Ballistic targeting method and system based on sobol Monte Carlo method

Abstract

The invention relates to the technical field of aerospace, in particular to a sobo Monte Carlo method-based ballistic targeting method and system, and the method comprises the steps of generating a ballistic parameter sample by using a sobo sequence for ballistic parameters; generating a sample matrix according to the ballistic parameter samples; substituting the sample matrix into a Monte Carlo model for targeting to obtain a corresponding output vector; calculating a Sobol index according to the output vector; and outputting a sensitivity analysis result of the ballistic parameters according to the Sobol index. According to the method, ballistic design can be balanced in performance and design workload, so that the method is suitable for design work of scheme rapid argumentation and rapid iteration.

Description

Technical Field

[0001] This application relates to the field of aerospace technology, and in particular to a ballistic target-firing method and system based on the Sobol Monte Carlo method. Background Technology

[0002] Currently, ballistic design processes dealing with multiple deviation factors rely on deviation envelope design, either using extreme deviation combinations or probabilistic design with random deviation combinations. The former verifies the design by selecting a small number of extreme deviation conditions or fixed deviation boundaries, covering only a limited number of critical conditions. While simple to operate, this approach imposes overly strict design constraints, leading to redundant design margins and failing to achieve an optimal balance between cost and performance. The latter design envelope presents a more favorable distribution of deviation probabilities, but requires massive simulation calculations and complex condition designs, resulting in an extremely large workload and high time costs. Therefore, current ballistic design methods struggle to simultaneously address the core requirements of "design margin optimization" and "design efficiency improvement," failing to achieve a balance between performance and workload, and are unsuitable for rapid feasibility studies and iterative design processes.

[0003] Furthermore, in traditional ballistic design methods, random combinations of deviations are used, and then ballistic simulation software is used to simulate and calculate the design results for each combination. The sensitivity of different deviation combinations to the design results is analyzed, and critical deviation combinations that cause the design results to fail to meet the performance requirements are identified. However, this ballistic design method is inefficient and requires extensive simulation support.

[0004] Therefore, how to achieve a balance between performance and workload in ballistic design to make it suitable for rapid demonstration and iteration of design schemes is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This application provides a ballistic target-firing method and system based on the Sobol Monte Carlo method, which achieves a balance between performance and workload in ballistic design, making it suitable for rapid scheme demonstration and rapid iterative design work.

[0006] To solve the above-mentioned technical problems, this application provides the following technical solution:

[0007] A ballistic target shooting method based on the Sobol Monte Carlo method includes the following steps: Step S110, generating ballistic parameter samples using a Sobol sequence for the ballistic parameters; Step S120, generating a sample matrix based on the ballistic parameter samples; Step S130, substituting the sample matrix into a Monte Carlo model for target shooting to obtain the corresponding output vector; Step S140, calculating the Sobol exponent based on the output vector; Step S150, outputting the sensitivity analysis results of the ballistic parameters based on the Sobol exponent.

[0008] The ballistic target shooting method based on the Sobol Monte Carlo method described above preferably includes generating ballistic parameter samples by: generating a Sobol sequence that follows a uniform distribution of U(0,1); determining the cumulative distribution function and inverse cumulative distribution function of each ballistic parameter; using the inverse cumulative distribution function of each ballistic parameter to convert each uniform random number in the Sobol sequence into a ballistic parameter sample; and substituting the converted ballistic parameter sample into the cumulative distribution function of the ballistic parameter to verify the conversion effect of the random number in the Sobol sequence into the ballistic parameter sample.

[0009] The ballistic target acquisition method based on the Sobol Monte Carlo method described above preferably includes generating a sample matrix by: constructing two independent N*k sampling sample matrices A and B based on the ballistic parameter samples, where N is the sample size and k is the number of input sample parameters; and generating a perturbation sample matrix C for each input sample parameter j (j = 1, 2, ..., k). j The construction rule for the perturbation sample matrix is ​​as follows: Perturbation sample matrix C j The j-th column is replaced with the j-th column of the sample matrix B, while the remaining columns remain consistent with the sample matrix A.

[0010] The ballistic target-firing method based on the Sobol Monte Carlo method described above is characterized by the following steps: calculating the Sobol exponents, which includes: after obtaining the output vectors through the Monte Carlo model, calculating the first-order Sobol exponent and the total-order Sobol exponent based on these output vectors.

[0011] A ballistic target shooting system based on the Sobol Monte Carlo method, preferably comprising: a sample generation unit, a sample matrix generation unit, a target shooting unit, an exponent calculation unit, and a result output unit; wherein, the sample generation unit uses a Sobol sequence to generate ballistic parameter samples for the ballistic parameters; the sample matrix generation unit generates a sample matrix based on the ballistic parameter samples; the target shooting unit substitutes the sample matrix into a Monte Carlo model for target shooting to obtain the corresponding output vector; the exponent calculation unit calculates the Sobol exponent based on the output vector; and the result output unit outputs the ballistic parameter sensitivity analysis results based on the Sobol exponent.

[0012] In the ballistic target system based on the Sobol Monte Carlo method described above, preferably, the sample generation unit generates a Sobol sequence that follows a uniform distribution of U(0,1), determines the cumulative distribution function and inverse cumulative distribution function of each ballistic parameter, uses its inverse cumulative distribution function to convert each uniform random number in the Sobol sequence into a ballistic parameter sample, and substitutes the converted ballistic parameter sample into the cumulative distribution function of the ballistic parameter to verify the conversion effect of the random number in the Sobol sequence into the ballistic parameter sample.

[0013] In the ballistic target acquisition system based on the Sobol Monte Carlo method described above, preferably, the sample matrix generation unit constructs two independent N*k sampling sample matrices A and B based on the ballistic parameter samples, where N is the sample size and k is the number of input sample parameters. For each input sample parameter j (j = 1, 2, ..., k), a perturbation sample matrix C is generated. j The construction rule for the perturbation sample matrix is ​​as follows: Perturbation sample matrix C j The j-th column is replaced with the j-th column of the sample matrix B, while the remaining columns remain consistent with the sample matrix A.

[0014] In the ballistic target system based on the Sobol Monte Carlo method described above, preferably, after obtaining the output vector through the Monte Carlo model, the exponent calculation unit calculates the first-order Sobol exponent and the total-order Sobol exponent based on these output vectors.

[0015] Compared to the aforementioned background technology, this application combines the Monte Carlo model with the Sobol sequence. By utilizing the low-discrepancy samples in the [0,1) interval of the Sobol sequence's original output, the influence of design variables can be obtained by using a small sample design condition. This allows for the efficient execution of Monte Carlo target practice, avoiding the use of traditional pseudo-random numbers in the Monte Carlo model. Consequently, a balance can be achieved between ballistic design performance and workload, making it suitable for rapid scheme demonstration and rapid iteration design work. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0017] Figure 1 This is a flowchart of the ballistic target shooting method based on the Sobol Monte Carlo method provided in this application;

[0018] Figure 2 This is a schematic diagram of the ballistic target system based on the Sobol Monte Carlo method provided in this application. Detailed Implementation

[0019] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0020] Example 1

[0021] like Figure 1 As shown, this application provides a ballistic target-firing method based on the Sobol Monte Carlo method, including the following steps:

[0022] Step S110: Use the Sobol sequence to generate ballistic parameter samples for the ballistic parameters;

[0023] First, a Sobol sequence following a uniform distribution U(0,1) is generated. Since the Sobol sequence is uniformly distributed, omissions or duplicates that may occur during random sampling can be avoided. Then, the cumulative distribution function and inverse cumulative distribution function of each ballistic parameter are determined. For each ballistic parameter, its inverse cumulative distribution function is used to transform each uniformly random number in the Sobol sequence into a ballistic parameter sample x. i =F -1 (p i ); where x i For the i-th ballistic parameter sample, p i F is the i-th random number in the Sobol sequence. -1 (·) is the inverse cumulative distribution function.

[0024] Furthermore, the generated ballistic parameter samples x i Substituting the cumulative distribution function F(x) into the ballistic parameters i The result is determined to be a uniform or approximately uniform distribution, i.e., to restore the uniformity of the Sobol sequence, in order to verify the conversion effect of the random number conversion of the Sobol sequence into ballistic parameter samples.

[0025] In addition, some ballistic parameters have hard constraints (e.g., fuel combustion efficiency cannot exceed 1.0). After converting the ballistic parameters into ballistic parameter samples, outliers need to be filtered out. For ballistic parameters with strong physical correlation (e.g., thrust coefficient and fuel consumption rate), after converting the ballistic parameters into ballistic parameter samples, logical checks can be added to the ballistic parameter samples (e.g., synchronously adjusting fuel consumption when thrust is too high).

[0026] Step S120: Generate sample matrices A, B, and C based on the ballistic parameter samples. j ;

[0027] After generating ballistic parameter samples, two independent N*k sampling sample matrices A and B are constructed based on the ballistic parameter samples, where N is the sample size and k is the number of input sample parameters. Each element in the sampling sample matrix follows the marginal distribution of the sample parameters (e.g., uniform distribution, normal distribution).

[0028] Example: If there are 2 input sample parameters (k=2) and 1000 samples (N=1000), then the sampling sample matrix A = {a 11 ,a 12 ;a 21 ,a 22 ;…;a 10001 ,a 10002}, where a 11 Let a be the first input sample parameter in the first group of the sample matrix A. 12 Let a be the second input sample parameter in the first group of the sample matrix A. 21 Let a be the first input sample parameter in the second group of the sample matrix A. 22 Let a be the second input sample parameter in the second group of the sample matrix A. 10001 Let a be the first input sample parameter of the 1000th group in the sampling sample matrix A. 10002 This is the second input sample parameter in the 1000th group of the sampling sample matrix A, and the same applies to the sampling sample matrix B.

[0029] In addition, for each input sample parameter j (j = 1, 2, ..., k), a perturbation sample matrix C is generated. j The construction rule for the perturbation sample matrix is ​​as follows: Perturbation sample matrix C j The j-th column is replaced with the j-th column of the sample matrix B, while the remaining columns remain consistent with the sample matrix A. Example: When k=2, C 1 =[B1,A2], C 2 = [A1, B2]; where C 1 For the first perturbation sample matrix, C 2 Let A1 be the first column of sample matrix A, A2 be the second column of sample matrix A, B1 be the first column of sample matrix B, and B2 be the second column of sample matrix B.

[0030] Step S130: Combine sample matrices A, B, and C. j Substitute the values ​​into the Monte Carlo model to perform target shooting, and obtain the corresponding output vector;

[0031] Sample matrix A, sample matrix B, and all perturbation sample matrix C are used. j Substituting into the Monte Carlo model f(·), we obtain the corresponding output vector;

[0032] Y_A = f(A)

[0033] Y_B=f(B)

[0034] Y_C j =f(C j )

[0035] Where Y_A is the output vector corresponding to the sample matrix A, Y_B is the output vector corresponding to the sample matrix B, and Y_C j For the perturbation sample matrix C j The corresponding output vector.

[0036] Step S140: Calculate the Sobol exponent based on the output vector;

[0037] The output vectors Y_A, Y_B, and Y_C are obtained through the Monte Carlo model. j Then, based on these output vectors Y_A, Y_B, and Y_C j The first-order Sobol exponent and the total-order Sobol exponent are calculated.

[0038] Specifically, the total variance V is first calculated using the output vector Y_A. The expression for the total variance V is as follows:

[0039]

[0040] Where Var(·) is the variance. Let Y_A be the mean.

[0041] Then, through the total variance V, output vectors Y_A, Y_B, and Y_C j The first-order Sobol exponent S was calculated. j The first-order Sobol exponent S j The expression is as follows:

[0042] S j =V j / V

[0043] in,

[0044] Additionally, the total variance V, output vectors Y_A, Y_B, and Y_C are used to... j The total order Sobol exponent S_T is calculated. j The total order Sobol exponent S_T j The expression is as follows:

[0045] S_T j =1-V_{-j} / V

[0046] in,

[0047] Step S150: Output the ballistic parameter sensitivity analysis results based on the Sobol index;

[0048] First-order Sobol exponent S j Or the total order Sobol exponent S_T j The closer the value is to 1, the greater the influence of the ballistic parameter on the output; conversely, the smaller the value is, the smaller the influence. The degree of influence of the ballistic parameter on the output is used as the output of the ballistic parameter sensitivity analysis. Based on the ballistic parameter sensitivity analysis results, improvements are implemented for highly sensitive trajectory parameters through an iterative design process to obtain optimized results.

[0049] Furthermore, by comparing and analyzing the deviations between different combinations of working conditions, a ranking of the weights of sensitive ballistic parameters is formed. This analysis process can quantify the "influence of the design variables themselves" (first-order Sobol index) and the "interaction between the design variables and other factors" (total-order Sobol index), which is the implementation process of sensitivity analysis.

[0050] Example 2

[0051] like Figure 2 As shown, this application provides a ballistic target shooting system 200 based on the Sobol Monte Carlo method, including: a sample generation unit 210, a sample matrix generation unit 220, a target shooting unit 230, an index calculation unit 240, and a result output unit 250.

[0052] The sample generation unit 210 uses the Sobol sequence to generate ballistic parameter samples for the ballistic parameters.

[0053] First, a Sobol sequence following a uniform distribution U(0,1) is generated. Since the Sobol sequence is uniformly distributed, omissions or duplicates that may occur during random sampling can be avoided. Then, the cumulative distribution function and inverse cumulative distribution function of each ballistic parameter are determined. For each ballistic parameter, its inverse cumulative distribution function is used to transform each uniformly random number in the Sobol sequence into a ballistic parameter sample x. i =F -1 (p i ); where x i For the i-th ballistic parameter sample, p i F is the i-th random number in the Sobol sequence. -1 (·) is the inverse cumulative distribution function.

[0054] Furthermore, the generated ballistic parameter samples x i Substituting the cumulative distribution function F(x) into the ballistic parameters i The result is determined to be a uniform or approximately uniform distribution, i.e., to restore the uniformity of the Sobol sequence, in order to verify the conversion effect of the random number conversion of the Sobol sequence into ballistic parameter samples.

[0055] In addition, some ballistic parameters have hard constraints (e.g., fuel combustion efficiency cannot exceed 1.0). After converting the ballistic parameters into ballistic parameter samples, outliers need to be filtered out. For ballistic parameters with strong physical correlation (e.g., thrust coefficient and fuel consumption rate), after converting the ballistic parameters into ballistic parameter samples, logical checks can be added to the ballistic parameter samples (e.g., synchronously adjusting fuel consumption when thrust is too high).

[0056] Sample matrix generation unit 220 generates sample matrices A, B, and C based on ballistic parameter samples. j .

[0057] After generating ballistic parameter samples, two independent N*k sampling sample matrices A and B are constructed based on the ballistic parameter samples, where N is the sample size and k is the number of input sample parameters. Each element in the sampling sample matrix follows the marginal distribution of the sample parameters (e.g., uniform distribution, normal distribution).

[0058] Example: If there are 2 input sample parameters (k=2) and 1000 samples (N=1000), then the sampling sample matrix A = {a 11 ,a 12 ;a 21 ,a 22 ;…;a 10001 ,a 10002}, where a 11 Let a be the first input sample parameter in the first group of the sample matrix A. 12 Let a be the second input sample parameter in the first group of the sample matrix A. 21 Let a be the first input sample parameter in the second group of the sample matrix A. 22 Let a be the second input sample parameter in the second group of the sample matrix A. 10001 Let a be the first input sample parameter of the 1000th group in the sampling sample matrix A. 10002 This is the second input sample parameter in the 1000th group of the sampling sample matrix A, and the same applies to the sampling sample matrix B.

[0059] In addition, for each input sample parameter j (j = 1, 2, ..., k), a perturbation sample matrix C is generated. j The construction rule for the perturbation sample matrix is ​​as follows: Perturbation sample matrix C jThe j-th column is replaced with the j-th column of the sample matrix B, while the remaining columns remain consistent with the sample matrix A. Example: When k=2, C 1 =[B1,A2], C 2 = [A1, B2]; where C 1 For the first perturbation sample matrix, C 2 Let A1 be the first column of sample matrix A, A2 be the second column of sample matrix A, B1 be the first column of sample matrix B, and B2 be the second column of sample matrix B.

[0060] Targeting unit 230 will use sample matrices A, B, and C j Substitute the values ​​into the Monte Carlo model to perform target practice, and obtain the corresponding output vector.

[0061] Sample matrix A, sample matrix B, and all perturbation sample matrix C are used. j Substituting into the Monte Carlo model f(·), we obtain the corresponding output vector;

[0062] Y_A = f(A)

[0063] Y_B=f(B)

[0064] Y_C j =f(C j )

[0065] Where Y_A is the output vector corresponding to the sample matrix A, Y_B is the output vector corresponding to the sample matrix B, and Y_C j For the perturbation sample matrix C j The corresponding output vector.

[0066] The index calculation unit 240 calculates the Sobol index based on the output vector.

[0067] The output vectors Y_A, Y_B, and Y_C are obtained through the Monte Carlo model. j Then, based on these output vectors Y_A, Y_B, and Y_C j The first-order Sobol exponent and the total-order Sobol exponent are calculated.

[0068] Specifically, the total variance V is first calculated using the output vector Y_A. The expression for the total variance V is as follows:

[0069]

[0070] Where Var(·) is the variance. Let Y_A be the mean.

[0071] Then, through the total variance V, output vectors Y_A, Y_B, and Y_C jThe first-order Sobol exponent S was calculated. j The first-order Sobol exponent S j The expression is as follows:

[0072] S j =V j / V

[0073] in,

[0074] Additionally, the total variance V, output vectors Y_A, Y_B, and Y_C are used to... j The total order Sobol exponent S_T is calculated. j The total order Sobol exponent S_T j The expression is as follows:

[0075] S_T j =1-V_{-j} / V

[0076] in,

[0077] The output unit 250 outputs the ballistic parameter sensitivity analysis results based on the Sobol index.

[0078] First-order Sobol exponent S j Or the total order Sobol exponent S_T j The closer the value is to 1, the greater the influence of the ballistic parameter on the output; conversely, the smaller the value is, the smaller the influence. The degree of influence of the ballistic parameter on the output is used as the output of the ballistic parameter sensitivity analysis. Based on the ballistic parameter sensitivity analysis results, improvements are implemented for highly sensitive trajectory parameters through an iterative design process to obtain optimized results.

[0079] Furthermore, by comparing and analyzing the deviations between different combinations of working conditions, a ranking of the weights of sensitive ballistic parameters is formed. This analysis process can quantify the "influence of the design variables themselves" (first-order Sobol index) and the "interaction between the design variables and other factors" (total-order Sobol index), which is the implementation process of sensitivity analysis.

[0080] This application combines the Monte Carlo model with the Sobol sequence. By utilizing the low-discrepancy samples in the [0,1) interval of the Sobol sequence's original output, the influence of design variables can be obtained by using a small sample design condition. This allows for the efficient execution of Monte Carlo target practice, avoiding the use of traditional pseudo-random numbers in the Monte Carlo model. Consequently, a balance can be achieved between ballistic design performance and workload, making it suitable for rapid scheme demonstration and rapid iterative design work.

[0081] As an example, in ballistic simulation, to determine whether the design results conform to the design constraints, analysis is required:

[0082] The design variables are grouped according to the Sobol sequence. When generating test cases using the Sobol sequence, it is best to use a power of 2 as the total number of sample cases. Taking 3 samples as an example, the following are examples to satisfy the requirements of uniform spatial distribution, comprehensive coverage, good orthogonality, and the ability to explore the entire design space.

[0083]

[0084] Based on the Sobol operating condition sequence, preliminary simulations are performed, followed by Monte Carlo simulation analysis to obtain the overall design result distribution (generally represented by a histogram to show normal distribution and other relationships), and then sensitivity analysis is conducted.

[0085] Sensitivity analysis results: The influence of input variables on output variables, after normalization, the lower the value, the smaller the influence, and the higher the value, the greater the influence. Negative values ​​indicate a negative correlation.

[0086]

[0087] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0088] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A ballistic target-firing method based on the Sobol Monte Carlo method, characterized in that, Includes the following steps: Step S110: Use the Sobol sequence to generate ballistic parameter samples for the ballistic parameters; Step S120: Generate a sample matrix based on the ballistic parameter samples; Step S130: Substitute the sample matrix into the Monte Carlo model to perform target shooting and obtain the corresponding output vector; Step S140: Calculate the Sobol exponent based on the output vector; Step S150: Output the sensitivity analysis results of the ballistic parameters based on the Sobol index.

2. The ballistic target-firing method based on the Sobol Monte Carlo method according to claim 1, characterized in that, Generate ballistic parameter samples, including: Generate Sobol sequences that follow a uniform distribution of U(0,1); Determine the cumulative distribution function and inverse cumulative distribution function for each ballistic parameter, and use its inverse cumulative distribution function to transform each uniform random number in the Sobol sequence into a ballistic parameter sample. The generated ballistic parameter samples were substituted into the cumulative distribution function of the ballistic parameters to verify the transformation effect of the random number transformation of the Sobol sequence into ballistic parameter samples.

3. The ballistic target-firing method based on the Sobol Monte Carlo method according to claim 1 or 2, characterized in that, Generate a sample matrix, including: Two independent N*k sampling matrix A and B are constructed based on the ballistic parameter samples, where N is the sample size and k is the number of input sample parameters; For each input sample parameter j (j = 1, 2, ..., k), generate a perturbation sample matrix C. j ; The construction rule for the perturbation sample matrix is ​​as follows: Perturbation sample matrix C j The j-th column is replaced with the j-th column of the sample matrix B, while the remaining columns remain consistent with the sample matrix A.

4. The ballistic target-firing method based on the Sobol Monte Carlo method according to claim 1 or 2, characterized in that, Calculating the Sobol index includes: After obtaining the output vectors through the Monte Carlo model, the first-order Sobol exponent and the total-order Sobol exponent are calculated based on these output vectors.

5. A ballistic target-firing system based on the Sobol Monte Carlo method, characterized in that, include: Sample generation unit, sample matrix generation unit, target shooting unit, index calculation unit, and result output unit; The sample generation unit uses the Sobol sequence to generate ballistic parameter samples for the ballistic parameters. The sample matrix generation unit generates a sample matrix based on the ballistic parameter samples; The target unit substitutes the sample matrix into the Monte Carlo model to perform target shooting and obtains the corresponding output vector. The exponent calculation unit calculates the Sobol exponent based on the output vector; The output unit outputs the ballistic parameter sensitivity analysis results based on the Sobol exponent.

6. The ballistic target system based on the Sobol Monte Carlo method according to claim 5, characterized in that, The sample generation unit generates a Sobol sequence that follows a uniform distribution of U(0,1), determines the cumulative distribution function and inverse cumulative distribution function of each ballistic parameter, and uses its inverse cumulative distribution function to transform each uniform random number in the Sobol sequence into a ballistic parameter sample. The transformed ballistic parameter sample is then substituted into the cumulative distribution function of the ballistic parameter to verify the transformation effect of the random number in the Sobol sequence into a ballistic parameter sample.

7. The ballistic target system based on the Sobol Monte Carlo method according to claim 5 or 6, characterized in that, The sample matrix generation unit constructs two independent N*k sampling sample matrices A and B based on the ballistic parameter samples, where N is the sample size and k is the number of input sample parameters. For each input sample parameter j (j = 1, 2, ..., k), a perturbation sample matrix C is generated. j The construction rule for the perturbation sample matrix is ​​as follows: Perturbation sample matrix C j The j-th column is replaced with the j-th column of the sample matrix B, while the remaining columns remain consistent with the sample matrix A.

8. The ballistic target system based on the Sobol Monte Carlo method according to claim 5 or 6, characterized in that, After obtaining the output vector through the Monte Carlo model, the exponent calculation unit calculates the first-order Sobol exponent and the total-order Sobol exponent based on these output vectors.

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