Multi-objective optimization method and system for electrode array parameters of non-invasive voltage sensor

Abstract

The present invention relates to a multi-objective optimization method and system for electrode array parameters of a non-invasive voltage sensor, and belongs to the technical field of electrode array parameter optimization. The total amount of array induced charge, the first distance sensitivity, and the second distance sensitivity are selected as evaluation indicators, and the shape parameters of the electrode array are optimized through simulation experiments to determine the optimal array shape and the optimal electrode shape. Then, a multi-objective optimization model is established, and the multi-objective optimization model is optimized and solved using a multi-objective genetic algorithm to obtain an optimal solution to optimize the structural parameters of the electrode array and determine the optimal number of electrodes, single electrode area, and single electrode thickness. Therefore, the present invention can optimize the array shape of the electrode array and the number of electrodes, electrode shape, single electrode area, and single electrode thickness in the electrode array, thereby improving the array measurement performance and reducing the design cost at the same time.

Description

Technical Field

[0001] The present invention relates to the technical field of electrode array parameter optimization, and in particular to a multi-objective optimization method and system for electrode array parameters of a non-invasive voltage sensor. Background Art

[0002] Sensing and measurement technology, as the basic technology for obtaining real-time information on the power grid, is a prerequisite for realizing smart grids. Among them, voltage measurement is a key link in the operation of the power system and has a significant impact on energy metering, automation equipment, etc. Non-invasive voltage measurement has gradually been widely used due to its high safety, no need to damage the cable insulation layer, and easy installation.

[0003] Non-invasive voltage measurement methods primarily rely on placing sensing electrodes around the cable under test and indirectly measuring the electric field strength using the induced charge on the sensing electrodes, thereby measuring the cable voltage. Prior art non-contact voltage measurement devices employ a metal plate between the cable under test and a virtual ground to achieve non-contact measurement. However, these devices employ a single-electrode design. While this design is convenient for installation and testing, it cannot fully describe the spatial distribution of the electric field, which can affect the accuracy of voltage measurement. To overcome the drawbacks of a single electrode, researchers often employ electrode array designs that combine multiple electrodes, such as dual-electrode, multi-electrode, and interleaved-electrode designs. Non-invasive voltage sensors employing electrode arrays distribute electrodes around the cable under test. Compared to single electrodes, these sensors effectively improve the acquisition of electric field information around the cable, enhancing measurement accuracy and stability. However, optimization of the electrode array itself is not considered. Variations in the electrode array parameters in non-invasive voltage sensors can affect array measurement performance and design cost. Optimizing electrode array parameters to improve array measurement performance while reducing design cost is an urgent problem that needs to be addressed. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-objective optimization method and system for electrode array parameters of a non-invasive voltage sensor, which optimizes the array shape of the electrode array as well as the number of electrodes, electrode shape, single electrode area and single electrode thickness in the electrode array, thereby improving the array measurement performance and reducing the design cost at the same time.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A multi-objective optimization method for non-invasive voltage sensor electrode array parameters, the multi-objective optimization method comprising:

[0007] The total amount of array induced charge, the first distance sensitivity, and the second distance sensitivity are selected as evaluation indicators, and the optimal array shape of the electrode array of the non-invasive voltage sensor and the optimal electrode shape of a single electrode in the electrode array are determined through simulation experiments;

[0008] Establishing a multi-objective optimization model; the multi-objective optimization model includes a total charge objective function, a design cost objective function, upper and lower limit constraints on the number of electrodes in the electrode array, upper and lower limit constraints on the area of ​​a single electrode in the electrode array, and upper and lower limit constraints on the thickness of a single electrode in the electrode array;

[0009] The multi-objective optimization model is optimized and solved using a multi-objective genetic algorithm to obtain multiple optimization schemes, and one optimization scheme is selected from the multiple optimization schemes as the optimal scheme; the optimization scheme includes the respective values ​​of the number of electrodes, the area of ​​the single electrode, and the thickness of the single electrode.

[0010] A non-invasive voltage sensor electrode array parameter multi-objective optimization system, the multi-objective optimization system comprising:

[0011] a shape optimization module, configured to select the total amount of array induced charge, the first distance sensitivity, and the second distance sensitivity as evaluation indicators, and determine, through simulation experiments, the optimal array shape of the electrode array of the non-invasive voltage sensor and the optimal electrode shape of a single electrode in the electrode array;

[0012] A model building module for establishing a multi-objective optimization model; the multi-objective optimization model includes a total charge objective function, a design cost objective function, upper and lower limit constraints on the number of electrodes in the electrode array, upper and lower limit constraints on the area of ​​a single electrode in the electrode array, and upper and lower limit constraints on the thickness of a single electrode in the electrode array;

[0013] A structural parameter optimization module is used to optimize and solve the multi-objective optimization model using a multi-objective genetic algorithm to obtain multiple optimization schemes, and select one of the multiple optimization schemes as the optimal scheme; the optimization scheme includes the respective values ​​of the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode.

[0014] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0015] The present invention provides a multi-objective optimization method and system for electrode array parameters in a non-invasive voltage sensor. The method selects the total amount of array induced charge, first distance sensitivity, and second distance sensitivity as evaluation indicators. Through simulation experiments, the shape parameters of the electrode array are optimized to determine the optimal array shape and electrode shape. A multi-objective optimization model is then established and solved using a multi-objective genetic algorithm to obtain an optimal solution. This solution is then used to optimize the structural parameters of the electrode array and determine the optimal number of electrodes, individual electrode area, and individual electrode thickness. This method optimizes the array shape, number of electrodes, electrode shape, individual electrode area, and individual electrode thickness within the electrode array, improving array measurement performance while reducing design costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0017] Figure 1 A schematic structural diagram of an optional non-invasive voltage sensor provided in Example 1 of the present invention;

[0018] Figure 2 This is a principle block diagram of the multi-objective optimization method provided in Example 1 of the present invention;

[0019] Figure 3 A flowchart of the multi-objective optimization method provided in Example 1 of the present invention;

[0020] Figure 4 A schematic diagram of an optional array shape provided in Example 1 of the present invention;

[0021] Figure 5 A schematic diagram of structural parameters of the electrode array provided in Example 1 of the present invention;

[0022] Figure 6 Schematic diagram of the optimization process of the NSGA-II algorithm provided in Example 1 of the present invention;

[0023] Figure 7 A schematic diagram showing the comparison of evaluation indicators provided in Example 1 of the present invention;

[0024] Figure 8 A schematic diagram of the Pareto optimal solution set results provided by Example 1 of the present invention;

[0025] Figure 9This is a schematic diagram of the VIKOR decision result provided in Example 1 of the present invention;

[0026] Figure 10 This is a system block diagram of the multi-objective optimization system provided in Example 2 of the present invention.

[0027] Explanation of symbols:

[0028] 110 - cable to be tested; 120 - current transformer; 130 - electrode array; 140 - sensing electrode; 150 - fixing member; 160 - sensing area. DETAILED DESCRIPTION

[0029] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0030] The purpose of the present invention is to provide a multi-objective optimization method and system for electrode array parameters of a non-invasive voltage sensor, which optimizes the array shape of the electrode array as well as the number of electrodes, electrode shape, single electrode area and single electrode thickness in the electrode array, thereby improving the array measurement performance and reducing the design cost at the same time.

[0031] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] Example 1:

[0033] Here, this embodiment first illustrates the necessity of optimizing the electrode array parameters in this embodiment through the structure of a specific non-invasive voltage sensor. However, it should be noted that the structure of the non-invasive voltage sensor here is only an example, and the multi-objective optimization method of this embodiment can be applied to any non-invasive voltage sensor.

[0034] like Figure 1, which is a schematic diagram of the structure of an optional non-invasive voltage sensor, composed of a current transformer 120 and an electrode array 130. The current transformer 120 measures the cable current, and the electrode array 130 measures the cable voltage. The electrode array 130 is composed of several sensing electrodes 140, a fixture 150, and a sensing area 160. The sensing electrodes 140 are embedded in the center of the fixture 150 and evenly arranged around the sensing area 160. They induce and collect charge in the electric field around the cable. The fixture 150 is used to fix the sensing electrodes 140. The sensing area 160 is located in the center of the fixture 150 and serves as the test area for the cable 110 to be tested. During the measurement process, the cable 110 under test passes through the sensing area 160 of the electrode array 130. Inductive charges are generated on the sensing electrodes 140. These charges change over time, generating induced currents. The induced currents pass through the sampling resistors, generating induced voltages. This induced voltage is collected by a data acquisition system, and the collected voltage data is post-processed to obtain the cable voltage signal, enabling non-invasive voltage measurement of energized cables. However, variations in the parameters of the electrode array 130 in the non-invasive voltage sensor, such as the array shape, electrode shape, number of electrodes, individual electrode area, and individual electrode thickness, can affect the array's measurement performance and design cost, necessitating optimization of these parameters.

[0035] like Figure 2 As shown, to optimize electrode array parameters, this embodiment provides a multi-objective optimization method for electrode array parameters. The method first determines the array arrangement. Based on array performance evaluation indicators, simulation analysis is performed on the electrode and array shapes to determine the optimal array arrangement and improve the overall performance of the array. Simulation experiments are then conducted using three electrode array structural parameters: the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode. An experimental dataset is established to compare the relationship between the changes in different electrode array structural parameters and the total amount of array induced charge Q. Based on the experimental dataset, a regression model is constructed to determine the total amount of array induced charge and the electrode array structural parameters. The number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode are used as decision variables, and their constraints are determined based on actual engineering requirements. A multi-objective optimization model is established with the optimization objectives of maximizing the total amount of array induced charge and minimizing the design cost. A multi-objective genetic algorithm is then used to optimize and solve the multi-objective optimization model. A compromise ranking method is then used to determine the optimal solution from multiple optimization schemes. The optimized array parameters significantly improve the total amount of array induced charge while significantly reducing the design cost.

[0036] To achieve the above objectives, this embodiment is used to provide a multi-objective optimization method for non-invasive voltage sensor electrode array parameters, such as Figure 3 As shown, the multi-objective optimization method includes:

[0037] S1: selecting the total amount of array induced charge, the first distance sensitivity, and the second distance sensitivity as evaluation indicators, and determining the optimal array shape of the electrode array of the non-invasive voltage sensor and the optimal electrode shape of a single electrode in the electrode array through simulation experiments;

[0038] During the optimization process of shape parameters (array shape and electrode shape), it is necessary to determine array performance evaluation indicators that can evaluate the overall quality of the electrode array.

[0039] During the measurement process of the non-invasive voltage sensor, the total amount of array induced charge sensed by the electrode array is closely related to the final measurement result. The total amount of array induced charge can reflect the measurement performance of the electrode array and the change in the cable voltage of the cable to be tested. The greater the cable voltage, the greater the total amount of array induced charge. Therefore, this embodiment uses the total amount of array induced charge Q as an evaluation indicator. The calculation formula for the total amount of array induced charge is:

[0040]

[0041] In formula (1), Q is the total amount of induced charge in the array, the larger the value, the better; n is the number of electrodes in the electrode array, i = 1, 2, ..., n; m is the number of spatial positions of the cable to be tested in the measurement area composed of the electrode array, j = 1, 2, ..., m; q ij is the induced charge of the i-th electrode at the j-th spatial position;

[0042] Changes in the relative distance between the cable under test and the electrode directly lead to changes in the charge on the electrode surface, which in turn causes changes in the measured voltage. Therefore, it is necessary to select an indicator that can effectively reflect changes in the relative distance between the cable under test and the electrode. Based on this, this embodiment introduces first distance sensitivity S1 and second distance sensitivity S2 as evaluation indicators. The first distance sensitivity S1 describes the change in charge at the current spatial position of the cable under test relative to its previous spatial position, and is used to evaluate the impact of electrode shape on array performance. The second distance sensitivity S2 describes the change in charge at the current spatial position of the cable under test relative to the center of the sensing area, and is used to evaluate the impact of array shape on array performance.

[0043] The calculation formula for the first distance sensitivity is:

[0044]

[0045] In formula (2), S1 is the first distance sensitivity, the larger the value, the better; Q j Q is the total amount of induced charge of the cable under test at the jth spatial position, which is equal to the sum of the induced charges of all electrodes when the cable under test is at the jth spatial position; j-1is the total amount of induced charge of the cable under test at the j-1th spatial position;

[0046] The calculation formula for the second distance sensitivity is:

[0047]

[0048] In formula (3), S2 is the second distance sensitivity, and the larger the value, the better; Q0 is the total amount of induced charge of the cable under test at the center point of the measurement area composed of the electrode array.

[0049] This embodiment uses the three evaluation indicators above to optimize the shape parameters of the electrode array and determine the optimal arrangement of the array. Specifically, the optimal shape parameters and the optimal arrangement of the array are determined by comparing the evaluation indicators under different arrangements. The optimal arrangement of the array means that the electrode array adopts the optimal array shape, and each electrode in the electrode array adopts the optimal electrode shape.

[0050] The process of determining the optimal array arrangement, i.e., S1, may include:

[0051] (1) Setting the electrode and the cable to be tested in the simulation software, changing the electrode shape, obtaining the induced charge of the electrode under each electrode shape, and calculating the first distance sensitivity based on the induced charge, and determining the optimal electrode shape based on the induced charge and the first distance sensitivity;

[0052] The simulation software of this embodiment can be any finite element analysis software for simulation testing, such as Ansys Electronics. In this simulation software, a cable to be tested is first set up with alternating current flowing through it. An induced electric field is generated around it. Electrodes (metal electrodes) are placed in this induced electric field, and induced charges are generated on the electrode surface. The induced charge q of a single electrode is calculated as follows:

[0053]

[0054] In formula (4), A0 is the surface area of ​​a single electrode; ε0 is the dielectric constant of vacuum; and E0 is the electric field strength in the space where the electrodes are placed.

[0055] Through the above formula (4), this embodiment can calculate the induced charge of a single electrode in the simulation software, and can further use formulas (1) to (3) to calculate three evaluation indicators. Subsequently, the induced charge q of a single electrode, the total induced charge Q of the array, the first distance sensitivity S1, and the second distance sensitivity S2 are used as judgment criteria to optimize the electrode shape and the array shape, and determine the optimal electrode shape and the optimal array shape.

[0056] When determining the optimal electrode shape for a single electrode, use simulation software to design single electrodes of various shapes, such as square and circular. Maintain a constant electrode thickness and a constant relative position between the electrode and the cable under test. For example, the electrode plane can be placed parallel to the cable under test. Compare the induced charge q and distance sensitivity S1 of various electrode shapes with different electrode areas. After comprehensive comparison, select the electrode shape with the largest q and S1 as the optimal electrode shape.

[0057] (2) An electrode array and a cable to be tested are set in the simulation software. The electrode array includes a plurality of electrodes, and the electrode shape of the electrodes adopts the optimal electrode shape determined above. The array shape of the electrode array is changed to obtain the induced charge of each electrode under each array shape, and the total induced charge of the array, the first distance sensitivity, and the second distance sensitivity are calculated based on the induced charge of each electrode to determine the optimal array shape of the electrode array.

[0058] The arrangement shape of the electrode array in space (i.e., array shape) has a significant impact on the overall performance of the array. Based on the determination of the optimal electrode shape of a single electrode, different array shapes are designed, such as square, side-by-side, ring, etc. Figure 4 As shown in the figure, this is an optional ring array, in which the electrode shape of a single electrode is square. Through simulation analysis of the Q, S1, and S2 values ​​under different array shapes, after comprehensive comparison, the array shape with the best Q, S1, and S2 is selected as the optimal array shape.

[0059] This embodiment mainly determines the optimal arrangement of the electrode array. First, the optimal electrode shape of a single electrode is determined. Based on the determination of the optimal electrode shape of the single electrode, the optimal array shape of the array is determined, thereby determining the optimal arrangement of the electrode array.

[0060] S2: Establishing a multi-objective optimization model; the multi-objective optimization model includes a total charge objective function, a design cost objective function, upper and lower limit constraints on the number of electrodes in the electrode array, upper and lower limit constraints on the area of ​​a single electrode in the electrode array, and upper and lower limit constraints on the thickness of a single electrode in the electrode array;

[0061] After optimizing the shape parameters of the electrode array using S1, this embodiment further optimizes the structural parameters of the electrode array, such as Figure 5 As shown, it is a schematic diagram of the structural parameters of the electrode array. Figure 5 It is an optional ring-shaped array, and its structural parameters mainly include the number of electrodes A, the area of ​​a single electrode B and the thickness of a single electrode C.

[0062] In this embodiment, the total charge objective function can be constructed based on the optimal array arrangement determined by S1, and the construction method is:

[0063] (1) Based on the optimal array shape and the optimal electrode shape, simulation experiments were conducted to determine the total amount of array induced charge corresponding to various structural parameters, and obtain an experimental data set; the structural parameters include the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode;

[0064] After determining the optimal array arrangement, simulation experiments were conducted to establish a test data set for the structural parameters and the total array induced charge Q. Specifically, the electrode array and the cable to be tested were set up in the simulation software. The electrode array was arranged in the optimal arrangement, and the values ​​of the structural parameters of the electrode array were varied. The total array induced charge corresponding to each value of the structural parameters was obtained to establish the test data set. During the simulation process, the area of ​​a single electrode can be varied by changing the electrode length L.

[0065] (2) Perform regression analysis on the experimental data set and construct a multivariate linear regression model between the structural parameters and the total amount of induced charge of the array;

[0066] The total amount of array induced charge directly determines the size of the induced voltage, and the total amount of array induced charge can reflect the measurement performance of the electrode array. Therefore, the total amount of array induced charge Q is selected as the charge evaluation index. The simulation test of the array structural parameters and the total amount of array induced charge Q is designed, and a multiple linear regression model of the structural parameters and the total amount of array induced charge Q is constructed. The multiple linear regression model is as follows:

[0067] Q=ω0+W T X; (5)

[0068] In formula (5), ω0 is the intercept; W = [w1,…,w n ] is the regression coefficient matrix, w n is the regression coefficient of the nth structural parameter; X=[x1,…,x n ] is an input variable consisting of structural parameters, and n is the number of structural parameters; the structural parameters include the number of electrodes, the area of ​​a single electrode and the thickness of a single electrode.

[0069] In the specific calculation and analysis process, this embodiment can use the least squares method to quickly obtain the estimated value of each regression coefficient in the regression coefficient matrix. The matrix method solution of the least squares method is as follows:

[0070] W=(X T X) -1 X T Y; (6)

[0071] In formula (6), Y is the target value, that is, the total amount of array induced charge Q in the test data set.

[0072] During the construction of the multiple linear regression model, this embodiment will first clean up the abnormal data of the test data set of input variables and target values, including filling in missing values ​​and removing excessively large and small values. The test data set will then be divided into a training set and a test set. Finally, data modeling is performed, that is, the linear regression model of machine learning is constructed to obtain a multiple linear regression model.

[0073] This embodiment can also test the constructed multiple linear regression model to see whether the prediction accuracy of the multiple linear regression model meets the requirements. Specifically, the prediction accuracy of the multiple linear regression model is expressed as the residual error e. r (Residual Error, RE) and average error e a (Average Error, AE) for quantitative evaluation, residual e r and the average error e a The calculation formula is as follows:

[0074] e r =y i -y real ; (7)

[0075] In formula (7), y i is the predicted value of the target value, y real is the actual value of the target value.

[0076]

[0077] In formula (8), e ri is the residual of the i-th data group; y reali is the actual value of the target value of the i-th data group; n is the number of data groups; a data group consists of structural parameters and their corresponding total array induced charge (target value).

[0078] (3) Negate the multivariate linear regression model to obtain the total charge objective function.

[0079] Changes in the structural parameters of the electrode array are directly reflected in changes in the total amount of induced charge in the array. Therefore, this embodiment selects the total amount of induced charge in the array as an optimization objective. Furthermore, for the electrode array, the larger the total amount of induced charge Q, the better. However, in the process of solving the problem using a multi-objective genetic algorithm, the smaller the objective function, the better. To achieve the goal of a smaller objective function, this embodiment negates the multivariate linear regression model of Equation (5) to obtain the total charge objective function.

[0080] The total charge objective function is:

[0081] F1=-(ω0+W T X); (9)

[0082] In formula (9), F1 is the target value of the total charge; ω0 is the intercept; W is the regression coefficient matrix; and X is the structural parameter.

[0083] Preferably, in order to improve the prediction accuracy of the total amount of array induced charge, the present embodiment expands the structural parameters, and the structural parameters at this time also include the product of the number of electrodes and the area of ​​a single electrode, the product of the number of electrodes and the thickness of a single electrode, and the product of the area of ​​a single electrode and the thickness of a single electrode.

[0084] To process the electrode signal, a post-processing circuit needs to be added to each electrode in the electrode array, so the electrode cost needs to be considered. The cost consists of 0.7 yuan / element for components and 500 yuan / m for materials. 2 , thickness processing fee is 1000 yuan / m·piece, other process fees are 1 yuan / piece, so this embodiment constructs the design cost target function, the design cost target function is:

[0085] F2=1.7A+500A×B+1000A×C; (10)

[0086] In formula (10), F2 is the design cost target value; A is the number of electrodes; B is the area of ​​a single electrode; and C is the thickness of a single electrode.

[0087] Based on the above two objective functions, this embodiment establishes a multi-objective optimization model with the optimization goals of maximizing the total amount of array induced charge and minimizing the design cost:

[0088]

[0089] In the actual optimization process, it is also necessary to constrain the upper and lower limits of the design variables according to the actual situation. The multi-objective optimization model of this embodiment includes the following three constraints:

[0090] (1) Upper and lower limit constraints on the number of electrodes:

[0091] The contactless voltage sensor uses an electrode array for measurement. The electrode array requires at least two electrodes. However, the installation space for the electrode array is limited, which imposes an upper limit on the number of electrodes. The specific constraints are as follows:

[0092] LB a <A<UB a ,A∈N; (12)

[0093] In formula (12), LB a UB is the lower limit of the number of electrodes in the electrode array, which can be determined according to actual needs. In this embodiment, it is set to 2; a The upper limit of the number of electrodes in the electrode array can be determined according to actual needs. In this embodiment, it is set to 8.

[0094] (2) Upper and lower limit constraints of a single electrode area:

[0095] Post-processing circuits need to be placed on the electrodes, and a certain amount of space is required for the welding of components. Therefore, the area of ​​a single electrode should not be too small. At the same time, a single electrode area that is too large will affect the installation. The specific constraints are as follows:

[0096] LB b ≤B≤UB b ,B∈1×10 -5 N; (13)

[0097] In formula (13), LB b The lower limit of the area of ​​a single electrode can be determined according to actual needs. In this embodiment, it is set to 4×10 -4 m 2 UB b The upper limit of the area of ​​a single electrode can be determined according to actual needs. In this embodiment, it is set to 1×10 -3 m 2 .

[0098] (3) Upper and lower limit constraints of the thickness of a single electrode:

[0099] The electrodes in the electrode array are subject to thickness constraints. Due to manufacturing process limitations, there is a minimum limit on the thickness of copper electrodes. The specific constraints are as follows:

[0100] LB c <C<UB c ,C∈1×10 -4 N; (14)

[0101] In formula (14), LB c The lower limit of the thickness of a single electrode can be determined according to actual needs. In this embodiment, it is set to 1×10 -4 m;UB c The upper limit of the thickness of a single electrode can be determined according to actual needs. In this embodiment, it is set to 8×10 - 4 m.

[0102] S3: Optimize and solve the multi-objective optimization model using a multi-objective genetic algorithm to obtain multiple optimization schemes, and select one of the multiple optimization schemes as the optimal scheme; the optimization scheme includes the respective values ​​of the number of electrodes, the area of ​​the single electrode, and the thickness of the single electrode.

[0103] In this embodiment, any multi-objective genetic algorithm can be used to optimize and solve the multi-objective optimization model established by S2. Here, this embodiment takes the NSGA-Ⅱ algorithm as an example to introduce the solution process of the multi-objective optimization model:

[0104] like Figure 6 As shown, the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode are first encoded in integer coding, the initial population is established, the decision variables are constrained, and the number of individuals N in the appropriate initial population and the crossover rate P are selected. C , mutation rate P M and the number of iterations M. The algorithm's fast non-dominated sorting method rapidly stratifies the population, obtaining the number of non-dominated layers of individuals within the population and bringing superior individuals closer to the Pareto front. Crowding is calculated as the local crowding distance between each point in the target space and two adjacent points on the same layer, which helps maintain individual diversity. Selection prevents the loss of effective genes and filters out ineffective individuals, aligning the optimization process toward a Pareto front solution. Alternating crossover and mutation operations help improve the algorithm's search performance. An elite strategy retains superior individuals from the parent generation and directly transfers them to the offspring. The population formed by recombining parent and offspring individuals is then screened again based on individual fitness to form a population for the next generation of evolution, ultimately yielding a Pareto solution set for the electrode structure parameters. The multi-objective optimization model is solved using the NSGA-II algorithm, an intelligent optimization algorithm, to obtain a series of optimization solutions.

[0105] This embodiment can select an optimization scheme from multiple optimization schemes as the optimal scheme based on actual needs. In order to select the most appropriate optimization scheme from the Pareto solution set of electrode structure parameters, this embodiment adopts the VIKOR method for decision-making. The VIKOR method is a multi-attribute compromise sorting method. By determining positive and negative ideal solutions, calculating the distance between each optimization scheme and the ideal solution and sorting them, a compromise solution is obtained. That is, this embodiment uses the VIKOR method to select an optimization scheme as the optimal scheme from multiple optimization schemes. The specific steps are as follows:

[0106] (1) Determine the corresponding positive ideal solution (y + ) and the negative ideal solution (y - ), the calculation formula is as follows:

[0107]

[0108] In formula (15), m represents the number of optimization schemes; n represents the number of optimization targets. In this embodiment, there are two optimization targets, so n is 2; y m (j) is the target value of the jth optimization objective of the mth optimization solution.

[0109] (2) Obtain the weight w of each optimization objective through the independence weight method j .

[0110] First, the original evaluation index matrix is ​​transformed into a dimensionless non-negative standard matrix R = (r ij ) m×n .

[0111]

[0112] In formula (16), row number i represents the i-th optimization solution, column number j represents the j-th optimization goal, and r ij The target value of the jth optimization objective of the i-th optimization solution is the normalized value.

[0113] The electrode array evaluation index r of the jth optimization target j The complex correlation coefficient R (that is, the vector matrix composed of the j-th column elements of the standard matrix R) j The calculation formula is:

[0114]

[0115] In formula (17), is the average value of the standard matrix R, Remove r from the standard matrix R j The remaining matrix after .

[0116] Since R j There is an inverse relationship between and weight, so the complex correlation coefficient R j The reciprocal of can be normalized to obtain the weight of each optimization objective. The weight calculation formula is:

[0117]

[0118] In formula (18), wj is the weight of the j-th optimization objective.

[0119] (3) Calculate the maximum group benefit S of each optimization scheme i and the minimum individual regret value R i .

[0120]

[0121] In formula (19), y + (j) is the positive ideal solution of the j-th optimization objective; y - (j) is the negative ideal solution of the j-th optimization objective. S i The smaller it is, the higher the group benefit of the optimization plan is, and vice versa.

[0122]

[0123] In formula (20), R iThe smaller it is, the lower the individual regret value of the optimization scheme is, and vice versa.

[0124] (4) Calculate the comprehensive evaluation value Q of the benefits of each optimization scheme i .

[0125]

[0126] In formula (21), v is the decision-making mechanism coefficient, v = 0.5, which means choosing a solution in the balance between group benefit and individual regret. i Sort and optimize by size, Q i The smaller it is, the higher the comprehensive benefit of the optimization scheme is. Therefore, in this embodiment, Q i The smallest optimized solution is taken as the best solution.

[0127] The multi-objective optimization method of this embodiment is further introduced below with reference to a specific example. It should be noted that this example is only used to more clearly describe the technical solution of this embodiment and cannot be used to limit the scope of protection of the present invention.

[0128] First, the optimal electrode shape for a single electrode is determined. In this example, rectangular and circular electrode shapes are used. The induced charge q and first distance sensitivity S1 are compared for four electrode areas. The comparison results are shown in Table 1. As can be seen from Table 1, the induced charge of the rectangular electrode exceeds that of the circular electrode by 12.23%, while the first distance sensitivity of the circular electrode exceeds that of the rectangular electrode by 1.11%. Based on this comprehensive comparison, the rectangular electrode is adopted as the optimal electrode shape.

[0129] Table 1 Comparison of electrode shapes

[0130]

[0131] Based on the determination of the optimal electrode shape for a single electrode, this example compares three array shapes: side-by-side, circular, and square, when the number of electrodes is 8. Through simulation experiments, a comparison chart of array performance evaluation indicators Q, S1, and S2 is obtained. Figure 7 As shown, Figure 7 (a) and Figure 7 The horizontal axis of (b) represents the data collection point. Figure 7 The horizontal axis of (c) represents the electrode number in the electrode array. Figure 7 (a) It can be clearly seen that the total amount of induced charge Q of the ring array is higher than that of the other two array arrangements, where the average Q of the ring array is 196.8×10 -12 C, the Q mean of the side-by-side array is 167.8×10 -12 C, the Q mean of the square array is 186.2×10 -12C. From the perspective of S1, Figure 7 (b) It can be seen that the average S1 of the side-by-side array is 6.16%, the average S1 of the circular array is 8.30%, and the average S1 of the square array is 3.61%. The circular array is 2.14% higher than the side-by-side array and 4.69% higher than the square array. Figure 7 (c) It can be seen that the S2 value of the ring array also significantly exceeds that of the other two array arrangements. After comprehensive comparison, the ring array shape is selected as the optimal array shape.

[0132] The experimental design of the array's structural parameters A, B, and C and the total amount of array induced charge Q was carried out. The three levels of the number of electrodes A were set to 4, 5, and 6, and the three levels of the single electrode area B were set to 4.5×10 -4 , 5.2×10 -4 , 6.0×10 -4 m 2 , the thickness of a single electrode C is 3×10 -4 , 4×10 -4 , 5×10 -4 m, to investigate the influence of these three structural parameters on the total amount of induced charge Q of the array, L9(3 3 ) orthogonal table to arrange the experiment, and the experimental data are shown in Table 2.

[0133] Table 2 L9(3 3 )Table test

[0134]

[0135]

[0136] To improve the accuracy of the model, in addition to the variables of electrode number A, single electrode area B, and single electrode thickness C, the pairwise product of the variables was also added when selecting the input variables. Therefore, the input variables of the model are A, B, C, A×B, A×C, and B×C, a total of 6. A multivariate linear regression model of the total amount of induced charge Q of the array was established based on the experimental data set:

[0137] Q=117.863+W T X; (22)

[0138] In formula (22), the regression coefficient matrix Input variable X = [A, B, C, A×B, A×C, B×C] T .

[0139] To verify the accuracy of the regression model, 9 sets of test data were designed to compare the predicted values ​​with the actual values. The comparison results of the multivariate linear regression model of the total induced charge of the array are shown in Table 3. It can be seen that the two are very close, with an average error of less than 1%, indicating that the multivariate linear regression model fits the orthogonal test results better and it is feasible to use the multivariate linear regression model to predict the total induced charge of the array.

[0140] Table 3 The fitting of the regression model to the experimental results

[0141]

[0142] The total charge objective function is obtained by negating the multivariate linear regression model of the total array induced charge. Then, the design cost objective function is established, and a multi-objective optimization model with the optimization objectives of maximizing the total array induced charge and minimizing the design cost is constructed as follows:

[0143]

[0144] Based on the multi-objective optimization model, this example uses the NSGA-Ⅱ algorithm for optimization and solution. The initial population of the NSGA-Ⅱ algorithm is set to 20, the maximum number of iterations is 200, the crossover probability is selected to 0.8, and the mutation probability is selected to 0.05. Matlab programming is used to obtain the Pareto solution set as follows: Figure 8 The optimal electrode array structural parameters are shown in Table 4. From the optimization results, it can be seen that compared with the original electrode array structural parameters: A = 4, B = 0.00048, C = 0.0003, the absolute value of the total array induced charge is 225.627, and the cost is 8.96 yuan. This method can achieve good results in both the total array induced charge and cost control.

[0145] Table 4 Electrode structure parameter optimization scheme

[0146]

[0147]

[0148] The VIKOR decision analysis is performed on the optimization scheme in Table 4. The analysis results are as follows: Figure 9 As shown in the figure, optimization schemes 1 to 20 correspond to the 20 optimization schemes in the table, and scheme 21 is the existing electrode array structure parameter scheme (the absolute value of the total induced charge of the array is 225.627 and the cost is 8.96). The comprehensive evaluation value of each scheme is on the right side of the bar chart. Figure 9 By comparison, the Q of Scheme 5 (the absolute value of the total induced charge of the array is 355.870 and the cost is 4.60) is iThe final design parameter optimization scheme has the smallest value and the highest comprehensive benefit. Compared with the existing scheme, the total amount of array induced charge is increased by 30.98% and the array cost is reduced by 48.66%.

[0149] The multi-objective optimization method provided in this embodiment establishes an array charge total amount index and a distance sensitivity index for evaluating the overall performance of the array. The optimal array arrangement is determined by the evaluation index, and the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode are used as decision variables to perform multi-objective optimization on the total amount of array induced charge and the design cost. Specifically, the optimal electrode shape and array shape are first determined through simulation analysis. Based on this, experiments are designed to establish a data set of different numbers of electrodes, areas of single electrodes, thicknesses of single electrodes, and total amount of array induced charge. A regression model of the total amount of array induced charge and structural parameters is constructed based on the experimental data, and a total amount of charge objective function is established. Based on the intelligent optimization algorithm, an optimization scheme is obtained with the total amount of array induced charge and design cost as the optimization objectives. A compromise ranking method is used to make decisions on each optimization scheme to obtain the optimal electrode array parameter scheme, thereby achieving a multi-objective optimization solution for this type of problem, and ultimately achieving a significant increase in the total amount of electrode array induced charge and a substantial reduction in design costs.

[0150] Example 2:

[0151] This embodiment is used to provide a non-invasive voltage sensor electrode array parameter multi-objective optimization system, such as Figure 10 As shown, the multi-objective optimization system includes:

[0152] A shape optimization module M1 is configured to select the total amount of array induced charge, the first distance sensitivity, and the second distance sensitivity as evaluation indicators, and determine the optimal array shape of the electrode array of the non-invasive voltage sensor and the optimal electrode shape of a single electrode in the electrode array through simulation experiments;

[0153] A model building module M2 is used to establish a multi-objective optimization model; the multi-objective optimization model includes a total charge objective function, a design cost objective function, upper and lower limit constraints on the number of electrodes in the electrode array, upper and lower limit constraints on the area of ​​a single electrode in the electrode array, and upper and lower limit constraints on the thickness of a single electrode in the electrode array;

[0154] The structural parameter optimization module M3 is used to optimize and solve the multi-objective optimization model using a multi-objective genetic algorithm to obtain multiple optimization schemes, and select one of the multiple optimization schemes as the optimal scheme; the optimization scheme includes the respective values ​​of the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode.

[0155] Each embodiment in this specification focuses on the differences from other embodiments, and the same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0156] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A multi-objective optimization method for electrode array parameters of a non-invasive voltage sensor, characterized in that: The multi-objective optimization method comprises: The total amount of array induced charge, the first distance sensitivity, and the second distance sensitivity are selected as evaluation indicators, and the optimal array shape of the electrode array of the non-invasive voltage sensor and the optimal electrode shape of a single electrode in the electrode array are determined through simulation experiments; Establishing a multi-objective optimization model; the multi-objective optimization model includes a total charge objective function, a design cost objective function, upper and lower limit constraints on the number of electrodes in the electrode array, upper and lower limit constraints on the area of ​​a single electrode in the electrode array, and upper and lower limit constraints on the thickness of a single electrode in the electrode array; Utilizing a multi-objective genetic algorithm to optimize and solve the multi-objective optimization model, a plurality of optimization schemes are obtained, and one of the plurality of optimization schemes is selected as the optimal scheme; the optimization scheme includes respective values ​​of the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode; The calculation formula of the first distance sensitivity is: ； in, S 1 is the first distance sensitivity; Q j For the cable under test j The total amount of induced charge at a certain spatial position; Q j-1 For the cable under test j- The total amount of induced charge at one spatial position; The calculation formula of the second distance sensitivity is: ； in, S 2 is the second distance sensitivity; Q 0 is the total amount of induced charge of the cable under test at the center of the measurement area composed of the electrode array; The method for constructing the total charge objective function is: Performing simulation tests based on the optimal array shape and the optimal electrode shape to determine the total amount of array induced charge corresponding to various structural parameters, thereby obtaining a test data set; the structural parameters include the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode; Performing regression analysis on the test data set to construct a multiple linear regression model between the structural parameters and the total amount of induced charge of the array; The multivariate linear regression model is negated to obtain the total charge objective function.

2. The multi-objective optimization method according to claim 1, characterized in that: The selecting of the total amount of array induced charge, the first distance sensitivity, and the second distance sensitivity as evaluation indicators and determining the optimal array shape of the electrode array of the non-invasive voltage sensor and the optimal electrode shape of a single electrode in the electrode array through simulation experiments specifically include: Setting an electrode and a cable to be tested in simulation software, changing the electrode shape, obtaining the induced charge of the electrode under each electrode shape, calculating the first distance sensitivity based on the induced charge, and determining the optimal electrode shape of the electrode based on the induced charge and the first distance sensitivity; An electrode array and the cable to be tested are set in simulation software, wherein the electrode array includes a plurality of electrodes, and the electrode shape of the electrodes adopts the optimal electrode shape; the array shape of the electrode array is changed, and the induced charge of each electrode under each array shape is obtained. The total induced charge of the array, the first distance sensitivity, and the second distance sensitivity are calculated based on the induced charge of each electrode, and the optimal array shape of the electrode array is determined.

3. The multi-objective optimization method according to claim 1 or 2, characterized in that: The calculation formula of the total amount of induced charge of the array is: ； in, Q is the total amount of induced charge in the array; n is the number of electrodes in the electrode array; m is the number of spatial positions of the cable to be tested in the measurement area formed by the electrode array; q ij For the i The electrode in j The amount of induced charge at a certain spatial position.

4. The multi-objective optimization method according to claim 1, characterized in that: The structural parameters also include the product of the number of electrodes and the area of ​​a single electrode, the product of the number of electrodes and the thickness of a single electrode, and the product of the area of ​​a single electrode and the thickness of a single electrode.

5. The multi-objective optimization method according to claim 1, characterized in that: The total charge objective function is: ； in, F 1 is the target value of total charge; ω 0 is the intercept; W is the regression coefficient matrix; X are structural parameters, including the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode.

6. The multi-objective optimization method according to claim 1, characterized in that: The design cost objective function is: ； in, F 2 is the design cost target value; A is the number of electrodes; B is the area of ​​a single electrode; C is the thickness of a single electrode.

7. The multi-objective optimization method according to claim 1, characterized in that: The multi-objective genetic algorithm is the NSGA-II algorithm.

8. The multi-objective optimization method according to claim 1, characterized in that: The selecting one of the optimization schemes as the optimal scheme from the multiple optimization schemes specifically includes: selecting one of the optimization schemes as the optimal scheme from the multiple optimization schemes using the VIKOR method.

9. A multi-objective optimization system for non-invasive voltage sensor electrode array parameters, characterized in that: The multi-objective optimization system comprises: a shape optimization module, configured to select the total amount of array induced charge, the first distance sensitivity, and the second distance sensitivity as evaluation indicators, and determine, through simulation experiments, the optimal array shape of the electrode array of the non-invasive voltage sensor and the optimal electrode shape of a single electrode in the electrode array; A model building module for establishing a multi-objective optimization model; the multi-objective optimization model includes a total charge objective function, a design cost objective function, upper and lower limit constraints on the number of electrodes in the electrode array, upper and lower limit constraints on the area of ​​a single electrode in the electrode array, and upper and lower limit constraints on the thickness of a single electrode in the electrode array; a structural parameter optimization module, configured to optimize and solve the multi-objective optimization model using a multi-objective genetic algorithm to obtain multiple optimization schemes, and select one of the multiple optimization schemes as the optimal scheme; the optimization scheme includes respective values ​​of the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode; The calculation formula of the first distance sensitivity is: ； in, S 1 is the first distance sensitivity; Q j For the cable under test j The total amount of induced charge at a certain spatial position; Q j-1 For the cable under test j- The total amount of induced charge at one spatial position; The calculation formula of the second distance sensitivity is: ； in, S 2 is the second distance sensitivity; Q 0 is the total amount of induced charge of the cable under test at the center of the measurement area composed of the electrode array; The method for constructing the total charge objective function is: Performing simulation tests based on the optimal array shape and the optimal electrode shape to determine the total amount of array induced charge corresponding to various structural parameters, thereby obtaining a test data set; the structural parameters include the number of electrodes, the area of ​​a single electrode, and the thickness of a single electrode; Performing regression analysis on the test data set to construct a multiple linear regression model between the structural parameters and the total amount of induced charge of the array; The multivariate linear regression model is negated to obtain the total charge objective function.

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