Improved regularized radial gate support arm pulsating load time domain identification method

Abstract

The invention discloses an improved regularized radial gate support arm pulsating load time domain identification method, and belongs to the technical field of radial gate flood discharge vibration monitoring. Comprising the steps of collecting a vibration signal and performing noise reduction; constructing a three-dimensional finite element mathematical model of the radial gate support arm and calculating a unit impulse response function matrix; displacement response of the radial gate support arm under discharge excitation is obtained through Duhamel integration, and an inverse analysis mathematical model is constructed; solving is carried out through a Tikhonov regularization algorithm, regularization parameters are obtained through an ICAA regularization selection method, and the inverse analysis mathematical model is corrected; the vibration displacement response obtained after noise reduction serves as input, iterative solution is conducted on the corrected inverse analysis mathematical model, and the water flow pulsation load is obtained. According to the method, the difficulty that the pulsating load cannot be directly measured or the pulsating load S cannot be solved according to the dynamic response variable in the prior art is solved, the selection accuracy of the regularization parameters is improved, the interference of noise is weakened to a certain extent, and the load identification precision is improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of monitoring the vibration of an arc gate during flood discharge, and particularly relates to a method for identifying the time-domain fluctuating load of an arc gate support arm by improving regularization. BACKGROUND

[0002] Arc gates are often used as working gates of water discharge structures such as spillway surface outlets and deep flood discharge tunnels, and their safe service is related to the normal operation of the entire water conservancy hub and the safety of life and property of downstream people. With the improvement of dam building technology, arc gates in China are facing the development trend of high water head, large flow and light weight, so the problem of vibration induced by water flow fluctuating load on arc gates is increasingly attracting attention. As a relatively weak component of the entire arc gate system, the support arm of the arc gate is not uncommon to see engineering damage cases caused by instability of the arc gate during local flood discharge. The phenomenon of flood discharge vibration is particularly worth attention in the problem of flow-induced vibration.

[0003] At present, the vibration monitoring indicators of arc gates are mainly the vibration acceleration and vibration stress directly collected by sensors. Although such indicators are more intuitive in reflecting the vibration problem of the gate, the existing technical means cannot analyze the water flow fluctuating load acting on the support arm of the gate from the monitored vibration data, and cannot predict in advance whether the vibration of the support arm is abnormal. Or in the prototype observation, the fluctuating pressure sensors are arranged at the bolt holes of the center line of the gate panel and the water stop rubber, only the point fluctuating pressure P of the high-speed water flow acting on the gate panel can be obtained, and the fluctuating load S cannot be directly measured in the actual prototype observation.

[0004] Therefore, the existing technology cannot directly measure the fluctuating load S acting on the support arm of the arc gate. The existing technology has not carried out inverse problem research of structural dynamics according to the dynamic response (such as dynamic acceleration, dynamic displacement or dynamic stress) data of the support arm of the arc gate, and there are few reports on the inversion of the fluctuating load S on the support arm. However, the cases of arc gate accidents and the projects with large gate vibration degree are all characterized by buckling instability of the support arm, severe vibration of the support arm and other phenomena. The occurrence of the above problems is closely related to the structural dynamics characteristics of the support arm itself and the fluctuating load S acting on the support arm. The structural dynamics characteristics of the support arm itself are generally analyzed by carrying out finite element modal calculation and water elasticity gate modal parameter test in the early design of the gate. Therefore, the unknown condition for the vibration system of the gate support arm is the fluctuating load S. On the one hand, when the energy of the water flow fluctuating load is large, it will excite the support arm of the gate to have forced vibration with large vibration intensity. When the main frequency of the fluctuating load is close to the natural frequency of the support arm, it will induce severe "beat vibration" or parametric vibration of the support arm. Therefore, it is very important to carry out inverse problem research of the arc gate support arm under flood discharge excitation, obtain the fluctuating load acting on the support arm, and then improve the early dynamics design of the support arm of the arc gate and ensure the safe operation and operation of the arc gate during local operation.

[0005] With the development of dynamic load time domain identification theory and technology, it is more and more used in dynamic excitation identification which is difficult to directly measure the vibration of structure, however, due to the noise interference and the performance limitation of sensor, the signal collected to construct the load time domain identification matrix often presents the ill-conditioned problem, and the existing regularization technology is difficult to find the accurate regularization parameter value based on the L curve method and GCV method. In summary, the existing technology has the defects of large noise interference of response signal, low efficiency of regularization parameter selection, etc. SUMMARY

[0006] The purpose of the present application is to overcome the defects of the prior art, based on the measured vibration displacement response of the radial gate support arm, the inverse problem of the support arm dynamic load is studied. A regularization parameter selection combined Tikhonov regularization pre-optimization GMRES algorithm based on inverse calculation-contrast-adjustment-approximation (ICAA) is provided. Firstly, CEEMDAN-wavelet threshold is used to denoise the measured vibration displacement of the gate support arm, and at the same time, a three-dimensional finite element mathematical model of the gate support arm is established by means of finite element modeling software. The modal calculation of the gate support arm finite element model is carried out by using Matlab software to obtain the natural frequency and mode shape vector of each order, and the unit impulse response function matrix is calculated. Based on this, the inverse problem model of the gate support arm fluctuating load time domain identification is constructed by means of Duhamel integral. The initial Tikhonov regularization parameter value is determined by combining the ICAA method. Finally, the GMRES algorithm is used for iterative solution to obtain the water flow fluctuating load acting on the radial gate support arm. The results show that the improved radial gate support arm fluctuating load time domain identification method provided by the present application is more accurate and has strong anti-interference ability than the existing regularization technology. The improved method can efficiently implement the dynamic identification and inversion of the radial gate support arm fluctuating load, so as to realize the real-time monitoring of the gate flood discharge vibration. The method provides a new idea for the vibration monitoring of the gate during the local opening operation.

[0007] Specifically, the present application provides an improved regularization radial gate support arm fluctuating load time domain identification method, comprising the following steps: S1, collecting the vibration signal of the radial working gate support arm under the flood discharge excitation and denoising the collected vibration signal by means of CEEMDAN combined wavelet threshold denoising; S2, constructing a three-dimensional finite element mathematical model of the radial gate support arm and carrying out modal calculation to obtain the natural frequency and mode shape vector of each order, and calculating the unit impulse response function matrix; S3, obtaining the displacement response of the radial gate support arm under the discharge excitation by means of Duhamel integral, and constructing the inverse analysis mathematical model among the displacement response matrix, the unit impulse response and the fluctuating load; S4, solving the inverse analysis mathematical model by a Tikhonov regularization algorithm, obtaining a regularization parameter and correcting the inverse analysis mathematical model by a regularization selection method of ICAA, and obtaining a corrected inverse analysis mathematical model; S5, taking the vibration displacement response after noise reduction in S1 as input, and iteratively solving the corrected inverse analysis mathematical model by a GMRES algorithm to obtain the water flow fluctuating load acting on the branch arm of the radial gate.

[0008] Preferably, S1 comprises: S11, collecting a vibration displacement signal of a local discharge flow of the radial working gate branch arm under flood discharge excitation as a raw signal, and decomposing the raw signal by a CEEMDAN algorithm to obtain a plurality of intrinsic mode function components and a residual; S12, calculating a multi-scale permutation entropy for each intrinsic mode function component, regarding the multi-scale permutation entropy higher than 0.6 as a high-frequency noise component, and regarding the multi-scale permutation entropy lower than 0.6 as a pure component; S13, performing noise reduction on the component with the multi-scale permutation entropy between 0.6 and 0.7 by an improved wavelet threshold function; S14, superimposing the signal components after noise reduction and the intrinsic mode function components with the multi-scale permutation entropy lower than 0.6 to obtain a reconstructed dynamic displacement signal.

[0009] Preferably, the improved wavelet threshold function is specifically represented as: ; In the formula, wherein, represents the improved wavelet threshold function, and λ represents a threshold value.

[0010] Preferably, S2 specifically comprises: S21, establishing a three-dimensional finite element mathematical model of the radial gate branch arm based on modeling software, wherein the geometric features of the branch arm connection system are mainly retained, and the modeling is performed by using solid elements; S22, based on the three-dimensional finite element mathematical model, performing grid preprocessing by a finite element grid division software, and then dividing the grid of the structure of the branch arm according to the function of the surface element grid, and assigning the corresponding material properties, thickness properties and element properties; S23, checking the grid element quality, and applying boundary conditions, adding a concentrated mass element to each front end plate of the gate branch arm to simulate the influence of the additional mass generated by the panel and beam system, and coupling all the degrees of freedom of each node on the front end plate with the corresponding additional mass element point by using a rigid element; S24, based on the three-dimensional finite element mathematical model of the radial gate branch arm, carrying out modal analysis and outputting the mass matrix and stiffness matrix of the gate branch arm; S25. Based on the mass matrix and stiffness matrix, the first N natural frequencies and mode shapes of the gate arm are calculated using the modal superposition method through calculation software to obtain the vector of the first N natural frequencies and mode shapes. S26. Based on the solution of the mode shape vectors, the first N order mode shape vectors are regularized to calculate the generalized mass, generalized stiffness and generalized damping matrix. S27. Based on the regularized mode shape, select the mode shape vector at the excitation point and the mode shape vector at the response point, and use them to form the mode shape matrix at the excitation point and the mode shape matrix at the response point, thereby constructing the unit impulse response.

[0011] Preferably, the mesh preprocessing includes mid-surface extraction, hybrid mesh generation, and contact processing.

[0012] Preferably, step S3 includes the following steps: S31. Structural dynamics equations of a multi-degree-of-freedom system based on a gate: Based on the principle of orthogonal mode shapes, obtain the dynamic displacement of the gate arm at any time and decouple it into equations in modal coordinates. S32. Construct expressions for the influence of displacement and velocity on the initial moment of the multi-degree-of-freedom system of the gate. Based on the equations in the modal coordinates, derive the zero-input response expression and the zero-state response expression of the modal displacement, respectively. S33. Substitute the zero-input response expression and the zero-state response expression of the modal displacement into the equation under the modal coordinates to obtain the system displacement; S34. Based on the system displacement and the dynamic displacement response calculated according to the Duhamel integral, the impulse response function is obtained; S35. Assemble the impulse response functions of each response point to a single-point excitation to obtain the corresponding unit impulse response function matrix. Concatenate the displacement vectors of each response point by row or column to obtain the displacement response matrix. S36. After discretizing the pulsating load in the time domain, and combining it with the displacement response matrix of the unit impulse response function matrix, a system of linear equations under single-point excitation is obtained. S37. Based on the actual situation, the linear expression of the multivariate pulsating load is obtained according to the principle of superposition of linear systems, and then the inverse analysis mathematical model is obtained.

[0013] Preferably, the dynamic displacement of the gate arm at any given time is specifically expressed as follows: ; In the formula, The modal shape matrix, y(t) is the displacement vector in modal coordinates; i represents the modal order; t represents time; n represents the number of modes of the reconstructed displacement y(t).

[0014] Preferably, the equation in modal coordinates is specifically expressed as: ; In the formula, , , These represent the acceleration, velocity, and displacement at the s-th order in modal coordinates, respectively. , Let be the modal mass and modal load of the i-th order, respectively; Let i be the modal damping ratio at the i-th order. Indicates the natural frequency.

[0015] Preferably, the zero-input response expression of the modal displacement is: ; The zero-state response expression for the modal displacement is: ; In the formula, It is the damped vibration frequency. , The initial displacement and initial velocity are in modal coordinates. Indicates a time delay.

[0016] Preferably, the expression for the impulse response function is: ; In the formula, It is an impulse response function; It is the normalized mode shape vector of the i-th mode; It is the mode vector The transpose of .

[0017] Preferably, the linear expression for the multi-element pulsating load is: In the formula, K is the number of excitations to be identified; J is the number of dynamic displacement response points; Y J The discrete displacement response at the measuring point with degree of freedom i; S K G is the discrete excitation vector at the load point with degree of freedom j; JK This represents the impulse response function matrix at the Kth measurement point when a unit impulse is applied at the Jth excitation point; The inverse analysis mathematical model is as follows: ; In the formula, It is a response matrix, which can be obtained by directly concatenating the displacement vectors of each response point by row (or by column); It is the unit impulse response function; It is the water flow pulsation load matrix.

[0018] Preferably, S4 specifically includes: S41. Based on the aforementioned inverse analysis mathematical model, define the inverse problem and construct the objective function of Tikhonov regularization, and introduce positive regularization parameters; S42. Transform the objective function of Tikhonov regularization into a regularization equation, calculate the expression of the Tikhonov regularization solution, and optimize the regularization parameters using the ICCA method. When the error is iterated to the minimum value, the regularization parameters are obtained. S43. By defining the initial value of regularization and the generalized inverse, a regularization pre-optimization process is constructed based on this. Assuming that the correction factor is known, the deviation function is constructed by combining the deviation expression between the calculated response and the measured response, and the response deviation is calculated. S44. Solve for the minimum value of the deviation function and derive the expression for the correction factor; S45. Substitute the expression of the correction factor into the pre-optimization process formula to obtain the modified back-analysis mathematical model.

[0019] Preferably, the correction factor is specifically expressed as: ; In the formula, It is the generalized inverse of Tikhonov regularization; It is response bias; represents the identity matrix; T represents the transpose of the matrix.

[0020] Preferably, the modified inverse analysis mathematical model is specifically expressed as follows: ; In the formula, It is the transpose of the unit pulsating response function G; This is the regularization parameter.

[0021] Preferably, in step S5, the GMRES algorithm is used for iterative solution as follows: Sa, set the initial solution and calculate the residual, and generate the orthogonal basis matrix and the upper Hessenberg matrix through the Arnoldi process; Sb, construct the Krylov subspace; Sc. Solve for the optimal coefficients in the subspace using a least squares problem and update the approximate solution; Sd, check if the residual meets the accuracy requirements. If it does not converge, restart the iteration and repeat the above process until the termination condition is met, and derive the expression for the water flow pulsation load.

[0022] Preferably, the water flow pulsation load is specifically represented as follows: ; In the formula, This represents the initial approximate solution vector of the fluctuating load during the iterative solution process of the GMRES algorithm. It is the solution vector of minimizing the subproblem. It is a Lanczos matrix.

[0023] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This method proposes for the first time an identification method for the load of the arc gate arm, solving the difficulty of existing technologies in directly measuring pulsating loads or solving for the pulsating load S based on dynamic response variables. Moreover, compared with traditional load time-domain identification methods, the proposed load time-domain identification method improves the accuracy of regularization parameter selection by introducing the ICCA combined with the GMRES algorithm, reduces noise interference to a certain extent, and greatly improves the load identification accuracy. It has broad application prospects in the field of flow-induced vibration monitoring of arc gates.

[0024] 2. The improved load inversion method proposed in this invention provides a novel approach to vibration monitoring for partially open flood discharge of arc-shaped working gates. By introducing advanced load inversion technology, the vibration of the gate during partially open flood discharge can be monitored and analyzed more accurately, effectively improving the safety and stability of gate operation. This method opens up a new path for the development of vibration monitoring technology in the field of water conservancy engineering, and has significant application value and innovative significance.

[0025] 3. The ICCA regularization parameter selection method proposed in this invention, combined with GMRES pre-optimization, significantly improves the accuracy of load time-domain identification and enhances the stability of load inversion by selecting the appropriate regularization parameter. (The highlighted content may contain some repetition.) Traditional load identification methods face problems of low identification accuracy and poor stability when dealing with complex loads. The ICCA regularization parameter selection method combined with GMRES pre-optimization in this invention effectively solves these problems by introducing the aforementioned optimization strategy.

[0026] 4. The improved threshold function proposed in this invention is continuous at the threshold point, thus overcoming the disadvantage of discontinuity of the hard threshold function at the threshold. It also satisfies the condition of an odd function, enabling the same effect to be achieved for both positive and negative signals when processing signals. In addition, the asymptote of the improved threshold function rapidly approaches the hard threshold function after the threshold value is exceeded, which can retain the energy of the finite signal and overcome the constant error problem in the soft threshold function. Attached Figure Description

[0027] Figure 1This is a schematic diagram of the overall process of load time-domain identification according to an embodiment of the present invention; Figure 2 The following are upstream and downstream views of the partial opening flood discharge of the arc-shaped gate according to an embodiment of the present invention: (a) downstream view of the surface spillway; (b) upstream top view of the partial opening flood discharge of the gate. Figure 3 This is a schematic diagram of an arc-shaped gate according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the three-dimensional finite element mesh generation of the gate arm, the arrangement of the arm response measurement points, and the three equivalent concentrated loads in an embodiment of the present invention. Figure 5 The visualization result of the gate support arm system matrix in an embodiment of the present invention; Figure 6 The results of the gate arm dynamics calculations in this embodiment of the invention are as follows; Figure 7 The rigid rectangular plate is an embodiment of the present invention; Figure 8 This is a schematic diagram of the improved wavelet threshold function used in an embodiment of the present invention; Figure 9 This is a comparison diagram of the noise reduction of the dynamic displacement response under random excitation of node number 3 on a rectangular plate according to an embodiment of the present invention; Figure 10 A diagram illustrating the process of determining regularization parameters for the GCV and L curves of a single pulsating load on a rectangular plate according to an embodiment of the present invention. Figure 11 This is a graph showing the ICCA optimization process of a noisy signal on a rectangular plate according to an embodiment of the present invention. Figure 12 The results of identifying single loads on a rectangular plate containing noisy signals according to embodiments of the present invention; Figure 13 This is a comparison diagram of the dynamic displacement response of the verification point after the forward analysis following the inversion of a single load on a rectangular plate according to an embodiment of the present invention. Figure 14 This is a comparison chart of the results of identifying multiple loads using various methods on a rectangular plate according to an embodiment of the present invention; Figure 15 This is a time-domain diagram of the three equivalent vertical loads on the arc-shaped gate arm according to an embodiment of the present invention; Figure 16 The displacement response and correlation coefficients at four measuring points are obtained from the positive analysis of three equivalent vertical loads on the arc-shaped gate arm in this embodiment of the invention.

[0028] Figure 17 This is a comparison diagram and correlation coefficient of the measured dynamic displacement response and the dynamic displacement response of the inverted load forward analysis at measuring point 5# of the lower support arm of the arc gate in an embodiment of the present invention. Detailed Implementation

[0029] Example 1: As Figures 1-17 As shown, this invention provides an improved regularized method for time-domain identification of pulsating loads on the support arm of an arc gate, comprising the following steps: S1. Collect the vibration signal of the partial discharge vibration of the arc-shaped working gate arm under the excitation of flood discharge, and use CEEMDAN combined with wavelet threshold denoising to denoise the collected vibration signal.

[0030] S1 specifically includes the following steps: S11: Add white noise to the original signal x(t). ,in Let be the amplitude coefficient of the white noise added for the first time. Then the signal at the i-th time can be expressed as: For each The first-order components of each signal after the i-th decomposition are obtained through EMD. and residual For all The first-order components of the whole obtained by averaging The residual signal is .

[0031] The final original signal can be represented as: (1) In the formula, W is the total number of intrinsic mode functions (IMFs) obtained through EMD decomposition. Indicates the trend.

[0032] S12. Calculate the multi-scale permutation entropy for each intrinsic mode function component. If the multi-scale permutation entropy is higher than 0.6, it is considered to contain high-frequency noise components. If the multi-scale permutation entropy is lower than 0.6, it is considered to be a pure component. S13. For components with multi-scale permutation entropy between 0.6 and 0.7, an improved wavelet threshold function is used for noise reduction. Based on existing research, an improved threshold function is adopted, which combines the characteristics of soft thresholding and hard thresholding. Specifically: (2) In the formula, Let λ represent the improved wavelet threshold function, where λ represents the threshold.

[0033] This function is continuous at the threshold point, thus overcoming the disadvantage of discontinuity at the threshold of the hard threshold function. It also satisfies the condition of an odd function, enabling the same effect to be achieved for both positive and negative signals. Furthermore, the asymptote of this improved threshold function rapidly approaches that of the hard threshold function after the threshold value is exceeded, thus preserving the energy of a finite signal and overcoming the constant error problem in the soft threshold function.

[0034] S14. The reconstructed dynamic displacement signal is obtained by superimposing the denoised signal components and the eigenmode function components with multi-scale arrangement entropy less than 0.6.

[0035] This step has beneficial effects such as enhancing feature information extraction capabilities, improving noise reduction effects, and adapting to non-stationary and nonlinear signals.

[0036] Specifically, CEEMDAN can decompose complex vibration signals into multiple intrinsic mode functions (IMFs), each IMF representing a vibration component at a different frequency, thereby effectively separating external interference from the true signal components. Wavelet thresholding denoising removes noise from the signal by setting a threshold, retaining the useful signal and improving signal accuracy.

[0037] Enhanced feature information extraction capability: By combining CEEMDAN and wavelet thresholding, feature information such as frequency and amplitude in gate vibration signals can be extracted more accurately, providing reliable data for subsequent structural health monitoring and safety assessment.

[0038] Improved noise reduction performance: Compared with single noise reduction methods, CEEMDAN combined with wavelet thresholding can more effectively remove noise from the signal, improve the signal-to-noise ratio, and reduce the root mean square error, thereby achieving higher quality noise reduction results.

[0039] Adaptable to non-stationary and nonlinear signals: The CEEMDAN algorithm can effectively handle non-stationary and nonlinear vibration signals, avoiding the problems of mode aliasing and low computational efficiency that may occur when traditional methods are used to process such signals.

[0040] S2. Construct a three-dimensional finite element mathematical model of the arc-shaped gate arm and perform modal calculations to obtain the natural frequencies and mode shape vectors of each order, and then calculate the unit impulse response function matrix based on these.

[0041] S21: Use 3D modeling software to create a 3D model of the arc gate. Solid elements are used when modeling the gate. The details of the gate support system, especially the complex connection structure, should be reproduced as much as possible during modeling. S22: The arc gate support arm is processed by extracting the mid-surface using professional finite element meshing software. Then, the entire structure of the support arm is meshed according to the surface element meshing function, and corresponding material properties, thickness properties and element properties are assigned. S23: After mesh generation, check the quality of the mesh elements and apply the following boundary conditions: The transverse rotational degree of freedom is released on the rear end plate of the gate arm, while the rotational degree of freedom is constrained on the front end plate of the arm. Lumped mass elements are added to each of the three front end plates of the arm to simulate the effect of the additional mass, and rigid elements are used to couple all degrees of freedom (including displacement and rotation) of all nodes on each front end plate.

[0042] S24: Perform modal analysis and output the mass and stiffness matrices of the gate arm system after the modal analysis is completed.

[0043] S25: Complete the preprocessing operations of S21~S24. The subsequent steps are as follows: First, the system matrix of the gate arm is input into the Matlab software. Based on the basic idea of ​​the modal superposition method, the first N natural frequencies and mode shapes of the gate arm are calculated to obtain the first ten natural frequencies V and mode shape vector D. Secondly, based on the solution of the mode shape vector, the mode shape is regularized, and the generalized mass, generalized stiffness and generalized damping matrix are calculated to realize the decoupling of multiple degrees of freedom into a single degree of freedom; Finally, based on the regularized mode shape, the mode shape vectors at the excitation point and the response point are selected to form the mode shape matrix at the excitation point and the mode shape matrix at the response point, thus completing the preparation work for constructing the unit impulse response G.

[0044] In this step, modal analysis is used to obtain the natural frequencies and mode shape vectors of the arc-shaped gate arm. This helps to understand the dynamic characteristics of the structure, avoid resonance in actual operation, and thus optimize the structural design and improve its safety and reliability.

[0045] Furthermore, fault diagnosis and condition monitoring using natural frequencies and mode vectors are important steps in structural health monitoring. By comparing modal parameters under different operating conditions, structural damage or anomalies can be detected in a timely manner, providing a basis for fault diagnosis and condition monitoring.

[0046] The unit impulse response function matrix is ​​an important parameter describing the dynamic response characteristics of a structure. The mode shape vectors obtained through modal calculations can be used to further calculate the unit impulse response function matrix, providing basic data for subsequent dynamic response analysis.

[0047] S3. The displacement response of the arc gate arm under discharge excitation is obtained by Duhamel integral, and an inverse analysis mathematical model is constructed between the displacement response matrix, the unit impulse response and the pulsating load.

[0048] S3 specifically includes the following steps: S31. Structural dynamics equations of a multi-degree-of-freedom system based on a gate: Based on the principle of orthogonal mode shapes, obtain the dynamic displacement of the gate arm at any time and decouple it into equations in modal coordinates. Specifically, the structural dynamics equations of the gate's multi-degree-of-freedom system can be expressed as: (3) In the formula, M, C, and K are the overall mass matrix, overall damping matrix, and overall stiffness matrix of the gate, respectively. , , These are the acceleration, velocity, and displacement in the system's physical coordinates. It is the external load on the system, which is generally a pulsating load in the field of flow-induced vibration of arc gates.

[0049] Based on the principle of orthogonal mode shapes, the dynamic displacement of its support structure at any given time can be expressed as follows: (4) In the formula The modal shape matrix, y(t) is the displacement vector in modal coordinates; i represents the modal order; t represents time; n represents the number of modes of the reconstructed displacement y(t).

[0050] This decouples the structural dynamics equations in physical coordinates into equations in modal coordinates: (5) In the formula , , Let x, y, y be the acceleration, velocity, and displacement of the system at the i-th order in modal coordinates, respectively. , Let be the modal mass and modal load of the i-th order of the system, respectively, and their expressions are as follows: , , Let i be the modal damping ratio at the i-th order. Indicates the natural frequency.

[0051] S32. Construct expressions for the influence of displacement and velocity on the initial moment of the multi-degree-of-freedom system of the gate. Based on the equations in modal coordinates, derive the zero-input response expression and the zero-state response expression of the modal displacement, respectively. S33. Substitute the zero-input response expression and the zero-state response expression of the modal displacement into the equations in modal coordinates to obtain the system displacement.

[0052] The effects of displacement and velocity at the initial moment of system testing can be expressed as: (6) In the formula, the general solution This corresponds to a system without external loads. The system's subsequent modal displacements Only with initial velocity and initial displacement Related, due to the system <1, Homogeneous solution of equation (4) The expression is: (7) (8) (9) In the formula, It is the damped vibration frequency. , The initial displacement and initial velocity are in modal coordinates; This represents the physical coordinate displacement vector of the system at the initial time (t=0), i.e., the initial displacement; This represents the physical coordinate velocity vector of the system at the initial moment (t=0), i.e., the initial velocity.

[0053] Zero-state response It is independent of the initial conditions of the system, therefore its expression is: (10) make: (11) (12) In the formula, τ represents the time delay.

[0054] At this point, the system displacement y is: (13) S34. Based on the system displacement and the dynamic displacement response calculated according to the Duhamel integral, the impulse response function is derived.

[0055] Based on the Duhamel integral, the dynamic displacement response of a linear system under a dynamic load in the continuous time domain can be expressed as the convolution of the unit impulse response function and the dynamic load. (14) Combining equations (14) and (15) above, the impulse response function can be obtained. Specific forms of expression: (15) In the formula, It is an impulse response function; It is the normalized mode shape vector of the i-th mode; It is the mode vector The transpose of .

[0056] S35. Assemble the impulse response functions of each response point to a single-point excitation to obtain the corresponding unit impulse response function matrix. Concatenate the displacement vectors of each response point by row or column to obtain the displacement response matrix. S36. After discretizing the pulsating load in the time domain, the linear equations under single-point excitation are obtained by combining the unit impulse response function matrix and the displacement response matrix. After discretizing the pulsating load in the time domain, the linear equations under single-point excitation are as follows: (16) The above formula can be written as: (17) In the formula, For time step, , , They are respectively Dynamic displacement response, unit impulse response function, and load to be identified; This represents the displacement response time vector at degree of freedom b; This represents the time vector of the fluctuating load at degree of freedom p.

[0057] S37. Based on the actual situation, the linear expression of the multivariate pulsating load is obtained according to the principle of superposition of linear systems, and then the inverse analysis mathematical model is obtained.

[0058] If the actual structure is subjected to multiple excitations, let the number of excitations to be identified be K and the number of dynamic displacement response points be J. Generally, the number of dynamic displacement response points K > the number of excitations to be identified K. According to equations (16) and (17), the unit impulse response function matrix under multivariate pulsating load is obtained. as follows: (18) In the formula, This represents the discrete displacement response at the measurement point with degree of freedom i. Let be the discrete excitation vector at the load point with degree of freedom j; Based on the principle of superposition of linear systems, the linear expression for multi-element pulsating load is: (19) Since a single load can be considered a special case of multiple loads, the concepts of single-source load and multi-source load are unified as follows: (20) In the formula, It is a response matrix, which can be obtained by directly concatenating the displacement vectors of each response point by row (or by column); It is the unit impulse response function; It is the pulsating load of the water flow.

[0059] S4. Solve the inverse analysis mathematical model using the Tikhonov regularization algorithm. Obtain the regularization parameters and modify the inverse analysis mathematical model using the ICAA regularization selection method to obtain the modified inverse analysis mathematical model.

[0060] S41. Based on the inverse analysis mathematical model, define the inverse problem and construct the objective function of Tikhonov regularization and introduce positive regularization parameters; S42. Transform the objective function of Tikhonov regularization into a regularization equation, calculate the expression of the Tikhonov regularization solution, and optimize the regularization parameters using the ICCA method. When the error is iterated to the minimum value, the regularization parameters are obtained.

[0061] The basic idea of ​​the Tikhonov regularization method is to transform the inverse problem into a functional minimization problem of the residual function and the norm term of the solution with regularization parameters, that is: (twenty one) In the formula: Describing the L2 norm, This is the regularization parameter, which is a positive number and relates to the accuracy of regularization.

[0062] The minimization problem of the above equation can be written as: (twenty two) The Tikhonov regular solution to the above equation is: (twenty three) In the formula: This represents the Tikhonov regularization operator. Represents the identity matrix.

[0063] S43. By defining the initial value of regularization and the generalized inverse, a regularization pre-optimization process is constructed based on this. Assuming that the correction factor is known, the deviation function is constructed by combining the deviation expression between the calculated response and the measured response, and the response deviation is calculated. make (twenty four) In the formula: This indicates that the initial value of the fluctuating load is obtained according to the Tikhonov canonical solution; This represents the generalized inverse of Tikhonov regularization.

[0064] The regularization pre-optimization process can be represented as follows: (25) In the formula: This indicates the deviation between the initially identified pulsating load and the actual pulsating load. Indicates response deviation; This represents the calculated response; This represents the correction factor.

[0065] If we assume that α is known in the above formula, then the deviation between the calculated response and the measured response can be expressed as: (26) To construct the constructor: (27) S44. Solve for the minimum value of the above deviation function and derive the expression for the correction factor; To solve the above deviation function The minimum value of is obtained by taking its partial derivative with respect to the correction factor α, and then setting the partial derivative to zero. (28) Further solving the above equation yields: (29) In the formula, It is the generalized inverse of Tikhonov regularization; It is response bias; represents the identity matrix; T represents the transpose of the matrix.

[0066] Substituting the correction factor α into the equation, we get: (30) The above formula can be simplified as follows: (31) In the formula: , representing the corrected unit pulse response function; , representing the corrected response matrix.

[0067] The regularization parameter selection method proposed in this invention, which combines ICCA and GMRES for pre-optimization, not only significantly improves the accuracy of load time-domain identification by selecting regularization parameters, but also significantly enhances the stability of load inversion.

[0068] Traditional load identification methods suffer from low accuracy and poor stability when dealing with complex loads. The regularization parameter selection method using ICCA combined with GMRES pre-optimization employed in this invention effectively solves these problems through the aforementioned optimization strategy.

[0069] First, this method utilizes ICCA (Independent Component Analysis, correctly termed Inverse Calculation-Comparison-Adjustment-Approximation) for data preprocessing, decomposing complex multidimensional signals into independent components, thereby simplifying the subsequent load feature extraction process. Based on this, GMRES (Generalized Minimum Residual Method) is combined for pre-optimization, further improving the accuracy and stability of load identification.

[0070] First, this method uses CEEMDAN and multi-scale permutation entropy to improve the wavelet threshold function for dynamic response data preprocessing, effectively eliminating noise components affected by the acquisition environment.

[0071] Based on this, an improved regularization parameter selection method, namely ICCA (Inverse Calculation-Comparison-Adjustment-Approximation) algorithm, is proposed according to the modified load inversion model. Furthermore, GMRES (Generalized Minimum Residual Method) is combined for pre-optimization, which further improves the accuracy and stability of load identification.

[0072] The GMRES algorithm is a powerful iterative method, particularly suitable for solving large sparse linear equation systems. By adjusting its parameters such as restart (number of restarts), tol (error tolerance), and maxit (maximum number of iterations), the convergence speed and stability of the algorithm can be optimized.

[0073] Furthermore, the selection of regularization parameters also plays a crucial role in this invention. By employing L1 and L2 regularization methods, the complexity of the model is effectively controlled, avoiding overfitting and underfitting. L1 regularization can generate a sparse model, enabling feature selection, while L2 regularization improves the model's generalization ability by maintaining parameter smoothness.

[0074] S5. Using the noise-reduced vibration displacement response after S1 as input, the modified inverse analysis mathematical model is iteratively solved using the GMRES algorithm to obtain the water flow pulsation load acting on the arc-shaped gate arm.

[0075] In S5, the GMRES algorithm is used for iterative solution as follows: Sa, set the initial solution and calculate the residual, and generate the orthogonal basis matrix and the upper Hessenberg matrix through the Arnoldi process; Sb, construct the Krylov subspace; Sc. Solve for the optimal coefficients in the subspace using a least squares problem and update the approximate solution; Sd, check if the residual meets the accuracy requirements. If it does not converge, restart the iteration and repeat the above process until the termination condition is met, and derive the expression for the water flow pulsation load.

[0076] Specifically, the GMRES (Generalized Minimum Residual Method) is used to iteratively solve equation (32). This method is widely used in solving large-scale asymmetric sparse equation systems and is beneficial for the stable inversion of dynamic loads. For solving... ,set up Initial vector The algorithm solution process is as follows: (1) Calculation , ;in, Represents the initial residual vector; This represents the first Arnoldi orthogonal basis vector; Represents the initial approximate solution vector; (2) By selecting an appropriate m, the Arnoldi process is carried out to obtain... And the Hessenberg matrix ;in, This represents the set of orthogonal basis vectors generated by the Arnoldi process, also known as the Krylov subspace basis; (3) Minimization Derive the solution vector of the minimization subproblem β represents the L2 norm of the initial residual r0; Represents the first unit coordinate vector; Represents the candidate vector for minimization; This represents the solution vector for minimizing the subproblem; (4) Order ,in, S represents the Lanczos matrix; m This represents the solution vector for the approximate fluctuating load at step m; (5) Calculation ;in, This represents the new residual vector at step m; This represents the load vector.

[0077] If the requirements are met, stop the iterative calculation; otherwise, let Return to process (2) and restart the iterative calculation. m is generally taken as 3~6. Finally, based on the GMRES iterative algorithm, the S-form expression of the water flow pulsation load is obtained as follows: (32) In the formula, It represents the approximate solution of the initial fluctuating load during the iterative solution of the GMRES algorithm, that is, the first guess of the unknown fluctuating load S at the beginning of the algorithm.

[0078] This invention proposes for the first time a method for identifying the load of an arc-shaped gate arm, solving the difficulty of existing technologies in directly measuring pulsating loads or solving for the pulsating load S based on dynamic response variables. Furthermore, compared with traditional load time-domain identification methods, the proposed load time-domain identification method improves the accuracy of regularization parameter selection by introducing the ICCA combined with the GMRES algorithm, reduces noise interference to a certain extent, and greatly improves the load identification accuracy.

[0079] Example 2: Figure 1 - Figure 17 As shown, this invention discloses an improved method for time-domain identification of pulsating loads on the support arm of an arc-shaped gate. Figure 1 This is a schematic diagram of the process proposed in this embodiment. This embodiment is based on embodiment 1 and includes a specific engineering simulation.

[0080] Figure 2 See the schematic diagram for the arc-shaped floodgate discharge. Figure 3 This is a 3D schematic diagram of the arc-shaped gate in this project case. The arc-shaped gate has three main horizontal beams and inclined arms. The middle and lower arms and the middle and lower main beams are box-shaped structures, while the top arm and the top main beam are welded I-beam structures. The main material of the gate leaf is Q345B, and the main material of the gate arm is Q345B. Figure 4 A schematic diagram of three-dimensional finite element mesh generation of the gate arm, arrangement of arm response measurement points, and three equivalent concentrated loads is provided. A total of 5 sensors are arranged on the upper, middle and lower arms of the arm to pick up the dynamic displacement response of the flood discharge vibration. Figure 5 The visualization result of the gate arm system matrix; Figure 6 The dynamic calculation results of the gate arm are used to construct the gate arm load identification.

[0081] First, a 3D model of the project was created based on the actual 2D drawings and using 3D modeling software. Solid elements were used for all gate models. The modeling process aimed to accurately represent the details of the gate support system, especially complex connection structures, avoiding excessive simplification that could lead to significant deviations from the actual project. Secondly, the support arm is processed by extracting the mid-surface using Hypermesh software. Then, the entire structure of the support arm is meshed using 2D elements based on the 2D mesh function. For the overlapping areas between some extracted mid-surfaces, common node processing is adopted to ensure stress transfer. After mesh generation, the quality of the mesh elements was checked. Once the quality was deemed acceptable, the SHELL181 element was used to simulate the gate arm, as shown in Figure 4. The total number of elements was 4996, with 5337 nodes. Boundary conditions were set as follows: the rotational degree of freedom in the transverse direction was released at the gate hinge, and the rotational degree of freedom of the front plate of the arm was constrained. Non-load-bearing components such as the maintenance ladder on the arm were ignored. Furthermore, to simulate the effect of the gate leaf on the arm, MASS21 elements were added to each of the three front plates of the arm to simulate the influence of additional mass. Similar to the deep-hole arc gate for flood discharge, to avoid uneven stress distribution, stress concentration, or excessive local deformation at structural nodes, rigid elements were used to couple all degrees of freedom (including displacement and rotation) of all nodes on each front plate, ensuring consistent deformation among the nodes.

[0082] After the above-mentioned 3D modeling, mesh generation, and boundary condition settings, the Lanczos eigenvalue method was used to solve for the first 10 modes (i.e., 10 natural frequencies and corresponding mode shapes). Using ANSYS MECHANICAL ADPL, the first natural frequency of the orifice gate arm was calculated to be 2.422 Hz, with its mode shape being the vertical vibration of the arm; its second natural frequency was 4.488 Hz, with its mode shape being the lateral vibration of the arm. After the modal analysis was completed, a decimal file was obtained by running the "HBMAT" command in ANSYS. This completed the basic preprocessing work in ANSYS. Subsequent steps are as follows: (1) Input the system matrix of the gate arm into Matlab software. The implementation method is to use the "spy" command to obtain the visualization result of the gate arm system, see [link to Matlab software]. Figure 5 As shown; (2) Based on this, the first ten natural frequencies and mode shapes of the gate arm are calculated according to the basic idea of ​​the modal superposition method. The implementation method is to use Matlab software with the help of "[V v D d The command `eigs(K, M, 10, 'smallestabs', 'Tolerance', 1e-3);` obtains the first ten natural frequencies V. v And mode vector D d The first ten natural frequencies obtained by this program are compared with those obtained by ANSYS software. See [link to relevant documentation]. Figure 6 As shown, the natural frequency values ​​of the two methods are basically the same; (3) Based on the solution of the mode shape vector, the mode shape is regularized and the generalized mass, generalized stiffness and generalized damping matrix are calculated to realize the decoupling of multiple degrees of freedom into a single degree of freedom; (4) Based on the regularized mode shapes, select the mode shape vectors at the excitation point and the response point, thereby forming the excitation point mode shape matrix and the response point mode shape matrix, see... Figure 6 As shown.

[0083] (5) Using existing mode shapes, mass, damping and stiffness, form a unit impulse response G and construct a mathematical model for load identification.

[0084] Through the above key steps, the three-dimensional modeling, mesh generation, boundary condition setting, and system matrix extraction of the surface-hole arc gate arm can be realized. Furthermore, the unit pulsating response matrix can be formed with the help of Matlab software, and a dynamic load inversion mathematical model can be built. The realization process of dynamic load inversion of the bottom-hole arc gate arm is basically similar to the steps of the surface-hole gate.

[0085] Based on the observation results of similar arched gate prototypes, it can be seen that the vibration of the arched gate arm is mainly vertical. Therefore, the excitation of the vertical vibration of the gate arm is simplified to three concentrated loads acting on the arm. At this time, J=5 and K=3, satisfying J>K, and load inversion is performed accordingly.

[0086] To verify the accuracy and feasibility of the time-domain load identification method in this embodiment, a rectangular plate model was established for verification. (See...) Figure 7 The rectangular plate is fixed at one end and unconstrained on the other three sides. It measures 1500mm x 750mm and has a density of 7850m³. 3 / s, elastic modulus is 206GPa, Poisson's ratio is 0.3.

[0087] The rectangular plate was meshed using finite element method (FEM) software, and its first 10 natural frequencies and mode shape vectors were calculated. The mass matrix and stiffness matrix of the rectangular plate were extracted. Two random loads (the pulsating pressure of measured water flow was selected as the pulsating load input) were applied at two different locations on the rectangular plate for 1 second each, with a sampling frequency of 1000 Hz, accumulating 1000 discrete time history points. The vibration characteristics of the rectangular plate were calculated using the modal superposition method. The dynamic displacement response under six random excitations was picked on the rectangular plate, with nodes 3#, 4#, 5#, 6#, and 7# as load inversion points and node 8# as the load verification point.

[0088] Given that signals acquired in actual engineering projects are often affected by noise and thus contain errors, a certain level of noise is added to the above six dynamic displacement responses to simulate the measured responses. The noise level is defined as follows: (31) Where a represents the acceleration sequence of a certain channel, σ a The standard deviation of acceleration, Indicates the level of added noise intensity. This means generating a standard normal white noise with the exact same size as the acceleration a sequence.

[0089] White noise of 10% (the standard deviation of the added noise is 10% of the standard deviation of the acceleration) was applied to the dynamic displacement acquisition data of each channel, and the results were compared with those under the condition of no noise.

[0090] Figure 8 This is a schematic diagram of the improved wavelet thresholding function used in this embodiment. This function combines the characteristics of soft thresholding and hard thresholding, and its expression is as follows: (33) Depend on Figure 8 It can be seen that the function is continuous at the threshold point, thus overcoming the disadvantage of the discontinuity of the hard threshold function at the threshold. It also satisfies the condition of an odd function, so that the same effect can be achieved for positive and negative signals when processing signals. The asymptote of the improved function rapidly approaches the hard threshold function after the threshold is exceeded, which can retain the energy of the finite signal and overcome the constant error problem in the soft threshold function.

[0091] Figure 9 The image shows a comparison of noise reduction in the dynamic displacement response of a rectangular plate under random excitation with node number 3. Figure 9 It can be seen that the dynamic displacement curve after adding noise has a large number of "spiking" interferences. In order to remove the noise interference, the CEEMDAN combined with the improved wavelet threshold denoising method of this embodiment is adopted. As shown in the figure, the denoised signal is smoother and the denoised signal is closer to the original signal. It can be seen that this method achieves better denoising effect while preserving the details of the original signal.

[0092] Figure 10 The process of determining the regularization parameter for the GCV and L curves under a single pulsating load is shown in the figure. As can be seen from the figure, the optimal regularization parameter determined by the L curve method is 7.917e-5, the optimal regularization parameter found by the GCV method is 4.3472e-4, and the optimal regularization parameter determined by ICCA is 4.4228e-7. The optimization curves of the ICCA method are shown in the figure. Figure 11 As shown. Figure 12 This diagram illustrates the results of single-load identification using various methods under noisy signals. To measure the similarity between the identified fluctuating load and the actual fluctuating load, a correlation coefficient is introduced, expressed as follows: (34) In the formula, Represents the mathematical expectation; This represents the actual pulsating load; This indicates the identified pulsating load.

[0093] The closer the correlation coefficient c is to 1, the higher the correlation between the identified value and the actual value, and the more accurate the inversion result; conversely, the closer the correlation coefficient c is to 1, the lower the correlation coefficient c is to 1.

[0094] Table 1 compares the correlation coefficients of different identification methods for single random loads. When the noise level is 10%, the traditional generalized inverse method is affected by noise, and its correlation coefficient is poor, only 0.03. When the commonly used L-curve and GCV methods are used to determine the regularization parameters, their correlation coefficients are all below 0.80.

[0095] Table 1 Time-domain identification results of single random load During the optimization iteration process, the following principles were followed: Point 8 was designated as the verification point, i.e., based on the regularization parameters initially established using the GCV method or L-curve method, the initial load was identified; the identified fluctuating load was substituted into the program based on the modal superposition method for forward analysis, yielding the response result of point 6, further confirming the regularization optimization direction that reduces the error at this verification point; optimization was stopped when the verification error curve rose (i.e., the minimum value was found) or the point error change threshold fell below 1% (i.e., the error approached the minimum value), and the regularization parameters at this point were determined. The GMRES algorithm was then used for iterative solution. The verification point results are shown below. Figure 13 As shown.

[0096] The ICCA method (inverse calculation-comparison-adjustment-approximation regularization parameter selection method) proposed in this invention is further combined with the GMRES method for pre-optimization, and the correlation coefficient is further improved to 0.92, which can meet the engineering accuracy requirements. The correlation coefficient between the dynamic displacement of the verification point (8# measuring point) obtained after the inverse dynamic load positive analysis and the actual dynamic displacement is as high as 0.995, which proves the accuracy of the program.

[0097] Table 2 compares the correlation coefficients of different identification methods for dual random loads. Figure 14 Table 2 shows a comparison of the time history curves for load identification under noisy conditions under dual loads. As can be seen from the results in Table 2, when the noise level is 10%, the traditional generalized inverse method is affected by noise, with a correlation coefficient of less than 0.1 for dual loads. The correlation coefficients for dual loads identified by the L-curve method are only 0.52 and 0.32, and the correlation coefficients for the GCV method are also only 0.63 and 0.43, both below 0.8, making it difficult to meet the accuracy requirements of engineering projects. In contrast, the ICCA-GMRES method proposed in this invention has a minimum correlation coefficient of 0.89, and its identification accuracy is far superior to existing technologies.

[0098] Table 2 Time-domain identification results of dual random loads Note: In the table, 0.90 and 0.89 represent the correlation coefficients between load F1 and the original load, and between F2 and the original load, respectively. In summary, based on the results of single and multi-load time-domain identification, when the signal is subject to noise interference, the correlation coefficient of the proposed method is much higher than that of the generalized inverse, L-curve, and GCV methods. The identified response matches the original response well, and the correlation of the identification results of the proposed method is extremely strong. This verifies the limitations of the improved load time-domain identification method proposed in this patent and demonstrates the noise resistance, accuracy, and stability of the program.

[0099] Example 3: To verify the feasibility of the developed program on the prototype arc gate arm, the No. 4 arc gate arm with a relative opening of 25% and an upstream reservoir water level of 362.82m was selected as the case for load time domain identification.

[0100] Figure 15 Three equivalent inversion discharge load time history curves are presented, each with a duration of 20 seconds and a sampling time interval of 0.01 seconds, i.e., a sampling frequency of 100 Hz. Figure 15 It can be seen that the three dynamic vertical loads obtained through inversion exhibit obvious pulsating characteristics, which are quite similar to the pulsating loads of water flow, indicating that the inverted loads are mainly caused by the pulsating pressure of water flow. The root mean square of the pulsating loads of the upper, middle, and lower supports obtained through inversion are 0.551 × 10⁻⁶, respectively. 4 N, 0.779×10 4 N and 1.036×10 4 N, the intensity of the pulsating load on the lower outrigger is 1.88 times that of the upper outrigger. Therefore, the pulsating load on the lower outrigger is stronger than that on the middle outrigger, and the upper outrigger is the weakest. The peak value of the pulsating load also shows this pattern.

[0101] After substituting the pulsating load obtained from the inverse analysis into the modal superposition method forward analysis program, the dynamic displacement of the measured point obtained from the forward analysis and the actual dynamic displacement of the measured point are compared. Figure 16 Among them, the correlation coefficients of measuring points 1, 2, and 4 are all higher than 0.8, indicating extremely high correlation. However, the correlation coefficient of measuring point 3 on the middle arm is 0.759, which is slightly lower than the other measuring points. The reason for this is that this measuring point is located at the end of the arm. On the one hand, this point is far from the excitation point, resulting in a large attenuation in power transmission; on the other hand, this point is close to the main hinge system. The connection between the movable hinge and the fixed hinge through the hinge shaft is difficult to distinguish from the rigid connection assumed by the finite element method. However, the correlation coefficient of this point is still higher than 0.7, which belongs to the category of strong correlation.

[0102] Figure 17 The diagram shows the comparison between the dynamic displacement of measurement point 5 obtained by inversion and the measured dynamic displacement. Unlike measurement point 3, the dynamic displacement information of this point has not yet been input into the load identification inverse problem model as a known condition. The correlation coefficient between the dynamic displacement obtained by inversion and forward analysis and the measured dynamic displacement is 0.882, which belongs to the level of extremely strong correlation, further verifying the accuracy of the load inversion results in this case.

[0103] This invention proposes for the first time a method for identifying the load on the support arm of an arc gate, solving the difficulty of existing technologies in directly measuring pulsating loads or solving for the pulsating load S based on dynamic response variables. Moreover, compared with traditional load time-domain identification methods, the proposed load time-domain identification method improves the accuracy of regularization parameter selection by introducing the ICCA combined with the GMRES algorithm, reduces noise interference to a certain extent, and greatly improves the load identification accuracy. It has broad application prospects in the field of flow-induced vibration monitoring of arc gates.

Claims

1. An improved regularized method for time-domain identification of pulsating loads on the support arm of an arc gate, characterized in that, Includes the following steps: S1. Collect the vibration signal of the partial discharge vibration of the arc-shaped working gate arm under the excitation of flood discharge, and use CEEMDAN combined with wavelet threshold noise reduction to denoise the collected vibration signal. S2. Construct a three-dimensional finite element mathematical model of the arc-shaped gate arm and perform modal calculations to obtain the natural frequencies and mode shape vectors of each order, and use these to calculate the unit impulse response function matrix; S3. The displacement response of the arc gate arm under discharge excitation is obtained by Duhamel integral, and an inverse analysis mathematical model is constructed between the displacement response matrix, the unit impulse response and the pulsating load. S4. Solve the inverse analysis mathematical model using the Tikhonov regularization algorithm, obtain the regularization parameters using the ICAA regularization selection method, and modify the inverse analysis mathematical model to obtain the modified inverse analysis mathematical model. S5. Using the noise-reduced vibration displacement response from S1 as input, the GMRES algorithm is used to iteratively solve the modified back-analysis mathematical model to obtain the water flow pulsation load acting on the arc-shaped gate arm.

2. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 1, characterized in that, S1 includes: S11. Collect the vibration displacement signal of the arc-shaped working gate arm under the flood discharge excitation as the original signal, and decompose the original signal using the CEEMDAN algorithm to obtain several intrinsic mode function components and residuals. S12. Calculate the multi-scale permutation entropy for each intrinsic mode function component. If the multi-scale permutation entropy is higher than 0.6, it is considered to contain high-frequency noise components. If the multi-scale permutation entropy is lower than 0.6, it is considered to be a pure component. S13. Denoising is performed on components with multi-scale arrangement entropy between 0.6 and 0.7 using an improved wavelet threshold function; S14. The reconstructed dynamic displacement signal is obtained by superimposing the denoised signal components and the intrinsic mode function components with multi-scale arrangement entropy less than 0.

6.

3. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 2, characterized in that, The improved wavelet threshold function is specifically expressed as follows: ； In the formula, Let λ represent the improved wavelet threshold function, where λ represents the threshold.

4. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 1, characterized in that, S2 specifically includes: S21. Establish a three-dimensional finite element mathematical model of the arc gate arm based on modeling software, focusing on preserving the geometric features of the arm connection system and using solid elements for modeling. S22. Based on the three-dimensional finite element mathematical model, mesh preprocessing is performed using finite element mesh generation software. Then, the structure of the support arm is meshed according to the surface element mesh function, and corresponding material properties, thickness properties, and element properties are assigned. S23. Check the quality of the mesh elements and apply boundary conditions. Add concentrated mass elements to each front plate of the gate arm to simulate the influence of the additional mass generated by the panel and beam structure. At the same time, use rigid elements to couple all degrees of freedom of all nodes on each front plate with the corresponding additional mass element points. S24. Based on the three-dimensional finite element mathematical model of the arc-shaped gate arm, perform modal analysis and output the mass matrix and stiffness matrix of the gate arm; S25. Based on the mass matrix and stiffness matrix, the first N natural frequencies and mode shapes of the gate arm are calculated using the modal superposition method through calculation software to obtain the vector of the first N natural frequencies and mode shapes. S26. Based on the solution of the mode shape vectors, the first N order mode shape vectors are regularized to calculate the generalized mass, generalized stiffness and generalized damping matrix. S27. Based on the regularized mode shape, select the mode shape vector at the excitation point and the mode shape vector at the response point, and use them to form the mode shape matrix at the excitation point and the mode shape matrix at the response point, thereby constructing the unit impulse response.

5. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 4, characterized in that, The mesh preprocessing includes mid-surface extraction, hybrid mesh generation, and contact processing.

6. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 1, characterized in that, S3 includes the following steps: S31. Structural dynamics equations of a multi-degree-of-freedom system based on a gate: Based on the principle of orthogonal mode shapes, obtain the dynamic displacement of the gate arm at any time and decouple it into equations in modal coordinates. S32. Construct expressions for the influence of displacement and velocity on the initial moment of the multi-degree-of-freedom system of the gate. Based on the equations in the modal coordinates, derive the zero-input response expression and the zero-state response expression of the modal displacement, respectively. S33. Substitute the zero-input response expression and the zero-state response expression of the modal displacement into the equation under the modal coordinates to obtain the system displacement; S34. Based on the system displacement and the dynamic displacement response calculated according to the Duhamel integral, the impulse response function is obtained; S35. Assemble the impulse response functions of each response point to a single-point excitation to obtain the corresponding unit impulse response function matrix. Concatenate the displacement vectors of each response point by row or column to obtain the displacement response matrix. S36. After discretizing the pulsating load in the time domain, the linear equations under single-point excitation are obtained by combining the unit impulse response function matrix and the displacement response matrix. S37. Based on the actual situation, the linear expression of the multivariate pulsating load is obtained according to the principle of superposition of linear systems, and then the inverse analysis mathematical model is obtained.

7. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 6, characterized in that, The dynamic displacement of the gate arm at any given time is specifically expressed as follows: ； In the formula, The modal shape matrix, y(t) is the displacement vector in modal coordinates; i represents the modal order; t represents time; n represents the number of modes of the reconstructed displacement y(t).

8. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 6, characterized in that, The equation in modal coordinates is specifically expressed as follows: ； In the formula, , , Let x, y, y be the acceleration, velocity, and displacement of the i-th order in modal coordinates, respectively. , Let be the modal mass and modal load of the i-th order, respectively; Let i be the modal damping ratio at the i-th order. Indicates the natural frequency.

9. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 6, characterized in that, The zero-input response expression for the modal displacement is: ； The zero-state response expression for the modal displacement is: ； In the formula, It is the damped vibration frequency. , The initial displacement and initial velocity are in modal coordinates. Indicates a time delay.

10. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 6, characterized in that, The expression for the impulse response function is: ； In the formula, It is an impulse response function; It is the normalized mode shape vector of the i-th mode; It is the mode vector The transpose of .

11. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 6, characterized in that, The linear expression for the multi-element pulsating load is: In the formula, K is the number of excitations to be identified; J is the number of dynamic displacement response points; Y J The discrete displacement response at the position with degree of freedom i at the measuring point; S K It is the discrete fluctuating load vector at the load point with degree of freedom j; G JK This represents the impulse response function matrix at the Kth measurement point when a unit impulse is applied at the Jth excitation point; The inverse analysis mathematical model is as follows: ； In the formula, It is the response matrix; It is the unit impulse response function; It is the water flow pulsation load matrix.

12. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 1, characterized in that, S4 specifically includes: S41. Based on the aforementioned inverse analysis mathematical model, define the inverse problem and construct the objective function of Tikhonov regularization, and introduce positive regularization parameters; S42. Transform the objective function of Tikhonov regularization into a regularization equation, calculate the expression of the Tikhonov regularization solution, and optimize the regularization parameters using the ICCA method. When the error is iterated to the minimum value, the regularization parameters are obtained. S43. By defining the initial value of regularization and the generalized inverse, a regularization pre-optimization process is constructed based on this. Assuming that the correction factor is known, the deviation function is constructed by combining the deviation expression between the calculated response and the measured response, and the response deviation is calculated. S44. Solve for the minimum value of the deviation function and derive the expression for the correction factor; S45. Substitute the expression of the correction factor into the pre-optimization process formula to obtain the modified back-analysis mathematical model.

13. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 12, characterized in that, The correction factor is specifically expressed as follows: ； In the formula, It is the generalized inverse of Tikhonov regularization; It is response bias; represents the identity matrix; T represents the transpose of the matrix.

14. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 12, characterized in that, The modified inverse analysis mathematical model is specifically expressed as follows: ； In the formula, It is the transpose of the unit pulsating response function G; This is the regularization parameter.

15. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 1, characterized in that, In S5, the GMRES algorithm is used for iterative solution as follows: Sa, set the initial solution and calculate the residual, and generate the orthogonal basis matrix and the upper Hessenberg matrix through the Arnoldi process; Sb, construct the Krylov subspace; Sc. Solve for the optimal coefficients in the subspace using a least squares problem and update the approximate solution; Sd, check if the residual meets the accuracy requirements. If it does not converge, restart the iteration and repeat the above process until the termination condition is met, and derive the expression for the water flow pulsation load.

16. The improved regularized time-domain identification method for pulsating loads on the support arm of an arc gate according to claim 15, characterized in that, The specific representation of the water flow pulsation load is as follows: ； In the formula, This represents the initial approximate solution vector of the fluctuating load during the iterative solution process of the GMRES algorithm. It is the solution vector of minimizing the subproblem. It is a Lanczos matrix.

Images