A method for quantifying human exposure uncertainty of wireless power transfer device

Abstract

The application discloses a human body exposure uncertainty quantification method of a wireless power transmission device, and comprises the following steps: establishing a generalized chaotic polynomial model of human body electromagnetic exposure according to an orthogonal basis of input variables and combining human body electromagnetic exposure specific absorption rate theory; calculating coefficients of generalized chaotic polynomial expansion terms based on a random greedy algorithm of an orthogonal matching pursuit method to obtain a sparse chaotic polynomial proxy model; calculating a probability density distribution function of a mean value of SAR of some organs of a human body exposed to electromagnetic radiation of a WPT system when the human body is beside an electric vehicle based on the sparse chaotic polynomial; and rewriting the sparse chaotic polynomial into an incremental summation form to analyze global sensitivity indexes of input variables. The application uses the sparse chaotic polynomial to analyze human body electromagnetic exposure uncertainty quantification problems of an electric vehicle WPT system, and quantifies the influence degree of different input variables on human body SAR, so as to provide reasonable suggestions for human body electromagnetic exposure protection in the future.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle technology, specifically a method for quantifying the uncertainty of human exposure to wireless power transmission devices. Background Technology

[0002] To ensure the safety and usability of electric vehicle WPT systems, their electromagnetic field leakage must comply with relevant standards, and product qualification must be demonstrated according to basic limiting criteria. International organizations such as the International Commission on Non-Ionizing Radiation Protection (ICNIPR) and the Institute of Electrical and Electronics Engineers (IEEE) have established relevant standards that impose certain limitations on the absorption rate and induced electric field. Firstly, SAR is limited, simulating tissue heat in the 100kHz-10GHz frequency range. Secondly, the induced electric field is evenly distributed across human tissue to prevent nerve stimulation. With the development of electric vehicle WPT technologies, research on human electromagnetic exposure safety is also continuously expanding. Considering the near impracticality of experimentally measuring electromagnetic radiation inside the human body, researchers typically use computational methods or simulation software to determine the electromagnetic field distribution of electric vehicle WPT systems. Currently, much research has been conducted on human safety issues related to electric vehicle WPT systems, but most studies focus on electromagnetic exposure under specific fixed conditions, considering only a very limited set of scenarios and ignoring the greater possibilities arising from uncertainties. Therefore, there is still considerable room for research on human electromagnetic exposure issues related to electric vehicle WPT systems.

[0003] To address the uncertainty quantification problem of human electromagnetic exposure in electric vehicle WPT systems, considering the complexity of both the electric vehicle WPT system and the human anatomical model, the Monte Carlo method, while highly accurate, is also computationally expensive and unsuitable. In recent years, uncertainty quantification methods based on machine learning theory have been extensively studied. Besides machine learning-related methods, surrogate model methods have also been widely used in engineering uncertainty quantification analysis, with chaotic polynomial-based methods being particularly prevalent. When dealing with small-sample uncertainty quantification problems, chaotic polynomial-based surrogate model methods require less training data to achieve computational accuracy comparable to machine learning-related methods. For the uncertainty quantification problem of human electromagnetic exposure, considering the uncertainty of material electrical parameters, non-interferometric PCE is used for calculations in both one-dimensional and two-dimensional variable cases. Existing uncertainties in human electromagnetic exposure quantification analyses consider relatively low-dimensional random input variables, even failing to cause the curse of dimensionality. Summary of the Invention

[0004] The purpose of this invention is to provide a method for quantifying the uncertainty of human exposure to wireless power transmission devices, so as to solve the problem of quantifying the uncertainty of human electromagnetic exposure in electric vehicle WPT systems.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for quantifying the uncertainty of human exposure to wireless power transmission devices includes the following steps:

[0007] (1) Based on the electromagnetic exposure environment of the human body, the possible situations of the WPT system in actual application and the relevant parameters of the compensation circuit, determine the input variables;

[0008] (2) Determine the distribution type corresponding to the input variables based on the input variables;

[0009] (3) Determine the orthogonal basis corresponding to the input variables based on the distribution type of the input variables;

[0010] (4) Based on the orthogonal basis of the input variables, establish a generalized chaotic polynomial model of human electromagnetic exposure and obtain the expansion of the generalized chaotic polynomial.

[0011] (5) The generalized chaotic polynomial proxy model is sparsified according to the OMP-based random greedy algorithm to obtain a sparse chaotic polynomial;

[0012] (6) Calculate the probability density distribution function of the mean organ SAR of the human body exposed to electromagnetic radiation from the WPT system when the human body is located on the side and behind the electric vehicle based on the sparse chaotic polynomial.

[0013] (7) Rewrite the sparse chaotic polynomial into an increasing summation form and use the global sensitivity analysis method to analyze the global sensitivity index of the input variable.

[0014] Based on the above technical solutions, the present invention also provides the following optional technical solutions:

[0015] In one alternative: the expansion of the generalized chaotic polynomial is achieved by utilizing multidimensional orthogonal polynomials. The original model Expand infinitely, in the following ways:

[0016]

[0017] Simplified to

[0018] (1)

[0019] in, Here, is the coefficient of the polynomial to be solved, and d is the dimension of the model input variables. Dimensional input variables , It is a multi-index of size d. The mixed orthogonal polynomial of order n is: Dimensional input variables The function.

[0020] In one alternative approach: for practical application in the analysis, equation (1) is truncated, with the truncation order being p. The truncated chaotic polynomial can then be expressed as:

[0021] (2);

[0022] Among them, the truncated multi-index for And the number of terms P in the truncated chaotic polynomial expansion is:

[0023] (3)

[0024] The key to constructing the generalized chaotic polynomial proxy model lies in solving... .

[0025] In one alternative approach: the generalized chaotic polynomial surrogate model is sparsified in the following way: (1) Orthogonal matching pursuit method, OMP is a greedy algorithm based on compressed sensing theory, which can accurately reconstruct the output of the model when N is small; OMP is a sequential process, which greedily selects terms from the dictionary D of the basis functions. In the kth iteration, OMP selects terms from the candidate set. Find the basis function most relevant to the residual r. And add it to the activity set, where The selection process can be represented as:

[0026] (4)

[0027] The polynomial coefficients corresponding to the kth iteration are: The matrix at this time The columns in the table contain the results of the current basis function selection, and the training residuals can be obtained through... Once the basis functions are selected, the new PC coefficients are calculated using least squares. The above steps are repeated until the l2 norm of the residuals meets the requirements.

[0028] (2) Random Greedy Algorithm

[0029] This algorithm adds a randomization step before finding basis functions and optimizes the calculation of polynomial coefficients and the selection of basis functions in the OMP algorithm;

[0030] 1) Update strategy

[0031] The matrix is ​​factored using the thinQR factorization method. Decompose into the product of an orthogonal matrix Q and an upper triangular matrix R:

[0032] (5)

[0033] in and This can be abbreviated as Q and R. In each iterative calculation, the number of basis functions increases after selection, while... A new column will be added to the calculation. To solve for the coefficients of the current chaotic polynomial and update the residuals, Q and R need to be updated in each iteration. The Gram-Schmidt process is used to update Q and R, and the coefficients of the chaotic polynomial in the current iteration can be calculated by factoring the updated Q and R and solving the upper triangular equation.

[0034] (6)

[0035] Meanwhile, using QR factorization for updating can quickly calculate the residual of the current iteration without solving for the coefficients of the chaotic polynomial. The residual can be updated using equation (7):

[0036] (7)

[0037] 2) Selection of candidate set function

[0038] To rank the candidate basis functions in each iteration, an expression is used to represent the future residuals. To accurately calculate the changes in the residuals, a projection matrix is ​​used. If the model contains the j-th basis function, then the precise future residual in the k-th iteration can be expressed as:

[0039] (8)

[0040] Where P is the projection matrix, and in the k-th iteration, P can be expressed as:

[0041] (9)

[0042] The computational cost associated with calculating accurate future residuals mainly lies in the denominator of equation (8). Using QR factorization, equation (8) can be rewritten as:

[0043] (10)

[0044] Considering the basis functions in each candidate set The computational cost remains significant, therefore... Updated to:

[0045] (11)

[0046] denominator Represented as ,and The initialization is set to In each iteration of the calculation, equation (12) is used for updating:

[0047] (12)

[0048] Then, in the k-th iteration, the basis function most relevant to the future residual can be selected from the candidate set using equation (13).

[0049] (13)

[0050] Through the above calculations, the future residuals can be calculated by focusing on the denominator of each candidate in each iteration.

[0051] 3) Random Greedy Step

[0052] To reduce the computational cost of selecting the optimal basis function from all candidate basis functions in each iteration of the greedy algorithm, a probabilistic acceleration method is used to construct a compressed representation of the involved matrices during the greedy iteration process. At the start of each iteration, a basis function is randomly selected from the candidate dictionary D. Choose the basis functions from them and select the optimal basis function; Selection using probability-related methods can usually make It is 60;

[0053] By optimizing and improving the OMP algorithm through the above three parts, the random greedy algorithm can be obtained.

[0054] In one alternative approach, the global sensitivity index is calculated by quantifying the contribution of the interaction between individual or multiple variables to the output variance; this is known as the global sensitivity analysis method. Specifically, the original model is decomposed into a sum of increasing terms.

[0055] (14)

[0056] In equation (14), the terms are orthogonal to each other, where Since is a constant and represents the mean of the output model, in order to obtain the variance decomposition formula, the variance is taken on both sides of equation (14):

[0057] (15)

[0058] In equation (15), each decomposition term represents the influence of different input variables and the interactions between variables on the output variance. The Sobol sensitivity index is defined as:

[0059] (16)

[0060] In equation (16) The first-order sensitivity index represents the contribution of a single variable to the output variance. The total sensitivity index is defined as the sum of the first-order sensitivity index of a variable and the sensitivity indices of the interaction between that variable and other variables.

[0061] (17).

[0062] In one alternative approach: the formula for sparsifying the generalized chaotic multinomial surrogate model is converted into an increasing summation form using an OMP-based stochastic greedy algorithm. The global sensitivity index of the input variables is then analyzed using a global sensitivity analysis method, specifically including:

[0063] 1) Obtain the sparse chaotic polynomial;

[0064] 2) Convert the sparse chaotic polynomial into an expansion of increasing summation form;

[0065] 3) Recursively calculate the expansion of the increasing summation form using the integration method, solve for the corresponding coefficients of the decomposition terms, and obtain the expansion of the increasing summation form with known coefficients; take the variance of both sides of the expansion of the increasing summation form with known coefficients to obtain the variance decomposition form.

[0066] 4) Obtain the global sensitivity index based on the variance decomposition formula;

[0067] 5) The global sensitivity index includes the sensitivity index and the total sensitivity index.

[0068] The expansion of the incremental summation form is:

[0069] (18)

[0070] In formula (18)

[0071] (19)

[0072] Further calculations yielded the following:

[0073] (20)

[0074] Based on the orthogonality of the basis functions of chaotic polynomials, we can obtain:

[0075] (twenty one)

[0076] By combining equation (21) and equation (16), the global sensitivity index of each variable in the chaotic polynomial surrogate model can be calculated.

[0077] In one alternative: the global sensitivity index includes a first-order sensitivity index and a total sensitivity index.

[0078] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0079] 1. This invention will utilize sparse PCE to analyze the uncertainty quantification problem of human electromagnetic exposure in electric vehicle WPT system, and quantify the influence of different input variables on human SAR, so as to provide reasonable suggestions for future human electromagnetic exposure protection.

[0080] 2. This invention calculates the SAR values ​​of certain human organs exposed to electromagnetic radiation from the WPT system of an electric vehicle. A surrogate model for the SAR of each organ is established using RGA-PCE. This method optimizes the update of residuals and the selection of basis functions during iterative calculations, based on OMP-PCE, further improving computational efficiency. Considering the shielding effect of the electric vehicle body, the SAR values ​​of certain organs are calculated when the human body is located on the side and rear of the electric vehicle. Furthermore, taking into account the human body displacement, uncertainty quantification analysis is performed on the SAR mean values ​​of certain organs.

[0081] 3. The calculation results of RGA-PCE are compared with those of OMP-PCE and MC to demonstrate that the RGA-PCE algorithm can quickly and effectively quantify the uncertainty of the mean SAR values ​​of organs exposed to electromagnetic radiation from the WPT system. Finally, by combining with Sobol, the influence of different variables on the mean SAR values ​​of human organs is calculated, providing reasonable suggestions for future research on human electromagnetic exposure safety. Attached Figure Description

[0082] Figure 1 A simulation model for electric vehicles and WPT systems.

[0083] Figure 2 This is the compensation circuit model for the WPT system.

[0084] Figure 3 This is a schematic diagram of an adult male human body model and its mesh division.

[0085] Figure 4 A simulation model and mesh partitioning diagram of the brain, heart, lungs, kidneys, and liver.

[0086] Figure 5 This is a schematic diagram showing a human body positioned on the side of a vehicle in a scene where a human model is exposed.

[0087] Figure 6 This is a schematic diagram showing a human body located at the rear of a vehicle in a scene where a human model is exposed.

[0088] Figure 7 This diagram illustrates the changes in position of a human body when positioned to the side and rear of a vehicle.

[0089] Figure 8 This is a schematic diagram showing the distribution of SAR (Specific Angiography) of the heart at different locations in the human body.

[0090] Figure 9 This diagram illustrates the mean probability density of SAR (Specific Absorption Rate) of the brain organs when a human is exposed to electromagnetic radiation from the WPT (Wireless Transmission Platform) system while positioned to the side or rear of an electric vehicle. The left column shows the human standing to the side of the vehicle, and the right column shows the human standing to the rear of the vehicle.

[0091] Figure 10 This diagram illustrates the mean probability density of SAR (Specific Absorption Rate) of the heart organ in the electromagnetic radiation of the WPT system when a human is positioned on the side or behind an electric vehicle. The left column shows the human standing on the side of the vehicle, and the right column shows the human standing behind the vehicle.

[0092] Figure 11 This diagram illustrates the mean probability density of lung SAR in the electromagnetic radiation of the WPT system when a human is positioned on the side and behind an electric vehicle. The left column shows the human standing on the side of the vehicle, and the right column shows the human standing behind the vehicle.

[0093] Figure 12 This diagram illustrates the mean probability density of SAR (Specific Absorption Rate) of the kidney organs in the WPT (Wireless Transmission Platform) electromagnetic radiation when a human is positioned on the side or behind an electric vehicle. The left column represents a human standing on the side of the vehicle, and the right column represents a human standing behind the vehicle.

[0094] Figure 13 This diagram illustrates the mean probability density of SAR (Specific Absorption Rate) of the liver organ when a human is exposed to electromagnetic radiation from the WPT (Wireless Power Transmission) system while positioned to the side or rear of an electric vehicle. The left column represents a human standing to the side of the vehicle, and the right column represents a human standing to the rear of the vehicle.

[0095] Figure 14 This diagram illustrates the mean probability density of SAR of the reproductive organs when a human is exposed to electromagnetic radiation from the WPT system while positioned on the side and rear of an electric vehicle. The left column shows the human standing on the side of the vehicle, and the right column shows the human standing behind the vehicle.

[0096] Figure 15 This is a comparison chart of the total sensitivity index of relevant variables for quantifying the uncertainty of electromagnetic exposure of the human heart and organs in the WPT system of electric vehicles. The left column shows the human body standing on the side of the vehicle, and the right column shows the human body standing behind the vehicle.

[0097] Figure 16This is a comparison chart of the total sensitivity index of relevant variables for quantifying the uncertainty of electromagnetic exposure of human lung organs in electric vehicle WPT system. The left column shows the human body standing on the side of the vehicle, and the right column shows the human body standing behind the vehicle.

[0098] Figure 17 This is a comparison chart of the total sensitivity index of relevant variables for quantifying the uncertainty of electromagnetic exposure of the human kidney organ in the WPT system of electric vehicles. The left column shows the human body standing on the side of the vehicle, and the right column shows the human body standing behind the vehicle.

[0099] Figure 18 This is a comparison chart of the total sensitivity index of relevant variables for quantifying the uncertainty of electromagnetic exposure of the human liver organ in the WPT system of electric vehicles. The left column shows the human body standing on the side of the vehicle, and the right column shows the human body standing behind the vehicle.

[0100] Figure 19 This is a comparison chart of the total sensitivity index of relevant variables for quantifying the uncertainty of electromagnetic exposure of the human liver in the WPT system of electric vehicles. The left column shows the human body standing on the side of the vehicle, and the right column shows the human body standing behind the vehicle.

[0101] Figure 20 This is a comparison chart of the total sensitivity index of relevant variables for quantifying the uncertainty of electromagnetic exposure of human reproductive organs in electric vehicle WPT systems. The left column shows the human body standing on the side of the vehicle, and the right column shows the human body standing behind the vehicle. Detailed Implementation

[0102] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The embodiments listed herein are merely illustrative and not intended to limit the scope of the invention. Any obvious modifications or alterations made to this invention do not depart from the spirit and scope of the invention.

[0103] The purpose of this invention is to provide a method for accurately analyzing the degree of influence of various uncertain input variables on the human body and organs; to achieve the above objective, this invention provides the following technical solution:

[0104] (1) Based on the electromagnetic exposure environment of the human body, the possible situations of the WPT system in actual application and the relevant parameters of the compensation circuit, determine the input variables;

[0105] (2) Determine the distribution type corresponding to the input variables based on the input variables;

[0106] (3) Determine the orthogonal basis corresponding to the input variables based on the distribution type of the input variables;

[0107] (4) Based on the orthogonal basis of the input variables, establish a generalized chaotic polynomial model of human electromagnetic exposure and obtain the expansion of the generalized chaotic polynomial.

[0108] (5) The generalized chaotic polynomial proxy model is sparsified according to the OMP-based random greedy algorithm to obtain a sparse chaotic polynomial;

[0109] (6) Calculate the probability density distribution function of the mean organ SAR of the human body exposed to electromagnetic radiation from the WPT system when the human body is located on the side and behind the electric vehicle based on the sparse chaotic polynomial.

[0110] (7) Rewrite the sparse chaotic polynomial into an increasing summation form and use the global sensitivity analysis method to analyze the global sensitivity index of the input variable.

[0111] Uncertainty Quantization Algorithm

[0112] To address the uncertainty quantification problem of human electromagnetic exposure in electric vehicle WPT systems, considering the complexity of the WPT system and the displacement of the human body exposed to electromagnetic radiation, this invention employs RGA-PCE to quantify the uncertainty of SAR (Specific Absorption Regulator) of various organs in the human body. RGA-PCE is based on PCE and OMP (Optical Multiplication Table), where the Wiener chaotic polynomial is extended to PCE using the Askey scheme proposed by Xiu, and is widely used for uncertainty quantification in related engineering problems. Based on the distribution type of each dimension of the variables, multidimensional orthogonal polynomials are used... The original model Expand indefinitely:

[0113]

[0114] c (1)

[0115] in Here, is the coefficient of the polynomial to be solved, and d is the dimension of the model input variables. Dimensional input variables , It is a multi-index of size d. The mixed orthogonal polynomial of order n is: Dimensional input variables The function. Considering the computational cost in practical application analysis, it is impractical to use an infinitely expanded chaotic polynomial for calculation. Therefore, equation (1) should be truncated, with the truncation order being p. The truncated chaotic polynomial can be expressed as:

[0116] (2)

[0117] The truncated multi-index for And the number of terms P in the truncated chaotic polynomial expansion is:

[0118] (3)

[0119] The key to constructing a generalized chaotic polynomial proxy model lies in solving... This invention uses a regression method for calculation, typically sampling N times based on the random distribution type of each input variable. Generally, N should conform to the oversampling principle, i.e. Finally, the result can be calculated using the least quadratic regression method. As model complexity increases and the dimension d of input variables grows, the demand for the number of sample points N and the truncation order p of the chaotic polynomial surrogate model also increases. The essence of sampling is to obtain the response value y of the original model. If the computational cost of the original model is high, it will lead to the curse of dimensionality. Considering the complexity of the human electromagnetic exposure model of the electric vehicle WPT system and the large number of input variables involved, it inevitably faces the curse of dimensionality problem. To alleviate the above problems, and to make the chaotic polynomial in... Even under certain circumstances, accurate results can be obtained. This invention uses an OMP-based random greedy algorithm to sparsify the generalized chaotic polynomial surrogate model.

[0120] 1. Orthogonal matching pursuit method

[0121] OMP is a greedy algorithm based on compressed sensing theory that can accurately reconstruct the model's output when N is relatively small. OMP is a sequential process that greedily selects terms from the dictionary D of basis functions. In the k-th iteration, OMP selects terms from the candidate set... Find the basis function most relevant to the residual r. And add it to the activity set, where The selection process can be represented as:

[0122] (4)

[0123] The polynomial coefficients corresponding to the kth iteration are The matrix at this time The columns in the table contain the results of the current basis function selection, and the training residuals can be obtained through... Once the basis functions are selected, the new PC coefficients can be calculated using least squares. Repeat the above steps until the l2 norm of the residuals meets the requirements—to achieve loop termination in OMP, a tolerance needs to be defined. To minimize the input error during training, cross-validation is typically used for estimation. The calculation process of the OMP algorithm is shown in Algorithm 1:

[0124] Algorithm1OrthogonalMarchingPursuit Input: Basis functions The dictionary D; the sampling points of the input variables The corresponding output . Output: Index of the selected basis function ; Polynomial coefficients c. 1: Iteration ; ; ; . 2: Set cross-validation error . 3:while do 4: k = k + 1 5: Through Choose the basis functions most relevant to the residuals. 6: Update the selected basis function index: 7: Update the candidate dictionary: 8: Solve for the polynomial coefficients at this point: ,in Include , . 9: Update residuals: 10:endwhile

[0125] Cross-validation requires repeated running of the OMP algorithm. According to (3), when the truncation order p and the dimension d of the input variables of the model increase, the candidate set dictionary in the OMP algorithm will also increase significantly. The OMP algorithm needs to search all the basis functions in the dictionary for calculation, which leads to the computational complexity of the OMP algorithm increasing with the increase of the truncation order p and the dimension d of the input variables, ultimately resulting in excessive computational cost.

[0126] 2. Random Greedy Algorithm

[0127] To address the increased computational cost of finding the most relevant basis functions and calculating cross-validation in each iteration of the OMP algorithm, this section introduces a stochastic greedy algorithm. This algorithm adds a randomization step before finding basis functions and optimizes the calculation of polynomial coefficients and the selection of basis functions in the OMP algorithm.

[0128] 1) Update strategy

[0129] The matrix is ​​factored using the thinQR factorization method. Decompose into the product of an orthogonal matrix Q and an upper triangular matrix R:

[0130] (5)

[0131] in and This can be abbreviated as Q and R. In each iterative calculation, the number of basis functions increases after selection, while... A new column will be added to the calculation. To solve for the coefficients of the current chaotic polynomial and update the residuals, Q and R need to be updated in each iteration. The Gram-Schmidt process is used to update Q and R, and the coefficients of the chaotic polynomial in the current iteration can be calculated by factoring the updated Q and R and solving the upper triangular equation.

[0132] (6)

[0133] Meanwhile, using QR factorization for updating can quickly calculate the residual of the current iteration without solving for the coefficients of the chaotic polynomial. The residual can be updated using equation (7):

[0134] (7)

[0135] 2) Selection of candidate set function

[0136] To rank the candidate basis functions in each iteration, an expression is used to represent the future residuals. To accurately calculate the changes in the residuals, a projection matrix is ​​used. If the model contains the j-th basis function, then the precise future residual in the k-th iteration can be expressed as:

[0137] (8)

[0138] Where P is the projection matrix, and in the k-th iteration, P can be expressed as:

[0139] (9)

[0140] The computational cost associated with calculating accurate future residuals mainly lies in the denominator of equation (8). Using QR factorization, equation (8) can be rewritten as:

[0141] (10)

[0142] Considering the basis functions in each candidate set The computational cost remains significant, therefore... Updated to:

[0143] (11)

[0144] denominator Represented as ,and The initialization is set to In each iteration of the calculation, equation (12) is used for updating:

[0145] (12)

[0146] Then, in the k-th iteration, the basis function most relevant to the future residual can be selected from the candidate set using equation (13).

[0147] (13)

[0148] Through the above calculations, the future residuals can be calculated by focusing on the denominator of each candidate in each iteration, thereby significantly reducing computational costs.

[0149] 3) Random Greedy Steps

[0150] To reduce the computational cost of selecting the optimal basis function from all candidate basis functions in each iteration of the greedy algorithm, a probabilistic acceleration method is used to construct a compressed representation of the involved matrices during the greedy iteration process. At the start of each iteration, a basis function is randomly selected from the candidate dictionary D. Calculate the basis functions and select the optimal basis function from them. Selection can be made using probability-related methods, typically allowing... It is 60.

[0151] After optimizing and improving the OMP algorithm through the above three parts, the random greedy algorithm can be obtained. The calculation process of the random greedy algorithm is shown in Algorithm 2.

[0152] Algorithm2RandomizedGreedyAlgorithm Input: Basis functions The dictionary D; the sampling points of the input variables The corresponding output . Output: Index of the selected basis function ;Polynomial coefficients c. 1: Iteration ; ; ; . 2:whilestoppingcriteriaarenotmetdo 3: k = k + 1 4:selectsubset 5: Through Choose the basis functions most relevant to the residuals. 6: Update the selected basis function index: 7: Update the candidate dictionary: 8: Update residuals 9: Determine if the stopping criteria are met. 10:endwhile 11: Solving for the coefficients of the chaotic polynomial ,in Includes basis functions , .

[0153] When faced with high-dimensional and highly truncated models, the stochastic greedy algorithm can keep the computational cost at a low level, so that the computational efficiency does not increase significantly with the increase of the dimension of the model input variables and the truncation order. Therefore, this invention will use RGA-based PCE to calculate the uncertainty quantification problem of human electromagnetic exposure in electric vehicle WPT system.

[0154] 3. Sobol Global Sensitivity Analysis

[0155] The uncertainty quantification problem of human electromagnetic exposure in electric vehicle WPT systems involves many variables. Quantifying the impact of different input variables on human electromagnetic exposure safety can provide an important theoretical basis for electromagnetic safety protection. Therefore, based on RGA-PCE, this invention combines the Sobol method to solve for the global sensitivity index of different variables. The Sobol method, based on the idea of ​​variance decomposition, calculates the global sensitivity index by quantifying the contribution of the interaction between single or multiple variables to the output variance. It is a widely used global sensitivity analysis method. The original model is decomposed into the form of a sum of increasing terms:

[0156] (14)

[0157] In equation (14), the terms are orthogonal to each other, where Since is a constant and represents the mean of the output model, in order to obtain the variance decomposition formula, the variance is taken on both sides of equation (14):

[0158] (15)

[0159] In equation (15), each decomposition term represents the influence of different input variables and the interactions between variables on the output variance. The Sobol sensitivity index is defined as:

[0160] (16)

[0161] In equation (16) The first-order sensitivity index represents the contribution of a single variable to the output variance. The total sensitivity index is defined as the sum of the first-order sensitivity index of a variable and the sensitivity indices of the interaction between that variable and other variables.

[0162] (17)

[0163] Combining the chaotic polynomial surrogate model with the Sobol method can significantly improve computational efficiency. Optionally, the formula for sparsifying the generalized chaotic polynomial surrogate model using an OMP-based stochastic greedy algorithm is converted into an incremental summation form, and the global sensitivity index of the input variable is analyzed using a global sensitivity analysis method, specifically including:

[0164] 1) Obtain the sparse chaotic polynomial;

[0165] 2) Convert the sparse chaotic polynomial into an expansion of increasing summation form;

[0166] 3) Recursively calculate the expansion of the increasing summation form using the integration method, solve for the corresponding coefficients of the decomposition terms, and obtain the expansion of the increasing summation form with known coefficients; take the variance of both sides of the expansion of the increasing summation form with known coefficients to obtain the variance decomposition form.

[0167] 4) Obtain the global sensitivity index based on the variance decomposition formula;

[0168] 5) The global sensitivity index includes the sensitivity index and the total sensitivity index.

[0169] Optionally, the expansion of the incremental summation form is:

[0170] (18)

[0171] In formula (18)

[0172] (19)

[0173] Further calculations can be performed to obtain:

[0174] (20)

[0175] Based on the orthogonality of the basis functions of chaotic polynomials, we can obtain:

[0176] (twenty one)

[0177] By combining equation (21) and equation (16), the global sensitivity index of each variable in the chaotic polynomial surrogate model can be calculated, including the first-order sensitivity index and the total sensitivity index.

[0178] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: The present invention combines a random greedy algorithm and a generalized chaotic polynomial, and uses an OMP-based random greedy algorithm to sparsify the generalized chaotic polynomial surrogate model, establishes a surrogate model to analyze the uncertainty quantification problem of human electromagnetic exposure, and combines the Sobol method to analyze the global sensitivity of the input variables, thereby analyzing and calculating the uncertainty quantification problem of human electromagnetic exposure more efficiently with lower computational cost while ensuring computational accuracy.

[0179] Example

[0180] 1. Simulation model of electric vehicle WPT system

[0181] The electric vehicle model and WPT model used in this invention are as follows: Figure 1 As shown, the dimensions of the electric vehicle are 4.5 × 2 × 1.5 m (length × width × height). Figure 1 As shown in (a), the dimensions are basically consistent with most family cars on the market, providing some reference value. Thanks to the precise modeling software, the geometry of each part of the electric vehicle is accurately considered, with the main material of the body being aluminum. To ensure the accuracy of the simulation results, non-metallic parts of the electric vehicle are also considered, such as glass for windows and rubber for tires, although this increases the computational complexity of the simulation. The WPT system, as shown... Figure 1 As shown in (b), it includes a transmitting coil TX and a receiving coil RX, as well as a transmitting shield and a receiving shield. The external dimensions of both the transmitting coil TX and the receiving coil RX are 0.6 × 0.6 m (A × A), and the internal dimensions are 0.3 × 0.3 m (a × a). The coil cross-sectional area is 2e-6 mm², and the number of coil turns is 11. The material used is copper. Considering that the ground clearance of most passenger cars on the market is 0.15-0.2 mm, the distance between the transmitting coil TX and the receiving coil RX is set to 0.2 m in this invention. The shield has the same dimensions as the coil, a thickness of 1 cm, and is primarily made of lossless soft iron. The WPT system uses an SS-type compensation circuit at a frequency of 80 kHz; the compensation circuit is as follows... Figure 2 As shown.

[0182] 2. Human body model

[0183] In this invention, a human body model was established based on an adult male, such as... Figure 3 As shown, this invention mainly focuses on the calculation and analysis of the uncertainty of SAR in human organs. Therefore, the human body model also includes the major organs of the human body, such as the heart, lungs, liver, kidneys, brain, and reproductive organs. Figure 4As shown in the figure. The height of this human model is 1.8m and the weight is 75kg, which is within the range of height and weight for some adult males. The electrical parameters and densities of some organs at 80kHz are shown in Table I.

[0184] Table 1. Electrical parameters and densities of some organs and tissues at 80 kHz

[0185] Conductivity (s / m) Relative permittivity Density (kg / m3) human body 0.27 5400 1050 lung 0.126 3890 450 heart 0.276 14500 1069 liver 0.064 12050 1151 kidney 0.156 10510 1147 brain 0.138 4990 1040 Reproductive organs 0.490 6390 1092

[0186] 3. Exposure scenario

[0187] To study the uncertainty quantification problem of human electromagnetic exposure to electric vehicle WPT systems, this invention establishes the aforementioned electric vehicle WPT system model and human anatomical model. Considering possible scenarios in real life, the positional relationship between people and the WPT system is mainly manifested at the rear of the electric vehicle, the side of the electric vehicle, and the passenger position within the electric vehicle. Given that the metal body of the electric vehicle is not a uniform plane, the shielding effect of the vehicle body is inconsistent when a person stands on the side of the vehicle versus at the rear. In both cases, even if the distance between the person and the WPT system is the same, the SAR of internal organs is not consistent. Therefore, the positional relationship between the person and the WPT system cannot be simply described using a single distance; the situations where the person stands on the side of the vehicle versus at the rear should be analyzed separately. For the above reasons, this invention considers the following exposure scenarios, such as... Figure 5 and Figure 6 As shown in the figure, it simultaneously demonstrates Figure 4 The diagram shows the organs involved.

[0188] V. Quantitative Analysis of Uncertainty

[0189] To quantify the uncertainty of human electromagnetic exposure to the WPT system of electric vehicles, this invention mainly focuses on the impact of electromagnetic radiation on certain organs of the human body (such as...) when exposed to electromagnetic radiation from the WPT system. Figure 4 This invention focuses on the SAR (Self-Protective Aspect) of electric vehicles. Considering the uncertainties in the parameters of the compensation circuit of the electric vehicle WPT (Wide-Pole Transmission) system during manufacturing, the uncertainties caused by the driver stopping in real-life applications, and the uncertainties in the position of a person standing around the WPT system, this invention assigns the variables involved in these uncertainties to the distribution types and parameters in Table II, where U represents a uniform distribution and N represents a normal distribution. It should be noted that due to the uneven shielding effect of the electric vehicle body, this invention divides the standing posture analysis into two cases: the person is located at the rear of the electric vehicle and the person is located on the side of the electric vehicle. Therefore, when setting the uncertainty variables, the relevant parameters of the person's position are also set separately, as illustrated in the diagram below. Figure 7 As shown.

[0190] Table II. Variables for Safety Assessment of Human Electromagnetic Exposure to WPT Systems in Electric Vehicles

[0191] Random input variables Distributed and parameter unit Coil distance d0 U(0.15,0.2) m TX lateral offset z0 U(-0.2,0.2) m TX vertical offset x0 U(-0.2,0.2) m TX cross-sectional area s0 N(3e-6, 1e-7) m2 RX cross-sectional area s1 N(3e-6, 1e-7) m2 TX compensation capacitor C1 N(114.01,6.2005) nF RX compensation capacitor C2 N(121.2392,6.662) nF TX resistor R1 N(0.1,0.005) Ω RX resistor R2 N(5,0.25) Ω Excitation current I N(50,2.5) A Lateral displacement Zs of the vehicle side U(-0.5,0.5) m Vehicle side longitudinal displacement Xs U(0,0.5) m Lateral displacement Zb of the vehicle U(0,0.5) m Rear longitudinal displacement Xb U(-0.5,0.5) m

[0192] In the practical application of the WPT system in electric vehicles, when a human body is located around the WPT system, the distribution of SAR (Specific Absorption Rate) of organs within the body changes with the body's position, particularly the location of the SAR's maximum value. Taking the SAR distribution of the heart in different body positions as an example... Figure 8 As shown, the SAR distribution of the heart has changed significantly, especially the location of the maximum SAR value. Using the maximum SAR value as the object of uncertainty quantification would present significant challenges. Therefore, this invention primarily uses the mean SAR value of different organs in the human body as the object of uncertainty quantification.

[0193] Based on different locations on the human body, the random greedy algorithm described in Section 3 is used to quantify the uncertainty of the distribution mean SAR of human organs exposed to electromagnetic radiation from the electric vehicle WPT system. These organs include the brain, heart, lungs, kidneys, liver, and reproductive organs. The truncation order p of the chaotic polynomial is 4, and the number of sampling points is 240. To verify the effectiveness of the method, the probability density distribution function of the SAR mean for each organ is calculated by comparing OMP-PCE with the 2000-time Monte Carlo method. The comparison results are as follows: Figures 9-14 As shown:

[0194] according to Figures 9-14 The probability density distribution functions of the SAR mean values ​​of different organs in the human body, as presented in this invention, show good consistency between the RGA-PCE method and the MC method. Since the truncation order and number of sampling points remain consistent in both OMP-PCE and RGA-PCE, it can be assumed that the computation time of the two methods should be the same during the sampling phase and the phase of calling the original model for calculation. This is mainly determined by the computation time of the simulation software. However, when calculating the chaotic polynomial coefficients, the computation time of the RGA-PCE algorithm is approximately 0.7 seconds, while the computation time of the OMP-PCE algorithm is approximately 3.6 seconds, demonstrating a significant improvement in the computational efficiency of RGA-PCE. Furthermore, to quantify the influence of different input variables on the SAR mean values ​​of different organs in the human body, the overall sensitivity index of each variable is calculated in conjunction with the Sobol method. The calculation results are as follows: Figures 15-20 As shown.

[0195] observe Figures 15-20The overall sensitivity index of various variables reveals that, regardless of whether the human body is standing on the side or behind the vehicle, the variables with the greatest impact on the SAR of human organs are the offset between the transmitting coil TX and the receiving coil RX of the WPT system, and the positional variable of the human body relative to the WPT system. These variables are not effectively controllable during the design of the electric vehicle WPT system. Furthermore, when the human body is standing on the side of the vehicle, the receiver resistance R2 also has a significant impact on the brain, heart, and reproductive organs. For the sake of human electromagnetic exposure safety, the configuration of R2 should be emphasized during the design phase of the electric vehicle WPT system. The above results demonstrate that the RGA-PCE method used in this invention can effectively calculate the uncertainty quantification problem of human electromagnetic exposure in electric vehicle WPT systems, and quantify the influence of different input variables based on the global sensitivity analysis results, providing an effective and reasonable basis for the protection of human electromagnetic exposure safety, and possessing high engineering application value.

[0196] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A method for quantifying the uncertainty of human exposure to wireless power transmission devices, characterized in that, Includes the following steps: (1) Based on the electromagnetic exposure environment of the human body, the possible situations of the WPT system in actual application and the relevant parameters of the compensation circuit, determine the input variables; (2) Determine the distribution type corresponding to the input variables based on the input variables; (3) Determine the orthogonal basis corresponding to the input variables based on the distribution type of the input variables; (4) Based on the orthogonal basis of the input variables, establish a generalized chaotic polynomial model of human electromagnetic exposure and obtain the expansion of the generalized chaotic polynomial. (5) The generalized chaotic polynomial proxy model is sparsified according to the OMP-based random greedy algorithm to obtain a sparse chaotic polynomial; (6) Calculate the probability density distribution function of the mean organ SAR of the human body exposed to electromagnetic radiation from the WPT system when the human body is located on the side and behind the electric vehicle based on the sparse chaotic polynomial. (7) Rewrite the sparse chaotic polynomial into an increasing summation form and use the global sensitivity analysis method to analyze the global sensitivity index of the input variable; The expansion of the generalized chaotic polynomial is achieved by utilizing multidimensional orthogonal polynomials. The original model Expand infinitely, in the following ways: Simplified to （1） in, Here, is the coefficient of the polynomial to be solved, and d is the dimension of the model input variables. Dimensional input variables , It is a multi-index of size d. The mixed orthogonal polynomial of order n is: Dimensional input variables The function.

2. The method for quantifying the uncertainty of human exposure to wireless power transmission devices according to claim 1, characterized in that, For practical application in analysis, equation (1) is truncated, with the truncation order being p. The truncated chaotic polynomial is expressed as: （2）； Among them, the truncated multi-index for And the number of terms P in the truncated chaotic polynomial expansion is: （3） The key to constructing the generalized chaotic polynomial proxy model lies in solving... .

3. The method for quantifying the uncertainty of human exposure to wireless power transmission devices according to claim 1, characterized in that, The sparsity processing method for the generalized chaotic polynomial surrogate model is as follows: (1) Orthogonal matching pursuit method. OMP is a greedy algorithm based on compressed sensing theory. When N is small, it accurately reconstructs the output of the model. OMP is a sequential process. It greedily selects terms from the dictionary D of the basis functions. In the k-th iteration, OMP selects terms from the candidate set. Find the basis function most relevant to the residual r. And add it to the activity set, where The selection process is represented as follows: （4） The polynomial coefficients corresponding to the kth iteration are: The matrix at this time The columns in the table contain the results of the current basis function selection, and the training residuals are obtained through... Once the basis functions are selected, the new PC coefficients are calculated using least squares. The above steps are repeated until the l2 norm of the residuals meets the requirements. (2) Random Greedy Algorithm This algorithm adds a randomization step before finding basis functions and optimizes the calculation of polynomial coefficients and the selection of basis functions in the OMP algorithm; 1) Update strategy The matrix is ​​factored using the thinQR factorization method. Decompose into the product of an orthogonal matrix Q and an upper triangular matrix R: （5） in and Abbreviated as Q and R, in each iteration of the calculation, the number of basis functions increases after selection, and at the same time... A new column will be added. To solve for the coefficients of the current chaotic polynomial and update the residuals, Q and R need to be updated in each iteration. The Gram-Schmidt process is used to update Q and R, and the coefficients of the chaotic polynomial in the current iteration can be calculated by factoring the updated Q and R and solving the upper triangular equation. （6） Meanwhile, QR factorization is used to quickly calculate the residual of the current iteration without solving for the coefficients of the chaotic polynomial. The residual is updated using equation (7): （7） 2) Selection of candidate set function To rank the candidate basis functions in each iteration, an expression is used to represent the future residuals. To accurately calculate the changes in the residuals, a projection matrix is ​​used. If the model contains the j-th basis function, then the precise future residual in the k-th iteration is represented as: （8） Where P is the projection matrix, and in the k-th iteration, P is represented as: （9） The computational cost associated with calculating accurate future residuals mainly lies in the denominator of equation (8). Using QR factorization, equation (8) can be rewritten as: （10） Considering the basis functions in each candidate set The computational cost remains significant, therefore... Updated to: （11） denominator Represented as ,and The initialization is set to In each iteration of the calculation, equation (12) is used for updating: （12） Then, in the k-th iteration, the basis function most relevant to the future residual is selected from the candidate set using equation (13). （13） Through the above calculations, the future residual can be calculated by focusing on the denominator of each candidate in each iteration. (3) Random Greedy Step To reduce the computational cost of selecting the optimal basis function from all candidate basis functions in each iteration of the greedy algorithm, a probabilistic acceleration method is used to construct a compressed representation of the involved matrices during the greedy iteration process. At the start of each iteration, a basis function is randomly selected from the candidate dictionary D. Choose the basis functions from them and select the optimal basis function; Selection is typically made using probability-related methods, usually by letting It is 60; By optimizing and improving the OMP algorithm through the above three parts, the random greedy algorithm can be obtained.

4. The method for quantifying the uncertainty of human exposure to wireless power transmission devices according to claim 1, characterized in that, The global sensitivity index is calculated by quantifying the contribution of the interaction between a single variable or multiple variables to the output variance; this is known as the global sensitivity analysis method. Specifically, the original model is decomposed into a sum of increasing terms. （14） In equation (14), the terms are orthogonal to each other, where Since is a constant and represents the mean of the output model, in order to obtain the variance decomposition formula, the variance is taken on both sides of equation (14): （15） In equation (15), each decomposition term represents the influence of different input variables and the interactions between variables on the output variance. The Sobol sensitivity index is defined as: （16） In equation (16) The first-order sensitivity index represents the contribution of a single variable to the output variance. The total sensitivity index is defined as the sum of the first-order sensitivity index of a variable and the sensitivity indices of the interaction between that variable and other variables. （17）。 5. The method for quantifying the uncertainty of human exposure to wireless power transmission devices according to claim 1, characterized in that, The formula for sparsifying the generalized chaotic multinomial surrogate model using an OMP-based stochastic greedy algorithm is converted into an increasing summation form. Global sensitivity analysis is then used to analyze the global sensitivity index of the input variables, specifically including: 1) Obtain the sparse chaotic polynomial; 2) Convert the sparse chaotic polynomial into an expansion of increasing summation form; 3) Recursively calculate the expansion of the increasing summation form using the integration method, solve for the corresponding coefficients of the decomposition terms, and obtain the expansion of the increasing summation form with known coefficients; take the variance of both sides of the expansion of the increasing summation form with known coefficients to obtain the variance decomposition form. 4) Obtain the global sensitivity index based on the variance decomposition formula; 5) The global sensitivity index includes the sensitivity index and the overall sensitivity index; The expansion of the incremental summation form is: （18） In formula (18) （19） Further calculations yielded the following: （20） Based on the orthogonality of the basis functions of chaotic polynomials, we obtain: （21） By combining equation (21) and equation (16), the global sensitivity index of each variable in the chaotic polynomial surrogate model can be calculated.

6. The method for quantifying the uncertainty of human exposure to wireless power transmission devices according to claim 1, characterized in that, The global sensitivity index includes the first-order sensitivity index and the total sensitivity index.

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