vector of all 1s where each normalized index takes the maximum value under the optimization objective.
[0038] Therefore, based on the previous preference ranking of the options... Obtain the consistency index of the comparison relationship Inconsistency indicators For example, believing the solution Superior Solution Then, the inconsistency index is: ; Consistency Indicators: ; Based on the above indicators, the optimization model of the LINMAP method with L2 regularization is obtained. Its constraints are: ; In the formula, For the plan and plan Comparison of ordered preferences for sets For the first The weighted squared Euclidean distance between each solution and the ideal solution. This is the consistency threshold. The goal of setting lower limits for the weights of each optimization objective is to ensure that each weight is greater than 0. Through the steps described above, we can calculate the final weights using the formula... We can obtain the weighted squared Euclidean distance of each solution from the ideal solution. To prevent extreme cases of certain weights in LINMAP, i.e., to make the final weights obtained by LINMAP more uniform, L2 regularization is introduced. Its core element is to introduce a penalty term into the function, usually the L2 norm of the weight parameters. In this embodiment, it is taken as the sum of the squares of each weight, i.e. Then the optimization objective function with L2 regularization is: ; In the formula, This is the preference weight; the larger the value, the more preferentially the optimization process considers the results of the LINMAP method itself. In this embodiment, it is set to 0.5. The regularization strength is 0.9; a larger value results in a more even weight distribution, thus achieving a more balanced weight allocation. In this embodiment, it is set to 0.9. In addition, since the subjective optimization objectives of wireless charging engineering vary across different scenarios, a subjective weight coefficient is added to the engineering process. This can be done by referring to the idea of the AHP method, assigning a subjective importance coefficient to all optimization objectives for ranking. To reflect subjective preferences or expert opinions, this coefficient is multiplied in the distance contribution of each indicator in the Euclidean distance calculation process to obtain a more subjective weight value. In this example, the subjective preference ranking added is [4,2,1,2], which are efficiency, offset efficiency loss rate, price, and output power, respectively. The weighted squared Euclidean distance after introducing these factors is as follows: ; In the formula, For the first The importance coefficient of subjective preferences for each optimization objective. Furthermore, since normalization has normalized all indices to positive indices, the ideal solution is directly set to all 1s. The final optimization model and constraints of the L2-LINMAP method are as follows: ; ; In the formula, The index weights are obtained by the algorithm. In this embodiment... Set it to 0.05. Taking a value of 0.5, after solving the problem, the optimized weights and importance coefficients are multiplied element-wise again, and the product is then normalized to obtain the final comprehensive weights. The final weights are [0.4728, 0.1345, 0.1110, 0.2816], and the optimal solution is A. 25 .
[0039] After determining the optimal discrete variables, the continuous variables are optimized based on them. In this example, there are four continuous variables: the outer radius of the coil, the inner radius of the coil, the transmission air gap spacing, and the additional coverage of the magnetic core.
[0040] The optimization process for the lower-level continuous variables remains consistent with that for the upper-level discrete variables, but the selection strategy for the basic solutions differs. From the perspective of the number of variables, if the lower-level continuous variables also use the same discrete value selection method as the upper-level discrete variables, the number of solution combinations will increase exponentially, resulting in a huge waste of computational resources. Therefore, the lower-level optimization uses the Taguchi method to construct a five-level orthogonal array, as shown in Table 3, to select representative basic solutions, thereby significantly reducing computational overhead while ensuring optimization effectiveness.
[0041] Table 3: Parameter Settings for the Five-Level Orthogonal Array
[0042] The specific values for the orthogonal experiment are shown in Table 4.
[0043] Table 4: Orthogonal Experiment Parameter Settings
[0044] The normalized matrix is shown in Table 5.
[0045] Table 5: Normalized matrix results
[0046] The selected preference pairs were 23 better than 16, 20 better than 23, 23 better than 9, 20 better than 21, and 16 better than 13. The subjective preference ranking remained [4, 2, 1, 2]. The final optimization result was scheme 20, with a comprehensive weight index of [0.4875, 0.2318, 0.0540, 0.2268]. The final selected optimal scheme had an efficiency of 97.95% and an output power of 9789W, which, under the same simulation conditions, was significantly better than the previous 97.73% and 1558W.
[0047] It should be noted that the various ranges given in the topology of this embodiment do not represent the maximum range that this optimization method can optimize. The various optimization variables and optimization objectives given do not represent all variables and objectives that this optimization method can optimize. The given preference order does not represent all preference orderings that can be optimized. They are only used to illustrate the specific working method of topology optimization in this embodiment. In fact, they can be arbitrarily selected according to the actual wireless charging working scenario and ordered arbitrarily according to subjective preferences. The selection of preference pairs does not mean that the preference pair must be selected. You can choose according to your needs.
[0048] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A multi-objective optimization method for wireless charging coils based on improved LINMAP, characterized in that, Includes the following steps: S1. Obtain the basic design structure of the wireless charging coil and determine multiple optimization objectives and multiple optimization variables; S2. Deconstruct and hierarchically divide the optimization variables into upper-level discrete variables and lower-level continuous variables, and reduce the solution space by using a hierarchical solution method. S3. Construct a basic solution set for the upper-level discrete variables, and obtain the optimization objective parameter values for each scheme through simulation calculation; S4. Normalize the optimization target parameter values of all schemes, and convert positive and negative indicators into positive evaluation indicators to construct an initial evaluation matrix. S5. Based on the application scenario, set the importance of subjective preferences for optimization objectives, construct an ordered set of preference pairs for pairwise comparison of solutions, and set regularization parameters, weight lower bound parameters, and consistency threshold parameters. S6. The improved LINMAP method, which introduces L2 regularization and subjective preference weights, is used to solve the initial evaluation matrix to obtain the comprehensive weights of each optimization objective and to select the optimal solution that is closest to the ideal solution. S7. Based on the optimal solution of the upper-level discrete variables, the same improved LINMAP method is used to optimize the lower-level continuous variables to obtain the comprehensive optimal combination of wireless charging coil topology parameters.
2. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 1, characterized in that: The upper-level discrete variables include coil shape and number of turns in the winding; The lower-level continuous variables include the outer radius of the coil, the inner radius of the coil, the additional coverage of the magnetic core, and the transmission air gap spacing.
3. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 1, characterized in that: For the upper-level discrete variables, an enumeration method is used to construct all design combinations as the basic solution set; for the lower-level continuous variables, the Taguchi method or uniform design method is used to construct experimental schemes, and representative solutions are selected to form the basic solution set; when the number of basic solution schemes exceeds the preset number of basic solution sets, non-dominated sorting is performed on the basic solution set, the Pareto optimal solution set is extracted as the input for the subsequent LINMAP method, and dominated inferior solutions are eliminated to reduce the computational load.
4. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 1, characterized in that: In S4, the index is normalized using the Max-Min linear normalization method, specifically as follows: For positive metrics such as transmission efficiency and output power, a positive normalization formula is used: ； For negative indicators such as manufacturing cost and offset efficiency loss rate, an inverse normalization formula is used: ； In the formula, For the first The first scheme is in the The original evaluation values under each optimization objective For all schemes in the first The maximum value under each optimization objective For all schemes in the first Minimum value under each optimization objective This is the normalized evaluation value.
5. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 1, characterized in that: The optimization objectives include transmission efficiency, offset resistance, manufacturing cost, and output power; among which offset resistance is quantified using the offset efficiency loss rate. The calculation formula is: ； In the formula, The transmission efficiency before coil offset, This represents the transmission efficiency after the coil is offset.
6. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 4, characterized in that: In S6, a weighted squared Euclidean distance is used to measure the difference between each solution and the ideal solution. A subjective preference weight coefficient is introduced into the distance calculation. The specific calculation formula is as follows: ； In the formula, For the first The weighted squared Euclidean distance between each solution and the ideal solution. To optimize the number of targets, For the first An algorithm for solving weights with an optimization objective. For the first The importance coefficient of subjective preferences for each optimization objective. For the ideal correct solution, in the first... The ideal solution is set as a vector of all 1s where each normalized index takes the maximum value under the optimization objective.
7. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 6, characterized in that: In S6, consistency and inconsistency indices are constructed based on the set of alternative preferences. An improved LINMAP linear programming objective function is then constructed by combining this with an L2 regularization penalty term. Specifically: Inconsistent Indicators for: ； Consistency Indicators for: ； The objective function of the optimization model with L2 regularization is: ； In the formula, For the plan and plan Comparison of ordered preferences for sets For the first The weighted squared Euclidean distance between each solution and the ideal solution. For preference weights, , The regularization intensity coefficient is . , This is the L2 regularization penalty term, which is the sum of squares of the weights of each optimization objective.
8. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 7, characterized in that: The constraints for the optimization model with L2 regularization are: ； In the formula, This is the consistency threshold. These are the lower limits for the weights of each optimization objective; After obtaining the initial weights, a second normalization is performed by combining the subjective preference weight coefficients to obtain the final comprehensive weights.
9. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 1, characterized in that: In S7, the optimization reuse of the normalization processing, parameter setting and improved LINMAP solution process of the upper layer is used to optimize the continuous variables of the lower layer. Under the premise of fixing the optimal discrete parameters of the upper layer, orthogonal experimental design and optimization solution are carried out on the dimension of continuous variables to obtain the comprehensive optimal combination of coil topology parameters.
10. The multi-objective optimization method for wireless charging coils based on improved LINMAP according to claim 1, characterized in that: In S3, the self-inductance and mutual inductance parameters of each coil topology are obtained through finite element simulation. The self-inductance and mutual inductance parameters are then substituted into the wireless charging system circuit model to calculate the transmission efficiency and output power optimization target parameter values corresponding to each scheme.