CN-122020824-A - Thin plate member deformation reconstruction method in high-speed airflow based on sparse measurement points

CN122020824ACN 122020824 ACN122020824 ACN 122020824ACN-122020824-A

Abstract

The application belongs to the field of aircraft design and experiments, and discloses a method for reconstructing deformation of sheet members in high-speed air flow based on sparse measuring points, which uses a high-resolution camera to monitor the sheet members in the air flow and constructs a characteristic load library, the deformation field constructed by the thin plate is obtained by utilizing a finite element method, the deformation field basis function is obtained by utilizing POD dimension reduction, and then a physical control equation is embedded by utilizing a pinns method, so that the purpose of inverting the real deformation of the thin plate by utilizing limited sparse measuring points is achieved, and an effective means is provided for structural deformation measurement and structural safety evaluation.

Inventors

TIAN BAOWEI
ZHANG ZHAO
CHEN ZHI
WANG LIANGFENG
TANG XINWU
LIU ZHIYONG
PENG HAO
YU HAO
FENG LIMING

Assignees

中国空气动力研究与发展中心高速空气动力研究所

Dates

Publication Date: 20260512
Application Date: 20260414

Claims (8)

1. The method for reconstructing the deformation of the thin plate member in the high-speed air flow based on the sparse measurement points is characterized by comprising the following steps of: S1, monitoring thin plate type components in air flow by using a high-resolution camera, and constructing a characteristic load library; s2, solving and obtaining a deformation field corresponding to the thin plate by using a finite element method, thereby obtaining a load-displacement/deformation database; S3, acquiring a deformation basis function by using a POD dimension reduction method based on the load-displacement/deformation database obtained in the S2; and S4, embedding a physical control equation by a pinns method to realize the reconstruction of the real deformation of the thin plate based on the sparse measurement point.
2. The method for reconstructing deformation of a thin plate member in high-speed airflow based on sparse measurement points according to claim 1, wherein the characteristic load library constructed in the step S1 comprises uniform load, linear distribution load, sinusoidal load, step load, linear load, single-point load, symmetrical-point load and random-point load.
3. The method for reconstructing deformation of a thin plate member in a high-speed airflow based on sparse measurement points according to claim 2, wherein the linear load is realized by defining a load width and a load distribution mode, and the symmetrical point load and the random point load are constructed by single point load.
4. A method for reconstructing deformation of a thin plate member in a high-speed airflow based on sparse measurement points according to claim 3, wherein the thin plate solution domain is discretized to form a structured grid, and the shape is formed as follows And each load distribution corresponds to a table, wherein x and y are length and width positions based on a global coordinate system oxy constructed for the sheet, Indicating the load size.
5. The method for reconstructing deformation of a thin plate member in high-speed airflow based on sparse measurement points as set forth in claim 1, wherein in step S2, the control equation of the thin plate elastomer under the action of static load is a complete partial differential equation set formed by a geometric equation, constitutive relation and equilibrium equation, and the deformation field corresponding to the thin plate is obtained by solving through a finite element method.
6. The method for reconstructing deformation of a thin plate member in a high-speed airflow based on sparse measurement points according to claim 1, wherein step S3 comprises: Compressing any deformation field according to a preset node arrangement mode to form a one-dimensional column vector, arranging the deformation fields in a load-displacement/deformation database according to columns to form a deformation matrix A, wherein each deformation basis function is also a column vector formed according to the same node arrangement mode and is recorded as The deformation basis functions can form a deformation basis matrix according to the arrangement of the columns The deformed basis matrix is defined as follows: wherein n represents the number of basis functions, deformation matrix A and deformation basis functions The method is realized by using a POD dimension reduction method.
7. The method for reconstructing deformation of a thin plate member in a high-speed airflow based on sparse measurement points according to claim 6, wherein in step S3, the deformation basis function construction process includes: assuming that the number of deformation fields is m, the degree of freedom of each column is n, and a deformation field matrix is composed: Wherein, the Is a deformation field matrix I is a positive integer less than or equal to m, and Representation of Is a real number matrix of (a); First, an average deformation field is calculated : Centralized data matrix : Wherein, the Representing a transpose of the matrix; Calculating covariance matrix : Wherein, the For centring data matrix Is a transposed matrix of (a); solving a eigenvalue problem: Wherein, the Representing the eigenvalue corresponding to the ith basis function, thereby obtaining the basis function 。
8. The method for reconstructing deformation of a thin plate member in a high-speed airflow based on sparse measurement points according to claim 7, wherein step S4 comprises: deformation field corresponding to krichhoff equation under arbitrary load and preset boundary condition and physical parameter Expressed in discrete form as a two-dimensional matrix Can be represented as a linear combination of p-order modes as follows: Measuring point sequence I.e. there are m coincident stations, when When two-dimensional matrix Equation is closed, and p can be solved Solution of equation Can be represented; When the mode number is greater than the measuring point number, the two-dimensional matrix If the equation is not statically determined, the weak form of the krichhoff equation is constrained by pinns to solve, and the best fit to the weak form is determined Value of up to reconstruction Form (iv); The weak form of krichhoff equation is obtained by performing area integration on differential equation and converting through green formula, and the final form is as follows: wherein D represents the bending stiffness of the panel, Indicating the deflection of the sheet, The area of the board is indicated and, Representing a half-section of the plate, 、 The projections of normal vectors representing the plate boundaries on the x, y coordinate axes, The double-tone sum operator is represented, The surface bins are represented by the surface bins, Representing the load applied to the plate, dxdy representing the area element of the plate plane; In code writing, for rectangular sheets, orthogonal grids are used for discretization, and the equation after discretization is as follows: Wherein, the 、 Represents the grid size in the x, y directions of an orthogonal grid cell, Is shown in Centered on Is the average value of the load in the rectangle with wide height; And is noted as: Wherein, the Representing a generalized differential operator of the type described above, Indicating the deflection of the sheet, For the gradient of the deflection in the x-direction, Parameters representing other constant properties; and solving through pinns to obtain the proper coefficients of each order Any deformation field can be characterized by the following formula: Wherein, the A deflection-distributed field is shown, I.e. pinns resulting in a deflection field Is a function of x, y, Is the average deflection field of the beam, Representing the i-th order basis function.

Description

Thin plate member deformation reconstruction method in high-speed airflow based on sparse measurement points Technical Field The application belongs to the field of aircraft design and experiments, and particularly relates to a deformation reconstruction method for a thin plate member in high-speed airflow based on sparse measurement points. Background The detection of the construction deformation of the thin plate is important in engineering, such as the deformation of a bridge under wind load, the construction deformation of a deep sea drilling platform under the action of ocean currents, and the like, and the deformation measurement of the construction is divided into three types at the present stage, namely mechanical instrument measurement, such as bending deformation of members such as beams, plates and the like by using a dial indicator and a deflectometer, electric sensors, such as a linear variable differential transformer, a resistance strain gauge and the like, displacement measurement by electric signal detection, and optical measurement methods, such as an interferometry, an image correlation method, a distributed optical fiber method and the like. One common feature of the three methods is that the single point or local displacement is mainly focused on construction, and the overall displacement distribution of the construction cannot be given. The deformation distribution of the full field is reconstructed by using limited sparse measuring points, and common methods in engineering include a reconstruction method based on a neighborhood, a reconstruction method based on a subdomain and a reconstruction method based on a function. The main idea of the neighborhood-based method is that the function value in the corresponding region is estimated by utilizing the value of the nearest neighbor discrete measuring point, the finally obtained reconstructed field is a field formed by splicing a plurality of fragments in constant, the most typical representation is a nearest neighbor method, a moving average method and a distance weighting method, but the method has poor reconstruction effect on the sparse measuring point, can not give error estimation, and can give error estimation on the region with more severe deformation distribution. And the corresponding method implies linear assumption that the reconstruction function is discontinuous in fragments, and has extremely poor reconstruction effect on sparse measurement points in severe deformation areas. The reconstruction method based on the subdomains is represented by a finite element reconstruction method, the space is divided into a plurality of subdomains, a distribution form is preset in each subdomain, and the measuring points are utilized to determine coefficients of the distribution form. The method can accurately meet the measurement point data, has higher calculation efficiency, is sensitive to boundaries and abnormal points, and the distribution of the reconstruction field is seriously dependent on the selection of a function space and the arrangement of measurement point positions. And the corresponding method cannot give more accurate deformation distribution for sparse measuring points. The function-based reconstruction method has the main ideas of giving a distribution assumption of a deformation field, for example, the deformation field is assumed to consist of a series of radial basis functions, the coefficients of the basis functions are determined by utilizing limited measuring points, the recently popular Gaussian process regression and the neural network method can be regarded as expansion of the method, the method can fit a complex function, and is expected to give more accurate deformation distribution, but the conventional neural network method needs more measuring points (more measuring point cost is often higher in engineering), and the obtained result is a black box model with poor interpretation. In the situations of aircraft control surface test, large-scale stadium choosing roof windload and the like, the method is extremely important for measuring and monitoring the deformation of a sheet-like structure, but in the special situations, the acquisition of the deformation of a relatively comprehensive part is difficult, a small number of measuring points are generally arranged, the deformation of the whole structure is represented by the small number of measuring points, the method is accurate when the structural deformation is small, but when the part is relatively complex under the load, the deformation of the part is also complex, the deformation of the whole part is difficult to represent by the deformation of the small number of measuring points, and a new means is needed. Aiming at the limitations of the existing method for reconstructing the distribution field based on the sparse measurement points, the application provides a thin plate deformation reconstruction method which simultaneously considers a control equa