Full-field response reconstruction method and system for beam structure, electronic equipment and storage medium

Abstract

The invention discloses a beam structure full-field response reconstruction method and system, electronic equipment and a storage medium. The method comprises the steps that a dictionary used for sparsely representing full-field response of a target beam structure is constructed based on sine series; analyzing the number of motivated structural modals of the target beam structure and the number of sine functions required for fitting each order vibration mode of the target beam structure, and determining the number of vibration detection sensors required for sparse measurement of the target beam structure; a Latin hypercube sampling method is adopted to determine the installation position of a vibration detection sensor; solving a sparse representation vector responded by the target beam structure by using an orthogonal tracking matching algorithm based on a measured value of the vibration detection sensor; and reconstructing a response field of the target beam structure based on the sparse representation vector and the dictionary. According to the method, high-precision reconstruction of the full-field response of the beam structure under sparse measurement is realized based on the space compressed sensing theory, the implementation efficiency is high, the universality is high, the method does not depend on a complex model, and the method has wide applicability and engineering practical value.

Description

Technical Field

[0001] The present application relates to the technical field of health monitoring and vibration analysis of beam structures, and in particular to a method, system, electronic device and storage medium for reconstructing the full-field response of a beam structure based on the theory of spatial compressed sensing, which is suitable for reconstructing the full-field dynamic response of a beam structure with high precision from the measurement data of a small number of sensors. Background Art

[0002] In actual engineering monitoring, sensors are often sparsely distributed at only a few key locations on beam structures due to factors such as high sensor costs and limited installation space. This limited sensor layout results in low spatial resolution of the acquired beam response data, making it difficult to fully and accurately reflect the overall vibration state of the beam structure, thus significantly hindering the precise analysis and reliable assessment of beam structures.

[0003] However, in the health monitoring of beam structures, accurately obtaining the full-field response of the beam structure (such as displacement, velocity, and acceleration) is crucial for the vibration analysis and state assessment of the beam structure. It plays an indispensable role in key links such as damage detection, boundary constraint identification, control equation discovery, and maximum load estimation of the beam structure.

[0004] Computer vision methods are a non-contact beam structure response measurement technique that has garnered significant attention in recent years. They measure beam vibrations by identifying and tracking characteristic points within a video. In this approach, each pixel in the image can be treated as a virtual sensor, promising high-resolution responses. However, these methods are extremely sensitive to environmental factors; background interference and changes in lighting conditions can severely affect measurement accuracy. Furthermore, the camera's limited field of view and long computational processing times pose significant challenges for practical application in large-scale beam structure monitoring.

[0005] Contact sensors, such as displacement meters and accelerometers, are the most widely used vibration testing equipment for beam structures, offering advantages such as low cost and good noise immunity. Consequently, traditional methods rely on densely arranged sensors to capture the full-field response of beam structures. However, this approach suffers from high cost, complex implementation, and low efficiency.

[0006] Methods that reconstruct the full-field response of beam structures based on the measurements of a small number of such sensors have significant advantages, such as being able to utilize existing monitoring systems and conforming to the work habits of engineering personnel. However, existing methods for reconstructing the full-field response of beam structures based on the measurements of a small number of contact sensors such as displacement meters and accelerometers have many limitations. For example, while the Kalman filter algorithm can estimate the full-field state of a beam structure using the responses of a limited number of measurement points, this method relies on a complex mathematical model of the beam structure (such as a finite element model) to determine the sensor installation locations. While transfer function or transfer matrix methods can use the responses at measurement points to infer the responses at non-measurement points, they rely on the modal characteristics of the beam structure, which are generally unknown before testing. This greatly limits the application of such methods in practical engineering.

[0007] Therefore, there is an urgent need to develop a method for reconstructing the full-field response of beam structures that is versatile, efficient, accurate, and independent of complex models to meet the needs of engineering practice. Summary of the Invention

[0008] In order to solve the above technical problems, the present application provides a method, system, electronic device and storage medium for reconstructing the full-field response of a beam structure, so as to solve the problems of difficulty, low accuracy and dependence on complex models in the existing technology in reconstructing the full-field response of a beam structure. Based on the theory of spatial compressed sensing, the measurement values ​​of a small number of vibration detection sensors are used to accurately reconstruct the full-field response of the beam structure, thereby improving the efficiency of structural vibration testing and the accuracy of vibration analysis. The method has strong versatility, wide applicability and practical engineering value.

[0009] The first objective of this application is to provide a method for reconstructing the full-field response of a beam structure.

[0010] The above-mentioned application objective 1 of this application is achieved through the following technical solutions:

[0011] A beam structure full-field response reconstruction method, the method comprising the following steps:

[0012] S1, constructs a dictionary based on sine series to sparsely represent the full-field response of the target beam structure represents a real number, its superscript represents the size of the matrix, m is the number of virtual measuring points evenly distributed on the target beam structure, and n is the order of the sine series expansion of the vibration mode;

[0013] S2, analyzing the number of excited structural modes of the target beam structure and the number of sine functions required to fit each order vibration mode of the target beam structure, and determining the number p of vibration detection sensors required for sparse measurement of the target beam structure;

[0014] S3, determining the installation positions of the p vibration detection sensors using a Latin hypercube sampling method;

[0015] S4, using the measured values ​​z∈R of the p vibration detection sensors p , the orthogonal matching algorithm is used to solve the sparse representation vector of the target beam structure

[0016] S5, reconstructing the response field of the target beam structure based on the sparse representation vector f and the dictionary D n s is the sampling time number of the vibration test.

[0017] Preferably, in step S1, constructing a dictionary D for sparsely representing the full-field response of the target beam structure based on a sine series includes:

[0018] Based on the modal superposition method, the vibration mode of the target beam structure is extended by an odd extension and then approximated by a sine series. The expression is:

[0019]

[0020] Among them, φ i (x) is the vibration mode of the i-th order vibration mode of the target beam structure, L is the beam length of the target beam structure, c ij is φ i (x) is the coefficient of the jth term of the series expansion, n is the order of the sine series expansion of the mode shape, and x is the coordinate along the length of the bridge;

[0021] The expression of dictionary D is:

[0022]

[0023] Among them, x1~x m are the coordinates of virtual measuring points evenly distributed on the target beam structure.

[0024] Preferably, in step S2, the number p of vibration detection sensors is greater than the sparsity K of the sparse representation vector f, wherein the sparsity K is determined by the number of excited modes of the target beam structure and the number of sinusoidal functions required for fitting the vibration mode.

[0025] Preferably, step S2 includes:

[0026] S21, obtaining the number of excited modes by performing modal analysis on the test data of the target beam structure;

[0027] S22, determining the number of sine functions required for each mode according to the amplitude attenuation characteristics of the sine series fitting coefficients of the vibration mode;

[0028] S23, adding the number of sine functions required for all excited modes to obtain the number p of the vibration detection sensors.

[0029] Preferably, step S3 includes:

[0030] S31, evenly dividing the target beam structure into p regions according to the length of the target beam structure;

[0031] S32 , randomly selecting a position from each area to obtain p positions, and using the p positions as installation positions of the p vibration detection sensors.

[0032] Preferably, step S4 includes:

[0033] S41, constructing a perception matrix based on the dictionary D and the determined position of the vibration detection sensor in, It is a measurement matrix composed of 0 and 1, each row of the matrix has an element of 1, corresponding to the position of a virtual measurement point where a vibration detection sensor is located, and the other elements of the matrix are 0;

[0034] S42, specifying an initial sparsity K, and initializing the residual to the measurement value z, and the sparse representation vector f to a zero vector;

[0035] S42, in each iteration, selecting the column in the perception matrix Φ that is most relevant to the residual, and updating the sparse representation vector f;

[0036] S43, when the residual norm is less than a preset threshold, the iteration is terminated to obtain the sparse representation vector f.

[0037] Preferably, step S5 includes:

[0038] S51, based on the sparse representation vector f and the dictionary D, obtain the full-field response y of the target beam structure at a certain moment, where:

[0039] y=Df (3);

[0040] S52, combination n s The full-field response y at each sampling moment is used to obtain the response field Y of the target beam structure.

[0041] The second object of this application is to provide a beam structure full-field response reconstruction system.

[0042] The second object of the present application is achieved through the following technical solutions:

[0043] A beam structure full-field response reconstruction system, the system comprising:

[0044] Dictionary building module for constructing a dictionary based on sine series for sparse representation of the full-field response of the target beam structure represents a real number, its superscript represents the size of the matrix, m is the number of virtual measuring points evenly distributed on the target beam structure, and n is the order of the sine series expansion of the vibration mode;

[0045] a sensor quantity determination module, configured to analyze the number of excited structural modes of the target beam structure and the number of sine functions required to fit each order vibration mode of the target beam structure, and determine the number p of vibration detection sensors required for sparse measurement of the target beam structure;

[0046] A sensor installation position determination module, configured to determine the installation positions of the p vibration detection sensors using a Latin hypercube sampling method;

[0047] A coefficient representation vector solving module for using the measured values ​​of p vibration detection sensors The orthogonal matching algorithm is used to solve the sparse representation vector of the target beam structure.

[0048] A structural response field reconstruction module is used to reconstruct the response field of the target beam structure based on the sparse representation vector f and the dictionary D. n s is the sampling time number of the vibration test.

[0049] Preferably, the dictionary construction module is specifically used to:

[0050] Based on the modal superposition method, the vibration mode of the target beam structure is extended by an odd extension and then approximated by a sine series. The expression is:

[0051]

[0052] Among them, φ i (x) is the vibration mode of the i-th order vibration mode of the target beam structure, L is the beam length of the target beam structure, c ij is φ i (x) is the coefficient of the jth term of the series expansion, n is the order of the sine series expansion of the mode shape, and x is the coordinate along the length of the bridge;

[0053] The expression of dictionary D is:

[0054]

[0055] Among them, x1~x m are the coordinates of virtual measuring points evenly distributed on the target beam structure.

[0056] Preferably, the number p of vibration detection sensors is greater than the sparsity K of the sparse representation vector f, wherein the sparsity K is determined by the number of excited modes of the target beam structure and the number of sinusoidal functions required for fitting the vibration mode.

[0057] Preferably, the sensor quantity determination module is specifically used to:

[0058] Obtaining the number of excited modes by performing modal analysis on the test data of the target beam structure;

[0059] According to the amplitude attenuation characteristics of the sine series fitting coefficients of the vibration mode, the number of sine functions required for each mode is determined;

[0060] The number of sine functions required for all excited modes is added together to obtain the number p of the vibration detection sensors.

[0061] Preferably, the sensor installation position determination module is specifically used to:

[0062] Evenly dividing the target beam structure into p regions according to the length of the target beam structure;

[0063] A position is randomly selected from each area to obtain p positions, and the p positions are used as installation positions of the p vibration detection sensors.

[0064] Preferably, the coefficient representation vector solving module is specifically used for:

[0065] Construct a perception matrix based on the dictionary D and the determined position of the vibration detection sensor in, It is a measurement matrix composed of 0 and 1, each row of the matrix has an element of 1, corresponding to the position of a virtual measurement point where a vibration detection sensor is located, and the other elements of the matrix are 0;

[0066] Specify an initial sparsity K, initialize the residual to the measurement value z, and the sparse representation vector f to a zero vector;

[0067] In each iteration, the column in the perception matrix Φ that is most relevant to the residual is selected to update the sparse representation vector f;

[0068] When the residual norm is less than a preset threshold, the iteration is terminated to obtain the sparse representation vector f.

[0069] Preferably, the structural response field reconstruction module is specifically used to:

[0070] Based on the sparse representation vector f and the dictionary D, the full-field response y of the target beam structure at a certain moment is obtained, where:

[0071] y=Df (3);

[0072] Combination n s The full-field response y at each sampling moment is used to obtain the response field Y of the target beam structure.

[0073] The third object of this application is to provide an electronic device.

[0074] The third object of the present application is achieved through the following technical solutions:

[0075] An electronic device, comprising:

[0076] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the method for reconstructing the full-field response of a beam structure as described in any one of the first objectives of the present application are implemented.

[0077] The fourth object of this application is to provide a computer-readable storage medium.

[0078] The fourth object of the present application is achieved through the following technical solutions:

[0079] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the beam structure full-field response reconstruction method described in any one of the first objectives of the present application.

[0080] Compared with the prior art, this application has the following beneficial effects:

[0081] 1. Strong versatility: The basis matrix constructed based on the characteristic that the sine series can quickly approximate the vibration modes of common beam structures is applicable to beam structures with various boundary conditions. Whether it is a simply supported beam, fixed-hinged beam, fixed-fixed beam, variable-section beam, or continuous beam, it can effectively describe its spatial vibration characteristics and has broad application prospects.

[0082] 2. High precision: By optimizing the number and installation locations of vibration detection sensors and using an efficient algorithm to solve the sparse representation vector, the full-field response of the beam structure can be accurately reconstructed;

[0083] 3. No need for complex models: Unlike traditional methods that rely on structural mathematical models or modal characteristics, this application uses the Latin hypercube sampling method to determine the sensor installation position. This eliminates the need to construct a finite element model of the beam structure, lowering the application threshold and improving the practicality and convenience of the method.

[0084] 4. Improved testing and analysis efficiency: The full-field response can be reconstructed using a small number of sensor measurements, significantly improving the efficiency of structural vibration testing compared to traditional methods that require a large number of sensors. At the same time, high-resolution response fields and vibration modes provide richer and more accurate information for structural vibration analysis and condition assessment, helping to improve the accuracy of vibration analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0086] Figure 1 This is a flow chart of a method for reconstructing the full-field response of a beam structure in one embodiment of the present application;

[0087] Figure 2 A comparison diagram of the reconstructed displacement field and the forward analysis results in a specific example of this application;

[0088] Figure 3 A comparison chart of the high-resolution mode shapes extracted from the specific example of the conventional interface beam in this application and the mode shapes extracted through modal analysis;

[0089] Figure 4 This is the response reconstruction diagram of the specific example of the variable cross-section beam in this application;

[0090] Figure 5 This is a structural diagram of a beam structure full-field response reconstruction system in one embodiment of the present application;

[0091] Figure 6 Schematic diagram of the structure of an electronic device in one embodiment of the present application. DETAILED DESCRIPTION

[0092] In order to help those skilled in the art better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making any creative efforts shall fall within the scope of protection of this application.

[0093] In the embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. The system embodiments described below are merely illustrative. For example, the division of units and modules is merely a logical function division. In actual implementation, there may be other division methods, such as: multiple units or modules can be combined, or can be integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the components shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0094] In addition, all functional units in the embodiments of the present application may be integrated into one processor, or each unit may be a separate device, or two or more units may be integrated into one device; each functional unit in the embodiments of the present application may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0095] Those skilled in the art will understand that all or part of the steps of the following method embodiments can be implemented by program instructions and related hardware. The aforementioned program instructions can be stored in a computer-readable storage medium. When the program instructions are executed, the steps of the following method embodiments are executed; and the aforementioned storage medium includes: mobile storage devices, read-only memories (ROM), magnetic disks or optical disks, and other media that can store program codes.

[0096] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of such features. Throughout the description of this application, "plurality" or "several" means two or more, unless otherwise specifically defined.

[0097] The embodiment of the present application provides a method for reconstructing the full-field response of a beam structure, such as Figure 1 As shown, the method may include the following steps:

[0098] S1, constructs a dictionary based on sine series to sparsely represent the full-field response of the target beam structure represents a real number, its superscript represents the size of the matrix, m is the number of virtual measuring points evenly distributed on the target beam structure, and n is the order of the sine series expansion of the vibration mode;

[0099] S2, analyzing the number of excited structural modes of the target beam structure and the number of sine functions required to fit each order vibration mode of the target beam structure, and determining the number p of vibration detection sensors required for sparse measurement of the target beam structure;

[0100] S3, using the Latin hypercube sampling method to determine the installation positions of p vibration detection sensors;

[0101] S4, using the measured values ​​of p vibration detection sensors The orthogonal matching algorithm is used to solve the sparse representation vector of the target beam structure;

[0102] S5, based on the sparse representation vector f and dictionary D, reconstruct the response field of the target beam structure n s is the sampling time number of the vibration test.

[0103] In the sparse measurement of beam structures, sparsely distributed sensors are equivalent to sampling the full-field response of the beam structure in the spatial domain, and the reconstruction of the full-field response can be reduced to the problem of recovering the spatial domain signal. The beam structure full-field response reconstruction method of this embodiment realizes the reconstruction of the full-field response of the beam structure under sparse measurement based on the theory of spatial compressed sensing. First, a dictionary for sparsely representing the full-field response of the target beam structure is constructed based on the sine series; then, the number of excited structural modes of the target beam structure and the number of sine functions required to fit the various vibration modes of the target beam structure are analyzed to determine the number of vibration detection sensors required for sparse measurement of the target beam structure; then, the Latin hypercube sampling method is used to determine the installation position of the vibration detection sensor; then, the sparse representation vector of the target beam structure is solved using the orthogonal matching algorithm based on the measurement values ​​of the vibration detection sensor; finally, based on the sparse representation vector and the dictionary, the response field of the target beam structure is reconstructed.

[0104] In this embodiment, the basis matrix constructed based on the characteristic of sine series that can quickly approximate the vibration modes of common beam structures is applicable to beam structures with various boundary conditions. Whether simply supported beams, fixed-hinged beams, fixed-fixed beams, variable-section beams, or continuous beams, it can effectively describe their spatial vibration characteristics and has broad application prospects. By optimizing the number and installation locations of vibration detection sensors and using an efficient algorithm to solve the sparse representation vector, the full-field response of the beam structure can be accurately reconstructed. Unlike traditional methods that rely on structural mathematical models or modal characteristics, this embodiment uses the Latin hypercube sampling method to determine the sensor installation locations, eliminating the need to construct a finite element model of the beam structure, lowering the application threshold and improving the practicality and convenience of the method. The full-field response can be reconstructed using a small number of sensor measurements, significantly improving the efficiency of structural vibration testing compared to traditional methods that require a large number of sensors. At the same time, the high-resolution response field and vibration modes provide richer and more accurate information for structural vibration analysis and condition assessment, helping to improve the accuracy of vibration analysis.

[0105] Specifically, in this embodiment, the vibration detection sensor can be one or any combination of a displacement sensor, a velocity sensor, and an acceleration sensor for detecting the displacement, velocity, and acceleration of the beam structure. Accordingly, the reconstructed response field of the beam structure can be one or any combination of a displacement field, a velocity field, and an acceleration field.

[0106] In one embodiment, in step S1, constructing a dictionary D for sparsely representing the full-field response of the target beam structure based on a sine series includes:

[0107] Based on the modal superposition method, the vibration mode of the target beam structure is extended by an odd extension and then approximated by a sine series. The expression is:

[0108]

[0109] Among them, φ i (x) is the vibration mode of the i-th order vibration mode of the target beam structure, L is the beam length of the target beam structure, c ij is φ i (x) is the coefficient of the jth term of the series expansion, n is the order of the sine series expansion of the mode shape, and x is the coordinate along the length of the bridge;

[0110] The expression of dictionary D is:

[0111]

[0112] Among them, x1~x m are the coordinates of virtual measuring points evenly distributed on the target beam structure.

[0113] Specifically, in the process of constructing the dictionary D, the value of the order n of the sine series expansion of the mode shape can be appropriately adjusted according to the actual beam structure characteristics and accuracy requirements. For example, if the accuracy requirements are high, the order n of the sine series expansion of the mode shape can be increased to make the dictionary's approximation of the mode shape more accurate.

[0114] In one embodiment, in step S2, the number p of vibration detection sensors is greater than the sparsity K of the sparse representation vector f, wherein the sparsity K is determined by the number of excited modes of the target beam structure and the number of sine functions required for fitting the vibration mode.

[0115] In this embodiment, the number of vibration detection sensors is made greater than the sparsity of the sparse representation vector so that the full-field response can be accurately reconstructed according to the linear equation solving theory. The sparsity of the sparse representation vector is jointly determined according to the number of excited modes of the target beam structure and the number of sinusoidal functions required for fitting the vibration mode. This makes the sparsity have dynamic correlation, adaptively matches the structural dynamic characteristics, improves the reconstruction accuracy, and avoids "oversampling" resulting from too many sensors and causing waste of resources, or "undersampling" resulting from too few sensors and reducing the reconstruction accuracy or even failure of reconstruction, thereby achieving an optimal balance between data acquisition and reconstruction accuracy.

[0116] In one embodiment, step S2 includes:

[0117] S21, obtaining the number of excited modes by performing modal analysis on the test data of the target beam structure;

[0118] S22, determining the number of sine functions required for each mode according to the amplitude attenuation characteristics of the sine series fitting coefficients of the vibration mode;

[0119] S23, adding the number of sine functions required for all excited modes to obtain the number p of vibration detection sensors.

[0120] In this embodiment, by combining modal analysis with the sparsity characteristics of sine series fitting, a scientific determination of the number of sparse measurement sensors for the beam structure is achieved. The specific analysis is as follows:

[0121] 1. Obtain the actual number of excited modes through modal analysis of test data, avoiding reliance on theoretical models or pre-set assumptions. This ensures that the number of sensors dynamically adapts to the actual vibration characteristics of the structure under test, accurately matches the structural dynamic characteristics, and optimizes sensor configuration. If the spectrum shows that only the first two modes are excited, only sensors need to be configured for these two modes, rather than redundantly arranging fixed higher-order modes. This significantly reduces the number of sensors and hardware costs while ensuring the accuracy of the full-field response reconstruction of the beam structure.

[0122] 2. Utilizing the matching characteristics between the mode shapes of beams under different boundary conditions and the sinusoidal basis functions, the minimum number of sinusoidal functions required for each mode is determined. Sparse representation is used to compress the problem size, avoid overfitting, improve computational efficiency, and achieve efficient fitting based on mode shape sparsity.

[0123] 3. Adding the number of sine functions required for each mode directly correlates to sparsity, meeting the sampling requirements in compressed sensing theory and providing clear engineering indicators to avoid reconstruction failures due to insufficient sensors or resource waste due to excessive sensors.

[0124] 4. Convert abstract mathematical sparsity (L1 norm) into operational engineering parameters such as the number of modes and the number of sine terms, lowering the threshold for algorithm application;

[0125] 5. Only test data is needed to complete sensor configuration, eliminating dependence on finite element models and making it more suitable for monitoring existing beam structures.

[0126] In one embodiment, step S3 includes:

[0127] S31, evenly dividing the target beam structure into p regions according to the length of the target beam structure;

[0128] S32 , randomly selecting a position from each area to obtain p positions, and using the p positions as installation positions of the p vibration detection sensors.

[0129] In this implementation, the Latin hypercube sampling method is used to evenly divide the structural space (such as the length of the beam) into intervals equal to the number of sensors, and a position is randomly selected in each interval to ensure that the distribution of vibration detection sensors covers the entire structural range, avoiding sensor clustering caused by traditional random sampling or empirical layout, and effectively capturing the spatial modal characteristics of structural vibration; compared with methods such as EFI-DPR that rely on finite element models, the Latin hypercube sampling method does not require prior vibration shape information and can meet the mathematical requirements of reconstruction only through spatial uniformity, reducing dependence on model accuracy; the Latin hypercube sampling method only requires the structural geometric dimensions and the number of sensors to generate a layout plan, without the need for complex calculations (such as modal kinetic energy analysis) or finite element modeling; in a noisy environment, the uniformity of the Latin hypercube sampling method can suppress local noise amplification and improve reconstruction robustness.

[0130] In one embodiment, step S4 includes:

[0131] S41, constructing a perception matrix based on the dictionary D and the determined position of the vibration detection sensor in, It is a measurement matrix composed of 0 and 1, each row of the matrix has an element of 1, corresponding to the position of a virtual measurement point where a vibration detection sensor is located, and the other elements of the matrix are 0;

[0132] S42, specify an initial sparsity K, initialize the residual to the measurement value z, and the sparse representation vector f to the zero vector;

[0133] S42, in each iteration, select the column in the perception matrix Φ that is most relevant to the residual and update the sparse representation vector f;

[0134] S43, when the residual norm is less than a preset threshold, the iteration is terminated to obtain a sparse representation vector f.

[0135] In this embodiment, in order to control the overfitting problem, a slightly larger initial sparsity K can be specified, and the norm of the fitting residual is monitored in each iteration. When the norm is less than a preset threshold (for example, 10-8 ) terminates the iteration process.

[0136] In one embodiment, step S5 includes:

[0137] S51, based on the sparse representation vector f and the dictionary D, obtain the full-field response y of the target beam structure at a certain moment, where

[0138] y=Df (3);

[0139] S52, combination n s The full-field response y at each sampling moment is used to obtain the response field Y of the target beam structure.

[0140] Specifically, the relationship between the measured value z and the full-field response y of the target beam structure at a certain moment is as follows:

[0141] z=Θy+v (4)

[0142] in, are independent and identically distributed, with mean 0 and covariance σ 2 I is the Gaussian noise, where I is the identity matrix.

[0143] Combining equations (3) and (4), we can obtain:

[0144] z=Φf+v (5).

[0145] In this embodiment, the obtained sparse representation vector f and the constructed dictionary D are substituted into formula (3) to obtain the full-field response y of the target beam structure at a certain moment, and then n s By combining the full-field responses y at each sampling moment, the response field of the target beam structure can be obtained.

[0146] In some other embodiments, after reconstructing the response field Y of the target beam structure, the singular value decomposition algorithm can be used to extract the inherent modes of the response field Y. The obtained results are high-resolution vibration shapes of the target beam structure, which provide rich information for vibration analysis and state assessment of the target beam structure and help to further improve the accuracy of vibration analysis.

[0147] Next, a specific example is used to illustrate the effect of the beam structure full-field response reconstruction method in this application:

[0148] In this example, the response reconstruction problem of a constant cross-section beam under moving load is investigated. The boundary conditions of the bridge are set as simply supported, fixed-hinge supported, and fixed-fixed.

[0149] The parameters of the beam are as follows: length 30m, mass per unit length 2500kg, elastic modulus 33.5GPa, moment of inertia 0.33m 4, the damping ratio of the first two modes is 0.01. A load with an amplitude of 100 kN passes from one end of the beam to the other at a speed of 1 m / s. 60 uniform two-dimensional Euler-Bernoulli beam elements are used to simulate the beam structure, and the finite element method is used to calculate the response of the beam. For the numerical example in this embodiment, this process is called forward analysis. The virtual measuring points are assumed to coincide with the finite element nodes, that is, the spacing is 0.5 m.

[0150] Here, only the response of the first two vibration modes is attempted to be reconstructed. The number of displacement sensors is specified as p = 8, corresponding to a ratio of real to virtual measurement points of 0.13. The sensor locations determined using the Latin hypercube method are the 2nd, 12th, 21st, 28th, 35th, 42nd, 52nd, and 59th nodes of the finite element model. The structural displacements at these locations are assembled into the measurement vector z. The sparsity K of the sparse representation vector f is specified to be 6, and then it is restored by the orthogonal matching pursuit method. The calculated sparse representation vector f is then substituted into equation (3) to restore the full-field response y of the target beam structure at a certain moment. Finally, the displacement field (i.e., response field Y) of the target beam structure is restored by assembling the full-field response y generated at each sampling moment. The recovered response is called the reconstructed response.

[0151] Figure 2 The three figures in the top section compare the displacement field of the beam structure obtained from the forward analysis (black mesh) with the displacement field reconstructed using spatial compressed sensing (red dots). As can be seen, the reconstructed displacements generally match the forward analysis results well. To quantitatively evaluate the reconstruction accuracy, the following mean relative error (MER) is defined:

[0152]

[0153] Where Y R (:,i) and Y F where (:,i) is the i-th column of the displacement matrix obtained from the reconstruction and forward analysis (i.e., the full-field displacement of the structure at the i-th time step). The MREs under the simply supported, fixed-hinge, and fixed-fixed boundary conditions are 0.64%, 3.28%, and 7.13%, respectively. Figure 2 The three figures at the bottom are the time history curves of the mid-span displacement of the bridge. Figure 2 It can be seen that the characteristics of beam vibration under the three boundary conditions of simply supported, fixed-pinned, and fixed-fixed are well captured.

[0154] To further check the quality of the reconstructed displacement field, the singular value decomposition algorithm can be used to extract the first two vibration modes of the beam structure, which correspond to the first two left singular vectors of the response field Y. As an example, only the results of the fixed-pinned boundary condition are shown in Figure 3For comparison, the figure also includes the theoretical vibration shapes obtained by modal analysis. As can be seen from the figure, the extracted vibration shapes are in good agreement with the theoretical values ​​as a whole. For the second-order vibration shapes, the extracted values ​​deviate slightly from the theoretical values ​​and show some fluctuations; despite this, the overall shape of the theoretical values ​​is still effectively captured. These phenomena indicate that the full-field response reconstruction method of the beam structure of this application can effectively recover the components of the low-order vibration modes. The vibration shapes extracted from the reconstructed response field have a spatial resolution of 0.5m. In contrast, the vibration shapes extracted directly from the measured response are low-resolution, that is, they can only provide the vibration shape amplitude at the sensor installation point; high-resolution vibration shapes provide richer information about the structural mass and stiffness distribution, which is crucial for structural vibration analysis and state assessment.

[0155] Figure 4 The response reconstruction of a variable cross-section beam is given. The material properties, external loads, number of sensors and their distribution are the same as those in the first example. The beam is fixed at both ends, the cross-section width is a constant value of 0.3m, and the height varies linearly, as shown in Figure 2. Figure 4 (a). The response of the beam is calculated using the finite element method. The response at the sensor location is used to reconstruct the full-field displacement. Figure 4 (b) shows the reconstruction results. As can be seen from the figure, the reconstruction values ​​(red dots) are in good agreement with the forward analysis results (black grid); the reconstruction error (MRE) is 4.23%. Figure 4 Figures (c) and (d) show the first two modes extracted from the reconstructed displacement field. The first mode matches the modal analysis result well. The extracted second mode has some fluctuations, but overall captures the theoretical mode shape well. This example demonstrates that the proposed method can also be used to reconstruct the response of variable-section beams.

[0156] like Figure 5 As shown, an embodiment of the present application further provides a beam structure full-field response reconstruction system, which may include:

[0157] Dictionary construction module 201, for constructing a dictionary for sparsely representing the full-field response of the target beam structure based on the sine series represents a real number, its superscript represents the size of the matrix, m is the number of virtual measuring points evenly distributed on the target beam structure, and n is the order of the sine series expansion of the vibration mode;

[0158] The sensor quantity determination module 202 is used to analyze the number of excited structural modes of the target beam structure and the number of sine functions required to fit each order vibration mode of the target beam structure, and determine the number p of vibration detection sensors required for sparse measurement of the target beam structure;

[0159] A sensor installation position determination module 203 is used to determine the installation positions of p vibration detection sensors using a Latin hypercube sampling method;

[0160] The coefficient representation vector solving module 204 is used to use the measurement values ​​of p vibration detection sensors The orthogonal matching algorithm is used to solve the sparse representation vector of the target beam structure;

[0161] The structural response field reconstruction module 205 is used to reconstruct the response field of the target beam structure based on the sparse representation vector f and the dictionary D. n s is the sampling time number of the vibration test.

[0162] In one embodiment, the dictionary building module 201 is specifically configured to:

[0163] Based on the modal superposition method, the vibration mode of the target beam structure is extended by an odd extension and then approximated by a sine series. The expression is:

[0164]

[0165] Among them, φ i (x) is the vibration mode of the i-th order vibration mode of the target beam structure, L is the beam length of the target beam structure, c ij is φ i (x) is the coefficient of the jth term of the series expansion, n is the order of the sine series expansion of the mode shape, and x is the coordinate along the length of the bridge;

[0166] The expression of dictionary D is:

[0167]

[0168] Among them, x1~x m are the coordinates of virtual measuring points evenly distributed on the target beam structure.

[0169] In one embodiment, the number p of vibration detection sensors is greater than the sparsity K of the sparse representation vector f, wherein the sparsity K is determined by the number of excited modes of the target beam structure and the number of sinusoidal functions required for fitting the vibration mode.

[0170] In one embodiment, the sensor quantity determination module 202 is specifically configured to:

[0171] The number of excited modes is obtained by performing modal analysis on the test data of the target beam structure;

[0172] According to the amplitude attenuation characteristics of the sine series fitting coefficients of the vibration mode, the number of sine functions required for each mode is determined;

[0173] The number of sine functions required for all excited modes is added together to obtain the number p of vibration detection sensors.

[0174] In one embodiment, the sensor installation position determination module 203 is specifically configured to:

[0175] The target beam structure is evenly divided into p regions according to the length of the target beam structure;

[0176] A position is randomly selected from each area to obtain p positions, and the p positions are used as installation positions of the p vibration detection sensors.

[0177] In one embodiment, the coefficient representation vector solving module 204 is specifically configured to:

[0178] Construct a perception matrix based on the dictionary D and the determined location of the vibration detection sensor in, It is a measurement matrix composed of 0 and 1, each row of the matrix has an element of 1, corresponding to the position of a virtual measurement point where a vibration detection sensor is located, and the other elements of the matrix are 0;

[0179] Specify an initial sparsity K, initialize the residual to the measurement value z, and the sparse representation vector f to the zero vector;

[0180] In each iteration, the column in the perception matrix Φ that is most relevant to the residual is selected to update the sparse representation vector f;

[0181] When the residual norm is less than the preset threshold, the iteration is terminated and the sparse representation vector f is obtained.

[0182] In one embodiment, the structural response field reconstruction module 205 is specifically configured to:

[0183] Based on the sparse representation vector f and the dictionary D, the full-field response y of the target beam structure at a certain moment is obtained, where

[0184] y=Df (3);

[0185] Combination n s The full-field response y at each sampling moment is used to obtain the response field Y of the target beam structure.

[0186] It should be noted that the beam structure full-field response reconstruction system in the above embodiment has the same working principle and technical effect as the beam structure full-field response reconstruction method in the above embodiment, which will not be repeated here.

[0187] like Figure 6 As shown, an embodiment of the present application further provides an electronic device, which may include:

[0188] A memory 301, a processor 302, and a computer program 303 stored in the memory 301 and executable on the processor 302, wherein the memory 301 and the processor 302 communicate with each other via a bus 304, and when the processor 302 executes the computer program 303, the steps of the beam structure full-field response reconstruction method of the above-mentioned method embodiment of the present application are implemented.

[0189] Specifically, the electronic device 3 can be an intelligent device with memory and processor, such as an industrial computer, a PC, or an intelligent mobile terminal, or a computer component with memory and processor, such as a CPU or a GPU.

[0190] An embodiment of the present application also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the method for reconstructing the full-field response of a beam structure of any one of the first purposes of the present application are implemented.

[0191] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0192] Professionals will further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented using electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the above description generally describes the components and steps of each example according to their functions. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0193] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0194] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. The present application will not be limited to the embodiments shown herein, but should conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for reconstructing the full-field response of a beam structure, characterized in that: The method comprises the following steps: S1, constructs a dictionary based on sine series to sparsely represent the full-field response of the target beam structure represents a real number, its superscript represents the size of the matrix, m is the number of virtual measuring points evenly distributed on the target beam structure, and n is the order of the sine series expansion of the vibration mode; S2, analyzing the number of excited structural modes of the target beam structure and the number of sine functions required to fit each order vibration mode of the target beam structure, and determining the number p of vibration detection sensors required for sparse measurement of the target beam structure; S3, determining the installation positions of the p vibration detection sensors using a Latin hypercube sampling method; S4, using the measured values ​​of p vibration detection sensors The orthogonal matching algorithm is used to solve the sparse representation vector of the target beam structure. S5, reconstructing the response field of the target beam structure based on the sparse representation vector f and the dictionary D n s is the sampling time number of the vibration test.

2. The beam structure full-field response reconstruction method according to claim 1, characterized in that: In step S1, the dictionary D for sparsely representing the full-field response of the target beam structure is constructed based on the sine series, including: Based on the modal superposition method, the vibration mode of the target beam structure is extended by an odd extension and then approximated by a sine series. The expression is: Among them, φ i (x) is the vibration mode of the i-th order vibration mode of the target beam structure, L is the beam length of the target beam structure, c ij is φ i (x) is the coefficient of the jth term of the series expansion, n is the order of the sine series expansion of the mode shape, and x is the coordinate along the length of the bridge; The expression of dictionary D is: Among them, x1~x m are the coordinates of virtual measuring points evenly distributed on the target beam structure.

3. The beam structure full-field response reconstruction method according to claim 1, characterized in that: In step S2, the number p of vibration detection sensors is greater than the sparsity K of the sparse representation vector f, wherein the sparsity K is determined by the number of excited modes of the target beam structure and the number of sine functions required for fitting vibration shapes.

4. The beam structure full-field response reconstruction method according to claim 3, characterized in that: Step S2 includes: S21, obtaining the number of excited modes by performing modal analysis on the test data of the target beam structure; S22, determining the number of sine functions required for each mode according to the amplitude attenuation characteristics of the sine series fitting coefficients of the vibration mode; S23, adding the number of sine functions required for all excited modes to obtain the number p of the vibration detection sensors.

5. The beam structure full-field response reconstruction method according to claim 1, characterized in that: Step S3 includes: S31, evenly dividing the target beam structure into p regions according to the length of the target beam structure; S32 , randomly selecting a position from each area to obtain p positions, and using the p positions as installation positions of the p vibration detection sensors.

6. The beam structure full-field response reconstruction method according to claim 1, characterized in that: Step S4 includes: S41, constructing a perception matrix based on the dictionary D and the determined position of the vibration detection sensor in, It is a measurement matrix composed of 0 and 1, each row of the matrix has an element of 1, corresponding to the position of a virtual measurement point where a vibration detection sensor is located, and the other elements of the matrix are 0; S42, specifying an initial sparsity K, and initializing the residual to the measurement value z, and the sparse representation vector f to a zero vector; S43, in each iteration, selecting the column in the perception matrix Φ that is most relevant to the residual, and updating the sparse representation vector f; S44, when the residual norm is less than a preset threshold, the iteration is terminated to obtain the sparse representation vector f.

7. The beam structure full-field response reconstruction method according to claim 1, characterized in that: Step S5 includes: S51, based on the sparse representation vector f and the dictionary D, obtain the full-field response y of the target beam structure at a certain moment, where: y=Df (3); S52, combination n s The response field Y of the target beam structure is obtained at the sampling moment y.

8. A beam structure full-field response reconstruction system, characterized in that: include: Dictionary building module for constructing a dictionary based on sine series for sparse representation of the full-field response of the target beam structure represents a real number, its superscript represents the size of the matrix, m is the number of virtual measuring points evenly distributed on the target beam structure, and n is the order of the sine series expansion of the vibration mode; a sensor quantity determination module, configured to analyze the number of excited structural modes of the target beam structure and the number of sine functions required to fit each order vibration mode of the target beam structure, and determine the number p of vibration detection sensors required for sparse measurement of the target beam structure; A sensor installation position determination module, configured to determine the installation positions of the p vibration detection sensors using a Latin hypercube sampling method; A coefficient representation vector solving module for using the measured values ​​of p vibration detection sensors The orthogonal matching algorithm is used to solve the sparse representation vector of the target beam structure. A structural response field reconstruction module is used to reconstruct the response field of the target beam structure based on the sparse representation vector f and the dictionary D. n s is the sampling time number of the vibration test.

9. An electronic device, characterized in that: The method comprises a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the beam structure full-field response reconstruction method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the beam structure full-field response reconstruction method according to any one of claims 1 to 7 are implemented.

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