A low-cost aircraft multidisciplinary hierarchical global sensitivity analysis method for mixed uncertainty

Abstract

The application discloses a kind of aircraft multidisciplinary layered global sensitivity analysis methods for mixed uncertainty, it is related to complex system engineering and multidisciplinary design optimization technical field, for solving the problem that existing method cannot effectively handle random and cognitive mixed uncertainty, high computing cost, analysis dimension is single and lacks knowledge fusion mechanism.The method adopts four-stage progressive strategy: step 1 is quickly screened by double-layer nested sampling strategy Non-sensitive parameter;Step 2 is calculated Sobol index and constructs inter-disciplinary coupling sensitivity matrix using proxy model;Step 3 is calculated matrix independent sensitivity index using Kolmogorov-Smirnov statistical quantity;Step 4 introduces time weight and expert confidence score mechanism to fuse prior knowledge.The application can efficiently handle mixed uncertainty under the premise of controllable computing cost, the calculation efficiency is improved by about two orders of magnitude, analysis dimension is more comprehensive, result is more in line with engineering practice, can directly guide multidisciplinary optimization strategy selection.

Description

Technical Field

[0001] This invention relates to the field of multidisciplinary design optimization technology, and in particular to a low-cost multidisciplinary hierarchical global sensitivity analysis method for aircraft facing mixed uncertainties. Background Technology

[0002] In the design phase of low-cost aircraft, it is necessary to comprehensively consider multiple closely coupled disciplines such as aerodynamics, structure, propulsion, guidance, detection, and execution. Two types of uncertainty are commonly present in the design of each discipline: first, stochastic uncertainty, stemming from inherent fluctuations in objective physical processes such as material properties (e.g., batch variations in skin density), manufacturing errors (e.g., machining tolerances of aircraft wing area), and environmental disturbances (e.g., random variations in the Mach number of the incoming flow), which can usually be described by probability distributions; second, cognitive uncertainty, stemming from insufficient subjective cognition such as model simplification (e.g., turbulence model coefficients), lack of parameter information (e.g., interval estimation of the elastic modulus of composite materials), and fuzzy expert experience, which are often described using interval theory and evidence theory.

[0003] Global sensitivity analysis aims to quantitatively assess the contribution of the uncertainty of each input parameter to the uncertainty of the system output response (such as life cycle cost, cruise drag coefficient, range, and mission execution probability), and is a key prerequisite for guiding the selection of design variables, resource allocation, and robust optimization.

[0004] Existing global sensitivity analysis methods mainly include the Sobol variance decomposition method and the Morris screening method. The Sobol variance decomposition method quantifies the contribution of parameters to the output variance by decomposing variance, and can distinguish between main effects and interaction effects of parameters. However, this method usually assumes that all input parameters have a clear probability distribution, and cannot effectively handle cognitive uncertainty (such as interval variables and evidence theory variables). The Morris screening method uses a trajectory sampling method of "one factor at a time" to quickly screen sensitive parameters by calculating basic effects. It has low computational cost, but only provides qualitative or semi-quantitative results, and also does not consider mixed uncertainty scenarios.

[0005] Therefore, existing methods have the following technical shortcomings in the multidisciplinary design of low-cost aircraft: First, they cannot effectively handle mixed scenarios involving both stochastic and cognitive uncertainties. For example, in the design of low-cost aircraft, the elastic modulus of a certain type of composite material may only have its range known without a precise distribution, making it difficult to directly apply the traditional Sobol method. Second, for high-dimensional complex systems containing hundreds of parameters (such as aerodynamic parameters, structural parameters, propulsion parameters, and control parameters), variance analysis methods based on Monte Carlo simulations require tens of thousands or even more model evaluations, resulting in a single high-fidelity aerodynamic-structural coupled simulation of a low-cost aircraft often taking several hours, making the computational cost prohibitive. Third, existing methods focus primarily on the variance (second moment) of the output response, neglecting key parameters that significantly influence the overall shape of the output probability distribution (such as high-risk tail regions and multimodal characteristics) but have a small contribution to variance. For example, the variance contribution of structural mass parameters may be small, but their fluctuations may lead to a high-cost long tail in the cost distribution, posing a significant risk to the economic viability required for low-cost design. Fourth, a large amount of historical design experience and expert knowledge from the early design phase were not effectively utilized to guide sensitivity analysis, which may lead to results that deviate from engineering reality.

[0006] Therefore, there is an urgent need for a low-cost global sensitivity analysis method for multidisciplinary aircraft systems that can efficiently and comprehensively handle mixed uncertainties and integrate prior knowledge. Summary of the Invention

[0007] The purpose of this invention is to provide a multidisciplinary hierarchical global sensitivity analysis method for aircraft facing mixed uncertainties, in order to solve the following technical problems existing in the prior art:

[0008] (1) It cannot effectively handle mixed scenarios where random uncertainty and cognitive uncertainty coexist. The traditional Sobol variance decomposition method is only applicable to parameters with a clear probability distribution.

[0009] (2) For high-dimensional complex systems containing hundreds of aerodynamic, structural, propulsion and control parameters, variance analysis based on Monte Carlo simulation requires tens of thousands of model evaluations, while a single high-fidelity aerodynamic-structural coupling simulation takes several hours, making the computational cost unbearable.

[0010] (3) Existing methods focus more on the variance of the output response and ignore key parameters that have an important impact on the high-risk region at the tail of the output probability distribution but do not contribute much to the variance;

[0011] (4) A large amount of historical design experience and expert knowledge were not effectively utilized in the early stages of the design, which may lead to the analysis results deviating from the actual engineering situation.

[0012] To achieve the above objectives, the present invention adopts the following technical solution:

[0013] This invention provides a low-cost, multidisciplinary, hierarchical global sensitivity analysis method for aircraft facing mixed uncertainties. It employs a four-stage progressive strategy of "rapid coarse screening - variance refinement - distribution supplementation - knowledge fusion," including the following steps:

[0014] Step 1: Preliminary parameter screening based on the improved Morris method.

[0015] For a low-cost multidisciplinary aircraft system model containing both random and cognitive uncertain parameter sets, a two-layer nested sampling strategy is implemented:

[0016] Outer sampling: Discretize the uncertainty space of the cognitive uncertainty parameter set to construct several fixed cognitive scenarios;

[0017] Inner layer sampling: Under each fixed cognitive scenario, the Morris trajectory sampling method is used to sample the set of random uncertain parameters and calculate the basic effect of each random parameter;

[0018] Calculate the screening criteria: Based on the sampling results from all cognitive scenarios, calculate the mean of the absolute values ​​of the basic effect of each parameter. and standard deviation ,Will The value is lower than the first threshold and Parameters with values ​​below the second threshold are initially identified as insensitive parameters and removed from subsequent analysis to obtain the key parameter set.

[0019] Step 2: Global sensitivity analysis based on variance decomposition.

[0020] For the parameters in the aforementioned key parameter set, perform a variance-based global sensitivity analysis:

[0021] Step 2.1: Using a surrogate model and Monte Carlo simulation, calculate the first-order Sobol exponent for each parameter. (Main effect index) and total order Sobol index ;

[0022] Step 2.2: Based on the difference between the first-order Sobol exponent and the total-order Sobol exponent, the main effect dominant parameters and the interaction effect dominant parameters are obtained from the key parameter set. The interdisciplinary coupling sensitivity matrix is ​​constructed to quantify the amplification or attenuation effect of uncertainty transmission between different disciplines through coupling variables, and to indicate the key coupling paths for multidisciplinary collaborative optimization.

[0023] Step 3: Moment-independent sensitivity analysis based on cumulative distribution.

[0024] Parameters that have a potential impact on the tail characteristics of the output response distribution are selected from the set of key parameters to form a parameter set for moment independence analysis. Perform moment-independent sensitivity analysis based on the cumulative distribution function for each parameter in the moment-independent analysis parameter set:

[0025] Step 3.1: Calculate the unconditional cumulative distribution function of the output of the low-cost aircraft system. ;

[0026] Step 3.2: Analyze the parameter set for moment independence Each input parameter in Fix it to different values Calculate the corresponding conditional cumulative distribution function. ;

[0027] Step 3.3: Use the Kolmogorov-Smirnov statistic to measure the maximum vertical distance between the conditional cumulative distribution function and the unconditional cumulative distribution function;

[0028] Step 3.4: Calculate the parameters based on the expected value of the Kolmogorov-Smirnov statistic. Moment-independent sensitivity index .

[0029] Step 4: Prior sensitivity fusion and parameter classification based on expert knowledge.

[0030] Step 4.1: Data Preparation and Normalization. Combine the overall sensitivity values ​​of each parameter in the current analysis report. Together with the combined sensitivity values ​​of the corresponding parameters in each historical report, the values ​​are normalized to a percentage impact:

[0031]

[0032] in Indicates the first Parameters in the report The overall sensitivity value, where the overall sensitivity value is taken from the value obtained in step 2. Compared with the result obtained in step 3 The weighted sum.

[0033] Step 4.2: Calculate the time weights for the current analysis report and historical reports. And expert confidence weight And according to time weight And expert confidence weight Weighted calculation report overall weight ;

[0034] Step 4.3: According to the formula

[0035]

[0036] Calculation parameters The weighted average impact reflects the parameter's influence. Overall importance based on all available information.

[0037] Step 4.4: Based on the comprehensive sensitivity score Step 2 and Step 3 The parameters are categorized by uncertainty type into performance-critical parameters, reliability-critical parameters, cognitive-critical parameters, coupling-critical parameters, interaction-sensitive parameters, and insensitive parameters. The final output includes a classification label, comprehensive sensitivity score, and ranking list for each parameter, available for use by multidisciplinary design optimization teams.

[0038] In a further preferred embodiment, the method for constructing the cognitive scene through outer-layer sampling in step 1 includes one or more of the following: vertex sampling, Latin hypercube sampling, focal element representative point sampling, or boundary and center combination sampling. These sampling methods can effectively cover the uncertainty space of cognitive parameters, ensuring the robustness of the screening results.

[0039] A further preferred embodiment is that, in step 1, the mean of the absolute values ​​of the basic effects is calculated. and standard deviation The specific formula is:

[0040]

[0041]

[0042]

[0043] in For the first Parameters In the The basic effects on the trajectory, This represents the total number of trajectories. These formulas provide a quantitative basis for parameter selection. Reflecting the average influence of the parameters, This reflects the stability of the parameters' impact under different cognitive scenarios.

[0044] A further preferred embodiment is that the first-order Sobol exponent in step 2... Sobol index of total order The calculation formula is:

[0045]

[0046]

[0047] in, The total variance of the system response. For the first Parameters Variance caused by individual effect To exclude the first Parameters The variance caused by all external parameters. The first-order Sobol exponent represents the main effect of the parameter, and the total-order Sobol exponent represents the total effect of the parameter (including the main effect and the interaction effect). The difference between the two quantifies the additional effect produced by the parameter through the interaction.

[0048] In a further preferred embodiment, in step 2.2, according to the formula...

[0049]

[0050] Calculate the first Parameters Interaction effect contribution Based on the contribution of the interaction effect, the main effect dominant parameters and the interaction effect dominant parameters are obtained from the key parameter set according to the following rules:

[0051] like and Then determine the first Parameters A parameter with a dominant main effect indicates that the fluctuation of this parameter itself has a significant impact on the output, has weak coupling with other parameters, and can be optimized independently.

[0052] like or Then determine the first Parameters The parameter is an interaction-dominated parameter, meaning that it significantly affects the output through coupling with other parameters and requires multidisciplinary collaborative optimization.

[0053] In a further preferred embodiment, step 2.2, the specific process of constructing the interdisciplinary coupling sensitivity matrix is ​​as follows:

[0054] Step 2.2.1: Subject decomposition and coupling variable identification:

[0055] First, the low-cost aircraft multidisciplinary system is decomposed into These are mutually coupled disciplinary subsystems, denoted as... .

[0056] For any two different disciplines and ( ), defined from Output to The input variables are coupling variables, denoted as... The specific methods for identifying coupling variables are as follows:

[0057] List The set of output variables ;

[0058] List input variable set ;

[0059] Find the intersection If each element in the set is a coupled variable, then each element in the set is a coupled variable. If there are multiple coupled variables, they can be processed separately or represented in a vectorized manner.

[0060] Step 2.2.2: Calculate the local sensitivity of the coupling variables to the system output:

[0061] For each coupling variable Calculate its response to the system's final output. The partial derivatives are denoted as:

[0062]

[0063] This partial derivative reflects the change in system output when the coupled variables change by a unit amount.

[0064] Step 2.2.3: Calculate the total effect of each input parameter on the coupling variables:

[0065] For each random input parameter Using the global sensitivity analysis process based on variance decomposition in step 2, calculate For coupling variables Total order Sobol index This index reflects Individual and their interaction Total contribution of uncertainty.

[0066] Step 2.2.4: Synthesize the interdisciplinary coupling sensitivity matrix :

[0067] Defining disciplines For the subject The coupling sensitivity is:

[0068]

[0069] in Traversal arrive All coupling variables. Combined into matrix Its diagonal elements Set to 0.

[0070] In a further optimized approach, step 3 involves selecting parameters from the set of key parameters that have a potential impact on the tail characteristics of the output response distribution, forming a parameter set for moment-independent analysis. The specific process is as follows:

[0071] First, perform quantitative screening based on probability thresholds:

[0072] Define a high-risk threshold for the output response. For parameters in the key parameter set ,calculate:

[0073] Will Fixed at its 5th percentile and 95th percentile ;

[0074] Calculate the output separately Exceed conditional probability and ;

[0075] Tail Sensitivity Indicators ,like If so, then this parameter will be included in the moment-independent analysis parameter set.

[0076] Secondly, a direct screening based on the type of cognitive uncertainty is performed: if the parameters in the key parameter set... Parameters belonging to any of the following types are unconditionally included in the moment-independent analysis parameter set: ① Interval-type parameters with unknown probability distributions but known only their range; ② Evidence-theoretic parameters described by multiple mutually exclusive evidence focal elements; ③ Fuzzy parameters with asymmetric membership functions. This process does not rely on numerical calculations but directly judges based on the parameter's type label (interval, evidence, fuzzy). Even parameters belonging to this type... The value is not high, and there may be potential tail risks due to unknown distribution. Therefore, it must be unconditionally included in the moment independence analysis parameter set.

[0077] Third, perform rapid filtering based on single-parameter extreme value scanning: [The parameters are then...] Take 11 sample points at equal intervals (covering 0% to 100% quantiles), and randomly sample other parameters for each fixed value, then calculate the output. 95th percentile Then calculate the coefficient of variation of the quantile sequence. ,in This indicates the calculation of the standard deviation. This indicates the calculation of the mean. If... Then the parameters Include the parameter set for moment-independent analysis. This is used to capture those parameters obtained through... This method cannot fully reflect parameters that do affect the high quantiles of the output. Because it involves relatively large computations, it is executed last as a supplementary measure.

[0078] In a further preferred embodiment, the formula for calculating the Kolmogorov-Smirnov statistic in step 3 is as follows:

[0079]

[0080] in, Let be the unconditional cumulative distribution function output by the low-cost aircraft system. For the first The parameters are fixed as follows: The conditional cumulative distribution function at time t.

[0081] A further preferred embodiment is that in step 3, according to the formula...

[0082]

[0083] Calculate input parameters Moment-independent sensitivity index ,in Represents the Kolmogorov-Smirnov statistic The expectation.

[0084] In a further preferred embodiment, the reporting weight in step 4 is:

[0085]

[0086] in, and These are the scaling factors for time and expert information, and their sum is 1. By adjusting these two scaling factors, the influence of historical data and expert experience can be balanced, enabling cross-validation between numerical analysis and engineering experience.

[0087] A further preferred embodiment is that the time weight is calculated using the following formula:

[0088]

[0089]

[0090] in, For the year corresponding to the k-th report, For reference years, To adjust the hyperparameters of time weighting, This represents the total number of reports. Time weights are applied using a sigmoid function to ensure that newer historical data receives higher weights while avoiding excessively large weight differences.

[0091] In a further optimized approach, step 4.4 defines the parameter classification rules as follows:

[0092] like If the parameter exceeds the third threshold and is a main effect-dominant parameter, it is classified as a performance-critical parameter. During design, the nominal value should be optimized first, tolerances should be strictly controlled, and it can be optimized independently. The third threshold is taken as 150% of the average sensitivity score of all parameters.

[0093] like If the parameter is greater than the third threshold and is a parameter dominated by interaction effects, it is classified as a coupling key parameter. It must be optimized collaboratively by multiple disciplines during the design process and cannot be adjusted alone.

[0094] like If it is classified as a key reliability parameter, tail risks must be considered during the design process, and reliability analysis and extreme condition verification must be carried out.

[0095] If the parameter is of the cognitive uncertainty type and If so, it is classified as a key cognitive parameter, and experimental resources must be invested in the design to reduce cognitive uncertainty;

[0096] like If a parameter is greater than 50% of the median of the overall sensitivity score of all parameters but lower than the third threshold, and the parameter is an interaction-effect dominant parameter, it is classified as an interaction-sensitive parameter and treated as a secondary variable in the collaborative optimization of the design process.

[0097] The remaining parameters that do not meet any of the above conditions are classified as insensitive parameters.

[0098] Beneficial effects

[0099] Compared with the prior art, the present invention has the following beneficial effects:

[0100] (1) This invention extends the Morris screening method to mixed uncertainty environment through a double-layer nested sampling strategy. Under the premise of controllable computational cost, it can quickly eliminate non-sensitive parameters from more than a hundred parameters, effectively overcome the "curse of dimensionality", and reduce the computational burden for subsequent detailed analysis.

[0101] (2) This invention adopts a four-stage progressive strategy of "rapid coarse screening - variance analysis - distribution supplementation - knowledge fusion" to concentrate computational resources on truly important parameters, reducing the number of model evaluations from millions to tens of thousands, and improving computational efficiency by about two orders of magnitude. Compared with the traditional Sobol method, which requires tens of thousands or even more model evaluations, the method of this invention significantly reduces computational costs while ensuring analytical accuracy through parameter screening.

[0102] (3) This invention not only focuses on parameters that affect the output variance, but also captures parameters that have a significant impact on the shape of the overall probability distribution of the output, especially the high-cost risk tail. The analysis dimensions are more comprehensive, and it can identify parameters that do not contribute much to the variance but have a significant impact on extreme risks. This comprehensive analytical capability enables the method of this invention to guide not only performance optimization, but also reliability design and risk control.

[0103] (4) For the first time, a time weighting and expert confidence scoring mechanism were introduced to quantify historical data and expert experience and cross-validate them with the results of pure numerical analysis, which significantly improved the engineering credibility of parameter classification. This knowledge fusion mechanism makes the analysis results more consistent with engineering practice and avoids the problem that pure numerical analysis may deviate from reality.

[0104] (5) The output parameter classification (performance critical, reliability critical, cognitive critical, coupling critical, interaction sensitive) can directly guide the selection of multidisciplinary optimization strategies, the focus of uncertainty quantification, and experimental design, so as to achieve the optimal trade-off between cost and performance. For example, for performance critical parameters (such as battery energy density), the main effort and budget should be invested in their selection and optimization; for interaction sensitive parameters (such as servo response error), a multidisciplinary collaborative optimization strategy should be adopted; for cognitive critical parameters (such as material elastic modulus), their uncertainty should be reduced through experiments.

[0105] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Detailed Implementation

[0106] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to specific embodiments. It should be noted that this embodiment uses the aerodynamic-structural-propulsion-guidance-detection-execution multidisciplinary system of a certain type of low-cost aircraft as an example to demonstrate the complete application process of the method of this invention. Those skilled in the art can apply the method of this invention to multidisciplinary sensitivity analysis of other low-cost aircraft or aerospace equipment based on the description herein.

[0107] This embodiment applies the method of the present invention to the design phase of a certain type of low-cost aircraft. First, a comprehensive performance analysis model of the low-cost aircraft is constructed, encompassing seven disciplines: aerodynamics, structure, propulsion, flight performance, guidance, detection, and execution. The input uncertainty parameters are identified and defined as follows:

[0108] (1) Random uncertainty parameters (12 in total), each of which is given a specific physical meaning:

[0109] Incoming Mach number: reflects the uncertainty of flight speed, originating from thrust fluctuations of the propulsion system and atmospheric disturbances, and follows a normal distribution.

[0110] Lift coefficient: determined by the aerodynamic shape and angle of attack of the aircraft, it fluctuates greatly during maneuvering flight and follows a normal distribution.

[0111] Drag coefficient: related to aircraft configuration and surface roughness, and follows a normal distribution.

[0112] Battery energy density: reflects the energy storage capacity of a power battery, is affected by the batch of cells, and follows a normal distribution.

[0113] Servo response error: reflects the delay time of the flight control system's control surface response, is affected by servo mass and control law, and follows a normal distribution.

[0114] Structural mass coefficient: reflects the weight efficiency of the aircraft's wings and fuselage structure, and follows a normal distribution.

[0115] Positioning error: reflects the overall positioning accuracy of the GPS / inertial navigation system and follows a normal distribution.

[0116] Target recognition distance: reflects the aircraft's ability to detect targets and follows a normal distribution.

[0117] Working load mass: The random deviation of the working load mass, which follows a normal distribution.

[0118] Thrust deviation: The deviation between the actual thrust of the engine and the nominal value, which follows a normal distribution.

[0119] Airfoil thickness deviation: Airfoil machining error, which follows a normal distribution.

[0120] Composite layup deviation: The error in the layup angle of composite materials follows a normal distribution.

[0121] (2) Cognitive uncertainty parameters (3 in total) have incomplete information and cannot be described by precise probability distributions:

[0122] Elastic modulus of structural materials: Using novel low-cost composite materials, only the range of values ​​is known, and it cannot be described by a precise probability distribution.

[0123] Empirical coefficients for aerodynamic models: empirical correction coefficients introduced when using turbulence models, described by evidence theory.

[0124] Initial mass distribution coefficient: a priori estimate of the mass proportion of each component within the aircraft, represented by a triangular fuzzy number.

[0125] (3) The system output response is a key performance indicator, including:

[0126] Life cycle cost (composed of structural cost, propulsion cost, workload cost, flight control cost, etc.); cruise drag coefficient (directly affects range); maximum range; mission execution probability.

[0127] In this embodiment, the total life cycle cost is the primary response.

[0128] Based on the above-mentioned overall performance analysis model for low-cost aircraft, the sensitivity analysis is performed using the method proposed in this invention. This method employs a four-stage progressive strategy of "rapid coarse screening - variance refinement - distribution supplementation - knowledge fusion," specifically including the following steps:

[0129] Step 1: Preliminary parameter screening based on the improved Morris method.

[0130] In the initial screening phase, a two-level nested sampling strategy is implemented:

[0131] Outer Sampling: For the three cognitive uncertainty parameters, the Latin hypercube sampling method is used to generate 20 cognitive scenarios, each corresponding to a fixed set of cognitive parameter values. The Latin hypercube sampling method can uniformly distribute sampling points within the uncertainty space of the cognitive parameters, ensuring sufficient coverage of the cognitive uncertainty space. The selection of 20 cognitive scenarios is based on a balance between computational resources and analysis accuracy, adequately representing the variation range of the cognitive parameters while avoiding the computational burden caused by too many scenarios. For example, the elastic modulus of composite materials is used as a cognitive parameter. We can take its upper and lower bounds and midpoint as typical cognitive scenarios.

[0132] Inner-layer sampling: In each cognitive scenario, Morris trajectory sampling is performed on the remaining 12 random uncertainty parameters. The parameter value range is discretized into 6 levels. The selection of 6 levels is based on standard Morris method practices, which can fully capture the changing trends of the parameters. 30 trajectories are generated for each scenario. The number of 30 trajectories is chosen based on the statistical requirement of obtaining stable basic effect estimates. Each trajectory contains 13 sample points (corresponding to 12 random parameters plus 1 initial point). The total number of system model evaluations is 20 scenarios multiplied by 30 trajectories multiplied by 13 sample points, which equals 7800 times. The system model uses a validated low-fidelity surrogate model (response surface model). A single evaluation takes approximately 0.1 seconds, and the total computation time is approximately 13 minutes. The use of the low-fidelity surrogate model is key to the rapid screening in step 1. Its accuracy has been validated by the high-fidelity model and can meet the accuracy requirements of parameter screening.

[0133] Calculate the screening criteria: Based on the sampling results from all cognitive scenarios, calculate the mean of the absolute values ​​of the basic effect of each parameter. and standard deviation Mean of the absolute value of the basic effect Standard deviation reflects the average influence of a parameter. This reflects the stability of the parameter's influence under different cognitive scenarios. The specific calculation formula is as follows:

[0134]

[0135]

[0136]

[0137] in For the first Parameters In the The basic effects on the trajectory, The total number of trajectories, in this embodiment This equals 20 scenes multiplied by 30 trajectories, which equals 600.

[0138] Set the first threshold to the value of all parameters. The second threshold is 10% of the mean, and the second threshold is the percentage of all parameters. The first threshold is set based on the relative importance of the average influence of parameters; parameters below this threshold have a smaller average impact on the system output. The second threshold is set based on the stability of parameter influence; parameters below this threshold show smaller fluctuations in influence across different cognitive scenarios, indicating that their sensitivity is not significantly affected by cognitive uncertainty. The results show that 5 out of the 12 random uncertainty parameters have a relatively small impact on the average influence of parameters. and All five parameters below the threshold were identified as non-sensitive and removed from subsequent analysis: airfoil thickness deviation, composite layup deviation, thrust deviation, target recognition distance, and working load mass. The remaining 10 parameters constituted the key parameter set: incoming flow Mach number, lift coefficient, drag coefficient, battery energy density, servo response error, structural mass coefficient, positioning error, structural material elastic modulus, aerodynamic model empirical coefficients, and initial mass distribution coefficient. Through the screening in step 1, the number of parameter dimensions was reduced from 15 to 10, reducing the computational burden for subsequent detailed analysis.

[0139] By employing this innovative double-layer nested sampling strategy, this invention extends the Morris screening method to environments with mixed uncertainties, enabling the rapid elimination of insensitive parameters from massive amounts of data while maintaining controllable computational costs, effectively overcoming the "curse of dimensionality".

[0140] Step 2: Global sensitivity analysis based on variance decomposition.

[0141] For the 10 selected key parameters, a high-precision surrogate model based on the Kriging model was constructed. The Kriging model is an interpolation method based on spatial correlation, which can significantly reduce computational costs while ensuring prediction accuracy. 500 training samples were generated using an optimal Latin hypercube design. Each sample invoked a high-fidelity, low-cost multidisciplinary analysis model for aircraft (including CFD aerodynamic calculations, finite element structural analysis, propulsion system model, and six-degree-of-freedom ballistic simulation). A validation set of 100 samples was used, and the model's coefficient of determination reached over 0.96. A coefficient of determination of 0.96 indicates that the Kriging surrogate model can explain more than 96% of the output response variance, and the prediction accuracy meets the requirements for subsequent sensitivity analysis.

[0142] Sobol global sensitivity analysis was performed using the Kriging surrogate model, and the first-order Sobol exponent for each parameter was calculated. Sobol index of total order The calculation formula is:

[0143]

[0144]

[0145] in, The total variance of the system response. For the first Parameters Variance caused by individual effect To exclude the first Parameters The variance caused by the effects of all external parameters. The first-order Sobol exponent represents the main effect of the parameter, that is, the contribution of the parameter's individual variation to the output variance. The total-order Sobol exponent represents the total effect of the parameter (including the main effect and the interaction effect). The difference between the two quantifies the additional influence produced by the parameter through the interaction.

[0146] Based on the difference between the first-order Sobol exponent and the total-order Sobol exponent, the main effect-dominant parameters and interaction effect-dominant parameters are obtained from the key parameter set. Specifically, according to the formula...

[0147]

[0148] Calculate the first Parameters Interaction effect contribution Based on the contribution of the interaction effect, the main effect dominant parameters and the interaction effect dominant parameters are obtained from the key parameter set according to the following rules:

[0149] like and Then determine the first Parameters A parameter with a dominant main effect indicates that the fluctuation of this parameter itself has a significant impact on the output, has weak coupling with other parameters, and can be optimized independently.

[0150] like or Then determine the first Parameters The parameter is an interaction-dominated parameter, meaning that it significantly affects the output through coupling with other parameters and requires multidisciplinary collaborative optimization.

[0151] In this embodiment, the Monte Carlo simulation method is used to calculate uncertainty propagation. The Monte Carlo simulation sample size is 10,000, and the selection of the sample size is based on the convergence requirement of the Sobol exponent estimation. Since the preliminary evaluation found that the Sobol exponents of the incoming Mach number, the empirical coefficients of the aerodynamic model, and the initial mass distribution coefficient are all less than 0.01, and are considered extremely insensitive parameters, they were further removed from the set of key parameters. Finally, seven representative parameters were retained, and the Sobol exponents were calculated as shown in the table below:

[0152]

[0153] The calculation results show that the main effect exponents of battery energy density, lift coefficient, and positioning error are relatively high, and have the greatest impact on the life cycle cost of low-cost aircraft. The total order exponent of servo response error is significantly greater than the first order exponent, indicating that it has a significant impact through interaction with other parameters (such as aerodynamic parameters and structural mass), and belongs to the interaction effect-dominated parameter.

[0154] In addition, an interdisciplinary coupling sensitivity matrix is ​​constructed to quantify the amplification or attenuation effect of uncertainty transmission between different disciplines through coupling variables, thus identifying key coupling paths for multidisciplinary collaborative optimization. The specific process is as follows:

[0155] First, the low-cost aircraft multidisciplinary system is decomposed into These are mutually coupled disciplinary subsystems, denoted as... In this embodiment, it is divided into the discipline of aerodynamics. Structural science Advance the discipline Control Science .

[0156] For any two different disciplines and ( ), defined from Output to The input variables are coupling variables, denoted as... The specific methods for identifying coupling variables are as follows:

[0157] List The set of output variables ;

[0158] List input variable set ;

[0159] Find the intersection If each element in the set is a coupled variable, then each element in the set is a coupled variable. If there are multiple coupled variables, they can be processed separately or represented in a vectorized manner.

[0160] This embodiment takes the aerodynamic-structural-control coupling of a low-cost aircraft as an example:

[0161] Output variables in aerodynamics include: aerodynamic pressure distribution Lift ,resistance Pitch moment wait;

[0162] Input variables for structural engineering include: lift. Torque wait;

[0163] therefore, .

[0164] The outputs of structural engineering include: elastic deformation Modal displacement wait;

[0165] Inputs to aerodynamics include: elastic deformation (Affects aerodynamic shape);

[0166] therefore, .

[0167] The outputs of control science include: rudder deflection. rudder surface speed ;

[0168] Inputs to aerodynamics include: control surface deflection. ;

[0169] Inputs to structural engineering include: rudder deflection. (Affects elastic load);

[0170] therefore, , .

[0171] Then calculate the local sensitivity of the coupling variables to the system output:

[0172] For each coupling variable Calculate its response to the system's final output. The partial derivatives are denoted as:

[0173]

[0174] This partial derivative reflects the change in system output when the coupled variable changes by a unit amount. The final output response of the system in this embodiment... Take the total life cycle cost This partial derivative can be obtained through the finite difference method (applying a small perturbation to the coupled variables and re-evaluating the system model), analytical methods (if the subject model is differentiable), or automatic differentiation using an established surrogate model. This embodiment calculates:

[0175]

[0176] Next, calculate the total effect of each input parameter on the coupling variables:

[0177] For each random input parameter Using the global sensitivity analysis process based on variance decomposition in step 2, calculate For coupling variables Total order Sobol index This index reflects Individual and their interaction The total contribution of uncertainty. Calculated in this embodiment:

[0178] , indicating the lift coefficient among all input parameters. It affects the lift of the coupled variables. The most important factor of uncertainty. The self and its interaction with other parameters together explain 65% of the total variance. (The remaining parameters) affect lift. The total order exponents are all much less than 0.65, and their contribution is negligible.

[0179] This indicates the influence of the elastic deformation of the coupled variables. The two dominant parameters are the structural quality coefficient. (Total order exponent 0.40) and elastic modulus of structural material (Total order exponent 0.45). Both explain... 85% of the total variance, of which The impact is slightly greater than .

[0180] , indicating the influence of the coupling variable, rudder surface deflection angle. The most important parameter is the servo response error. Its total order index is as high as 0.80.

[0181] Finally, the interdisciplinary coupling sensitivity matrix is ​​synthesized. :

[0182] Defining disciplines For the subject The coupling sensitivity is:

[0183]

[0184] in Traversal arrive All coupling variables. Combined into matrix Its diagonal elements Set to 0. In this embodiment, the interdisciplinary coupling sensitivity matrix is ​​finally obtained. for:

[0185]

[0186] in The maximum value indicates that the elastic deformation feedback between structure and aerodynamics is the strongest coupling path affecting cost uncertainty, and aerodynamic-structure co-optimization needs to be prioritized.

[0187] By calculating the interdisciplinary coupling sensitivity matrix Its physical meaning is: Quantifying the disciplines Uncertainty is transmitted to disciplines through coupling variables. This amplifies or attenuates the uncertainty of the final system output. The larger the value, the better from the perspective of the discipline. To the subject The more complex the coupling path, the more attention it requires. This matrix, as an independent analysis result, is directly available to the design team. Its uses include:

[0188] Identifying the key paths of uncertainty propagation: If If it is significantly larger than other elements, then the discipline should be considered during the design process. To impose stricter control on the output, or in the discipline Robust design for coupled inputs;

[0189] Guiding multidisciplinary decoupling or collaboration strategies: for strongly coupled paths ( (Very large), an integrated collaborative optimization method should be adopted; for weakly coupled paths ( (Very small), allowing for independent optimization of each discipline to improve efficiency;

[0190] To aid subsequent parameter classification: When a parameter is determined to be a parameter dominated by interaction effects, its classification should be combined with the disciplines involved. The value can be used to further determine which interdisciplinary couplings the parameter is primarily responsible for, thereby guiding the division of labor within the team.

[0191] Step 2 precisely quantifies the contribution of each parameter to the output variance through variance decomposition and reveals the coupling path between disciplines, providing a basis for multidisciplinary collaborative optimization.

[0192] Step 3: Moment-independent sensitivity analysis based on cumulative distribution.

[0193] Parameters that have a potential impact on the tail characteristics of the output response distribution are selected from the set of key parameters to form a parameter set for moment independence analysis. Perform moment-independent sensitivity analysis based on the cumulative distribution function for each parameter in the moment-independent analysis parameter set.

[0194] This step calculates the moment-independent sensitivity index based on the Kolmogorov-Smirnov statistic for parameters (structural quality coefficient, material elastic modulus) that may pose a risk to the tail of the output response (life-cycle cost). Moment-independent sensitivity analysis does not depend on specific moments (such as variance) and can identify parameters that have a decisive influence on the tail of the distribution.

[0195] In this embodiment, the specific process of selecting parameters that have a potential impact on the tail characteristics of the output response distribution from the set of key parameters to form the moment-independent analysis parameter set is as follows:

[0196] First, perform quantitative screening based on probability thresholds:

[0197] Define a high-risk threshold for the output response. In this embodiment, the cost exceeds 120% of the budget limit. This applies to parameters in the key parameter set. ,calculate:

[0198] Will Fixed at its 5th percentile and 95th percentile ;

[0199] Calculate the output separately Exceed conditional probability and ;

[0200] Tail Sensitivity Indicators ,like If so, then this parameter will be included in the moment-independent analysis parameter set.

[0201] In this embodiment, the structural quality coefficient The tail sensitivity index is 0.28, and the elastic modulus of the structural material is... The tail sensitivity index is 0.23, and the servo response error is... Its tail sensitivity index is 0.09, and its lift coefficient is... The tail sensitivity index is 0.11, so the structural quality coefficient is first set. and the elastic modulus of structural materials Include the parameter set for moment-independent analysis.

[0202] Secondly, a direct screening based on the type of cognitive uncertainty is performed: if the parameters in the key parameter set... Parameters belonging to any of the following types are unconditionally included in the moment-independent analysis parameter set: ① Interval-type parameters with unknown probability distributions but known only their range; ② Evidence-theoretic parameters described by multiple mutually exclusive evidence focal elements; ③ Fuzzy parameters with asymmetric membership functions. This process does not rely on numerical calculations but directly judges based on the parameter's type label (interval, evidence, fuzzy). Even parameters belonging to this type... The value is not high, and there may be potential tail risks due to unknown distribution. Therefore, it must be unconditionally included in the moment independence analysis parameter set.

[0203] In this embodiment, the elastic modulus of the structural material Since the parameter is an interval parameter, the elastic modulus of the structural material is determined once again. Include the parameter set for moment-independent analysis.

[0204] Third, perform rapid filtering based on single-parameter extreme value scanning: [The parameters are then...] Take 11 sample points at equal intervals (covering 0% to 100% quantiles), and randomly sample other parameters for each fixed value, then calculate the output. 95th percentile Then calculate the coefficient of variation of the quantile sequence. ,in This indicates the calculation of the standard deviation. This indicates the calculation of the mean. If... Then the parameters Include the parameter set for moment-independent analysis. This is used to capture those parameters obtained through... This method cannot fully reflect parameters that do affect the high quantiles of the output. Because it involves relatively large computations, it is executed last as a supplementary measure.

[0205] In this embodiment, the structural quality coefficient The coefficient of variation is 0.14, confirming that the structural quality coefficient... Include the parameter set for moment-independent analysis.

[0206] Then, a moment-independent sensitivity analysis based on the cumulative distribution function is performed on each parameter in the moment-independent analysis parameter set. The specific process is as follows:

[0207] Step 3.1: First, based on the Kriging surrogate model constructed in Step 2, obtain the unconditional cumulative distribution function of the system output through Monte Carlo simulation. Unconditional cumulative distribution function It reflects the overall probability distribution characteristics of the system output under the combined effects of uncertainties in all parameters. The Monte Carlo simulation uses 10,000 samples, and the selection of the sample size is based on the convergence requirements of the cumulative distribution function estimation.

[0208] Step 3.2: Analyze the parameter set for moment independence Each input parameter in Ten fixed values ​​are selected evenly within its range. For each fixed value, keep this parameter constant, and sample other parameters according to their original distribution to obtain the conditional cumulative distribution function. Conditional cumulative distribution function Reflects when parameters Fixed to a specific value The output probability distribution characteristics are given. For each fixed value, the Monte Carlo simulation sample size is 1000.

[0209] Step 3.3: Use the Kolmogorov-Smirnov statistic to measure the maximum vertical distance between the conditional cumulative distribution function and the unconditional cumulative distribution function; the specific calculation formula is as follows:

[0210]

[0211] in, Let be the unconditional cumulative distribution function output by the low-cost aircraft system. For the first The parameters are fixed as follows: The conditional cumulative distribution function. The KS statistic captures the overall influence of parameters on the shape of the output distribution by measuring the maximum vertical distance between two distribution functions, including mean, variance, skewness, kurtosis, and tail characteristics.

[0212] Step 3.4: Expectation based on the Kolmogorov-Smirnov statistic:

[0213]

[0214] Calculation parameters Moment-independent sensitivity index . The larger the value, the greater the impact of the uncertainty of this parameter on the shape of the tail of the output distribution, even if its variance contribution may be small.

[0215] In this embodiment, it is expected that the structural quality coefficient is obtained by averaging 10 fixed values ​​of the Kolmogorov-Smirnov statistic. The calculation results show that the structural quality coefficient... The moment-independent sensitivity index is 0.124, and the elastic modulus of the structural material is... The moment-independent sensitivity index (MISI) for the structural quality coefficient is 0.087. In contrast, the MISI for battery energy density is only 0.031. The MISI ranges from 0 to 1, with a higher value indicating a greater overall impact of the parameter on the output distribution. The MISI for the structural quality coefficient (0.124) is significantly higher than that for battery energy density (0.031), indicating that although the structural quality coefficient does not contribute much to the variance analysis, it has a significant impact on the tail of the cost distribution. The specific mechanism is as follows: when the elastic modulus of the material is low, the increased structural deformation requires additional stiffeners, leading to a sharp increase in cost and forming a high-cost long tail in the cost distribution.

[0216] Step 3 not only focuses on parameters that affect the output variance, but also captures parameters that have a significant impact on the shape of the overall probability distribution of the output (especially the high-cost risk tail), making the analysis more comprehensive.

[0217] Step 4: Prior sensitivity fusion and parameter classification based on expert knowledge.

[0218] This step focuses on the key parameter set, using the Sobol index output in step 2 and the moment-independent sensitivity index output in step 3 as the basis for the current analysis. It integrates historical reports and expert knowledge to calculate the comprehensive sensitivity score and output the final parameter classification.

[0219] In this embodiment, five sensitivity analysis reports on similar low-cost aircraft models from the past eight years were collected from our organization, and combined with the current report, for a total of six reports.

[0220] Step 4.1: Data Preparation and Normalization. Combine the overall sensitivity values ​​of each parameter in the current analysis report. Together with the combined sensitivity values ​​of the corresponding parameters in each historical report, the values ​​are normalized to a percentage impact:

[0221]

[0222] in Indicates the first Parameters in the report The overall sensitivity value, where the overall sensitivity value is taken from the value obtained in step 2. Compared with the result obtained in step 3 The weighted sum.

[0223] Step 4.2: Calculate the time weights for the current analysis report and historical reports. And expert confidence weight And according to time weight And expert confidence weight Weighted calculation report overall weight ;

[0224]

[0225] in, and These are the scaling factors for time and expert information, and their sum is 1. By adjusting these two scaling factors, the influence of historical data and expert experience can be balanced, enabling cross-validation between numerical analysis and engineering experience.

[0226] The formula for calculating the time weight is:

[0227]

[0228]

[0229] in, For the year corresponding to the k-th report, For reference years, To adjust the hyperparameters of time weighting, This represents the total number of reports. Time weights are applied using a sigmoid function to ensure that newer historical data receives higher weights while avoiding excessively large weight differences.

[0230] The expert experience was assessed by inviting three chief engineer-level experts (from aerodynamics, structure, and flight control respectively) to rate the results of the six reports on a confidence scale of 1 to 10, and the expert confidence weights were calculated. .

[0231] Step 4.3: According to the formula

[0232]

[0233] Calculation parameters The weighted average impact reflects the parameter's influence. Overall importance based on all available information.

[0234] In this embodiment, the final calculated weighted average influence is:

[0235]

[0236] Step 4.4: Based on the comprehensive sensitivity score Step 2 and Step 3 The parameters are categorized by uncertainty type into performance-critical parameters, reliability-critical parameters, cognitive-critical parameters, coupling-critical parameters, interaction-sensitive parameters, and insensitive parameters. The final output includes a classification label, comprehensive sensitivity score, and ranking list for each parameter, available for use by multidisciplinary design optimization teams.

[0237] The parameter classification rules are as follows:

[0238] like If the parameter is greater than the third threshold and is a main effect-dominant parameter, it is classified as a performance-critical parameter. During design, the nominal value should be optimized first, tolerances should be strictly controlled, and it can be optimized independently. The third threshold is taken as 150% of the average comprehensive sensitivity score of all parameters. In this embodiment, the average comprehensive sensitivity score of all parameters is 0.118, and 150% of the average comprehensive sensitivity score of all parameters is 0.177.

[0239] like If the parameter is greater than the third threshold and is a parameter dominated by interaction effects, it is classified as a coupling key parameter. It must be optimized collaboratively by multiple disciplines during the design process and cannot be adjusted alone.

[0240] like If it is classified as a key reliability parameter, tail risks must be considered during the design process, and reliability analysis and extreme condition verification must be carried out.

[0241] If the parameter is of the cognitive uncertainty type and If so, it is classified as a key cognitive parameter, and experimental resources must be invested in the design to reduce cognitive uncertainty;

[0242] like If a parameter is greater than 50% of the median of the overall sensitivity score of all parameters but lower than the third threshold, and the parameter is an interaction-dominant parameter, it is classified as an interaction-sensitive parameter and treated as a dependent variable in the collaborative optimization of the design process; the median of the overall sensitivity score of all parameters is 0.168, and 50% of the median of the overall sensitivity score of all parameters is 0.084.

[0243] The remaining parameters that do not meet any of the above conditions are classified as insensitive parameters.

[0244] In this embodiment, battery energy density and lift coefficient are key performance parameters, and tolerances need to be controlled first and optimized independently. In addition, it is noted that the weighted average influence of positioning error is 0.176 < 0.177, which is only slightly below the threshold, and it is a main effect-dominant parameter. Therefore, it is also recommended to control tolerances first and optimize independently during the design.

[0245] No parameter meets the requirements of the key coupling parameters, but the weighted average influence of the servo response error is 0.168 < 0.177, which is also slightly below the threshold. Moreover, it is a parameter dominated by interaction effects, so multidisciplinary collaborative optimization is required during the design.

[0246] structural quality coefficient The moment-independent sensitivity index is 0.124, and the elastic modulus of the structural material is... The moment-independent sensitivity index is 0.087, all greater than 0.08, therefore the structural quality coefficient is... and the elastic modulus of structural materials It is classified as a key reliability parameter, and tail risks must be considered during the design process, along with reliability analysis and extreme condition verification.

[0247] In addition, the elastic modulus of structural materials of It is also classified as a key cognitive parameter, and experimental resources must be invested in the design to reduce cognitive uncertainty. The range can be narrowed by arranging supplementary experiments.

[0248] The remaining parameters are insensitive parameters, with fixed nominal values, and their uncertainty is ignored.

[0249] This step introduces time weighting and expert confidence scoring mechanisms for the first time, quantifying historical data and expert experience and cross-validating them with pure numerical analysis results, which significantly improves the engineering credibility of the classification.

[0250] In this embodiment, based on the above sensitivity analysis results, the low-cost aircraft design team made the following decisions: Focus their main efforts and budget on selecting high-energy-density batteries (a key performance parameter), optimizing aerodynamic shape to improve the lift coefficient (a key performance parameter), and developing a high-precision positioning system (a key proximity performance parameter). For the servo system, a multidisciplinary collaborative optimization strategy was adopted, fully considering its coupling effects with control laws and aeroelasticity to reduce the uncertainty amplification caused by interaction effects. Specific measures included: establishing an aerodynamic-control-structure joint simulation model and designing robust control laws; conducting more refined static tests on the elastic modulus of structural materials (a key cognitive parameter) to reduce its cognitive uncertainty and improve the credibility of system reliability predictions; adopting lightweight design (such as topology optimization) within cost limits for the structural mass coefficient (a key reliability parameter) to control the tail risk of cost distribution; and ignoring parameters marked as insensitive, thereby significantly reducing the dimensionality of design variables in subsequent multidisciplinary optimization problems.

[0251] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A low-cost, multidisciplinary, hierarchical global sensitivity analysis method for aircraft facing mixed uncertainties, characterized in that: Includes the following steps: Step 1: Preliminary parameter screening based on the improved Morris method: For a low-cost multidisciplinary aircraft system model containing both random and cognitive uncertain parameter sets, a two-layer nested sampling strategy is implemented: Outer sampling: Discretize the uncertainty space of the cognitive uncertainty parameter set to construct several fixed cognitive scenarios; Inner layer sampling: Under each fixed cognitive scenario, the Morris trajectory sampling method is used to sample the set of random uncertain parameters and calculate the basic effect of each random parameter; Calculate the screening criteria: Based on the sampling results from all cognitive scenarios, calculate the mean of the absolute values ​​of the basic effect of each parameter. and standard deviation ,Will The value is lower than the first threshold and Parameters with values ​​below the second threshold are initially identified as insensitive parameters and removed from subsequent analysis to obtain the key parameter set; Step 2: Global Sensitivity Refinement Based on Variance Decomposition: For the parameters in the aforementioned key parameter set, perform a variance-based global sensitivity analysis: Step 2.1: Using a surrogate model and Monte Carlo simulation, calculate the first-order Sobol exponent for each parameter. Sobol index of total order ; Step 2.2: Based on the difference between the first-order Sobol exponent and the total-order Sobol exponent, obtain the main effect dominant parameters and the interaction effect dominant parameters from the key parameter set, and construct the interdisciplinary coupling sensitivity matrix; Step 3: Moment-independent sensitivity analysis based on cumulative distribution: Parameters that have a potential impact on the tail characteristics of the output response distribution are selected from the set of key parameters to form a parameter set for moment independence analysis. Perform moment-independent sensitivity analysis based on the cumulative distribution function for each parameter in the moment-independent analysis parameter set: Step 3.1: Calculate the unconditional cumulative distribution function of the output of the low-cost aircraft system. ; Step 3.2: Analyze the parameter set for moment independence Each input parameter in Fix it to different values Calculate the corresponding conditional cumulative distribution function. ; Step 3.3: Use the Kolmogorov-Smirnov statistic to measure the maximum vertical distance between the conditional cumulative distribution function and the unconditional cumulative distribution function; Step 3.4: Calculate the parameters based on the expected value of the Kolmogorov-Smirnov statistic. Moment-independent sensitivity index ; Step 4: Prior sensitivity fusion and parameter classification based on expert knowledge: Step 4.1: Data Preparation and Normalization: Combine the sensitivity values ​​of each parameter in the current analysis report. Together with the combined sensitivity values ​​of the corresponding parameters in each historical report, the values ​​are normalized to a percentage impact: in Indicates the first Parameters in the report The overall sensitivity value, where the overall sensitivity value is taken from the value obtained in step 2. Compared with the result obtained in step 3 The weighted sum; Step 4.2: Calculate the time weights for the current analysis report and historical reports. And expert confidence weight And according to time weight And expert confidence weight Weighted calculation report overall weight ; Step 4.3: According to the formula Calculation parameters The weighted average impact; Step 4.4: Based on the comprehensive sensitivity score Step 2 and Step 3 The system also considers the uncertainty type of parameters, classifying them into performance-critical parameters, reliability-critical parameters, cognitive-critical parameters, coupling-critical parameters, interaction-sensitive parameters, and insensitive parameters. Finally, it outputs the classification label, comprehensive sensitivity score, and ranking list for each parameter, which can be used for multidisciplinary design optimization.

2. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 1, characterized in that: In step 1, the mean of the absolute values ​​of the basic effects is calculated. and standard deviation The specific formula is: in For the first Parameters In the The basic effects on the trajectory, This represents the total number of trajectories.

3. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 1, characterized in that: The first-order Sobol exponent in step 2 Sobol index of total order The calculation formula is: in, The total variance of the system response. For the first Parameters Variance caused by individual effect To exclude the first Parameters The variance caused by the effects of all external parameters.

4. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 1, characterized in that: In step 2.2, according to the formula Calculate the first Parameters Interaction effect contribution Based on the contribution of the interaction effect, the main effect dominant parameters and the interaction effect dominant parameters are obtained from the key parameter set according to the following rules: like and Then determine the first Parameters A parameter with a dominant main effect indicates that the fluctuation of this parameter itself has a significant impact on the output, has weak coupling with other parameters, and can be optimized independently. like or Then determine the first Parameters The parameter is an interaction-driven parameter, meaning that it significantly affects the output through coupling with other parameters and requires multidisciplinary collaborative optimization.

5. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 1, characterized in that: In step 2.2, the specific process of constructing the interdisciplinary coupling sensitivity matrix is ​​as follows: Step 2.2.1: Subject decomposition and coupling variable identification: First, the low-cost aircraft multidisciplinary system is decomposed into These are mutually coupled disciplinary subsystems, denoted as... ; For any two different disciplines and ( ), defined from Output to The input variables are coupling variables, denoted as... ; Step 2.2.2: Calculate the local sensitivity of the coupling variables to the system output: For each coupling variable Calculate its response to the system's final output. The partial derivatives are denoted as: This partial derivative reflects the change in system output when the coupled variable changes by a unit amount; Step 2.2.3: Calculate the total effect of each input parameter on the coupling variables: For each random input parameter Using the global sensitivity analysis process based on variance decomposition in step 2, calculate For coupling variables Total order Sobol index This index reflects Individual and their interaction The total contribution of uncertainty; Step 2.2.4: Synthesize the interdisciplinary coupling sensitivity matrix : Defining disciplines For the subject The coupling sensitivity is: in Traversal arrive All coupling variables; all Combined into a matrix Its diagonal elements Set to 0.

6. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 5, characterized in that: The specific methods for identifying coupling variables are as follows: List The set of output variables ; List input variable set ; Find the intersection If so, then each element in the set is a coupling variable.

7. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 1, characterized in that: In step 3, the specific process of selecting parameters that have a potential impact on the tail characteristics of the output response distribution from the set of key parameters to form the parameter set for moment independence analysis is as follows: First, perform quantitative screening based on probability thresholds: Define a high-risk threshold for the output response. ; For parameters in the key parameter set ,calculate: Will Fixed at its 5th percentile and 95th percentile ; Calculate the output separately Exceed conditional probability and ; Tail Sensitivity Indicators ,like If so, then this parameter will be included in the moment-independent analysis parameter set; Secondly, a direct screening based on the type of cognitive uncertainty is performed: if the parameters in the key parameter set... If a parameter belongs to any of the following types, it is unconditionally included in the set of moment-independent analysis parameters: ① interval-type parameters whose probability distribution is unknown and only their range of values ​​is known; ② evidence theory-type parameters described by multiple mutually exclusive evidence focal elements; ③ fuzzy-type parameters whose membership function is asymmetric. Third, perform rapid filtering based on single-parameter extreme value scanning: [The parameters are then...] Eleven sample points were taken at equal intervals, covering the 0% to 100% quantiles. Other parameters were randomly sampled at each fixed value, and the output was calculated. 95th percentile Then calculate the coefficient of variation of the quantile sequence. ,in This indicates the calculation of the standard deviation. This indicates the calculation of the mean; if Then the parameters Include the parameter set for moment-independent analysis.

8. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 1, characterized in that: The formula for calculating the Kolmogorov-Smirnov statistic in step 3 is as follows: in, Let be the unconditional cumulative distribution function output by the low-cost aircraft system. For the first The parameters are fixed as follows: The conditional cumulative distribution function at time t.

9. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 1, characterized in that: The overall weighting for the report in step 4 is as follows: in, and The time weight is a proportionality coefficient to the expert information, and the sum of the two is 1; the formula for calculating the time weight is: in, For the year corresponding to the k-th report, For reference years, To adjust the hyperparameters of time weighting, This represents the total number of reports.

10. The method for multidisciplinary hierarchical global sensitivity analysis of low-cost aircraft oriented towards mixed uncertainties as described in claim 1, characterized in that: In step 4.4, the parameter classification rule is as follows: like If the parameter is greater than the third threshold and is a main effect-dominant parameter, it is classified as a key performance parameter; the third threshold is taken as 150% of the average sensitivity score of all parameters. like If the parameter is greater than the third threshold and is a parameter dominated by interaction effects, it is classified as a key coupling parameter. like If it is classified as a key reliability parameter, tail risks must be considered during the design process, and reliability analysis and extreme condition verification must be carried out. If the parameter is of the cognitive uncertainty type and If so, it is classified as a key cognitive parameter, and experimental resources must be invested in the design to reduce cognitive uncertainty; like If a parameter is greater than 50% of the median of the overall sensitivity score of all parameters but lower than the third threshold, and the parameter is an interaction-effect dominant parameter, it is classified as an interaction-sensitive parameter and treated as a secondary variable in the collaborative optimization of the design process. The remaining parameters that do not meet any of the above conditions are classified as insensitive parameters.

Images