Aircraft dynamic load uncertainty propagation analysis and efficient quantification method
By constructing the optimal chaotic polynomial model and Monte Carlo simulation method, the calculation efficiency and accuracy problems of aircraft dynamic load uncertainty evaluation are solved, and the uncertainty propagation analysis of aircraft dynamic load is realized efficiently, supporting the reliability design of aircraft.
Patent Information
- Application Number
- CN202510590620.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-08
- Publication Date
- 2025-08-15
AI Technical Summary
The prior art is difficult to effectively evaluate and quantify the dynamic load of aircraft under multi-source uncertainty, resulting in structural design and control difficulties, affecting the reliability and safety of aircraft.
The optimal chaotic polynomial model was constructed by Gegenbauer polynomial and orthogonal decomposition method. Combined with Monte Carlo simulation method, the impact of uncertainty in aircraft design parameters on dynamic load was quantitatively analyzed, and the model accuracy was optimized through Latin hypercube sampling and R2 criterion.
It realizes efficient and accurate quantification of uncertainty propagation of aircraft dynamic loads, improves calculation efficiency, provides a basis for aircraft reliability design, and is suitable for uncertainty analysis of high-dimensional design parameters.
Smart Images
Figure CN120493403A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to uncertainty assessment of aircraft dynamic loads, and in particular to an aircraft dynamic load uncertainty propagation analysis and efficient quantification method. Background Art
[0002] Aircraft are often subjected to a variety of dynamic loads during flight, including thrust loads during launch, pulse pressure during transonic flight, and strong aerodynamic loads during re-entry. With the rapid increase in flight speed, flight distance, maneuverability, and carrying capacity of aerospace vehicles, accurately acquiring dynamic loads has become a prerequisite for precise management of aircraft flight control and health monitoring. However, in actual engineering, the dynamic loads on aircraft are difficult to measure directly using force sensors. However, the structural response of an aircraft under load, such as displacement, acceleration, and structural strain, can be easily measured to a certain extent. Therefore, indirectly calculating the dynamic loads on an aircraft by measuring the dynamic response and structural characteristics of the aircraft structure and combining it with mature load inversion methods is a practical method.
[0003] Generally speaking, dynamic load analysis for aircraft is subject to multiple sources of uncertainty. On the one hand, each aircraft subsystem generally exhibits uncertainties arising from static factors (such as material dispersion, tolerances, manufacturing errors, and modeling errors) or time-varying parameters (such as boundary condition interference and instrument measurement deviations). Furthermore, the propagation of these uncertainties causes deviations in the actual mass, center of mass, and moment of inertia of the aircraft relative to the designed design. Furthermore, uncertainties arise from external excitations during launch and from gusts and transonic pressure fluctuations during ascent. These multidisciplinary uncertainties accumulate over the course of the aircraft's service life. Furthermore, the cross-coupling effects of these uncertainties generate a significant amount of noise independent of the actual dynamic loads, hindering the precise assessment of dynamic loads and creating difficulties for aircraft structural design and operational attitude control. Furthermore, these uncertainties propagate across disciplines and levels, including initial data, trajectory, attitude control, dynamics, and loads. In particular, dynamic loads caused by external excitations can have a significant impact on pre-launch instrument calibration and attitude control during operation. Therefore, the refined design of uncertain dynamic loads of aircraft is a key issue that needs to be solved urgently, and it is also an interdisciplinary topic between structural dynamics problems and uncertainty analysis. Summary of the Invention
[0004] The purpose of the present invention is to efficiently and quantitatively analyze the impact of the uncertainty of aircraft design parameters on the flight dynamic load response, obtain the moment information corresponding to the dynamic load, and provide a basis for aircraft reliability design.
[0005] The technical solution of the present invention is to provide a method for propagation analysis and efficient quantification of aircraft dynamic load uncertainty, comprising the following steps:
[0006] 1. A method for uncertainty propagation analysis and efficient quantification of aircraft dynamic loads, characterized by comprising the following steps:
[0007] Step 1: Establish a flight dynamics model and determine the uncertainty information of the aircraft design parameters based on engineering experience or experimental data;
[0008] Step 2: Sampling is performed based on Latin hypercube to obtain the initial sample points of the design parameters and the corresponding state parameter responses;
[0009] Step 3: Determine the maximum order of the polynomial and construct a completely chaotic polynomial model based on the Gegenbauer polynomial. Perform an orthogonal transformation on the completely chaotic polynomial and use structure selection technology to select orthogonal terms that contribute most to the reduction of the error function. Build the optimal chaotic polynomial model to replace the flight dynamics model.
[0010] Step 4: Extract test sample points based on the Latin hypercube method using R 2 The accuracy of the optimal chaotic polynomial model is evaluated by the criterion; if the accuracy requirement is not met, the test sample is added to the original sample and steps 3 and 4 are repeated to update the optimal chaotic polynomial model;
[0011] Step 5: Based on the high-precision approximate model finally established, use the Monte Carlo simulation method to perform uncertainty propagation analysis and obtain the moment information of the dynamic load.
[0012] Furthermore, the step 1 includes:
[0013] The design parameters mainly include the design parameters of the environment, structure, assembly and materials that need to be considered when designing the aircraft, including the aircraft structure mass deviation and structure thickness deviation.
[0014] Furthermore, the step 2 includes:
[0015] The dynamic loads of an aircraft include shear force, bending moment, and acceleration, which characterize the lateral dynamic loads on the aircraft when it is subjected to external interference such as shear wind and gusts in the atmosphere.
[0016] Furthermore, the step 3 constructs a completely chaotic polynomial model according to the following formula:
[0017]
[0018] Where, f(x1,x2,…,x q ) represents the state parameter response value, h is the maximum order of the selected Gegenbauer polynomial, represents an expression for any basis in the constructed polynomial model, where j i The value of (i=1,2,…,q) is any natural number from 0 to h, is the coefficient of the corresponding basis, q is the number of design parameters, and the polynomial of each design parameter is The calculation method is the same and can be obtained by the following formula:
[0019]
[0020] Where, is the general formula of the Gegenbauer polynomial:
[0021]
[0022] Where, (η i ) k =η i (η i +1)…(η i +k-1), η i The value is greater than 0.
[0023] Furthermore, in step 3, the optimal chaotic polynomial model is obtained by performing structural selection according to the following formula:
[0024]
[0025] Where M represents the total error value, L is the number of samples, f(s) is the response value of the state parameter of the sth sampling, N is the number of all bases included in formula (1), and p e (s) is the orthogonal term of the orthogonal transformation on the right side of equation (1), c e is the corresponding orthogonal term coefficient, ε e is the error reduction ratio of the e-th orthogonal term. The larger its value is, the easier it is to retain the orthogonal term.
[0026] Furthermore, the accuracy of step 4 is evaluated as follows:
[0027]
[0028] In the formula, G is the number of test samples, y m and are the actual response value and the test response value, respectively. is the mean of the true response values of G test samples, R 2 Indicates the overall accuracy. The larger the value, the higher the model accuracy.
[0029] Beneficial effects of the present invention:
[0030] (1) The present invention proposes a method for analyzing and efficiently quantifying the uncertainty propagation of aircraft dynamic loads. This method can quantitatively analyze the uncertainty transfer process from aircraft design parameters to flight dynamic loads, and then accurately evaluate the aircraft dynamic load moment information affected by multi-source uncertainty.
[0031] (2) The present invention can construct an optimal chaotic polynomial model to replace the aircraft flight dynamics model based on a small amount of sample data, so as to solve the computational efficiency bottleneck problem in uncertainty propagation analysis and improve the uncertainty assessment efficiency of aircraft dynamic loads.
[0032] (3) The flight load uncertainty analysis method proposed in this invention can effectively evaluate the impact of high-dimensional (23-dimensional) design parameter uncertainty on flight loads and has high universality. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.
[0034] Figure 1 It is a schematic diagram of the finite element model setting of the aircraft;
[0035] Figure 2 It is the accuracy verification of the optimal PCE model under 200 samples;
[0036] Figure 3 It is a comparison between the uncertainty propagation analysis results of the aircraft dynamic load and the results of 100,000 target shootings. DETAILED DESCRIPTION
[0037] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, which constitute a part of this application and are used to illustrate the principles of the present invention together with the embodiments of the present invention.
[0038] The method of the present invention can be adapted for uncertainty assessment of aircraft dynamic loads. To illustrate the technical solution of the present invention in more detail, an aircraft finite element model is used as an example. Specifically, a method for propagating uncertainty analysis and efficient quantification of aircraft dynamic loads includes the following steps:
[0039] Step 1: Establish a flight dynamics model and determine the uncertainty information of aircraft design parameters based on engineering experience or experimental data.
[0040] Figure 1 The aircraft finite element model is displayed, including relevant information such as sensor locations, some aerodynamic surfaces, selected cross-sectional load locations, etc. As shown in Table 1, this embodiment provides the uncertainty types and corresponding distribution information of 23-dimensional design parameters.
[0041] Step 2: Sampling is performed based on Latin hypercube to obtain the initial sample points of the design parameters and the corresponding state parameter responses.
[0042] In this example, 400 samples were extracted using the Latin hypercube method, resulting in a 400×23 matrix. Each row of this matrix represents a sample, and each column of each row represents the value of each design parameter in the sample. This example uses the aircraft finite element model to calculate the response values of three flight motion loads: shear force, bending moment, and resultant acceleration, corresponding to the 400 sample points.
[0043] Step 3: Determine the maximum order of the polynomial and construct a completely chaotic polynomial model based on the Gegenbauer polynomial. Perform an orthogonal transformation on the completely chaotic polynomial and, using structure selection techniques, select orthogonal terms that contribute significantly to reducing the error function. This results in an optimal chaotic polynomial model to replace the flight dynamics model.
[0044] Take h = 2 and construct the following completely chaotic polynomial model:
[0045]
[0046] Among them, there are a total of For the convenience of description, Equation (7) can be re-expressed as
[0047]
[0048] Where, t m (x1,x2,…,x 23 ) is the basis in formula (7). In order to solve the coefficient a m , perform orthogonal transformation on the right side of equation (8) to obtain the following equation
[0049]
[0050] Where p e (s) can be obtained by t m (x s ) is obtained through Gram-Schmidt orthogonalization, c e is the corresponding orthogonal term coefficient, which can be obtained by the following formula
[0051]
[0052] According to equations (4) and (5), find the orthogonal term that contributes most to reducing the total error value, and calculate the coefficient a in equation (8) by matrix multiplication. m , completing the construction of the optimal chaotic polynomial model.
[0053] Step 4: Extract test sample points based on the inherited Latin hypercube method, using R 2The accuracy of the optimal chaotic polynomial model is evaluated by the criterion. If the accuracy requirement is not met, the test sample is added to the original sample and steps 3 and 4 are repeated to update the optimal chaotic polynomial model.
[0054] This embodiment will randomly re-sample 200 groups of sample data to verify the accuracy of the final model. Figure 2 As shown in Table 2, a scatter plot is obtained, with the calculated response of the aircraft model as the horizontal axis and the optimal chaotic polynomial model as the vertical axis. As can be seen from the plot, most points fall on the straight line y = x, proving the accuracy of the model. For quantitative analysis, as shown in Table 2, the maximum relative error does not exceed 1%.
[0055] Step 5: Based on the high-precision approximate model finally established, use the Monte Carlo simulation method to perform uncertainty propagation analysis and obtain the moment information of the dynamic load.
[0056] In this example, the Monte Carlo method was used to perform 100,000 calculations on the constructed high-precision approximate model to obtain corresponding dynamic load data such as shear force, bending moment, and acceleration. The means and standard deviations of 100,000 sets of data were statistically analyzed to obtain quantitative uncertainty information. The dynamic load responses at different probability points were analyzed and compared with the results of 100,000 target shooting experiments. As shown in Table 3, the relative errors of the load results and moment information at each probability point were all less than 1%, indicating that the uncertainty propagation results based on the optimal PCE are true and reliable.
[0057] In the present invention, the high-precision model obtained in steps 3 and 4 performs well in the process of verification of 200 test sample points, such as Figure 2 As shown in Table 2, the validity of the subsequent calculation results is guaranteed. In addition, the method of the present invention calls the original model a total of 400 times. If the Monte Carlo method is used to directly simulate the entire propagation process, the original model needs to be called a total of 100,000 times. From the number of calls, the number of times required for the method of the present invention is less than 1% of the Monte Carlo method, which greatly improves the computational efficiency of the aircraft uncertainty propagation analysis and reflects the efficiency of the content of the present invention. In addition, the analysis results of the method of the present invention have a very small error compared with the results of 100,000 target shooting experiments, as shown in Table 3, which illustrates the accuracy of the content of the present invention.
[0058] Table 1 Uncertainty information of 23-dimensional design parameters
[0059]
[0060] Table 2 Error analysis of test samples
[0061]
[0062]
[0063] Table 3 Dynamic load analysis results and verification
[0064]
[0065] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.
Claims
1. A method for uncertainty propagation analysis and efficient quantification of aircraft dynamic loads, characterized by: The following steps are involved: Step 1: Establish a flight dynamics model and determine the uncertainty information of the aircraft design parameters based on engineering experience or experimental data; Step 2: Sampling is performed based on Latin hypercube to obtain the initial sample points of the design parameters and the corresponding state parameter responses; Step 3: Determine the maximum order of the polynomial and construct a completely chaotic polynomial model based on the Gegenbauer polynomial. Perform an orthogonal transformation on the completely chaotic polynomial and use structure selection technology to select orthogonal terms that contribute most to the reduction of the error function. Build the optimal chaotic polynomial model to replace the flight dynamics model. Step 4: Extract test sample points based on the Latin hypercube method using R 2 The accuracy of the optimal chaotic polynomial model is evaluated by the criterion; if the accuracy requirement is not met, the test sample is added to the original sample and steps 3 and 4 are repeated to update the optimal chaotic polynomial model; Step 5: Based on the high-precision approximate model finally established, use the Monte Carlo simulation method to perform uncertainty propagation analysis and obtain the moment information of the dynamic load.
2. The method for uncertainty propagation analysis and efficient quantification of aircraft dynamic loads according to claim 1, characterized in that: The step 1 further comprises: The design parameters mainly include the design parameters of the environment, structure, assembly and materials that need to be considered when designing the aircraft, including the aircraft structure mass deviation and structure thickness deviation.
3. The method for uncertainty propagation analysis and efficient quantification of aircraft dynamic loads according to claim 1, characterized in that: The step 2 further comprises: The dynamic loads of an aircraft include shear force, bending moment, and acceleration, which characterize the lateral dynamic loads on the aircraft when it is subjected to external interference such as shear wind and gusts in the atmosphere.
4. The method for uncertainty propagation analysis and efficient quantification of aircraft dynamic loads according to claim 1, characterized in that: The step 3 constructs a completely chaotic polynomial model according to the following formula: Where, f(x1,x2,…,x q ) represents the state parameter response value, h is the maximum order of the selected Gegenbauer polynomial, represents an expression for any basis in the constructed polynomial model, where j i The value of (i=1,2,…,q) is any natural number from 0 to h, is the coefficient of the corresponding basis, q is the number of design parameters, and the polynomial of each design parameter is The calculation method is the same and can be obtained by the following formula: Where, is the general formula of the Gegenbauer polynomial: Where, (η i ) k =η i (η i +1)…(η i +k-1), η i The value is greater than 0.
5. The method for uncertainty propagation analysis and efficient quantification of aircraft dynamic loads according to claim 1, characterized in that: In step 3, the optimal chaotic polynomial model is obtained by performing structural selection according to the following formula: Where M represents the total error value, L is the number of samples, f(s) is the response value of the state parameter of the sth sampling, N is the number of all bases included in formula (1), and p e (s) is the orthogonal term of the orthogonal transformation on the right side of equation (1), c e is the corresponding orthogonal term coefficient, ε e is the error reduction ratio of the e-th orthogonal term. The larger its value is, the easier it is to retain the orthogonal term.
6. The method for uncertainty propagation analysis and efficient quantification of aircraft dynamic loads according to claim 1, characterized in that: The accuracy evaluation of step 4 is performed as follows: In the formula, G is the number of test samples, y m and are the actual response value and the test response value, respectively. is the mean of the true response values of G test samples, R 2 Indicates the overall accuracy. The larger the value, the higher the model accuracy.