Uncertainty analysis method for aeroacoustic coupled system

Abstract

This invention discloses an uncertainty analysis method for a spacecraft thermoacoustic-vibration coupling system, relating to the field of aerospace computing. The method includes: discretizing the geometric model of the spacecraft's structure and internal sound field to obtain a thermoacoustic-vibration coupling finite element model; selecting sample points in the uncertainty parameter space to establish a data-driven multidimensional parallelepiped model; selecting observation points in the spacecraft's structure and internal sound field; selecting experimental points in the uncertainty parameter space and inputting them into the finite element model to perform thermoacoustic-vibration coupling finite element analysis, obtaining the corresponding structural velocity response and sound pressure level response values ​​at the observation points; establishing a radial basis function neural network model based on the experimental points and their corresponding response values; and calculating the response intervals of the structural velocity response and sound pressure level response of the multidimensional parallelepiped model based on the radial basis function neural network model. This invention improves the accuracy of uncertainty calculation for spacecraft thermoacoustic-vibration coupling systems while maintaining computational efficiency.

Description

Technical Field

[0001] This invention belongs to the field of aerospace computing, specifically relating to an uncertainty analysis method for a thermoacoustic-vibration coupled system of an aircraft. Background Technology

[0002] Compared to traditional aircraft, hypersonic vehicles possess advantages such as higher speed, greater maneuverability, and superior penetration capabilities. The development of hypersonic vehicles has become a crucial element in the struggle for space dominance among nations. When flying at high Mach numbers, hypersonic vehicles constantly operate in complex environments characterized by high temperatures and intense noise interference, resulting in extremely harsh service conditions and placing higher demands on their structural design.

[0003] The phenomenon of surface temperature rise caused by hypersonic speeds is known as the "aerodynamic heating effect." Under this effect, temperature changes cause variations in the material's intrinsic properties, leading to thermal deformation of the structure, affecting its aerodynamic layout and overall load-bearing capacity. Furthermore, uneven temperature distribution can induce thermal stress and even structural failure, posing a significant challenge to the structure's thermal protection performance and overall stiffness. In addition to the high-temperature environment, the structure also endures high-intensity noise loads; engine noise can exceed 180 dB, severely impacting the structure. The nonlinear relationship between materials and structures caused by high temperatures, the complex temperature distribution, and the coupling of high-intensity noise all significantly affect the state of hypersonic vehicles. Under the coupled effects of thermal and noise dynamic loads, the uncertainty of the structure's dynamic response increases dramatically. However, methods for uncertainty analysis of vehicles, especially hypersonic vehicles, in multi-field coupling are still lacking. Summary of the Invention

[0004] This invention provides an uncertainty analysis method for a thermoacoustic-vibration coupling system of an aircraft, so as to realize the thermoacoustic-vibration coupling analysis of the aircraft and fully consider the influence of parameter uncertainty.

[0005] The uncertainty analysis method for a spacecraft thermoacoustic-vibration coupling system provided by this invention includes:

[0006] Step 1: Discretize the geometric model of the aircraft's structure and internal sound field using a finite element mesh to obtain the thermoacoustic-vibration coupled finite element model of the aircraft;

[0007] Step 2: Obtain the uncertain parameter space based on the uncertain parameters, and select multiple sample points within the uncertain parameter space to obtain the center, radius, and correlation coefficient of the uncertain parameters, and establish a data-driven multidimensional parallelepiped model, wherein the uncertain parameters are interval parameters;

[0008] Step 3: Select structural observation points and sound field observation points in the structure and internal sound field of the aircraft, respectively;

[0009] Step 4: Select test points in the space of uncertain parameters using the Latin hypercube sampling method. Based on the test points, perform structural finite element thermal analysis in the thermo-acoustic-vibration coupled finite element model to obtain the structural thermal stress. Use the structural thermal stress as prestress to perform acoustic-vibration coupled finite element analysis to obtain the response values ​​of the structural velocity response and the sound pressure level response corresponding to the structural observation point and the sound field observation point, respectively.

[0010] Step 5: Based on the test points and the corresponding response values, a center is selected using a self-organizing learning method, and the weights are calculated using an orthogonal least squares algorithm to establish a radial basis function neural network model. The radial basis function neural network model is used to characterize the mapping relationship between the uncertain parameters and the structural velocity response and the sound field sound pressure level response.

[0011] Step 6: Based on the radial basis function neural network model, calculate the maximum and minimum values ​​of the structural velocity response and sound pressure level response of the multidimensional parallelepiped model, and use them as the structural velocity response range and the sound pressure level response range of the multidimensional parallelepiped model.

[0012] The uncertainty analysis method for the acoustic-thermal-vibration coupling system of an aircraft provided by the present invention has at least the following advantages:

[0013] (1) Compared with the traditional acoustic-vibration coupling response analysis model, the uncertainty analysis method provided by this invention takes into account the influence of uncertainty on parameters in actual engineering, and the calculation results have important guiding significance for thermo-acoustic-vibration coupling analysis and structural design.

[0014] (2) The data-driven multidimensional parallelepiped model in this invention requires fewer sample points, i.e. less data, and improves the calculation method of correlation coefficient, resulting in higher accuracy.

[0015] (3) The radial basis neural network model in this invention serves as a surrogate model. It has strong fitting ability for highly nonlinear systems such as acoustic-vibration coupling analysis that considers thermal stress, and greatly improves computational efficiency compared to the finite element model. Attached Figure Description

[0016] Figure 1 This is a flowchart of the uncertainty analysis method for the thermoacoustic-vibration coupling system of an aircraft in an embodiment of the present invention;

[0017] Figure 2 This is a simplified flowchart of the uncertainty analysis method for the aircraft thermoacoustic-vibration coupling system in an embodiment of the present invention;

[0018] Figure 3 This is a schematic diagram of the structure of the hypersonic vehicle in an embodiment of the present invention. Detailed Implementation

[0019] To make the above-mentioned objectives, features, and advantages of the embodiments of the present invention more apparent and understandable, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This invention is applicable to the analysis of acoustic-vibration coupled systems of aircraft considering thermal stress and containing uncertain parameters. Taking a hypersonic aircraft as an example, it specifically illustrates the uncertainty analysis method for the thermo-acoustic-vibration coupled system of an aircraft. A hypersonic aircraft refers to an aircraft whose flight speed can reach Mach 5 or higher. (Reference) Figure 1 and Figure 2 The uncertainty analysis method for the thermoacoustic-vibration coupled system of an aircraft includes the following steps:

[0021] Step 1: Discretize the geometric model of the aircraft's structure and internal sound field using a finite element mesh to obtain the thermo-acoustic-vibration coupled finite element model of the aircraft.

[0022] In this embodiment of the invention, different types of finite element meshes are used to discretize the geometric model of the aircraft's structure and internal sound field, and coupling boundaries and boundary conditions are set for the structure and internal sound field to obtain the thermoacoustic-vibrational coupled finite element model of the aircraft. This finite element model is subsequently used for finite element analysis to obtain the structural velocity response and sound pressure level response of the structure and internal sound field under sinusoidal loads at a set frequency under thermal stress.

[0023] In one possible embodiment, the structure of the aircraft and the geometric model of its internal sound field are as follows: Figure 3 As shown, the structure refers to the aircraft's physical structure, which includes the nose, fuselage, tail, and air intake. The fuselage is a cavity structure, and the air intake is located at the bottom of the fuselage. The internal sound field refers to the aircraft's internal sound field, which is the internal filling structure of the fuselage. The structure (i.e., nose, fuselage, tail, and air intake) is discretized using 9631 solid elements, and the internal sound field is discretized using 3344 fluid elements. The surface where the structure contacts the internal sound field is designated as the acoustic-vibration coupling surface.

[0024] A fixed boundary condition is applied to the tail of the aircraft fuselage, and a thermal boundary condition is set on the surface of the aircraft to obtain a thermoacoustic-vibration coupled finite element model of the aircraft.

[0025] Step 2: Obtain the space of uncertain parameters based on the uncertain parameters, and select multiple sample points in the space of uncertain parameters to obtain the center, radius and correlation coefficient of the uncertain parameters, and establish a data-driven multidimensional parallelepiped model, where the uncertain parameters are interval parameters.

[0026] The structure and internal sound field of an aircraft have multiple uncertain parameters. For example, the structure and internal sound field of an aircraft may have n uncertain parameters, where n is a positive integer greater than or equal to 1. These n uncertain parameters form an n-dimensional uncertain parameter vector, where x... i Let i represent the i-th uncertain parameter in the n-dimensional uncertain parameter vector, where i = 1, 2, ..., n.

[0027] Uncertain parameters are typically bounded interval parameters, which can be represented by interval numbers, specifically as follows: Where I indicates that the uncertain parameter is an interval parameter. and x They represent the interval parameter x respectively I The upper and lower bounds, and the space of uncertain parameters of the aircraft's structure and internal sound field can be expressed as:

[0028]

[0029] Here, "×" represents the Cartesian product operation. The uncertain parameter space Θ is a multidimensional cube obtained by performing Cartesian products on all uncertain parameters (interval parameters), where each uncertain parameter forms one dimension of the uncertain parameter space Θ. Let θ be the i-th dimension of the uncertain parameter space Θ.

[0030] For an n-dimensional uncertain parameter vector x = (x1, x2, ..., xn) in the uncertain parameter space Θ n ) T Obtain m sample points x for the n-dimensional uncertain parameter vector. (q) q = 1, 2, ..., m, where x q Let represent the q-th sample point. Since each uncertain parameter is an interval parameter, for the ith uncertain parameter, its upper and lower bounds can be represented by its center and radius. Based on the sample points, the center and radius of the uncertain parameter can be calculated as follows:

[0031]

[0032] in, and Let the center and radius of the i-th uncertain parameter be represented respectively. Let q be the value of the q-th sample point in the i-th dimension of the uncertain parameter space Θ.

[0033] The correlation between any two uncertain parameters can be represented by a correlation coefficient, which can be obtained based on the distribution characteristics of multiple sample points in the space of uncertain parameters. For two uncertain parameters i,j (i,j=1,2,……,n), when their center and radius are determined, there exists a corresponding correlation coefficient for the q-th sample point. If the sample point lies on the edge of the parallelogram constructed based on the correlation coefficient, then the correlation coefficient between the two uncertain parameters, i and j, is:

[0034]

[0035] Based on the center of each uncertain parameter radius And establish a data-driven multidimensional parallelepiped model Ω based on correlation coefficients. x The multidimensional parallelepiped model Ω x It includes all sample points (m sample points), specifically:

[0036] Ω x ={x|-e≤K(xx)} C )≤e}

[0037] in, Multidimensional parallelepiped model Ω x The characteristic matrix K is obtained by the following formula:

[0038]

[0039]

[0040]

[0041] In one possible embodiment, Figure 3 Based on the geometric model and corresponding finite element model of the aircraft's structure and internal sound field, the fuselage is made of alumina, and the internal sound field is air. The Young's modulus E, density ρ1, thermal conductivity λ of the alumina, and air density ρ2 are all uncertain parameters. These four uncertain parameters are represented by interval numbers E = [390, 430] GPa, ρ1 = [3800, 4200] kg / m³, respectively. 3 , λ=[23.5,26.5]W / (mK), ρ2=[1.125,1.325]kg / m 3 express.

[0042] A concentrated sinusoidal excitation load is applied at the center of the fuselage bottom, and its amplitude F0 is also an uncertain parameter, represented by the interval number F0 = [95, 105]N. The above five uncertain parameters form a five-dimensional uncertain parameter vector x = (E, ρ1, λ, ρ2, F0). TTo reduce numerical errors during uncertainty quantization, the corresponding uncertainty parameter space Θ is described as: Θ=[39,43]×[38,42]×[23.5,26.5]×[11.25,13.25]×[95,105].

[0043] Based on 40 sample points of uncertain parameter vectors obtained in the five-dimensional uncertain parameter space Θ, the center and radius of each uncertain parameter are calculated, as shown in Table 1.

[0044] Table 1. Center and radius of the uncertain parameters

[0045]

[0046] Considering the correlation between the uncertain parameters E and ρ1, and between ρ1 and λ, calculate the correlation coefficient between any two uncertain parameters. The correlation between the uncertain parameters can be represented by the following correlation coefficient matrix R:

[0047]

[0048] For the 40 sample points with the aforementioned uncertain parameters, a data-driven multidimensional parallelepiped model Ω containing all sample points can be established. x Specifically, based on the center, radius, and correlation coefficient matrix of each uncertain parameter, a multidimensional parallelepiped model can be obtained for the sample points, and its explicit equation is:

[0049]

[0050] Step 3: Select structural observation points and sound field observation points in the structure and internal sound field of the aircraft, respectively.

[0051] In the thermo-acoustic-vibration coupled finite element model of the aircraft, nodes at key structural and internal acoustic field locations were selected as structural observation points and acoustic field observation points, respectively. In the subsequent thermo-acoustic-vibration coupled finite element analysis of the aircraft, the structural velocity response at the structural observation points and the sound pressure level response at the acoustic field observation points were obtained as typical responses.

[0052] In one possible embodiment, the center node at the top of the fuselage is selected as the structural observation point of the aircraft under the applied load, and the center node at the top of the internal sound field is selected as the sound field observation point of the internal sound field under the applied load. In the subsequent thermoacoustic-vibration coupled finite element analysis of the aircraft, the structural velocity response is obtained at the structural observation point, and the sound pressure level response is obtained at the sound field observation point.

[0053] Step 4: Select test points in the uncertain parameter space using the Latin hypercube sampling method. Based on the test points, perform structural finite element thermal analysis in the thermo-acoustic-vibration coupled finite element model to obtain the structural thermal stress. Use the structural thermal stress as prestress and perform acoustic-vibration coupled finite element analysis to obtain the response values ​​of the structural velocity response and sound field sound pressure level response corresponding to the structural observation point and the sound field observation point, respectively.

[0054] Latin hypercube sampling is performed within the uncertain parameter space Θ to obtain multiple test points, which are used for thermo-acoustic-vibrational coupled finite element analysis (TAFE). The TFE includes structural finite element thermal analysis and acoustic-vibrational coupled finite element analysis. Structural thermal stress of the aircraft can be obtained through structural finite element thermal analysis. Then, based on the obtained structural thermal stress, acoustic-vibrational coupled finite element analysis is performed to obtain the structural velocity response and sound pressure level response values. Optionally, acoustic-vibrational coupled finite element analysis employs acoustic-vibrational coupled harmonic response finite element analysis.

[0055] Specifically, the following process is performed for each test point: The values ​​of the uncertain parameters at the test point are input into the thermo-acoustic-vibrational coupled finite element model of the aircraft. First, thermal loads are applied to the leading edges of the aircraft's nose, tail, and air intakes, and structural finite element thermal analysis is performed. The obtained structural thermal stress is used as prestress. Then, acoustic-vibrational coupled finite element analysis is performed to obtain the response values ​​of the structural velocity response at the structural observation point and the response values ​​of the sound pressure level response at the sound field observation point. All test points and their structural velocity response and sound pressure level response values ​​form the dataset required for the radial basis function neural network model.

[0056] In one possible embodiment, based on the Young's modulus E, density ρ1, thermal conductivity λ, air density ρ2, and amplitude F0 of the alumina material as uncertain parameters, Latin hypercube sampling is performed in the uncertain parameter space Θ to obtain multiple test points.

[0057] For each test point, the following process was performed: The values ​​of the uncertain parameters at the test point were substituted into the thermoacoustic-vibrational coupled finite element model of the aircraft. Thermal loads were applied to the thermoacoustic-vibrational coupled finite element model, for example, at the leading edge of the nose, tail, and air intake. Structural finite element thermal analysis was performed to calculate the structural thermal stress, which was then used as the prestress for subsequent finite element analyses. A concentrated sinusoidal excitation load was applied at the center of the aircraft's fuselage bottom. The frequencies of the sinusoidal excitation load were 30Hz, 40Hz, ..., 90Hz. Finite element analysis of the aircraft's acoustic-vibrational coupled harmonic response considering the prestress was performed at each frequency. The response values ​​of the structural velocity response at the structural observation points and the response values ​​of the sound pressure level response at the sound field observation points were obtained at different frequencies. All test points and their obtained response values ​​formed the dataset required for the subsequent establishment of the radial basis function neural network model.

[0058] Step 5: Based on the test points and corresponding response values, select the center using the self-organizing learning method, calculate the weights using the orthogonal least squares algorithm, and establish a radial basis function neural network model. The radial basis function neural network model is used to characterize the mapping relationship between uncertain parameters and structural velocity response and sound field sound pressure level response.

[0059] Based on the obtained dataset, a radial basis function (RBF) neural network model is established using the uncertain parameter x as the input parameter and the structural velocity response and sound pressure level response Y (hereinafter referred to as response Y) as the output parameters. First, k-means clustering is performed to select the basis function centers and calculate the variance. Then, the orthogonal least squares algorithm is used to calculate the connection weights between the hidden layer and the output layer. The final RBF neural network model is represented as Y = g(x), where g(·) represents the mapping relationship between the input and output parameters in the RBF neural network model.

[0060] In one possible embodiment, based on the dataset obtained in step four with sinusoidal excitation loads at frequencies of 30Hz, 40Hz, ..., 90Hz, a radial basis neural network model Y = g(x) representing the mapping relationship between uncertain input parameter x and response Y at different frequencies can be established, with the top center node of the fuselage as the structural observation point and the top center node of the internal sound field as the sound field observation point.

[0061] Step 6: Based on the radial basis function neural network model, calculate the maximum and minimum values ​​of the structural velocity response and sound pressure level response of the multidimensional parallelepiped model, and use them as the response ranges of the corresponding structural velocity response and sound pressure level response of the multidimensional parallelepiped model.

[0062] Using the radial basis function neural network (RBN) model as a surrogate model, based on the established RBN model Y=g(x) at different frequencies, it is possible to obtain the multidimensional parallelepiped model Ω. xThe response range Y of the structure velocity response and sound field sound pressure level response. I Specifically:

[0063]

[0064]

[0065] in, Y and The response intervals Y under the multidimensional parallelepiped model are respectively I The lower and upper bounds, and These are the lower and upper bounds of the response interval under the multidimensional parallelepiped model obtained from the radial basis function neural network model.

[0066] In one possible embodiment, a radial basis function neural network model is used to solve the response range of the structural velocity response and the response range of the sound pressure level response of the multidimensional parallelepiped model under different load frequencies, and the results are compared with those obtained by using the finite element model at different frequencies. The comparison results are shown in Table 2.

[0067] Table 2 Comparison of Response Results

[0068]

[0069]

[0070] As shown in the table above, the relative errors of the results obtained using the radial basis function neural network (RBN) model and the finite element method (FEM) model are both less than 3%, meeting engineering requirements. However, in performing the same response calculation, the FEM model method requires several hundred times more time than the RBN model method. This indicates that the computation time of the established RBN model is significantly shorter than that of the FEM model, demonstrating higher computational efficiency and making it more suitable for complex engineering problems. This advantage becomes more pronounced as the engineering problem becomes more complex.

[0071] In summary, the uncertainty analysis method for the thermoacoustic-vibration coupling system of an aircraft provided in this embodiment of the invention extracts the features of uncertain parameters from multiple sample points in the uncertain parameter space and quantifies the uncertain parameters using a multidimensional parallelepiped model. This is a data-driven and efficient model construction method. Using a radial basis function neural network model to calculate the structural velocity and sound pressure level response of the multidimensional parallelepiped model effectively reduces computational costs while maintaining computational accuracy compared to the finite element model.

[0072] The various embodiments or implementation methods described in this specification are presented in a progressive manner. Each embodiment focuses on the differences from other embodiments, and the same or similar parts between the embodiments can be referred to each other.

[0073] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An uncertainty analysis method for an aircraft thermoacoustic-vibration coupled system, characterized in that, include: Step 1: Discretize the geometric model of the aircraft's structure and internal sound field using a finite element mesh to obtain the thermoacoustic-vibration coupled finite element model of the aircraft; Step 2: Obtain the uncertain parameter space based on the uncertain parameters, and select multiple sample points within the uncertain parameter space to obtain the center, radius, and correlation coefficient of the uncertain parameters, and establish a data-driven multidimensional parallelepiped model, wherein the uncertain parameters are interval parameters; Step 3: Select structural observation points and sound field observation points in the structure and internal sound field of the aircraft, respectively; Step 4: Select test points in the space of uncertain parameters using the Latin hypercube sampling method. Based on the test points, perform structural finite element thermal analysis in the thermo-acoustic-vibration coupled finite element model to obtain the structural thermal stress. Use the structural thermal stress as prestress to perform acoustic-vibration coupled finite element analysis to obtain the response values ​​of the structural velocity response and the sound pressure level response corresponding to the structural observation point and the sound field observation point, respectively. Step 5: Based on the test points and the corresponding response values, a center is selected using a self-organizing learning method, and the weights are calculated using an orthogonal least squares algorithm to establish a radial basis function neural network model. The radial basis function neural network model is used to characterize the mapping relationship between the uncertain parameters and the structural velocity response and the sound field sound pressure level response. Step 6: Based on the radial basis function neural network model, calculate the maximum and minimum values ​​of the structural velocity response and sound pressure level response of the multidimensional parallelepiped model, and use them as the structural velocity response range and the sound pressure level response range of the multidimensional parallelepiped model.

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