Attitude and orbit control engine electromagnetic characteristic analysis and evaluation method

Abstract

The application provides a method for analyzing and evaluating electromagnetic characteristics of an attitude control engine, which comprises the following steps: firstly, modeling a complex electromagnetic environment model, modeling an electromagnetic sensitive device model, and parameterizing the models; judging whether the complex electromagnetic environment model is a radiation problem or a conduction problem according to the properties of the complex electromagnetic environment model; after classification, analyzing electromagnetic characteristics in combination with the parameterized models; performing parameter sensitivity analysis on the simulation analysis results to determine the deterministic relationship between input parameters and output responses; comparing simulation data and structure data to perform reverse parameter calibration; according to the calibrated parameters, correcting the input parameters of the environment model and the device model, returning to step three to perform simulation analysis again; and comparing simulation data and test data to evaluate simulation credibility. The application can provide comprehensive robustness / reliability evaluation and parameter optimization analysis.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic technology and relates to a method for analyzing and evaluating electromagnetic characteristics. Background Technology

[0002] The core task of electromagnetic characteristic analysis and evaluation technology for attitude and orbit control engines is to assess the reliability of electromagnetic characteristic coupling models. The reliability of electromagnetic characteristic coupling simulation models directly affects the usability of electromagnetic characteristic data and models. Major international electromagnetic characteristic modeling software has continuously improved its modeling accuracy through verification and validation using extensive experimental data.

[0003] Currently, China has established laboratory accreditation procedures for the electromagnetic properties of targets and their environments, and has completed the implementation of verification, validation, and accreditation (VV&A) of some electromagnetic models and measurement systems, which has improved the credibility of target and environmental electromagnetic property models and data. However, there is a lack of verification and validation of real dynamic electromagnetic property measurement data.

[0004] Attitude and orbit control electromagnetic environment effect modeling (referred to as effect modeling) is the process of mathematically abstracting and modeling the correlation between electromagnetic environment elements and attitude and orbit control engine performance. It mainly involves three aspects: environmental elements, the attitude and orbit control engine system, and the correlation. Among these, environmental elements and the attitude and orbit control engine system are the objects of modeling research, the correlation is the link between the two, and the purpose of effect modeling is to construct an attitude and orbit control engine system model that accurately reflects the correlation between electromagnetic environment elements and the performance of the attitude and orbit control engine system.

[0005] The core idea of ​​effect modeling is to summarize and analyze the mechanisms by which environmental factors affect the attitude and orbit control engine system, including key aspects and parameters. The modeling process emphasizes key elements and makes reasonable simplifications to ensure that the constructed model can realistically and sensitively reflect the effects of key aspects and parameters. This allows for the most realistic simulation and reproduction of the impact process and effects of environmental factors on the radar. Furthermore, the impact effects serve as a guide for selecting key modules and determining the granularity of the modeling process.

[0006] Currently, there are many problems in the analysis and evaluation of the electromagnetic characteristics of attitude and orbit control engines due to the lack of a systematic and widely accepted solution. Therefore, it is particularly necessary to provide a reasonable and reliable method for the analysis and evaluation of the electromagnetic characteristics of attitude and orbit control engines. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention provides a method for analyzing and evaluating the electromagnetic characteristics of an attitude and orbit control engine, which can provide a comprehensive robustness / reliability assessment and parameter optimization analysis.

[0008] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0009] Step 1: Modeling the complex electromagnetic environment and electromagnetically sensitive devices. The complex electromagnetic environment model refers to the electromagnetic compatibility test environment for various operating conditions of the attitude and orbit control engine, including the microwave anechoic chamber walls, absorbing materials, test benches, cables, antennas, etc. The three-dimensional structure of these components is modeled and corresponding material properties are assigned by the preprocessing module of the software platform that integrates the electromagnetic characteristic analysis and evaluation methods of the attitude and orbit control engine. The electromagnetically sensitive device model refers to the traces on each layer of the PCB board and the various types of resistors, capacitors, inductors, analog devices, and digital devices on them. The corresponding resistor, capacitor, inductance values ​​and interface performance files are configured for them.

[0010] Step 2: Model parameterization; this includes structural parameterization, material parameterization, and spectral parameterization.

[0011] Step 3: Determine whether the complex electromagnetic environment model is a radiation-type problem or a conduction-type problem based on its properties, and then perform electromagnetic characteristic analysis in conjunction with the parameterized model.

[0012] Step 4: Perform parameter sensitivity analysis on the simulation results to determine the deterministic relationship between the input parameters and the output response;

[0013] Step 5: Compare the simulation data and structural data, and perform reverse parameter calibration; then, based on the calibrated parameter correction, directly assign values ​​to the input parameters in the environment model and device model, and return to Step 3 to perform simulation analysis again;

[0014] Step 6: Compare the simulation data and test data to evaluate the credibility of the simulation.

[0015] The input parameters for step four include:

[0016] 1) Electromagnetic compatibility: Conductive coupling of power lines to the attitude and orbit control engine under airborne carrier, frequency range 10kHz~10MHz;

[0017] 2) Lightning: refers to indirect lightning interference signals, the impact of indirect lightning on attitude and orbit control engines, electric field strength 6×106 / (1+R2 / 50)1 / 2V / m, magnetic field strength 3.2×104A / m;

[0018] 3) Electromagnetic interference: The impact of active and passive interference on attitude and orbit control engines in airborne electronic warfare platforms, with a frequency range of 30MHz to 40GHz and a power range of 1W to 10MW.

[0019] 4) High-power electromagnetic aspects: The impact of high-power electromagnetic and electromagnetic pulse weapons on attitude and orbit control engines. The frequency range of high-power electromagnetic is 300MHz~300GHz, and the frequency of electromagnetic pulse is 500MHz~10GHz; the power is 1MW.

[0020] The output parameters for step four include:

[0021] The measured / simulated quantity is the corresponding port voltage or current. The test value of the port voltage is defined as Ut, the test value of the port current is It, the simulated value of the port voltage is Uc, and the test value of the port current is Ic.

[0022] In step four, parameter sensitivity analysis first scans the parameter design space to assess the sensitivity of the output response to the input parameters and identify important parameters. The key technologies involved are high-efficiency sample space sampling technology and high-quality sample space generation technology. During parameter sensitivity analysis, a high-quality response surface is established to describe the relationship between the output response and the input parameters.

[0023] In step four, while performing parameter sensitivity analysis, a numerical fitting method is used to establish a function describing the relationship between the response parameters and the input parameters, i.e., the response surface. The fitting model includes first-order and second-order polynomial regression, first-order, second-order, and interpolation-type moving least squares methods, etc. The fitting accuracy is evaluated by predicting the quality indicators CoD and CoP.

[0024] In step six, the method for calculating the simulation reliability is as follows: Let x and y be random variables in the simulation data and experimental data, respectively, with sample data {xi, i = 1, 2, ..., N1} and {yi′, i′ = 1, 2, ..., N2}, and population distribution functions F(x) and G(y), respectively. First, test whether the two random variables follow the same probability distribution. Based on the known distribution characteristics of F(x) and G(y), select the appropriate test method. If, after testing, the two population distribution functions F(x) and G(y) follow the same distribution, then it is necessary to test the statistical characteristic values ​​of the sample data of the two random variables. First, calculate the mean test statistic of the two sets of sample values ​​respectively:

[0025]

[0026] / >

[0027]

[0028]

[0029] Using the t-test method, calculate the mean test statistic, where T is a t-distribution with (N1+N2-2) degrees of freedom:

[0030]

[0031] If the test statistic T1-α / 2 = tα / 2, then the hypothesis is accepted, and it is considered that there is no significant difference between the mean of the simulation data and the experimental data at the significance level α; where tα / 2 can be obtained from the t-distribution table based on the confidence level α.

[0032] The beneficial effects of this invention are: it provides comprehensive robustness / reliability assessment and parameter optimization analysis capabilities.

[0033] 1) Parameter sensitivity analysis: CoD, CoI, COP, CC and other indicators accurately and objectively measure the degree of influence of random variables on the response.

[0034] 2) Multidisciplinary optimization: Advanced single-objective, multi-objective, and multi-parameter optimization algorithms, as well as global and local adaptive response surface methods, can greatly improve the solution efficiency of multivariable engineering optimization problems.

[0035] 3) Robustness assessment: Based on analysis of variance, the advanced Latin hypercube sampling method effectively reduces the correlation between variables, obtains more response information with fewer sample points, and effectively improves computational efficiency.

[0036] 4) Reliability Analysis: Based on probabilistic design methods, it provides advanced reliability analysis methods, effectively improving the accuracy of reliability calculation for low-probability events.

[0037] 5) Robust and Reliable Optimization Design: Robust reliability and optimization analysis are integrated to optimize product performance by taking into account the uncertainties in product design, thereby improving the robustness and reliability of the product and reducing the probability of failure.

[0038] The response surface model generated by this method can be used as an alternative solver in optimization iterations and robustness analysis. It eliminates the need to call the original solver, resulting in very high computational efficiency. Its advantages are particularly evident in multi-parameter optimization designs that require consideration of a large number of design parameters (hundreds or thousands). Solver-based solutions use electromagnetic algorithms to perform numerical calculations on the model, which are time-consuming and require significant hardware resources. Using the response surface model, results corresponding to multiple parameters can be directly retrieved via table lookup. Detailed Implementation

[0039] The present invention will be further described below with reference to the embodiments, which include, but are not limited to, the following embodiments.

[0040] The method for analyzing and evaluating the electromagnetic characteristics of an attitude and orbit control engine consists of the following steps:

[0041] Step 1: Modeling the complex electromagnetic environment and electromagnetically sensitive devices;

[0042] Since the main research content of this invention is the interference at two levels—intra-system and inter-system—namely, the electromagnetic influence of missiles and weapon platforms on the attitude and trajectory control engine, the granularity of the electronic component decomposition is set at the component level. That is, all electronic components that make up the entire attitude and trajectory control engine are decomposed to the component level, and the electronic connections between them are described, ultimately forming the following electronic decomposition table at the entire engine level.

[0043] Table 1. Component Breakdown Table for the Whole Machine

[0044]

[0045] According to the three elements of electromagnetic compatibility, the above eight components can be divided into three categories:

[0046] Electromagnetic interference sources: control module, switching power supply, communication / telemetry module, ignition circuit, ignition device, I / O module;

[0047] Electromagnetic sensors: control module, ignition circuit, communication / telemetry module, I / O module;

[0048] Propagation path: connecting cables (differential-mode conducted radiation and common-mode radiation exist), shielding housing (leaking radiation exists through pores and gaps).

[0049] Based on their electromagnetic simulation analysis characteristics, the above eight components can be divided into three categories:

[0050] Includes PCB board components: control module, switching power supply, ignition circuit, communication / telemetry module, and I / O module;

[0051] High-frequency electromagnetic components (radio frequency type): Ignition device (may generate high-frequency radiation to the outside during operation);

[0052] Cable harnesses and shielding: connecting cables and shielding housings.

[0053] Step 2: Model parameterization; this includes structural parameterization, material parameterization, and spectral parameterization.

[0054] Among them, structural parameterization refers to parameterizing the physical dimensions of the outline and details of each component to facilitate model modification; material parameterization refers to parameterizing the basic properties of materials, and a new material can be obtained by modifying the variable values; spectrum parameterization refers to parameterizing the frequency band to be simulated to facilitate modification of the simulation frequency band.

[0055] Since each working condition sample is independent of the others and they are not comparative experiments, but they have basically fixed and similar simulation scenarios and elements, the model parameterization mentioned here is for the purpose of facilitating calibration before the simulation model is finalized, and for facilitating the adjustment of the simulation scenario after the model is finalized, so as to improve the reusability of the model. It is not the input variable conditions of the sample.

[0056] Step 3: Determine whether the complex electromagnetic environment model is a radiation-type problem or a conduction-type problem based on its properties, and then perform electromagnetic characteristic analysis in conjunction with the parameterized model.

[0057] Based on the different stages of attitude and orbit control engine operation in air-to-air combat, three typical complex electromagnetic environment analysis backgrounds are established. Then, the main electromagnetic interference sources in each background are analyzed. Based on the characteristics of the specific interference sources, relevant standards are found, and the content, methods, and corresponding experimental content of the scenarios are determined according to the standards.

[0058] Based on the analysis of complex electromagnetic environments, three typical complex electromagnetic environments are briefly described as follows:

[0059] 1) Environment scenario in the state of readiness for launch

[0060] The pre-launch state primarily faces challenges from platform-based noise and the external electromagnetic environment. This invention mainly considers the electromagnetic adaptability of the airborne carrier. Because missile and aircraft components originate from different research and development units, their systems have different functions, including propulsion (power) devices, signal receiving and transmitting devices, guidance devices, various radars, and warheads. Therefore, electronic equipment includes multiple types of signal transmission sources, creating a relatively complex electromagnetic environment through conductive coupling or radiative coupling in space via cable bundles and connecting components. Analysis of typical interference threat scenarios reveals that for attitude control engines, the most crucial aspect is ensuring that the engine control system does not misfire or malfunction during the pre-launch state. The key is to ensure that the conducted radiation from power and signal lines does not affect the normal operation of the internal circuitry of the attitude control engine's ignition control components. In other words, the pre-launch environment scenario primarily considers non-confrontational radiation from the external electromagnetic environment (including high-power radiation from communication and radar), and airborne environmental interference from platform-based noise within the internal electromagnetic environment.

[0061] Non-countermeasures-based radiated interference mainly originates from electromagnetic radiation interference from high-power devices such as radar outside the aircraft, as well as electromagnetic radiation interference and electromagnetic induction interference from high-power, high-current devices such as power supply systems inside the aircraft. It also includes electromagnetic radiation interference that may exist in ground and space systems. The frequency range of these interference sources typically covers 10kHz-40GHz. The specific radiated power / electric field strength needs to be determined through actual testing on the actual airborne platform of the air-to-air missile. For radiation data that cannot be specifically tested, this invention proposes to adopt the data recommended in relevant standards (see Tables 2-3) as the electromagnetic radiation excitation amplitude for research.

[0062] Table 2: Non-confrontational radiation interference

[0063]

[0064]

[0065] Table 3: Airborne Environmental Radiation Interference

[0066]

[0067] 2) Mid-course flight scenario

[0068] Mid-course flight primarily faces external electromagnetic interference and platform-based noise. Since the missile has detached from the airborne platform at this stage, this invention mainly considers lightning interference and the missile's own interference characteristics. Through analysis of typical interference threat scenarios, we found that for the attitude and trajectory control engine, the most crucial aspect is ensuring that the engine's connecting cables and shielding housing do not fail or become damaged under the indirect influence of lightning interference during mid-course flight. In other words, the mid-course flight environment primarily considers lightning interference from natural radiation within the external electromagnetic environment and missile-based noise from the platform's own internal electromagnetic environment.

[0069] Lightning interference is often difficult to accurately collect. This invention proposes to adopt relevant standards and simulate current pulse waveforms commonly used in simulations and experiments. The pulse waveform is usually represented by a spike pulse containing a rising edge and a falling edge (the specific waveform function is usually not required, only the rise time, fall time, and peak current are specified, and it can be represented in the form of a double Gaussian pulse). The time-domain waveform requirements for indirect lightning strikes that this invention needs to focus on are shown in Table 4.

[0070] Table 4: Lightning Waveform Requirements

[0071]

[0072]

[0073] The specific sources of radiation interference for the missile itself include cables / harnesses (power cables and communication cables) in the missile's guidance system, command transponder, fuse system, telemetry system, power supply system, and communication system. The typical signal forms / frequencies and their strengths (power / field strength) are detailed in Table 5.

[0074] Table 5: Missile Radiation Interference

[0075]

[0076] 3) Final stage hostile state scenario

[0077] In the terminal phase, when facing the enemy, the main challenges are the external electromagnetic environment and platform noise. Since the missile has entered the interference range of enemy electromagnetic countermeasures weapons at this stage, this invention primarily considers interference from enemy electronic countermeasures and electromagnetic weapons. Specifically, the impact of electronic countermeasures and high-power electromagnetic interference (frequency range 300MHz–40GHz) on the attitude and trajectory control engine in the terminal phase of the missile's engagement scenario is considered a typical form of interference. Simultaneously, considering that the engine is typically in a highly maneuverable state during this phase, internal engine interference must also be considered.

[0078] Hostile electromagnetic countermeasures weapons (including electromagnetic pulses and high-power electromagnetic fields) are typically impossible to detect. This invention proposes to adopt relevant standards, and the transient electromagnetic field radiation of interest in this invention is specifically shown in Table 6.

[0079] Table 6: Transient Electromagnetic Field Radiation Requirements

[0080]

[0081]

[0082] The overall technical approach for electromagnetic simulation research of attitude and orbit control engines is as follows: first, analyze the electromagnetic components in groups according to their characteristics; then, find suitable calculation methods for each component; in the actual model building process, apply the corresponding methods to build a high-quality electromagnetic simulation model; and finally, use system analysis methods to integrate all the models into the electromagnetic simulation system for system-level modeling and analysis.

[0083] Electromagnetic analysis of PCB boards is a high-precision three-dimensional electromagnetic problem that requires the application of the finite element method. The classic theory for cable harness analysis is the telegraph equation, which needs to be solved numerically in a discrete form. The calculation of shielding effectiveness of shielding layers and lightning effects are usually time-domain electromagnetic problems that require the application of the finite-difference time-domain method. Finally, in system-level analysis, a system-level circuit needs to be built for field-circuit coupling analysis.

[0084] The specific computational methods involved include the finite element method, the finite-difference time-domain method, and the telegraph equation method. The core principles of each method are briefly described below:

[0085] The finite element method (FEM) is the mainstream computational method for electromagnetic field frequency domain calculations. It can solve electromagnetic field problems in any three-dimensional space. First, based on the frequency and wavelength of the problem to be solved, the physical prototype is divided into several tetrahedral initial meshes. On each tetrahedral mesh, the frequency domain form of the following Maxwell's equations is discretized:

[0086]

[0087]

[0088] After generating the coefficient matrix, the electromagnetic field distribution and port parameters are obtained. Then, adaptive mesh refinement is started to iterate the calculation of the problem. When the error between the two iterations is less than the predefined threshold, the converged calculation result is obtained. Finally, a wideband scan calculation is performed on the entire frequency band to obtain the wideband frequency response.

[0089] The finite-difference time-domain method is the mainstream computational method for electromagnetic field time-domain calculation. First, the orthogonal discrete step sizes Δx, Δy, and Δz of the solution space are determined according to the required computational accuracy, and the solution space is divided into small orthogonal grids.

[0090] Then, discretized sampled values ​​of electric and magnetic fields are defined on each grid.

[0091] Then, by applying spatial and temporal differences to approximate differential operations, the differential form of Maxwell's equations can be obtained:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] It is transformed into the difference form of the finite-difference time-domain method.

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] Considering that the orthogonal step size of the space gradually approaches 0, the calculation result of the finite-difference time-domain method approaches the true solution of Maxwell's equations. That is, for any required accuracy, a sufficiently small step size can always be found to meet the requirement.

[0106] The telegraph equation calculation method analyzes how to approximate the solution of the telegraph equations for a uniform transmission line using discrete numerical calculation methods:

[0107]

[0108]

[0109] Similar to the finite-difference time-domain method, the telegraph equations can be discretized in space and time, resulting in a form that can be solved using discrete numerical methods:

[0110]

[0111]

[0112] All three methods described above have the characteristic that as the spatial step size and time step size are gradually reduced, the calculation results gradually approach the solution of the corresponding differential equation.

[0113] Step 4: Perform parameter sensitivity analysis on the simulation results to determine the deterministic relationship between the input parameters and the output response;

[0114] Parameter sensitivity analysis provides parameter sensitivity indices to reflect the importance of parameters, including:

[0115] The classic sensitivity factor CoI is based on the coefficient of determination CoD in multinomial regression; the CoI of parameter Xa is the amount of reduction in CoD after excluding Xa from the regression model.

[0116] The sensitivity factor CoP is based on the optimal predictor meta-model MOP; the CoP of parameter Xa is the product of the output variation that Xa can explain and the MOP prediction coefficient; CoP is more reliable than CoI.

[0117] The correlation coefficient (CC) is used to evaluate the degree of correlation between parameters using primary and secondary correlation coefficients.

[0118] Step 5: Compare the test data with the response surface data and perform reverse parameter calibration. That is, find the corresponding input parameters from the curve in the response surface that is closest to the test data and calibrate them. Then, correct the environmental model and device model based on the calibrated parameters and perform simulation analysis again.

[0119] Step 6: Compare the simulation data and test data to evaluate the credibility of the simulation.

[0120] Based on the requirement that the credibility level be no less than 0.8, the following applies:

[0121]

[0122]

[0123] Furthermore, in this method, the input parameters are:

[0124] 1) Electromagnetic compatibility: Conductive coupling of power lines to the attitude and orbit control engine under airborne carrier, frequency range 10kHz~10MHz;

[0125] 2) Lightning: refers to indirect lightning interference signals, the impact of indirect lightning on attitude and orbit control engines, electric field strength 6×106 / (1+R2 / 50)1 / 2V / m, magnetic field strength 3.2×104A / m;

[0126] 3) Electromagnetic interference: The impact of active and passive interference on attitude and orbit control engines in airborne electronic warfare platforms, with a frequency range of 30MHz to 40GHz and a power range of 1W to 10MW.

[0127] 4) High-power electromagnetic aspects: The impact of high-power electromagnetic and electromagnetic pulse weapons on attitude and orbit control engines. The frequency range of high-power electromagnetic is 300MHz~300GHz, and the frequency of electromagnetic pulse is 500MHz~10GHz; the power is 1MW.

[0128] Furthermore, in this method: output parameters:

[0129] The quantity to be measured / simulated is the corresponding port voltage or current. The test value of the port voltage is defined as Ut, the test value of the port current is It, the simulation value of the port voltage is Uo, and the test value of the port current is Ic.

[0130] Furthermore, in step four shown: the parameter sensitivity analysis first scans the parameter design space, evaluates the sensitivity of the output response to the input parameters, and identifies important parameters; the key technologies are high-efficiency sample space sampling technology and high-quality sample space generation technology, which can establish a high-quality response surface to describe the relationship between the output response and the input parameters while performing parameter sensitivity analysis.

[0131] Furthermore, in step four: simultaneously with parameter sensitivity analysis, a numerical fitting method is used to establish a function describing the relationship between the response parameters and the input parameters, i.e., the response surface. The fitting models include first-order and second-order polynomial regression, first-order, second-order, and interpolation-based moving least squares methods, among which moving least squares can meet the need for accurate fitting of complex response surfaces with rapidly changing gradients. We can evaluate the fitting accuracy using the prediction quality indices CoD and CoP. CoD is the traditional coefficient of determination, reflecting the accuracy of the fitted model through the sample points, but its objectivity is poor when the sample size is small, and spurious interpolation may occur. CoP is the prediction coefficient, which uses cross-validation algorithms to avoid spurious interpolation and evaluate the accuracy of the fitted model, ensuring the objectivity of the CoP index.

[0132] In the response surface fitting process, a high-quality response surface, namely the MOP optimal predictive meta-model, is established for each response variable by searching for the optimal subset of parameters and the best-fitting model, i.e., the subset of parameters and the best-fitting model with the largest CoP. The MOP fitting quality is not affected by irrelevant interference parameters, and a high-quality response surface is established based on the most important subset of parameters and the best-fitting model using a limited number of sample points.

[0133] After establishing the MOP (Model-Oriented Programming) model, we can evaluate which input parameters (key parameters of the simulation model) primarily influence the output response (simulation results). Furthermore, based on test data and the MOP model, we can reverse-engineer the value ranges of these key parameters. Through the accumulation of extensive experimental data, the above methods can be applied to correct the errors between the simulation model and the experimental model, thus establishing a high-precision simulation model.

[0134] The Analytic Hierarchy Process (AHP) is a comprehensive evaluation method. Its basic idea is to construct a credibility evaluation index structure by hierarchically classifying the factors affecting the correctness of the simulation model, and then judging the degree of influence between the evaluation indicators at each level to obtain the weight of each indicator's influence on the indicator at the previous level. The specific implementation steps are as follows:

[0135] a) Establish a hierarchical evaluation model based on the set of evaluation indicators;

[0136] b) Select the appropriate verification method and calculate the simulation model verification results E=[e1,e2,…en] for each low-level evaluation index;

[0137] c) Calculate the judgment matrix A for each layer. The judgment matrix represents the importance of each evaluation index to the others. In this invention, the correlation coefficient of each evaluation index is calculated. The calculation method is consistent with the most predictive meta-model method in the inverse model calibration method, that is, sampling with a sufficiently large sample size, and then performing spatial fitting analysis to calculate the correlation coefficient, so A = [αij];

[0138] d) Based on the judgment matrix A, calculate the weight of each evaluation indicator at the same level on the indicator at the next higher level, and obtain the weight vector W = [β1, β2, ..., βn]. The specific calculation formula is as follows:

[0139]

[0140] e) Combining the test results of all evaluation indicators at the same level with the weight vector calculation, the credibility test results of higher-level indicators can be obtained:

[0141]

[0142] Where EH is the evaluation result value of the high-level evaluation index, E is the evaluation result vector of each low-level evaluation index, and W is the weight vector of each low-level evaluation index. And so on, until the credibility of the highest-level simulation model is obtained.

[0143] Furthermore, in step six, the method for calculating the simulation reliability is as follows: Let x and y be random variables in the simulation data and experimental data, respectively, with sample data {xi, i = 1, 2, ..., N1} and {yi, i = 1, 2, ..., N2}, and population distribution functions F(x) and G(y), respectively. First, we need to test whether the two random variables follow the same probability distribution. Depending on whether the distribution characteristics of F(x) and G(y) are known, appropriate testing methods can be selected. In this invention, since the simulation data can be complete, the distribution characteristics of F(x) can usually be obtained. Therefore, the above problem is reduced to a goodness-of-fit test to verify whether the unknown distribution function follows a known statistical distribution.

[0144] If, after testing, the two population distribution functions F(x) and G(y) follow the same distribution, then it is necessary to test the statistical characteristic values ​​of the sample data of the two random variables. First, calculate the mean test statistic for each of the two sets of sample values:

[0145]

[0146]

[0147]

[0148]

[0149] Using the t-test, we can calculate the mean test statistic, where T is a t-distribution with (N1+N2-2) degrees of freedom.

[0150]

[0151] If the test statistic T1-α / 2 = tα / 2, then the hypothesis can be accepted, indicating that there is no significant difference between the mean of the simulated data and the experimental data at the significance level α. Here, tα / 2 can be obtained from the t-distribution table based on the confidence level α.

[0152] Specifically, in the simulation project of electromagnetic characteristics of attitude and orbit control engines under complex electromagnetic environments, the existing index system for attitude and orbit control engines is mainly based on the system's supporting components and can be directly used for the design, development, and acceptance of attitude and orbit control engine products. However, when conducting boundary assessments of the electromagnetic characteristics of attitude and orbit control engines, it is necessary to consider the impact of complex electromagnetic environments on the electromagnetic characteristics of attitude and orbit control engines, optimize the index system structure, ignore index items unrelated to other models, and conduct hierarchical analysis of correlated indexes to construct the index system.

[0153] The hierarchical evaluation index system is structured from a top layer, several intermediate layers, and a bottom layer. The top layer represents the performance boundary assessment target, and the top-level indexes should characterize the final performance of the attitude and orbit control engine. The intermediate-level indexes are determined based on the specific model correlation of the actual evaluation object, mainly reflecting the relationship between the bottom-level and top-level indexes during the operational process of the attitude and orbit control engine. The bottom-level indexes are generally calculable and quantifiable performance and technical indicators.

[0154] Top-level indicators are a comprehensive representation of the electromagnetic characteristics of attitude and orbit control engines. They need to clearly and quantitatively describe the extent to which the attitude and orbit control engine completes its combat mission under given complex electromagnetic environment conditions. There are two ways to select top-level indicators:

[0155] a) A top-level index is derived by synthesizing existing system-level indices. System-level performance indices affected by complex electromagnetic environments are synthesized using a specific method to obtain a concrete quantitative index representing the electromagnetic characteristics of the attitude and orbit control engine. This method constructs a top-level index that comprehensively reflects the impact of various system-level indices; however, it lacks actual physical meaning, fails to demonstrate the relationships between different system-level indices, and possesses a degree of subjectivity, thus not accurately describing the attitude and orbit control engine's adaptability to complex electromagnetic environments.

[0156] b) In conjunction with the operational mission of the attitude and orbit control engine, a new top-level indicator is used to summarize and describe the electromagnetic characteristics of the attitude and orbit control engine.

[0157] Mid-level indicators are a decomposition of top-level indicators and an aggregation of bottom-level indicators. Based on the electromagnetic characteristics of the attitude and orbit control engine, mid-level indicators mainly include probability indicators, etc.

[0158] The underlying metrics are a set of indicators reflecting the electromagnetic characteristics of the attitude and orbit control engine. They are an important component of the electromagnetic characteristic index correlation system of the attitude and orbit control engine and a major content of model correlation testing. The index values ​​of the underlying metrics are reflected in the intermediate metrics through the transmission of information flow within the attitude and orbit control engine. The underlying metrics include performance and technical indicators of each stage.

[0159] Simulation credibility relies on correct and reasonable verification and validation, and requires the establishment of credibility assessment indicators using appropriate methods. By applying a hierarchical analysis method for credibility assessment, this invention decomposes the credibility indicators of the simulation data of the electromagnetic characteristics of an attitude and orbit control engine under complex electromagnetic environments layer by layer. Based on this, a comprehensive evaluation and analysis of credibility and reliability can be conducted, i.e., a comprehensive credibility assessment study.

[0160] The credibility assessment of simulation program models is a crucial step in the verification, validation, and analysis process of modeling and simulation. Its purpose is to determine the model's acceptability based on the results of previous verification and analysis stages. If only one factor influences the credibility of the simulation program model, or if only one aspect of the model's characteristics has been verified, then the model's credibility can be directly determined from this verification result. However, we know that the correctness of a simulation model is often influenced by multiple factors, and verifying only one aspect is clearly incomplete. Therefore, it is necessary to decompose the various factors affecting the electromagnetic characteristics of attitude and orbit control engines under complex electromagnetic environments.

[0161] The simulation and experimental data of this invention are composed of multiple samples from various scenarios, thus requiring a scientific method to calculate the simulation reliability. Without loss of generality, let x and y be random variables in the simulation and experimental data, respectively, with sample data {xi, i = 1, 2, ..., N1} and {yi, i = 1, 2, ..., N2}, and population distribution functions F(x) and G(y), respectively. The first step is to test whether the two random variables follow the same probability distribution. Depending on whether the distribution characteristics of F(x) and G(y) are known, an appropriate testing method can be selected. In this invention, since the simulation data can be complete, the distribution characteristics of F(x) can usually be obtained. Therefore, the above problem is reduced to a goodness-of-fit test to verify whether the unknown distribution function follows a known statistical distribution.

[0162] If, after testing, the two population distribution functions F(x) and G(y) follow the same distribution, then it is necessary to test the statistical characteristic values ​​of the sample data of the two random variables. First, calculate the mean test statistic for each of the two sets of sample values:

[0163]

[0164]

[0165]

[0166]

[0167] Using the t-test, we can calculate the mean test statistic, where T is a t-distribution with (N1+N2-2) degrees of freedom.

[0168]

[0169] If the test statistic T1-α / 2 = tα / 2, then the hypothesis can be accepted, indicating that there is no significant difference between the mean of the simulated data and the experimental data at the significance level α. Here, tα / 2 can be obtained from the t-distribution table based on the confidence level α.

[0170] Random sampling strategies are employed, including Monte Carlo methods, Design of Experiments (DoE) methods, Latin hypercube sampling, and its improved versions. Latin hypercube sampling, an improved version of Monte Carlo, offers more than 12 times the sample efficiency of Monte Carlo, minimizing sample correlation and avoiding clustering, thus ensuring the validity of each sample. This helps designers implement reasonable experimental designs and obtain accurate statistical results.

[0171] For existing calculation or experimental results, the optimal predictive meta-model is directly generated for use in parameter sensitivity analysis, establishing the optimal predictive meta-model (response surface model), optimization analysis, etc.

[0172] The Optimal Predictive Meta-Model (MOP) supports 2D and 3D graphical display and allows for uniform or non-uniform sampling of design variables to obtain the relationship function between input and output parameters. It uses an intuitive 2D / 3D blanket graph model to help users quickly understand the design space.

[0173] The MOP's fitting quality is unaffected by irrelevant interference parameters. Using a limited number of sample points, it establishes a high-quality response surface based on the most important parameter subset and the best-fit model, and can be used as an alternative solver. After establishing the MOP during the parameter analysis phase, subsequent optimization and robustness / reliability analyses can be performed using the MOP as a solver, eliminating the need for a CAE solver and thus significantly improving analysis efficiency.

[0174] Parameter sensitivity analysis provides parameter sensitivity indices to reflect the importance of parameters, including:

[0175] The classic sensitivity factor CoI is based on the coefficient of determination CoD in multinomial regression. The CoI of parameter Xa represents the reduction in CoD after excluding Xa from the regression model.

[0176] The sensitivity factor CoP is based on the optimal predictor meta-model (MOP). The CoP of parameter Xa is the product of the output variation explained by Xa and the MOP prediction coefficients. CoP is more reliable than CoI.

[0177] The correlation coefficient (CC) is used to evaluate the degree of correlation between parameters using primary and secondary correlation coefficients.

[0178] The response surface model generated by this method can be used as an alternative solver in the optimization iteration process and robustness analysis process. It eliminates the need to call the original solver, resulting in very high computational efficiency. Its advantages are particularly evident in multi-parameter optimization designs that require consideration of a large number of design parameters (hundreds or thousands).

[0179] The attitude and orbit control electromagnetic environment modeling includes the following three aspects: environmental elements, attitude and orbit control engine system, and correlation. Among them, environmental elements and attitude and orbit control engine system are the objects of modeling research, correlation is the link between the two, and the purpose of effect modeling is to construct an attitude and orbit control engine system model that can accurately reflect the correlation between electromagnetic environmental elements and the performance of attitude and orbit control engine system, that is, attitude and orbit control engine system electromagnetic environment effect model.

[0180] The core task of attitude and orbit control engine electromagnetic characteristic analysis and evaluation technology is to assess the reliability of the electromagnetic characteristic coupling model. The reliability of the electromagnetic characteristic coupling simulation model directly affects the usability of the electromagnetic characteristic data and model.

[0181] Attitude and orbit control electromagnetic environment effect modeling, or simply "effect modeling," is the process of mathematically abstracting and modeling the relationship between electromagnetic environment elements and attitude and orbit control engine performance. It mainly involves three aspects: environmental elements, the attitude and orbit control engine system, and the relationship. Among these, environmental elements and the attitude and orbit control engine system are the objects of modeling research, the relationship is the link between them, and the purpose of effect modeling is to construct an attitude and orbit control engine system model that accurately reflects the relationship between electromagnetic environment elements and the performance of the attitude and orbit control engine system—that is, the attitude and orbit control engine system electromagnetic environment effect model (referred to as the "effect model").

[0182] The core idea of ​​effect modeling is to summarize and analyze the mechanisms by which environmental factors affect the attitude and orbit control engine system, including key aspects and parameters. This is done by focusing on key areas and simplifying the model appropriately, ensuring that the constructed model accurately and sensitively reflects the effects of these key aspects and parameters. This allows for the realistic simulation and reproduction of the impact process and effects of environmental factors on the radar. Furthermore, the impact effect serves as a guide for selecting key modules and determining the granularity of the modeling process. This is a modeling method that embodies the concept of "impact effect."

[0183] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions conceived without inventive effort should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

Claims

1. A method for analyzing and evaluating the electromagnetic characteristics of an attitude and orbit control engine, characterized in that, Includes the following steps: Step 1: Modeling the complex electromagnetic environment and electromagnetically sensitive devices. The complex electromagnetic environment model refers to the electromagnetic compatibility test environment for various operating conditions of the attitude and orbit control engine, including the microwave anechoic chamber walls, absorbing materials, test bench, cables, and antennas. The three-dimensional structure of these components is modeled and corresponding material properties are assigned by the preprocessing module of the software platform that integrates the electromagnetic characteristic analysis and evaluation methods of the attitude and orbit control engine. The electromagnetically sensitive device model refers to the traces on each layer of the PCB board and the various types of resistors, capacitors, inductors, analog devices, and digital devices on them. The corresponding resistor, capacitor, inductance values ​​and interface performance files are configured for them. Step 2: Model parameterization; this includes structural parameterization, material parameterization, and spectral parameterization. Step 3: Determine whether the complex electromagnetic environment model is a radiation-type problem or a conduction-type problem based on its properties, and then perform electromagnetic characteristic analysis in conjunction with the parameterized model. Step 4: Perform parameter sensitivity analysis on the simulation results to determine the deterministic relationship between input parameters and output response; the input parameters include electromagnetic compatibility, lightning, electromagnetic interference, and high-power electromagnetic aspects; the output parameters include the measured / simulated quantities as the corresponding port voltages or currents. Step 5: Compare the simulation data and structural data to perform reverse parameter calibration; Then, based on the calibrated parameters, directly assign values ​​to the input parameters in the environment model and device model, and return to step three to perform simulation analysis again; Step 6: Compare the simulation data and test data to evaluate the credibility of the simulation.

2. The method for analyzing and evaluating the electromagnetic characteristics of an attitude and orbit control engine according to claim 1, characterized in that, The input parameters for step four include: 1) Electromagnetic compatibility: Conductive coupling of power lines to the attitude and orbit control engine under airborne carrier, frequency range 10kHz~10MHz; 2) Lightning: refers to indirect lightning interference signals, the impact of indirect lightning on attitude and orbit control engines, electric field strength 6×106 / (1+R2 / 50)1 / 2V / m, magnetic field strength 3.2×104A / m; 3) Electromagnetic interference: The impact of active and passive interference on attitude and orbit control engines in airborne electronic warfare platforms, with a frequency range of 30MHz to 40GHz and a power range of 1W to 10MW. 4) High-power electromagnetic aspects: The impact of high-power electromagnetic and electromagnetic pulse weapons on attitude and orbit control engines. The frequency range of high-power electromagnetic is 300MHz~300GHz, and the frequency of electromagnetic pulse is 500MHz~10GHz; the power is 1MW.

3. The method for analyzing and evaluating the electromagnetic characteristics of an attitude and orbit control engine according to claim 1, characterized in that, The output parameters in step four include: the measured / simulated quantity is the corresponding port voltage or current, the test value of the port voltage is defined as Ut, the test value of the port current is It, the simulated value of the port voltage is Uo, and the test value of the port current is Ic.

4. The method for analyzing and evaluating the electromagnetic characteristics of an attitude and orbit control engine according to claim 1, characterized in that, In step four, parameter sensitivity analysis first scans the parameter design space to assess the sensitivity of the output response to the input parameters and identify important parameters. The key technologies involved are high-efficiency sample space sampling technology and high-quality sample space generation technology. During parameter sensitivity analysis, a high-quality response surface is established to describe the relationship between the output response and the input parameters.

5. The method for analyzing and evaluating the electromagnetic characteristics of an attitude and orbit control engine according to claim 1, characterized in that, In step four, while performing parameter sensitivity analysis, a numerical fitting method is used to establish a function describing the relationship between the response parameters and the input parameters, i.e., the response surface; the fitting model includes first-order and second-order polynomial regression, first-order, second-order, and interpolation-type moving least squares methods; the fitting accuracy is evaluated by predicting the quality indicators CoD and CoP.

6. The method for analyzing and evaluating the electromagnetic characteristics of an attitude and orbit control engine according to claim 1, characterized in that, In step six, the method for calculating the simulation reliability is as follows: Let x and y be random variables in the simulation data and experimental data, respectively, with sample data {xi, i = 1, 2, ..., N1} and {yi′, i′ = 1, 2, ..., N2}, and population distribution functions F(x) and G(y), respectively. First, test whether the two random variables follow the same probability distribution. Based on the known distribution characteristics of F(x) and G(y), select the appropriate test method. If, after testing, the two population distribution functions F(x) and G(y) follow the same distribution, then it is necessary to test the statistical characteristic values ​​of the sample data of the two random variables. First, calculate the mean test statistic of the two sets of sample values ​​respectively: Using the t-test method, calculate the mean test statistic, where T is a t-distribution with (N1+N2-2) degrees of freedom: If the test statistic T1-α / 2 = tα / 2, then the hypothesis is accepted, and it is considered that there is no significant difference between the mean of the simulation data and the experimental data at the significance level α; where tα / 2 can be obtained from the t-distribution table based on the confidence level α.

Images