A method for identifying impact load of a plate structure based on improved elastic-net hybrid regularization

Abstract

The application discloses a kind of based on improved Elastic-net's hybrid regularization's panel structure impact load identification method, belong to impact load identification technical field.Step 1: obtain calibration system transfer matrix and measured response containing noise y noise ;Step 2: construct the improved Elastic-net identification model of introducing time weighting sparse term;Step 3: solve the improved Elastic-net identification model of step 2 using iterative shrinkage threshold algorithm ISTA;Step 4: based on system frequency response function, construct physical drive frequency domain weighted generalized cross-validation criterion to select regularization parameter, realize more in line with the impact load reconstruction result of physical mechanism.The present application is aimed at the ill-conditioned, instability and pre-ringing problem in the panel structure impact load identification.

Description

Technical Field

[0001] This invention belongs to the field of impact load identification technology, specifically relating to an impact load identification method for plate frame structures based on improved Elastic-net hybrid regularization. Background Technology

[0002] Ships encounter complex and diverse loads during operation, with impact loads being a typical form, such as cargo impacts, ice drop loads, and carrier-based aircraft landings. Information related to these impacts directly affects the safety and fatigue life of the structural frame. Related assessment techniques involve structural health monitoring, structural reliability analysis and design, and fatigue life prediction. In practical engineering, direct measurement is often impossible due to the unpredictable impact location; therefore, indirect measurement methods based on sensor responses are frequently employed. Impact load identification is essentially a typical ill-conditioned inverse problem: it requires inversely deducing information about the unknown excitation source from the response signals (such as acceleration and strain) at a limited number of measurement points on the structural surface. Due to measurement noise, model errors, and the ill-posedness of the system transfer function, this problem typically suffers from non-uniqueness and instability of solutions. Traditional dynamic load identification methods are primarily based on physical models and incorporate various algorithms and techniques, such as the conjugate gradient method, basis function expansion method, and regularization techniques, with regularization techniques being the most widely used.

[0003] While traditional regularization methods can alleviate ill-conditioning to some extent, they often struggle to balance sparsity and stability when dealing with multi-source impact scenarios or high-dimensional sparse excitations, leading to limited recognition accuracy. In recent years, with the development of computational techniques, many scholars have begun to focus on sparse regularization techniques. Chen decomposed the impact time domain based on envelope energy gradient characteristics, established a dimensionless evaluation index, and proposed a residual amplitude estimation method for decomposing multi-source impact signals. Lin proposed an improved Bayesian regularization algorithm based on a multi-sensor measurement system to solve the regularization problem of multi-source / continuous influence loads, avoiding ill-conditioning caused by direct inversion during regularization through Wavelet and Cholesky decomposition. Li, based on a structured Bayesian framework, introduced extended impulse and layer priors, introducing joint sparsity to reduce the dimensionality of the solution space, enabling accurate identification of complex spatiotemporally coupled distributed loads even under significant noise conditions. Liu directly introduced a Sparse Bayesian Wide Learning (SBBL) model and then introduced an adaptive input feature selection procedure, improving the computational efficiency and robustness of waveform curves. Wang proposed an improved fractional-order Tikhonov method that modifies singular values ​​by varying their magnitudes, and demonstrated its effectiveness through numerical and experimental results on a ship deck model.

[0004] Sparse regularization techniques can help us identify time-dependent external forces using function expansion methods, with L1 norm regularization being the most common. Lasso (L1 regularization) is widely used in load identification due to its inherent sparsity-enhancing ability; however, Lasso is prone to selection bias when variables are highly correlated (e.g., strong coupling between adjacent sensor responses) and is insufficient in suppressing non-sparse components. While Ridge (L2 regularization) effectively handles collinearity problems and improves solution stability, it cannot induce sparse solutions. Therefore, Zou and Hastie proposed the Elastic-Net regularization method in 2005, which enhances the model's generalization ability while maintaining sparsity by linearly combining L1 and L2 norms. Xing proposed an elastic network regularization method combined with a correlation coefficient model for time series prediction, transforming the optimization problem into an adaptive Lasso model, and the results showed that it performed well in prediction. Liu used fractional elastic network regularization for force identification, and the method retained the characteristics of fractional Tikhonov and fractional L1-norm regularization. On this basis, he proposed a strategy to determine the weights of different regularization parameters, achieving high-precision identification of various types of forces. Luo proposed a novel SDD method based on an improved modal shape sensitivity equation and elastic network regularization, and developed an adaptive strategy to determine the value of the regularization parameter in the iteration process. The identification results showed that the proposed method can effectively identify forces and has high identification accuracy under the influence of noise. Chen proposed a two-dimensional elastic network regularization method and embedded a hybrid penalty term L1+L2 directly applied to the correlation target for underwater sonar image analysis, which improved robustness and suppressed overfitting. Shi uses L1 / 2 regularization and shape functions to identify impact loads on ship reinforcement structures. The shape function method improves the identification accuracy, outperforming the traditional Green kernel function. Furthermore, the L1 / 2 norm provides sparser solutions than the L1 norm and has better noise resistance than the L2 norm.

[0005] Furthermore, the use of data-driven concepts in inversion calculations is becoming increasingly practical. Shi proposed a data-driven regression method to identify impact loads, and the results showed that the reconstructed impact loads were in good agreement with the experimental measurements. Kang developed a neural network architecture combining physical models and data to predict assembly deformation errors, and verified the effectiveness of the proposed MPDS-NN model through a case study of a high-pressure compressor rotor system. An proposed a Physically Augmented Deep Learning (PADL) framework for structural dynamic load identification, using the Frequency Response Function (FRF) to invert loads, and proved the effectiveness of the proposed PADL framework in structural dynamic load identification through an LSTM network. Xin studied low-frequency load identification methods under high noise levels, proposing a weighted summation least squares method. The results showed that using a weight matrix to consider unequal noise levels significantly reduced the identification bias.

[0006] In summary, L1 norm regularization is difficult to distinguish between features caused by external forces and measurement noise. On the contrary, L2 regularization, represented by Tikhonov regularization and truncated singular value decomposition, cannot obtain sparse solutions, which leads to excessive smoothing of the curve. Therefore, hybrid regularization is needed to balance transient sparse peaks with global stability and smoothness.

[0007] To address the aforementioned issues, this invention conducts a systematic study on typical plate frame structures. It introduces a hybrid regularization approach in both the system calibration and impact load identification stages. Furthermore, in the identification stage, it integrates first-order differential smoothing constraints. This prioritizes mitigating the continuous oscillations in the curves caused by the amplification of the inversion solution in the high-frequency subspace and the lack of constraints on temporal smoothness and physical continuity, effectively suppressing high-frequency numerical oscillations and avoiding non-physical pseudo-ringing. This achieves synchronous and high-precision recovery of peak amplitude and temporal morphology. In addition, a time-weighted sparsity penalty mechanism is introduced to effectively suppress non-physical pre-ringing phenomena before impact, thereby achieving impact load reconstruction results that are more consistent with physical mechanisms. Summary of the Invention

[0008] This invention provides a hybrid regularization-based method for identifying impact loads on plate frame structures using an improved Elastic-net, addressing the ill-conditioning, instability, and ringing problems in impact load identification of plate frame structures.

[0009] This invention is achieved through the following technical solution: A method for identifying impact loads on plate frame structures based on improved Elastic-net hybrid regularization, the method comprising the following steps: Step 1: Obtain the transfer matrix of the calibration system and measured response with noise ynoise ; Step 2: Construct an improved Elastic-net recognition model that incorporates time-weighted sparse terms; Step 3: Solve the improved Elastic-net recognition model from Step 2 using the Iterative Shrink Thresholding Algorithm ISTA; Step 4: Based on the system frequency response function, construct a physical driving frequency domain weighted generalized cross-validation criterion and select regularization parameters to achieve impact load reconstruction results that are more in line with the physical mechanism.

[0010] Furthermore, step 1 specifically includes the following steps: Step 1.1: Apply known rated loads to the structure. f true Collect corresponding responses y obs Establish convolutional relationships; Step 1.2: Construct an improved Elastic-net hybrid regularization method network model; Step 1.3: Obtain the optimal impulse response Then, construct the system transfer matrix. Its form is a lower triangular Toeplitz structure, which completes the system calibration.

[0011] Furthermore, the convolutional relationship in step 1.1 is specifically as follows: (2) in, h For the system impulse response, the matrix H f Constructed by load; The network model in step 1.2 is specifically as follows: (4) Where D is the difference operator for the discrete first derivative. .

[0012] Furthermore, step 1.3 specifically involves constructing the system transfer matrix: (8) The matrix maintains the lower triangular Toeplitz structure, satisfying the system's causality, thus completing the system calibration.

[0013] Furthermore, step 2 specifically involves: (10) in, f i These are time-weighted coefficients, and the weights are defined as follows: (11) in t p This is an estimate of the initial time of the impact. f pre >1 is used to enhance the suppression effect before impact.

[0014] Furthermore, step 3 specifically involves, based on the forward-backward splitting concept, the ISTA iteration format is as follows: (15) in, , k For the number of iterations, For the descent gradient: (16) Proximal operators have an analytic form: (17) Under the above assumptions, the step size condition of ISTA is satisfied: (18) That is, its convergence criterion is: (19).

[0015] Furthermore, step 4 specifically involves defining a system frequency sensitivity function based on the system frequency response matrix H(ω): (25) in, G ( oh k H( represents the overall sensitivity of the system to this frequency component.) oh k ) for the system at frequency oh k Frequency response matrix at the location; when G ( oh k When the value is small, it indicates that the frequency component is significantly attenuated during structural transmission and is easily lost during inversion; conversely, it indicates that the frequency is in the high-sensitivity region of the structure. Based on this, a physical driving frequency domain weighting function is constructed. w ( oh k ): (26) in, This represents the system's maximum sensitivity, used for normalization. e To prevent small constants with singular values, For weighted adjustment index; whenG ( oh k When the value is small, the system is not sensitive to this frequency. w ( oh k Increasing the value of ) can enhance the weight of the frequency residual, forcing the inversion to retain the high-frequency information of the impact that is attenuated by the structure.

[0016] Furthermore, when G ( oh k When it is large, w ( oh k The value of ) approaches 1, which can avoid overfitting noise in the low-frequency region; Finally, frequency-domain weighted generalized cross-validation is defined as follows: (28) Finally, this weight is introduced into the WGCV framework, i.e., formula (28), to construct the physical driving frequency domain weighting criterion; the minimum value of WGCV corresponds to the optimal regularization parameter: (29).

[0017] A hybrid regularization-based impact load identification system for plate frame structures using improved Elastic-net is provided. The system employs the aforementioned hybrid regularization-based impact load identification method for plate frame structures using improved Elastic-net. The system includes: Calibration unit: Obtain the transfer matrix of the calibration system. and measured response with noise y noise ; Model building unit: Constructing an improved Elastic-net recognition model that incorporates time-weighted sparse terms; Model calculation unit: The improved Elastic-net recognition model constructed by the model building unit is solved using the iterative shrinking threshold algorithm ISTA. Regularization parameter selection unit: Based on the system frequency response function, a physical driving frequency domain weighted generalized cross-validation criterion is constructed to select regularization parameters, so as to achieve impact load reconstruction results that are more in line with physical mechanisms.

[0018] An impact load identification method for plate frame structures based on improved Elastic-net and hybrid regularization, as described above, is applied to the identification of impact loads encountered by ships during operation.

[0019] The beneficial effects of this invention are: This invention focuses on a systematic study of typical plate frame structures.

[0020] This invention proposes a unified modeling framework of "sparseness + continuity": L1 sparsity maintains peak accuracy; the differential smoothing operator D ensures waveform stability; time weighting effectively suppresses the ringing phenomenon of the original EN method; and finally, adaptive parameter selection is achieved through WGCV to ensure the accuracy of the overall understanding. This invention constructs a time-weighted sparsity penalty mechanism to effectively eliminate the pre-ringing phenomenon: Addressing the common "energy leakage" problem in inverse problem solving, a time-weighted coefficient is introduced to impose a stronger penalty on the region before the impact occurs. Results show that this strategy can significantly reduce the pre-ringing energy error (PEER) and the initial energy error (PEE), making the inverted load more consistent with the actual physical process.

[0021] This invention proposes a physically driven frequency-domain weighted WGCV parameter selection method: frequency sensitivity weights are constructed using the system's frequency response function to characterize the structure's "observability." This method can enhance the recovery of effective information in the mid-to-high frequencies while suppressing noise amplification, achieving adaptive optimal selection of regularization parameters, and improving overall inversion accuracy and stability.

[0022] The parameter sensitivity analysis of this invention reveals the optimal working range of the method: through a systematic analysis of λ1, λ2, time weighting coefficient φpre and frequency domain weighting parameter γ, the influence of each parameter on sparsity, smoothness and spectral compensation capability is clarified, and a recommended value range with engineering practical value is given, which improves the operability and practicality of the method.

[0023] Numerical and experimental results of this invention verify the effectiveness and robustness of the method: Under a typical plate frame structure model, compared with TSVD and the traditional Elastic-net method, IENHR shows superior performance in terms of peak error (PRE), correlation (PCC), and impulse energy (IIE). Furthermore, under different signal-to-noise ratio conditions, this method maintains high peak identification accuracy and waveform stability, demonstrating good noise resistance. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the inversion calculation process of the present invention.

[0025] Figure 2 This is a diagram of the pre-looping phenomenon in traditional elastic network inversion.

[0026] Figure 3 This is a schematic diagram simulating load impact.

[0027] Figure 4 This is a schematic diagram of the corresponding results under different A1 and A2 values ​​of the present invention, wherein... Figure 4 (a) Schematic diagram of the impact of corresponding PRE results under different A1 and A2 values. Figure 4(b) Schematic diagram of PCC results under different A1 and A2 values. Figure 4 (c) Schematic diagram of the impact of IIE related results under different A1 and A2 values.

[0028] Figure 5 This is a schematic diagram of PEER and PEE values ​​under different λ values ​​according to the present invention.

[0029] Figure 6 This is a schematic diagram of PRE, PCC, IIE and HFER values ​​corresponding to different y values ​​of the present invention.

[0030] Figure 7 This is a schematic diagram of the load reversal curves corresponding to different y values ​​of the present invention.

[0031] Figure 8 This is a schematic diagram of the experimental model of the reinforced steel plate of the present invention.

[0032] Figure 9 This is a schematic diagram comparing the inversion results of different methods of the present invention.

[0033] Figure 10 This is a schematic diagram illustrating the accuracy of the present invention at different signal-to-noise ratio levels.

[0034] Figure 11 is a schematic diagram comparing the inversion results under different signal-to-noise ratios of the present invention, wherein (a) PRE (power level error) under different signal-to-noise ratio levels, (b) PCC (Pearson correlation coefficient) under different signal-to-noise ratio levels, and (c) IIE charts under different signal-to-noise ratio levels. Detailed Implementation

[0035] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0036] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0037] It should also be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0038] The following is in conjunction with the appendix to this application specification. Figure 1-1 1. The technical solutions in the embodiments of this application are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0039] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0040] Implementation Method 1 This embodiment provides a method for identifying impact loads on plate frame structures based on improved Elastic-net hybrid regularization. The identification method includes the following steps: Step 1: Obtain the transfer matrix of the calibration system and measured response with noise y noise ; Step 2: Construct an improved Elastic-net recognition model that incorporates time-weighted sparse terms; Step 3: Solve the improved Elastic-net recognition model from Step 2 using the Iterative Shrink Thresholding Algorithm ISTA; Step 4: Construct a physical drive frequency domain weighted generalized cross-validation (PF-WGCV) criterion based on the system frequency response function to select regularization parameters and achieve impact load reconstruction results that are more in line with the physical mechanism.

[0041] Further detailed explanation is as follows: Overall problem modeling: The structural system satisfies a linear convolution relationship in the discrete-time domain: (1) in: To measure the response, For impact load, For the transfer matrix, e For measuring noise.

[0042] Since the frequency response of a structural system typically exhibits rapid decay characteristics, the matrix H is often highly ill-conditioned. Direct least-squares inversion will lead to severe noise amplification. Therefore, this problem is a typical ill-conditioned inverse problem, and a regularization strategy must be introduced.

[0043] Improved construction of Elastic-net hybrid regularization model: In practical engineering, it is impossible to directly obtain relevant information about the structural system, let alone directly know the spatiotemporal information of the load. Therefore, the system needs to be calibrated before identification, which requires two inversion calculations. For detailed procedures, see [link to detailed process]. Figure 1 .

[0044] System calibration: A known calibration load was applied in the experiment. f true Collect corresponding responses y obs Convolutional relationships can be established: (2) in, h For the system impulse response, the matrix H f Constructed by load (3) The matrix has a lower triangular Toeplitz structure, satisfying the causality requirement. This model transforms the system calibration problem into a linear inverse problem.

[0045] To obtain a stable and physically meaningful impulse response, the classic formula for Elastic-Net regularization is introduced: (4) in, For the estimated model parameter vector, l h For regularization parameters, Control two types of regularization weights. The L1 term is... The aim is to enhance sparsity and suppress non-physical oscillations at the tail of the impulse response; the L2 term is... The aim is to improve numerical stability and ensure a smooth decay of the response.

[0046] Equation (4) is the classic elastic network algorithm. This model avoids the spectral distortion caused by singular value hard truncation and significantly improves noise resistance and stability. However, since the elastic network model imposes the same penalty on all parameters, the parameter estimation has a large bias, that is, an adaptive elastic network model is needed.

[0047] Based on this, the present invention proposes an improved Elastic-net hybrid regularization method (IENHR) network model: (5) The difference operator D introduced here is: (6) Formula (5) enhances data fitting ability while retaining the original data terms: L1 term As a way to distinguish it from traditional Tikhonov regularization or TSVD methods, it enhances the sparsity of the solution. The L2 term... The term is a newly introduced difference operator in this paper. Its essence is the discrete first derivative, and the difference penalty is essentially... .Right now: (7) The core function of the differential operator D is to suppress high-frequency oscillations and force the continuity and smoothness of the solution. This allows formula (5) to achieve the peak value of the load curve maintained by the L1 term and the stable shape of the load curve maintained by the L2 term, thereby solving the problem of sawtooth oscillations and high-frequency numerical noise that are very easy to occur in the inversion of impact loads.

[0048] Obtain the optimal impulse response Then, construct the system transfer matrix. (8) The matrix maintains the lower triangular Toeplitz structure, satisfying the system's causality, thus completing the system calibration.

[0049] Load identification: To simultaneously ensure the sparsity of the impact load and the continuity of time, the hybrid regularized model of formula (4) above is continued to be used: (9) in y noise This is the measured response with noise.

[0050] The model essentially embodies a "sparse + continuous" physical prior, effectively solving the high-frequency oscillation problem in traditional Elastic-Net inversion. However, in the actual inversion process, the starting point of signal acquisition is not necessarily the starting point of the load waveform. Since solving the inverse problem is a global optimization process, the high energy of the impact peak... Figure 2 As shown.

[0051] To suppress this effect, this invention introduces time-weighted sparsity regularization in the identification stage, imposing a stronger penalty on the load before the impact occurs, with the aim of effectively eliminating spurious fluctuations before the wave crest: (10) in, f i These are time-weighted coefficients, and the weights are defined as follows: (11) in t p This is an estimate of the initial time of the impact. f pre >1 is used to enhance the suppression effect before impact.

[0052] Numerical solution of the Iterative Shrink Thresholding Algorithm (ISTA): The proposed improved Elastic-Net hybrid regularization model includes L 1-norm sparsity penalty term and L 2-norm smoothing term. Because L The 1-norm is not differentiable at the origin (non-smooth), making it difficult to directly apply traditional gradient-based optimization algorithms (such as steepest descent or Newton's method) because they require the objective function to be differentiable everywhere. Furthermore, to obtain physically plausible sparse solutions, numerical algorithms need to be able to handle non-smooth constraints.

[0053] ISTA (Iterative Shrinkage Thresholding Algorithm) is an optimization algorithm for solving the Lasso problem, and it is particularly suitable for scenarios such as sparse signal recovery, compressed sensing, and feature selection.

[0054] Consider the following typical sparse regularization optimization problem: (12) The original function is decomposed as follows, taking the recognition process as an example: (13) (14) Among them, F( f ) is a smooth convex function, G( f ) is a non-smooth convex function.

[0055] Based on the concept of forward-backward splitting (Proximal Gradient), the ISTA iteration format is as follows: (15) in, , k For the number of iterations, For the descent gradient: (16) The proximal operator (soft threshold) has an analytical form: (17) Under the above assumptions, the step size condition of ISTA is satisfied: (18) That is, its convergence criterion is: (19) ISTA can efficiently solve linear inverse problems with sparse constraints, but it usually requires iteration to obtain satisfactory sparse code. The key parameter in the algorithm, the iteration step size, needs to be manually set in advance; in this invention, the algorithm step size is set to 3000 steps.

[0056] Frequency domain weighted WGCV regularization parameters: Consider the general form of the regularized inversion problem, for a linear estimator: (20) Its influence matrix is ​​defined as follows: (twenty one) The standard GCV format is: (twenty two) In real-world problems, high-frequency noise is more severe, and impact information is concentrated in the high-frequency region. Therefore, a weighting matrix W is introduced: (twenty three) Where W is the time-aware weight. w i Let be the weight of the i-th sampling point. c is the weighting adjustment factor. trace is the trace of the matrix, representing the smoothing intensity. In formula (22), the numerator is the weighted prediction error, and the denominator is the model degrees of freedom.

[0057] The significance of W lies in assigning different weights to different time points or frequency points. w i Its significance can be referenced from two standards: the time domain and the frequency domain.

[0058] Time weights can be divided based on the impact zone and the background zone: if a certain moment belongs to the impact zone, let... w i = w s ( w s If the time is within the impact zone, then a small residual at that point is required for accurate peak reconstruction; if it belongs to the background zone, then... w i = w b ( w b If the background time is used, then a larger residual can be allowed, i.e., smoothing can be tolerated.

[0059] Frequency domain weights can be used to perform FFT analysis on signals and construct the frequency spectrum. The frequency domain characteristics of impact loads are: low frequencies cover the overall structural response, mid frequencies cover the dominant impact component, and high frequencies cover the peak edges and noise. The peak position is mainly determined by the mid-to-high frequencies; excessive high-frequency suppression will flatten the peak, while neglecting high frequencies will amplify the noise. A weighting function can be defined, its classic form being: (twenty four) in, c As a weighting adjustment factor, oh For the current frequency, oh max This is the highest frequency of the signal.

[0060] This method improves peak reconstruction capability by enhancing mid-to-high frequency weights while suppressing low-frequency overfitting, thus enhancing inversion accuracy to some extent. However, the weighting function relies entirely on the frequency position itself and does not consider the non-uniform transmission effect of structural dynamics on different frequency components, resulting in a lack of physical basis. Furthermore, it ignores structural filtering effects, making it difficult to distinguish between signal and noise.

[0061] This invention further introduces the system frequency response function (FRF) as the basis for weight construction, and proposes a physically driven frequency-domain weighted generalized cross-validation (PF-WGCV) method. Its core idea is that the weights are no longer determined solely by the frequency location, but by the system's "observability" at that frequency.

[0062] First, the system frequency sensitivity function is defined based on the system frequency response matrix H(ω): (25) in, G ( oh k H( represents the overall sensitivity of the system to this frequency component.) oh k ) for the system at frequency oh k The frequency response matrix at that location.

[0063] when G ( oh k When the value is small, it indicates that the frequency component is significantly attenuated during the structural transmission process and is easily lost during the inversion process; conversely, it indicates that the frequency is in the high-sensitivity region of the structure.

[0064] Based on this, a physical driving frequency domain weighting function is constructed. w ( oh k ): (26) in, This represents the system's maximum sensitivity, used for normalization. e To prevent small constants with singular values, This is the weighted adjustment index.

[0065] when G ( oh k When the value is small, the system is not sensitive to this frequency. w ( oh k Increasing the value of ) can enhance the weight of the frequency residual, forcing the inversion to retain the high-frequency information of the impact that is attenuated by the structure.

[0066] when G ( oh k When it is large, w ( oh k The value of ) approaches 1, which can avoid overfitting noise in the low-frequency region.

[0067] Perform a Fourier transform on the residual term in the original formula (22): (27) Among them, Fourier[ [] represents the Fourier transform. Its purpose is to transform the residuals to the frequency domain.

[0068] Finally, the frequency domain weighted generalized cross-validation (FW-WGCV) is defined as follows: (28) Compared to traditional GCV, its molecular transformation is a frequency-domain weighted residual energy.

[0069] Finally, this weight is incorporated into the WGCV framework, i.e., formula (28), to construct the physical driving frequency domain weighting criterion. The minimum value of WGCV corresponds to the optimal regularization parameter: (29) Numerical simulation Relevant simulation information: To evaluate the IENHR proposed in this invention, a classic marine plate frame structure was used to assess the effectiveness of the inversion method. For example... Figure 3 As shown, the dimensions of the plate frame structure are l × w × h =1.2m×1.0m×0.01m, with two horizontal and two vertical T-shaped reinforcing ribs arranged under the main board. The dimensions of the horizontal ribs are... b f × t f × b w×h =20mm×4mm×4mm×40mm, the dimensions of the vertical member are... b f × t f × b w ×h =10mm×3mm×3mm×20mm. The elastic modulus of the steel is 206 GPa, and the density is 7850 kg / m³. 3 .

[0070] An external force F is set, with the impact load location randomized, and the signal curve references a sinusoidal curve of the impact load. A sensor is placed at the center of the plate, outputting an acceleration signal as the response yobs.

[0071] The time history curve will be inverted using the aforementioned simulation data. The regularization parameters λ1 and λ2, the pre-peak time weighting φi, and the WGCV frequency domain weighting adjustment factor γ in the IENHR method will be discussed.

[0072] Regularization parameters l 1 and l 2. Discussion: Formula (9) is a mixed regularization model. The L1 and L2 terms of the formula affect the sparsity and smoothness of the curve. The regularization parameter... l 1 and l The choice of option 2 is crucial. (The text continues...) l The choice of 2 is based on the existing calculation formulas in WGCV. l The choice of option 2 is based on experience. The range is... Generally speaking, based on the objective function formula (2), the empirical formula for calculating its value range is as follows: (30) Since we need to discuss a scenario involving impact loads and a noise background, the noise is approximated as Gaussian white noise with a standard deviation of [value missing]. s In this case, l The value of 1 is: (31) Where N is the dimension of the unknown.

[0073] Ensure noisy conditions during calculation l The calculated value of 1 should be kept within the range of formula (30).

[0074] To better evaluate regularization parameters l The performance under the IENHR method. We discard the aforementioned... l 1 and l The calculation formula for 2 is set. l1 and l The range of values ​​for 2 is

[10] . -7 10 -0.1 To objectively evaluate the accuracy of load identification, the following evaluation criteria are defined: The Peak Relative Error (PRE) is defined to primarily assess the difference between the peak value of the impact curve and the true load curve. (32) Where, max( f () represents the peak of the sinusoidal part of the curve.

[0075] Define the Pearson correlation coefficient (PCC) to describe the degree of linear correlation between curves: (33) in, and These represent the values ​​of the actual load and the inverted load curves at time i, respectively. This represents the mean of each curve.

[0076] The impact area error (IIE) is defined to evaluate the difference in impulse or energy (force-time integral) between sinusoidal portions of curves: (34) set up l 1 and l The reference line for 2, obtained from formula (31) and the value calculated by GCV without considering the weight matrix W, is (2.512e-03, 5.386e-02). Figure 4 The center is highlighted with a red dot.

[0077] Depend on Figure 4 It can be seen that the above method calculates... l 1 and l 2. It maintains high accuracy and exhibits a relatively clear "optimal region" or "optimal peak," within which PRE is at its maximum, PCC is at its maximum, and IIE is also at a high level. This indicates the existence of a robust parameter combination range, and the red dot is very close to the optimal region for each evaluation metric.

[0078] Further targeting l 1 and l 2. Perform separate analysis: l 1. Main control over the sparsity of solutions: when l When the value is too small, the model's noise suppression is insufficient, resulting in a large number of spurious non-zero elements (high-frequency oscillations) in the solution. This severely reduces PCC and IIE, meaning poor correlation and distorted integral energy. l When the value is too large, the model will over-penalize non-zero elements, causing the true impact peak to be over-compressed or even lost, thus significantly increasing PRE (large peak error).

[0079] l 2. The main control factors are the smoothness and stability of the solution. When l When the value is too small (2), the model cannot effectively suppress high-frequency numerical oscillations, resulting in an uneven waveform and affecting PCC and IIE. l When the value is too large, the model will become overly smoothed, which will flatten the transient characteristics of the impact load and also lead to an increase in PRE.

[0080] Pre-peak time weighting coefficient f pre discuss: The high energy at the peak of the elastic network method passes through Forward "leakage" causes a pre-ringing phenomenon before the peak arrives. As described in formulas (10) and (11): To suppress this effect, the present invention introduces time-weighted sparsity regularization in the identification stage, applies a stronger penalty to the load before the impact occurs, and sets a time-weighting coefficient. f i .

[0081] For evaluation f i The penalty effect is defined as the ratio of energy in the short time window before the transient to the energy in the main transient window, known as the energy leakage ratio PEER (Pre-echoEnergy Ratio). (35) The numerator, the pre-ringing window, calculates the inverted load energy before the impact. Ideally, this energy should be zero. Any non-zero value represents "energy leakage" caused by the ill-conditioning of the inversion algorithm. The denominator, the main impact window, calculates the inverted load energy during the main impact event, representing the main effective energy of the signal.

[0082] Simultaneously, the Pre-energy Error (PEE) is defined to measure the non-physical energy appearing in the inversion results before the impact occurs, essentially reflecting the pre-ringing intensity: (36) In response to different l Use a value of 1 for comparison.

[0083] Depend on Figure 5 It can be seen that, lThere exists a minimum value for PEER and PEE before the value of 1 is [0.1, 0.15]. Prove this. l 1. Within this range, the ringing phenomenon can be suppressed to the greatest extent. And as mentioned in the previous section, l The optimal value for 1 is 2.512e-03.

[0084] Then, from formula (11), the time weighting coefficient f pre The approximate range of values ​​is: (37) in, l min for Figure 5 The corresponding minimum value, l 1 is the optimal value.

[0085] From (37) f pre The value range is [40, 60]. In the experiment... f pre The median value is 50.

[0086] Discussion of WGCV frequency domain weights From the above formula, it can be seen that, c This is the weight adjustment index in the physical drive frequency domain weighting function, which determines the intensity of the influence of the system frequency sensitivity on the WGCV weight distribution. c The magnitude of the value directly determines the degree of preservation of different frequency components during the inversion process, thus affecting the peak reconstruction capability, noise immunity, and waveform stability of the impact load. Therefore, it is necessary to... c A systematic discussion was held.

[0087] For analysis c Regarding the impact on inversion performance, the evaluation system remains the same, using PRE, PCC, and IIE as evaluation criteria. Additionally, to characterize the impact of frequency domain modulation on high-frequency noise suppression capability, the following definition is added: High-Frequency Energy Ratio (HFER). (38) Among them, the high frequency region This refers to the portion of the total frequency band from 30% to 100%. A higher HFER indicates more severe high-frequency noise.

[0088] The optimal parameters obtained by fixing: l 1 = 2.512e-03, l 2 = 5.386e-02, f pre =50. Setting Scanning calculations were performed with a step size of 0.1 to obtain PRE, PCC, IIE, and HFER. c See the change curve. Figure 6 .

[0089] Depend on Figure 6 The following patterns can be observed: c When the value is small (γ<0.5), the peak value of the inversion curve is weakened, PRE decreases significantly, PCC and IIE decrease synchronously, and HFER remains at the lowest level; c Located in the middle range ( c When the P-value is approximately 0.8–1.5, PRE, PCC, and IIE reach their maximum peak values, while HFER remains at a relatively low level. c When too large ( c >2), PRE and PCC decreased simultaneously, IIE decreased the most severely, and HFER increased, meaning that the high-frequency weights were excessively amplified.

[0090] The above differences c The corresponding load inversion curves are compared with the actual loads; for details, please refer to [reference needed]. Figure 7 .

[0091] Therefore, we can conclude that when γ is too small, the frequency domain weights have little impact, but insufficient recovery of high-frequency information leads to peak loss. When γ is in the medium range [0.8, 1.5], the weakly sensitive frequencies of the system are moderately enhanced, high-frequency noise is not excessively amplified, and peak and waveform recovery is optimal; at this point, the model is in an optimal spectral balance state. When γ is too large, the high-frequency weights are significantly over-amplified, the peak value drops significantly, the curve exhibits severe sawtooth oscillations, and the significant enhancement of high-frequency noise leads to inversion instability.

[0092] In summary, γ essentially adjusts the frequency compensation capability and the risk of noise amplification, while... Figure 6 It can be seen that γ has an optimal equilibrium interval: [0.8, 1.5], where the optimal values ​​for PCC and IIE are 0.9. And from... Figure 7 It can be seen that the curve reaches its most stable state when γ=0.9. In the experiment, γ=0.9 is chosen to ensure that the value achieves the best trade-off between peak recovery, noise immunity, and stability.

[0093] Compared to traditional frequency position weighting, the γ adjustment in this invention has physical driving characteristics, enabling adaptive compensation for structural frequency filtering effects, significantly improving the recovery capability of mid-to-high frequency impulse information, and avoiding low-frequency overfitting and high-frequency noise amplification. The PF-WGCV method of this invention achieves an adaptive balance between spectral physical compensation and noise suppression through γ.

[0094] To better integrate with real-world engineering problems, this paper addresses the regularization operators discussed above. l Time-weighted before peak fi and WGCV frequency domain weighting adjustment factor c Substitute the model into experiments for verification.

[0095] The experimental material was a marine steel stiffened plate with the following parameters: density 7850 kg / m³. 3 Young's modulus 2.06e11 Pa, Poisson's ratio 0.3, dimensions are l × w × h =2m × 1.2m × 0.005m. T-shaped profiles with 4 horizontal and 5 vertical sections are installed under the steel plate. Relevant dimensions: Horizontal T-shaped profiles b f × t f × b w ×h =10mm×3.2mm×3.2mm×20mm, vertical T-section is b f × t f × b w ×h =20mm×4mm×4mm×40mm. See attached model photos for details. Figure 8 .

[0096] The experiment used a hammer to apply external force. An accelerometer was installed on the underside of the plate. Data was transmitted back to the computer via a signal acquisition device to save and record the time history of the impact load application and related acceleration response data. Continuing the experimental setup from the previous chapter, the impact load was applied at random locations, and an accelerometer was placed at the center of the square enclosed by the T-shaped profile. The response at this location was used in the inversion calculation.

[0097] To compare the effectiveness of the method described in this invention, the TSVD method and the ordinary Elastic-net method (EN) are introduced for comparison. Compared to the IENHR method, TSVD does not include an L1 regularization term, while the ordinary Elastic-net method includes L1 and L2 regularization terms but without any parameters. Detailed comparison diagrams are shown below. Figure 9 .

[0098] Table 1. Results Reference Based on Evaluation Criteria

[0099] pass Figure 9As shown in Table 1, IENHR has significant advantages over TSVD and EN methods. The TSVD method is based on the traditional Tikhonov method combined with SVD and GCV regularization operators. Its essence is L2 regularization plus singular value truncation, which directly discards high-frequency singular values, resulting in a noticeably "overly smooth" curve and temporal diffusion of impact energy. While the traditional Elastic-net (EN) adds an L1 term to preserve sparse peaks, it suffers from high-frequency sawtooth oscillations. Furthermore, the method lacks explicit constraints on temporal continuity, leading to amplification of high-frequency noise during inversion.

[0100] As can be seen from the figure, compared with the TSVD method, IENHR has better accuracy at sinusoidal peaks, especially in suppressing ill-conditioned accumulation at the regularization tail, showing a significant advantage, particularly in IIE. Compared with the traditional EN method, it exhibits better stability, showing advantages in both PRE and PCC. Although the traditional EN method is numerically superior to IENHR in IIE, the curves show that IENHR has a better effect on suppressing oscillations.

[0101] In summary, the IENHR proposed in this invention significantly suppresses pre-ringing through time-weighted sparsity penalty. Furthermore, it suppresses high-frequency numerical oscillations and ensures temporal continuity through differential operators, achieving peak heights closest to the actual load with smooth, jagged waveforms. Finally, a physically driven frequency-domain weighted generalized cross-validation method accurately locates the [load]. l This enhances the mid-to-high frequency weights to improve peak reconstruction capability, while suppressing low-frequency overfitting.

[0102] As mentioned earlier, the simulation first applies a known calibration load. f true Collect corresponding responses y obs Construct the transfer matrix H f Then, the corresponding response was collected. y obs Add noise to obtain a noisy response. y noise Then the response y noise With transfer matrix H f Substitute them together into the calculation to obtain the final inversion load. f .

[0103] Here we introduce amplitude signal-to-noise ratio and define SNR. dB for: (39) The final synthesized signal is: (40) in, It is standard Gaussian white noise. It is random noise in a unit direction. Let L2 be the target noise.

[0104] Generally, the signal-to-noise ratio (SNR) test range for wireless communication has the following characteristics: 0-10dB simulates a strong noise environment, 10-20dB represents typical operating conditions, and 20-30dB indicates a high-quality channel. Setting the SNR... dB There are 6 control groups with dB values ​​of 5, 10, 15, 20, 25, and 30 dB. See the detailed comparison chart for reference. Figure 10 .

[0105] Depend on Figure 10 It can be seen that as the SNRdB decreases and the environment becomes noisier, the curve maintains a certain smoothness and continuity in the sinusoidal part, but tends to be highly oscillating elsewhere. Furthermore, at the peak, except for the 15dB control group, the others remain roughly at the same level, indicating that the method has good noise resistance at both the waveform and peak values.

[0106] To avoid data uniformity, in addition to the original simulation, 48 groups of sensors at different locations were randomly set up as control groups. PRE, PCC and IIE were still used as evaluation criteria. See Figure 11 for detailed comparison.

[0107] As shown in Figure 11, even in a strong noise environment, the PRE and PCC results maintain high accuracy, with PRE not lower than 81% and PCC not lower than 76%. The more serious issue is with IIE, which, while maintaining over 80% accuracy under typical operating conditions, exhibits persistent high oscillations under strong noise interference. Combining PRE and PCC, it can be concluded that the method of this invention has good noise resistance at the waveform and peak values, but is significantly affected in non-sinusoidal pulse segments.

[0108] In summary, while IENHR inherits the pronounced high-frequency oscillation characteristic of EN, its suppression effect in noisy environments is significantly weakened. However, it maintains high smoothness and temporal continuity in the half-sine pulse segment and preserves high peak accuracy, demonstrating that the method of this invention has good noise immunity.

[0109] This invention addresses the problems of strong ill-conditioning, solution instability, significant pre-ringing, and severe high-frequency oscillations in the impact load identification process of plate frame structures. It proposes a hybrid regularization method (IENHR) based on an improved Elastic-net, and systematically studies its effectiveness and superiority through numerical simulation and experimental verification. The main conclusions are as follows: (1) A unified modeling framework of "sparseness + continuity" is proposed: L1 sparsity is used to maintain peak accuracy. The differential smoothing operator D is used to ensure waveform stability. Time weighting is used to effectively suppress the ringing phenomenon of the original EN method. Finally, adaptive parameter selection is achieved through WGCV to ensure the accuracy of understanding the whole. (2) A time-weighted sparsity penalty mechanism was constructed to effectively eliminate the pre-ringing phenomenon: To address the common "energy leakage" problem in inverse problem solving, a time-weighted coefficient was introduced to impose a stronger penalty on the region before the impact. The results show that this strategy can significantly reduce the pre-ringing energy (PEER) and the pre-amplitude energy error (PEE), making the inverted load more consistent with the actual physical process.

[0110] (3) A physical-driven frequency-domain weighted WGCV parameter selection method is proposed: frequency sensitivity weights are constructed using the system frequency response function to characterize the "observability" of the structure. This method can enhance the recovery capability of effective information in the mid-to-high frequency range while suppressing noise amplification, achieving adaptive optimal selection of regularization parameters, and improving the overall inversion accuracy and stability.

[0111] (4) Parameter sensitivity analysis reveals the optimal working range of the method: Through systematic analysis of λ1, λ2, time weighting coefficient φpre and frequency domain weighting parameter γ, the influence of each parameter on sparsity, smoothness and spectrum compensation capability is clarified, and a recommended range of values ​​with engineering practical value is given, which improves the operability and practicality of the method.

[0112] (5) Numerical and experimental results verify the effectiveness and robustness of the method: Under a typical plate frame structure model, compared with TSVD and the traditional Elastic-net method, IENHR shows better performance in terms of peak error (PRE), correlation (PCC), and impulse energy (IIE). At the same time, under different signal-to-noise ratio conditions, the method can still maintain high peak identification accuracy and waveform stability, demonstrating good noise resistance.

[0113] In summary, the IENHR method proposed in this invention achieves an effective balance between peak accuracy, waveform stability and noise immunity in the problem of impact load identification, providing a solution with physical constraints and engineering application potential for load inversion of complex structures.

[0114] Implementation Method 2 This embodiment provides an impact load identification system for plate frame structures based on improved Elastic-net and hybrid regularization. The identification system uses the impact load identification method for plate frame structures based on improved Elastic-net and hybrid regularization as described in Embodiment 1. The identification system includes: Calibration unit: Obtain the transfer matrix of the calibration system. and measured response with noise y noise ; Model building unit: Constructing an improved Elastic-net recognition model that incorporates time-weighted sparse terms; Model calculation unit: The improved Elastic-net recognition model constructed by the model building unit is solved using the iterative shrinking threshold algorithm ISTA. Regularization parameter selection unit: Based on the system frequency response function, the physical drive frequency domain weighted generalized cross-validation (PF-WGCV) criterion is constructed to select regularization parameters, so as to achieve impact load reconstruction results that are more in line with the physical mechanism.

[0115] Implementation Method 3 This invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor. The memory stores software programs and modules, and the processor executes various functional applications and data processing by running the software programs and modules stored in the memory. The memory and processor are connected via a bus. Specifically, the processor implements any step in Embodiment 1 by running the computer program stored in the memory.

[0116] It should be understood that, in the embodiments of the present invention, the processor may be a Central Processing Unit (CPU), but it may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0117] Memory may include read-only memory, flash memory, and random access memory, and provides instructions and data to the processor. Some or all of the memory may also include non-volatile random access memory.

[0118] Implementation Method 4 This embodiment provides a method for identifying impact loads on plate frame structures based on improved Elastic-net hybrid regularization, as described in Embodiment 1. The method is applied to the identification of impact loads encountered by ships during operation.

Claims

1. A method for identifying impact loads on plate frame structures based on improved Elastic-net hybrid regularization, characterized in that, The identification method includes the following steps: Step 1: Obtain the transfer matrix of the calibration system and measured response with noise y noise ; Step 2: Construct an improved Elastic-net recognition model that incorporates time-weighted sparse terms; Step 3: Solve the improved Elastic-net recognition model from Step 2 using the Iterative Shrink Thresholding Algorithm ISTA; Step 4: Based on the system frequency response function, construct a physical driving frequency domain weighted generalized cross-validation criterion and select regularization parameters to achieve impact load reconstruction results that are more in line with the physical mechanism.

2. The method for identifying impact loads on plate frame structures according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1: Apply known rated loads to the structure. f true Collect corresponding responses y obs Establish convolutional relationships; Step 1.2: Construct an improved Elastic-net hybrid regularization method network model; Step 1.3: Obtain the optimal impulse response Then, construct the system transfer matrix. Its form is a lower triangular Toeplitz structure, which completes the system calibration.

3. The method for identifying impact loads on plate frame structures according to claim 2, characterized in that, The convolutional relationship in step 1.1 is specifically as follows: （2） in, h For the system impulse response, the matrix H f Constructed by load; The network model in step 1.2 is specifically as follows: （4） Where D is the difference operator for the discrete first derivative. .

4. The method for identifying impact loads on plate frame structures according to claim 3, characterized in that, Step 1.3 specifically involves constructing the system transfer matrix: （8） The matrix maintains the lower triangular Toeplitz structure, satisfying the system's causality, thus completing the system calibration.

5. The method for identifying impact loads on plate frame structures according to claim 2, characterized in that, Step 2 specifically involves, （10） in, φ i These are time-weighted coefficients, and the weights are defined as follows: （11） in t p This is an estimate of the initial time of the impact. φ pre >1 is used to enhance the suppression effect before impact.

6. The method for identifying impact loads on plate frame structures according to claim 1, characterized in that, Step 3 specifically involves the following: Based on the forward-backward splitting concept, the ISTA iteration format is as follows: （15） in, , k For the number of iterations, For the descent gradient: （16） Proximal operators have an analytic form: （17） Under the above assumptions, the step size condition of ISTA is satisfied: （18） That is, its convergence criterion is: （19）。 7. The method for identifying impact loads on plate frame structures according to claim 1, characterized in that, Step 4 specifically involves defining a system frequency sensitivity function based on the system frequency response matrix H(ω): （25） in, G ( ω k H( represents the overall sensitivity of the system to this frequency component.) ω k ) for the system at frequency ω k Frequency response matrix at the location; when G ( ω k When the value is small, it indicates that the frequency component is significantly attenuated during structural transmission and is easily lost during inversion; conversely, it indicates that the frequency is in the high-sensitivity region of the structure. Based on this, a physical driving frequency domain weighting function is constructed. w ( ω k ): （26） in, This represents the system's maximum sensitivity, used for normalization. ε To prevent small constants with singular values, For weighted adjustment index; when G ( ω k When the value is small, the system is not sensitive to this frequency. w ( ω k Increasing the value of ) can enhance the weight of the frequency residual, forcing the inversion to retain the high-frequency information of the impact that is attenuated by the structure.

8. The method for identifying impact loads on plate frame structures according to claim 7, characterized in that, when G ( ω k When it is large, w ( ω k The value of ) approaches 1, which can avoid overfitting noise in the low-frequency region; Finally, frequency-domain weighted generalized cross-validation is defined as follows: （28） Finally, this weight is introduced into the WGCV framework, i.e., formula (28), to construct the physical driving frequency domain weighting criterion; the minimum value of WGCV corresponds to the optimal regularization parameter: （29）。 9. A system for identifying impact loads on plate frame structures based on improved Elastic-net and hybrid regularization, characterized in that, The identification system uses the improved Elastic-net-based hybrid regularization method for identifying impact loads on plate frame structures as described in any one of claims 1-8, and the identification system includes: Calibration unit: Obtain the transfer matrix of the calibration system. and measured response with noise y noise ; Model building unit: Constructing an improved Elastic-net recognition model that incorporates time-weighted sparse terms; Model calculation unit: The improved Elastic-net recognition model constructed by the model building unit is solved using the iterative shrinking threshold algorithm ISTA. Regularization parameter selection unit: Based on the system frequency response function, a physical driving frequency domain weighted generalized cross-validation criterion is constructed to select regularization parameters, so as to achieve impact load reconstruction results that are more in line with physical mechanisms.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the impact load identification method as described in any one of claims 1-8.

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