Confidence calculation method of underwater acoustic target strength simulation model based on orthogonal design

Abstract

The application discloses a confidence degree calculation method of a water acoustic target intensity simulation model based on orthogonal design, and comprises the following steps: S1, determining the calculation result and the uncertainty of the water acoustic target intensity simulation model; S2, determining the test result and the uncertainty of the water acoustic target intensity test; S3, determining the upper limit and the lower limit of the simulation model result and the upper limit and the lower limit of the test result, drawing a water acoustic target intensity simulation model confidence degree evaluation diagram, and calculating the confidence degree of the water acoustic target intensity simulation model. In view of the actual test difficulties of the water acoustic material component target intensity evaluation, such as far-field test limitation, low signal-to-noise ratio and accurate positioning difficulty, the simulation technology is used to make up for the deficiency of the actual test, the confidence degree of the simulation result is mainly considered, the calculation method improves the reliability of the simulation result, and belongs to an innovative method applied to the field of underwater electric acoustic parameter simulation and test.

Description

Technical Field

[0001] The invention belongs to the field of underwater electroacoustic parameter simulation and testing, and particularly relates to a method for calculating the confidence of an underwater acoustic target intensity simulation model based on orthogonal design. Background Art

[0002] Target strength assessment of underwater acoustic material components is a crucial task in the development of underwater acoustic technology and a key element in ensuring and enhancing the stealth and tactical advantages of naval and other underwater equipment. This assessment is crucial for verifying the effectiveness of new material technologies and ensuring the long-term stability and adaptability of equipment in complex marine environments. It is also crucial for advancing the development of underwater acoustic countermeasure strategies, optimizing underwater combat deployments, and promoting innovation in underwater acoustic signal processing and target recognition technologies. It bridges basic scientific research with practical application, and has strategic significance for maintaining national security and enhancing underwater combat and detection capabilities.

[0003] The actual testing of target strength of large-area samples of underwater acoustic material components is the primary evaluation method. However, due to technical difficulties such as the difficulty in meeting far-field test conditions in open waters, the difficulty in obtaining high signal-to-noise ratio signals, and the difficulty in achieving high-precision positioning and orientation, it is often difficult to obtain accurate component target strength values. Given the various challenges faced by underwater acoustic material component target strength testing, underwater acoustic target strength simulation has become an indispensable and important supplementary method. Using methods such as finite element analysis, underwater sound field propagation, material scattering characteristics, and the interaction between the target and the environment are reproduced in a simulated environment. This can assist in identifying the validity of test results while ensuring accurate calculations. However, when using simulation technology to evaluate the target strength of underwater acoustic material components, multiple key factors, including the degree of mesh refinement, the choice of calculation algorithm, the thickness of the perfectly matched layer (PML), and the scope of the simulated water area, can affect the calculation results. In order to measure the accuracy and reliability of simulation calculation results, it is necessary to establish a systematic confidence assessment method for underwater acoustic target strength simulation models.

[0004] Current methods for assessing the confidence of simulation models fall into two main categories: empirically based qualitative assessment methods and data-driven quantitative analysis methods. Qualitative assessment methods rely on the past experience of domain experts, subjectively determining the model's confidence level by comparing the degree of agreement between simulation data and measured data. While simple and convenient to operate, these methods are highly subjective and susceptible to personal judgment, limited experience, and external interference, making objectivity and consistency difficult to guarantee. Quantitative analysis methods employ mathematical statistical analysis, time / frequency domain, and time-frequency domain analysis methods to calculate the consistency, correlation, or similarity of data obtained from simulation and experimentation, thereby quantifying the confidence level of the simulation model. These methods offer the advantages of high objectivity and a well-defined scope of application.

[0005] Currently, there are few reports on the confidence level of underwater acoustic target intensity simulation models. An analysis of relevant literature and research findings on simulation model confidence assessment methods reveals that existing assessment methods primarily rely on quantitative analysis. While these methods consider the consistency and correlation between simulation and experimental data, they do not simultaneously assess the uncertainty of both simulation and experimental results to determine the confidence level of the simulation model. Summary of the Invention

[0006] In order to solve the problems existing in the existing underwater acoustic target intensity confidence assessment method technology, the present invention provides a method for calculating the confidence of an underwater acoustic target intensity simulation model, determines the uncertainty of the simulation results and the test results, and provides the evaluation standard of the simulation results - confidence based on the mutual envelope results of the simulation and test results, thereby ensuring the reliability of the simulation results.

[0007] The technical solution of the present invention is:

[0008] The confidence calculation method of the underwater acoustic target intensity simulation model based on orthogonal design is characterized by comprising the following steps:

[0009] S1. Determine the calculation results and uncertainty of the underwater acoustic target intensity simulation model:

[0010] S11. Establish a finite element model of the structure based on the structural parameters and material properties of the structure, and take the arithmetic average of the target strength calculated multiple times at each frequency point as the best estimate;

[0011] S12. Analyze the uncertainty or error sources of the underwater acoustic target intensity simulation test and select the important factors as the experimental orthogonal design level;

[0012] S13. Select an appropriate orthogonal table, determine the design plan for the underwater acoustic target intensity simulation test, conduct simulation tests according to the plan, analyze the standard deviation of the test results, and check whether important factors or interactions between important factors are omitted;

[0013] S14. Evaluate the uncertainty of type A and type B of the simulation model test, calculate the standard uncertainty of the model synthesis, and obtain the expanded uncertainty;

[0014] S2. Determine the test results and uncertainty of the underwater acoustic target intensity test:

[0015] S21. Under a stable test environment, measure the underwater acoustic target intensity of the structure that matches the simulation model, and take the arithmetic mean of multiple measurements at each frequency point as the best estimate;

[0016] S22. Evaluate the Class A and Class B uncertainty of the underwater acoustic target intensity test results, calculate the model synthesis standard uncertainty, and obtain the expanded uncertainty;

[0017] S3. Based on the simulation model calculation results and their expanded uncertainty, the test results and their expanded uncertainty, determine the upper and lower limits of the simulation model results, the upper and lower limits of the test results, draw the confidence evaluation diagram of the underwater acoustic target intensity simulation model, and calculate the confidence of the underwater acoustic target intensity simulation model based on the mutual envelope area of ​​the simulation and test results, that is,

[0018] ,

[0019] Where S 仿真模型∪试验 It is the union of the upper and lower limits of the simulation model calculation results and the upper and lower limits of the test results. The upper limit of the simulation model calculation results is the absolute value of the sum of the best estimate of the simulation model and its expanded uncertainty. The lower limit of the simulation model calculation results is the absolute value of the difference between the best estimate of the simulation model and its expanded uncertainty. The upper limit of the test result is the absolute value of the sum of the best estimate of the test result and its expanded uncertainty. The lower limit of the test result is the absolute value of the difference between the best estimate of the test result and its expanded uncertainty. S 仿真模型∩试验 It is the intersection of the upper and lower limits of the simulation model calculation results and the upper and lower limits of the test results.

[0020] Preferably, in step S11, the interior of the structure is air, the exterior of the structure is water, and the outer side connected to the water is a perfectly matched layer (PML).

[0021] Preferably, in step S11, the structural parameters of the structure include geometric parameters such as diameter and thickness, the material properties of the structure include elastic modulus, density, and Poisson's ratio, and the material properties of the water include density and sound velocity. Acoustic-solid coupling is considered in the finite element model of the structure, and the underwater acoustic target intensity of the structure is calculated according to the following formula:

[0022] TS =20lg│ P l · l │

[0023] Where, TS is the underwater acoustic target intensity, P l Calculated by the target strength simulation model l The external sound pressure value at the position, l For distance.

[0024] Preferably, in step S12, since the grid scale is an important parameter of the finite element calculation method in the process of solving the sound pressure in the frequency domain using the finite element method, the size setting of the water area will affect the calculation of the sound pressure, and the thickness of the perfect matching layer can ensure that the truncation error of the far-field sound pressure is within a controllable range. Different calculation algorithms have an impact on the accuracy, calculation efficiency, scope of application, stability and resource requirements of the underwater acoustic target intensity simulation model. Therefore, it is necessary to systematically analyze the factor levels in the underwater acoustic target intensity simulation model and select 3 to 5 factors as important factors.

[0025] Preferably, in step S12, the maximum grid size, water area range, perfectly matched layer (PML) thickness, calculation algorithm, etc. can be selected as important factors in the underwater acoustic target intensity simulation model, and the number of levels is selected based on experience, and the number of levels is 3.

[0026] Preferably, in step S13, the orthogonal array type is determined according to the appropriate number of factors and levels, and the interaction between factors is determined. In the underwater acoustic target intensity simulation model, the number of factors is 4 and the number of levels is 3. Considering the influence of the interaction, the orthogonal design table L27 (3 13 ), where the interactions are the interaction between the maximum grid size and the water area, the interaction between the maximum grid size and the thickness of the perfectly matched layer (PML), and the interaction between the water area and the thickness of the perfectly matched layer (PML).

[0027] Preferably, in step S14, the Class A uncertainty assessment mainly considers the repeatability of simulation calculation results under important factors and their interactions, and is calculated according to the following formula:

[0028] ,

[0029] ,

[0030] Where x i is the result obtained from the ith simulation calculation, is the average value of the n simulation calculation results, s(x) is the standard deviation of the n simulation calculation results, and u(x) represents the value of Class A uncertainty.

[0031] Preferably, in step S14, the Class B uncertainty assessment mainly considers the calculation errors existing in the numerical calculation algorithm, including the uncertainty caused by the truncation error and the iteration error. Since the iteration error is very small and can be ignored, the truncation error is mainly considered and considered as a uniform distribution, that is,

[0032] ,

[0033] Where δ is the iterative error value, estimated by Richardson extrapolation method, k is the inclusion factor, which is calculated as consider.

[0034] Preferably, in step S21, the stable test environment should meet the far-field test distance requirements of the structural test piece size and the requirements of high-precision positioning.

[0035] Preferably, in step S22, the Class A uncertainty assessment mainly considers the repeatability of the test results and is calculated using the standard deviation.

[0036] Preferably, in step S22, the Class B uncertainty assessment mainly considers factors such as inaccurate oscilloscope DC gain, horizontal fluctuations in hydrophone sensitivity, uneven incident sound field, distance measurement error, total harmonic distortion of the power amplifier, and uneven scattered sound field.

[0037] The beneficial effects of the present invention are: in response to the actual testing difficulties faced in the target strength assessment of underwater acoustic material components, such as far-field testing limitations, low signal-to-noise ratio and problems with precise positioning, the present invention uses simulation technology to make up for the shortcomings of actual measurement, focusing on the confidence level of the simulation results. The provided calculation method improves the reliability of the simulation results, and is an innovative method applied to the field of underwater electroacoustic parameter simulation and testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 The flowchart of the confidence calculation method of the underwater acoustic target intensity simulation model based on orthogonal design is shown;

[0039] Figure 2 This is a structural diagram of the underwater acoustic target intensity simulation model;

[0040] Figure 2 Middle: 10 is the structure, 20 is air, 30 is water, and 40 is the perfectly matched layer (PML);

[0041] Figure 3 Diagram of the sound field and test instrument structure for underwater acoustic target intensity test;

[0042] Figure 3 Middle: 1 is the lifting and rotating device, 2 is the target structure, 3 is the hydrophone connecting rod, 4 is the standard hydrophone, 5 is the transmitting converter, 6 is the computer, 7 is the oscilloscope, 8 is the power amplifier, and 9 is the signal source;

[0043] Figure 4 This is the confidence assessment diagram of the underwater acoustic target intensity simulation model. DETAILED DESCRIPTION

[0044] In the description of the present invention, it should be understood that the terms "inside", "outside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0045] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0046] The present invention provides a method for calculating the confidence of an underwater acoustic target intensity simulation model based on orthogonal design. By combining orthogonal design theory and introducing a systematic calculation process, the method comprehensively considers the uncertainty of the simulation model calculation results and the experimental test results for the first time to evaluate the confidence of the simulation model. The method first establishes an underwater acoustic target intensity simulation model through finite element analysis, systematically analyzes the sources of uncertainty in the model, selects key factors for orthogonal design, considers the interaction between the factors, and obtains the best estimate and uncertainty through multiple simulation calculations. Secondly, the uncertainty of the test results of the physical test of the underwater acoustic target intensity is evaluated. Finally, the confidence of the simulation model is obtained by calculating the area ratio of the intersection and union of the upper and lower limits of the simulation and experimental results. The present invention optimizes the confidence evaluation process of the underwater acoustic target intensity simulation through orthogonal design, thereby ensuring the reliability of the simulation results.

[0047] Reference Figure 1 The present invention provides a method for calculating the confidence of an underwater acoustic target intensity simulation model based on orthogonal design. The steps of a specific embodiment are as follows:

[0048] Step S1: Determine the calculation result and uncertainty of the underwater acoustic target intensity simulation model:

[0049] Step S11: Establish a finite element model of the structure according to the structural parameters and material properties of the structure, such as Figure 2 As shown, the structural parameters of the structure 10 (considered to be a rigid standard sphere) include its geometric parameters (diameter, thickness), the material properties of the structure 10 include elastic modulus, density, and Poisson's ratio, the interior of the structure 10 is air 20, and the material properties of the air 20 include density and sound velocity, the exterior of the structure 10 is water 30, and the material properties of the water 30 include density and sound velocity, and the outer side connected to the water is a perfectly matched layer (PML) 40. Acoustic-solid coupling is considered in the model, and the underwater acoustic target intensity of the structure 10 is calculated according to the following formula:

[0050] TS =20lg│ P l · l │

[0051] Where, TS is the underwater acoustic target intensity, P l Calculated by the target strength simulation model l The external sound pressure value at the position, l For distance.

[0052] In the above formula, the sound pressure values ​​at all positions can be calculated by solving the wave equation, and the fixed l The sound pressure value at the location.

[0053] Step S12: Analyze the uncertainty or error sources of the underwater acoustic target intensity simulation test, and select important factors as the experimental orthogonal design levels. After systematically analyzing the factor levels in the underwater acoustic target intensity simulation model, 3 to 5 factors are selected as important factor levels. In the underwater acoustic target intensity simulation model, the maximum grid scale, water area, perfectly matched layer (PML) thickness, calculation algorithm, etc. can be selected as important factors. The number of levels is selected based on experience, and the number of levels is 3, as shown in Table 1. In the table, lam represents the wavelength of the sound wave. D is the diameter of the spherical structural member.

[0054] Table 1. Levels of important factors in underwater acoustic target intensity simulation model

[0055]

[0056] Step S13: Select a suitable orthogonal table, determine the design scheme of the underwater acoustic target intensity simulation test, conduct simulation tests according to the scheme, perform standard deviation analysis on the test results, and check whether important factors or interactions between important factors are omitted. Determine the type of orthogonal table based on the appropriate number of factors and levels, and determine the interactions between factors. In the underwater acoustic target intensity simulation model, the number of factors is 4 and the number of levels is 3. The orthogonal design table L can be selected. 27 (3 13 ), where the interactions are the interaction between the maximum grid size and the water area, the interaction between the maximum grid size and the thickness of the perfectly matched layer (PML), and the interaction between the water area and the thickness of the perfectly matched layer (PML), as shown in Table 2.

[0057] Table 2 Orthogonal array design L 27 (3 13 )

[0058]

[0059] Note: The above table is an orthogonal table L 27 (3 13 )'s canonical structure, orthogonal table L 27 (3 13) is a commonly used orthogonal table, which is suitable for studying the experimental design of 13 three-level factors. The characteristic of this table is that in 27 experiments, the three levels of 13 factors (usually recorded as 1, 2, and 3) can be examined in a balanced manner, and the factors are orthogonal to each other.

[0060] The simulation test results are shown in Table 3, where: TS M is the target intensity.

[0061] Table 3 Simulation test calculation results

[0062]

[0063] The standard deviation analysis is shown in Table 4, where the variance is the quotient of the sum of squared deviations and the degrees of freedom. F is calculated based on the variance and error of each factor (including the interactions between factors) to determine the significance of the factor. The calculation formula is:

[0064] ,

[0065] Taking the first row of Table 4 as an example, the quotient of the sum of squares of the between-group deviations of A and the between-group degrees of freedom is 0.232, and the quotient of the sum of squares of the within-group deviations of Se (ABCD) and the within-group degrees of freedom is 0.013, so F=0.232 / 0.013=17.81;

[0066] Table 4 Standard deviation analysis

[0067] ,

[0068] Step S14: Simulation model test Class A uncertainty assessment, Class B uncertainty assessment, calculation model synthesis standard uncertainty, and obtain expanded uncertainty. Class A uncertainty assessment mainly considers the repeatability of simulation calculation results under important factors and their interactions, and is calculated according to the following formula:

[0069] ,

[0070] ,

[0071] Where, x i For the i The results obtained from the simulation calculations are for n The average value of the simulation results, s ( x )for n The standard deviation of the simulation results, u ( x) represents the value of Class A uncertainty (characterizing the repeatability of the model). Class B uncertainty assessment mainly considers the computational errors in the numerical calculation algorithm, including the uncertainty caused by truncation error and iteration error. Usually, the iteration error is very small and can be ignored. The focus is on the truncation error, which is considered as a uniform distribution, that is,

[0072] ,

[0073] Where, δ is the iterative error value, estimated by Richardson extrapolation method, k is the inclusion factor, when uniformly distributed, consider.

[0074] The calculation results are shown in Table 5. The combined standard uncertainty in the table is u c The expanded uncertainty is 0.66dB, and the expanded uncertainty is k times the combined standard uncertainty. When k is equal to 2, the expanded uncertainty is 1.32dB. According to the specification, take two significant figures, then the expanded uncertainty U sim for:

[0075] .

[0076] Table 5 Measurement uncertainty calculation table

[0077] ,

[0078] Note: The combined standard uncertainty is the square root of the square of each type A factor plus the square of each type B factor.

[0079] Step S2: Determine the test result and uncertainty of the underwater acoustic target intensity test:

[0080] Step S21: Under a stable test environment, measure the underwater acoustic target intensity of the structure that matches the simulation model, and take the arithmetic average of multiple measurements at each frequency point as the best estimate. The stable test environment should meet the far-field test distance requirements of the structure test piece size and the requirements of high-precision positioning. The sound field test layout diagram of the structure underwater acoustic target intensity is as follows: Figure 2 As shown, the target structure 2 is arranged in the water through the lifting and rotating device 1, the standard hydrophone 4 is arranged in the water through the hydrophone connecting rod 3, and then connected to the oscilloscope 7 through the line, and the oscilloscope 7 is connected to the computer 6 through the line, and the transmitter 5 is arranged in the water through the lifting and rotating device 1, and then connected to the power amplifier 8 through the line, and the power amplifier 8 is connected to the signal source 9 through the line.

[0081] Step S22: Evaluate the Type A and Type B uncertainties of the underwater acoustic target intensity test results, calculate the model's combined standard uncertainty, and obtain the expanded uncertainty. The Type A uncertainty evaluation primarily considers the repeatability of the test results and is calculated using the standard deviation. The Type B uncertainty evaluation primarily considers factors such as oscilloscope DC gain inaccuracy, horizontal fluctuations in hydrophone sensitivity, incident sound field non-uniformity, range measurement error, power amplifier total harmonic distortion, and scattered sound field non-uniformity (the values ​​of each factor are calculated according to GB / T 31014–2014, "Acoustics—Laboratory Method for Measurement of Underwater Acoustic Target Intensity"). The combined standard uncertainty (the square root of the square of each Type A factor plus the square of each Type B factor) is calculated using the same method as step S14.

[0082] On this basis, the expanded uncertainty is k times the combined standard uncertainty. When the combined standard uncertainty is 0.75dB and k is equal to 2, the expanded uncertainty U test for:

[0083] ,

[0084] The comparison between the underwater acoustic target intensity test results and the simulation calculation results is shown in Table 6.

[0085] Table 6 Comparison of underwater acoustic target intensity test results and simulation calculation results

[0086] ;

[0087] Step S3: Based on the simulation model calculation results and their expanded uncertainty, the test results and their expanded uncertainty, determine the upper and lower limits of the simulation model results, the upper and lower limits of the test results, draw a confidence assessment diagram of the underwater acoustic target intensity simulation model, and calculate the confidence of the underwater acoustic target intensity simulation model based on the mutual envelope area of ​​the simulation and test results, that is,

[0088] ,

[0089] Where S 仿真模型∪试验 It is the union of the upper and lower limits of the simulation model calculation results and the upper and lower limits of the test results. The upper limit of the simulation model calculation results is the absolute value of the sum of the best estimate of the simulation model and its expanded uncertainty. The lower limit of the simulation model calculation results is the absolute value of the difference between the best estimate of the simulation model and its expanded uncertainty. The upper limit of the test result is the absolute value of the sum of the best estimate of the test result and its expanded uncertainty. The lower limit of the test result is the absolute value of the difference between the best estimate of the test result and its expanded uncertainty. S 仿真模型∩试验 It is the intersection of the upper and lower limits of the simulation model calculation results and the upper and lower limits of the test results.

[0090] The confidence evaluation diagram of underwater acoustic target intensity simulation model is shown in Figure 3 ,in accordance with Figure 3 Calculate the union of the upper and lower limits of the simulation model calculation results and the upper and lower limits of the test results, and the intersection of the upper and lower limits of the simulation model calculation results and the upper and lower limits of the test results.

[0091] .

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A confidence calculation method for an underwater acoustic target intensity simulation model based on orthogonal design, characterized in that: The following steps are involved: S1. Determine the calculation results and uncertainty of the underwater acoustic target intensity simulation model: S11. Establish a finite element model of the structure based on the structural parameters and material properties of the structure, and take the arithmetic average of the target strength calculated multiple times at each frequency point as the best estimate; S12. Analyze the uncertainty or error sources of the underwater acoustic target intensity simulation test and select the important factors as the experimental orthogonal design level; S13. Select an appropriate orthogonal table, determine the design plan for the underwater acoustic target intensity simulation test, conduct simulation tests according to the plan, analyze the standard deviation of the test results, and check whether important factors or interactions between important factors are omitted; S14. Class A uncertainty assessment and Class B uncertainty assessment of simulation model test. Class A uncertainty assessment considers the repeatability of simulation results under important factors and their interactions. Class B uncertainty assessment considers the calculation errors existing in the numerical calculation algorithm, considers the truncation error, calculates the synthetic standard uncertainty of the simulation results of the model, and obtains the expanded uncertainty of the simulation results. S2. Determine the test results and uncertainty of the underwater acoustic target intensity test: S21. Under a stable test environment, measure the underwater acoustic target intensity of the structure that matches the simulation model, and take the arithmetic mean of multiple measurements at each frequency point as the best estimate; S22. Evaluation of Class A and Class B uncertainty of the underwater acoustic target intensity test results. Class A uncertainty evaluation considers the repeatability of the test results and is calculated using standard deviation. Class B uncertainty evaluation considers inaccurate oscilloscope DC gain, horizontal fluctuations in hydrophone sensitivity, uneven incident sound field, distance measurement error, total harmonic distortion of the power amplifier, and uneven scattered sound field. The standard uncertainty of the test results of the calculation model is synthesized to obtain the expanded uncertainty of the test results. S3. Based on the simulation model calculation results and the expanded uncertainty of the simulation results, the test results and the expanded uncertainty of the test results, determine the upper and lower limits of the simulation model results, the upper and lower limits of the test results, draw the confidence evaluation diagram of the underwater acoustic target intensity simulation model, and calculate the confidence of the underwater acoustic target intensity simulation model based on the mutual envelope area of ​​the simulation and test results, that is, ， Where S 仿真模型∪试验 is the union of the upper and lower limits of the simulation model calculation results and the upper and lower limits of the test results. The upper limit of the simulation model calculation results is the absolute value of the sum of the best estimate of the simulation model and the expanded uncertainty of the simulation results. The lower limit of the simulation model calculation results is the absolute value of the difference between the best estimate of the simulation model and the expanded uncertainty of the simulation results. The upper limit of the test result is the absolute value of the sum of the best estimate of the test result and the expanded uncertainty of the test result. The lower limit of the test result is the absolute value of the difference between the best estimate of the test result and the expanded uncertainty of the test result. S 仿真模型∩试验 It is the intersection of the upper and lower limits of the simulation model calculation results and the upper and lower limits of the test results.

2. The method for calculating the confidence of an underwater acoustic target intensity simulation model based on orthogonal design according to claim 1 is characterized in that: In step S11 , the interior of the structure is air, the exterior of the structure is water, and the outer side connected to the water is a perfectly matched layer (PML).

3. The method for calculating the confidence of the underwater acoustic target intensity simulation model based on orthogonal design according to claim 2 is characterized in that: In step S11, the structural parameters of the structure include geometric parameters such as diameter and thickness, the material properties of the structure include elastic modulus, density, and Poisson's ratio, and the material properties of the water include density and sound velocity. Acoustic-solid coupling is considered in the finite element model of the structure, and the underwater acoustic target intensity of the structure is calculated according to the following formula: TS =20lg│ P l · l │ Where, TS is the underwater acoustic target intensity, P l Calculated by the target strength simulation model l The external sound pressure value at the position, l For distance.

4. The method for calculating the confidence of an underwater acoustic target intensity simulation model based on orthogonal design according to claim 1 is characterized in that: In step S12, after systematically analyzing the factor levels in the underwater acoustic target intensity simulation model, 3 to 5 factors are selected as important factors.

5. The method for calculating the confidence of the underwater acoustic target intensity simulation model based on orthogonal design according to claim 4 is characterized in that: In step S12, the maximum grid size, water area, perfectly matched layer (PML) thickness, and calculation algorithm are selected as important factors in the underwater acoustic target intensity simulation model, and the number of levels is selected as 3.

6. The method for calculating the confidence of an underwater acoustic target intensity simulation model based on orthogonal design according to claim 1 is characterized in that: In step S13, the orthogonal table type is determined based on the appropriate number of factors and levels, and the interaction between factors is determined. In the underwater acoustic target intensity simulation model, the number of factors is 4 and the number of levels is 3. The orthogonal design table L27 (3 13 ), where the interactions are the interaction between the maximum grid size and the water area, the interaction between the maximum grid size and the thickness of the perfectly matched layer (PML), and the interaction between the water area and the thickness of the perfectly matched layer (PML).

7. The method for calculating the confidence of an underwater acoustic target intensity simulation model based on orthogonal design according to claim 1 is characterized in that: In step S14, the Class A uncertainty is calculated according to the following formula: ， ， Where x i is the result obtained from the ith simulation calculation, is the average value of the n simulation calculation results, s(x) is the standard deviation of the n simulation calculation results, and u(x) represents the value of Class A uncertainty.

8. The method for calculating the confidence of an underwater acoustic target intensity simulation model based on orthogonal design according to claim 1 is characterized in that: In step S14, the Class B uncertainty is calculated according to the following formula: ， Where δ is the iterative error value and k is the coverage factor.

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