Impact Force Identification Research Articles

A model-based deep learning approach to interpretable impact force localization and reconstruction

Model-based and deep learning-based methods have been widely studied for force identification. However, model-based methods usually have high computational complexity and face challenges in parameter setting, while the generic network structures in deep learning methods are mostly designed empirically. In this paper, a model-based deep learning network is proposed to simultaneously localize and reconstruct impact f[orces. The proposed network, dubbed NSC-Net, is obtained by unrolling the iterative shrinkage-thresholding algorithm (ISTA) for the non-negative sparse coding (NSC) model. NSC-Net combines the interpretability of the model-based ISTA with the powerful parameter learning capability of deep learning. The transfer matrix is embedded into the network as physical information through learnable scaling. The structure of NSC-Net is based on explicit theoretical analysis, which enhances its interpretability in terms of structural design. In contrast to ISTA, the parameters in NSC-Net can be trained end-to-end from the training data without manual setting. Simulations and experiments on composite panels are conducted to validate the performance of the proposed method. The results demonstrate that NSC-Net accurately localizes and reconstructs impact forces, outperforming both ISTA and learned iterative shrinkage-thresholding algorithm (LISTA) network. Additionally, NSC-Net exhibits excellent noise immunity. Furthermore, the systematic approach of constructing an algorithm unrolling network for impact force identification is summarized, aiming to facilitate further related research.

A fast impact force identification method via constructing a dynamic reduced dictionary

Impact force identification is an important aspect of structural health monitoring for online assessment of the integrity of engineering structures. Increasing the number of monitoring positions is undoubtedly beneficial to accurate force localization, however, it may increase sharply the dimension of the transfer matrix and thus lead to a large-scale inverse problem. In this case, traditional methods, such as the Iterative Shrinkage Threshold algorithm (IST) and the Two-Step Iterative Shrinkage Thresholding algorithm (TwIST), suffer from low solving efficiency. In this paper, the dynamic reduced dictionary is firstly introduced according to the sparsity of impact force in both time and spatial domains so as to lower significantly the dimension of the transfer matrix. Then, a new reduced unconstrained optimization problem is established via the dynamic reduced dictionary for impact force identification. By integrating the reduced unconstrained optimization problem into each iteration step of IST/TwIST, two novel algorithms, which are the reduced Newton iteration shrinkage threshold algorithm (rNIST) and the reduced Newton two-step iteration shrinkage threshold algorithm (rNTwIST), are proposed to solve quickly the large-scale impact force identification problem using ℓ1-norm sparse regularization. Meanwhile, the adaptive setting of regularization parameters strategy is used to construct force more fast and accurately. The proposed algorithms are numerically and experimentally demonstrated through identifying impact forces at 16-point and 81-point distributions of a plate using one sensor response. The results show that rNIST/rNTwIST can more quickly and accurately identify impact forces under numerous monitoring points compared with other ℓ1-norm regularization methods and nonconvex sparse regularization methods. Moreover, the more the number of monitoring points, the more obvious the efficiency improvement of the impact force identification by rNIST/rNTwIST method.

Research on the influence of impact damage on force identification for composite material

The invisible damage caused by low-velocity impacts are safety threats to engineering structures. Thus, impact force identification is crucial in the context of composite structures for both structure health monitoring (SHM) and composite structure design. This paper investigates the process of identifying impacts on composite structures subjected to low-velocity impact. Considering the damage evolution in the composite structure during impact, this paper explores the influence of impact damage on the accuracy of force identification. Impact experiments on carbon fiber reinforced polymer (CFRP) laminates were conducted to obtain impact force peaks and displacement responses. Furthermore, a validated finite element model (FEM) is established for more elaborate analysis on the mechanism. The findings reveal that the structural damage can lead to significant deviations in force identification if the damage is not considered. Finally, a neural network is employed to predict the force history taking impact damage into consideration. This research provides a reference for the composite structures design and health monitoring of engineering structures considering impact damage.

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice, simultaneous impact localization and time history reconstruction can hardly be achieved, due to the ill-posed and under-determined problems induced by the constrained and harsh measuring conditions. Although ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{1}$$\\end{document} regularization can be used to obtain sparse solutions, it tends to underestimate solution amplitudes as a biased estimator. To address this issue, a novel impact force identification method with ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization is proposed in this paper, using the alternating direction method of multipliers (ADMM). By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators, ADMM can address the challenge effectively. To mitigate the sensitivity to regularization parameters, an adaptive regularization parameter is derived based on the K-sparsity strategy. Then, an ADMM-based sparse regularization method is developed, which is capable of handling ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization with arbitrary p values using adaptively-updated parameters. The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure. Additionally, an investigation into the optimal p value for achieving high-accuracy solutions via ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization is conducted. It turns out that ℓ0.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{0.6}$$\\end{document} regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{1}$$\\end{document} regularization method. The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Impact force identification for composite structures using adaptive wavelet-regularised deconvolution

Impact force identification (IFI) through deconvolution methods from measured structural responses poses a challenge due to the ill-posed nature of the inversion problem. Regularisation techniques, such as Tikhonov, sparse, and wavelet regularisation, offer potential solutions to mitigate the ill-posedness. However, determining suitable regularisation parameters is time-consuming. This study presents an adaptive wavelet-regularised time-domain deconvolution method for efficient IFI, based on wavelet transform and multi-resolution analysis. By analysing impact sensor signals using wavelets, adaptive impact windows covering the entire impact duration are generated, reducing signal length for deconvolution. Multi-resolution analysis of sensor signals enables identification of wavelet bases for the multi-resolution representation of impact force history. Regularisation is achieved by filtering out insignificant wavelet bases based on their energy contributions. Validation is performed through experiments involving small-mass hammer and large-mass drop tower impacts, comparing against various deconvolution methods. Results demonstrate the superior computational efficiency and comparable accuracy of the proposed adaptive method in IFI across different time windows. Notably, accurate force deconvolution for large-mass impacts confirms the effectiveness of the deconvolution methods for IFI, particularly when the structure undergoes significant local deformation.

Impact force identification on a ferry dock bridge

Impact force identification on a ferry dock bridge

An efficient impact force identification methodology via a single sensor utilizing the concept of generalized transmissibility

The issue of localizing and reconstructing the impact force through double-inverse approaches is widely recognized as an ill-posed and computationally demanding problem. Such a challenge has emerged as a prominent research topic of interest and great concern in the field of structural health monitoring. This study proposes a novel and efficient hierarchical methodology that is adept at ascertaining both the location and time history of an impact force through data obtained from a single accelerometer. The proposed methodology entails an efficient retrieval of uncorrected modal constants with a ratio function referred to as generalized transmissibility. The generalized transmissibility symbolizes the ratio of responses from identical accelerometer subjected to two distinct impacting scenarios, one excited at a yet-to-be-identified location and the other at a pre-determined reference location. The theoretical disclosure of the correlation between the generalized transmissibility at pole frequencies and retrieved uncorrected modal constants is demonstrated in details herein. These modal constants are then served as a signature to identify the impact location. Following localization, the force reconstruction problem is tackled by fitting a parametric model, wherein a gaussian basis function is employed to effectively approximate the time history of impact force. Experimental demonstrations on a metallic plate and a composite wing were carried out to validate the efficient and accurate localization as well as the rapid reconstruction capabilities in response to an impact force applied anywhere on a 2D structure.

Non-contact impact load identification based on intelligent visual sensing technology

Accurate identification of impact loads is vital for structural assessment and design. Traditional methods rely on complex equipment, such as accelerometers or strain gauge, which can be expensive and prone to failure. This study introduces a non-contact intelligent identification approach incorporating visual sensing technology, providing a convenient means to identify impact loads. Numerical simulations explore the differences in identifying impact forces through acceleration and displacement responses, particularly by considering such variables as measurement noise and number of measurement points. A meticulously designed experiment verified the feasibility of the proposed method for measuring the displacement and velocity of rapidly moving targets, and evaluated its performance in terms of accuracy. A series of impact loading experiments were conducted on a simply supported girder bridge model to validate the effectiveness of the proposed impact force identification method. Results indicate strong agreement between displacement response measurements and percentile meters. The proposed non-contact method accurately identifies single or continuous impact loads, with a minimum peak relative error of 0.2%. This study represents a pioneering application of intelligent visual sensing technology in the field of impact load identification. Moreover, the current research introduces a novel approach to address the challenges faced by conventional methods in identifying impact loads. Future research can leverage the groundwork laid by this study to further optimize and expand the proposed method, enhancing its capabilities and fully harnessing its potential to offer advanced solutions in structural health monitoring.

Impact force localization and reconstruction via gated temporal convolutional network

Techniques for identifying impact forces are crucial for improving the operational reliability and safety of aerospace composite structures. To address the challenges of theoretical modeling that arise from the complexity of composite structures, we propose a Gated Temporal Convolutional Network (GTCN) method. This method establishes inverse mapping relationships between structural vibration responses and impact forces. The GTCN increases the receptive field through dilated convolution, concurrently employing gating mechanisms to extract pivotal features from input signals in the vertical direction. Simulations and experiments are conducted to robustly validate the efficacy and applicability of the proposed impact force identification method. The simulation results demonstrate that the GTCN method is capable of obtaining robust impact force localization and reconstruction results, even amidst conditions of elevated noise levels. The average localization error of the GTCN is kept within 20 mm even at a noise level of 5 dB. Meanwhile, the GTCN method achieves satisfactory identification results for different types of impact forces (Gaussian, semi-cosine, and sawtooth), with an average localization accuracy above 95%. The applicability of the GTCN method to real-world structure is verified in the experiments. The average relative error of the reconstructed forces by GTCN is less than 15%. GTCN achieves stable identification of impact forces when the number of sensors is larger than 2. In both simulations and experiments, the GTCN performs better than Temporal Convolutional Network (TCN) and Convolutional Neural Network (CNN) with higher identification accuracy. The proposed method demonstrates considerable potential for application in the health monitoring of aircraft composite structures.

Iterative-Based Impact Force Identification on a Bridge Concrete Deck.

Steel-reinforced concrete decks are prominently utilized in various civil structures such as bridges and railways, where they are susceptible to unforeseen impact forces during their operational lifespan. The precise identification of the impact events holds a pivotal role in the robust health monitoring of these structures. However, direct measurement is not usually possible due to structural limitations that restrict arbitrary sensor placement. To address this challenge, inverse identification emerges as a plausible solution, albeit afflicted by the issue of ill-posedness. In tackling such ill-conditioned challenges, the iterative regularization technique known as the Landweber method proves valuable. This technique leads to a more reliable and accurate solution compared with traditional direct regularization methods and it is, additionally, more suitable for large-scale problems due to the alleviated computation burden. This paper employs the Landweber method to perform a comprehensive impact force identification encompassing impact localization and impact time-history reconstruction. The incorporation of a low-pass filter within the Landweber-based identification procedure is proposed to augment the reconstruction process. Moreover, a standardized reconstruction error metric is presented, offering a more effective means of accuracy assessment. A detailed discussion on sensor placement and the optimal number of regularization iterations is presented. To automatedly localize the impact force, a Gaussian profile is proposed, against which reconstructed impact forces are compared. The efficacy of the proposed techniques is illustrated by utilizing the experimental data acquired from a bridge concrete deck reinforced with a steel beam.

Robust Nonconvex Sparse Optimization for Impact Force Identification

The inherent sparse structure of impact forces has garnered considerable attention in the field of impact force identification. However, conventional convex sparse regularization methods, including the widely used [Formula: see text] regularization, often encounter challenges such as underestimation of impact amplitudes and biased estimations. To address these limitations, we propose a robust nonconvex sparse regularization method for impact force identification. The key advantage of our method is the simultaneous retention of robustness and unbiasedness. The robustness of our method is primarily achieved through an efficient solver developed within the alternating direction method of multipliers (ADMM) framework. By combining convex and nonconvex strategies, the ADMM solver separates the intractable nonconvex problem into more manageable convex sub-problems. Additionally, the ADMM solver incorporates the firm-thresholding operator, which ensures an unbiased amplitude distribution and preserves the impact amplitudes. With a sparse and under-determined sensor configuration, our proposed method enables simultaneous impact localization and time-history reconstruction. We comprehensively demonstrate the algorithmic performance through a series of numerical simulations and laboratory experiments on typical composite structures. The comparative results clearly indicate that our proposed approach achieves significant improvements in identification accuracy compared to classical sparse regularization methods, such as [Formula: see text] and [Formula: see text] regularization.

Accelerated generalized minimax-concave sparse regularization for impact force reconstruction and localization

Impact force identification has always been of significance for structure health monitoring especially on the applications involving composite materials. As a typical inverse problem, impact force reconstruction and localization is undoubtedly a challenging task. The well-known ℓ1 sparse regularization has a tendency to underestimate the amplitude of impact forces. To alleviate this limitation, we propose an accelerated generalized minimax-concave (AGMC) for sparse regularization that employs a non-convex generalized minimax-concave (GMC) penalty as the regularizer and incorporates an acceleration technique to expedite the attainment of the global minimum. Compared with the classic ℓ1-norm penalty, the GMC penalty can not only induce sparsity in the estimation, but also maintain the convexity of the cost function, so that the global optimal solution can be obtained through convex optimization algorithms. This method is applied to solve the impact force identification problem with unknown force locations to simultaneously reconstruct and localize impact forces in the under-determined case utilizing a limited number of sensors. Meanwhile, K-sparsity criterion is used to adaptively select regularization parameters by taking advantage of the sparse prior knowledge on impact forces. Simulations and experiments are conducted on a composite plate to verify the computational efficiency and robustness of the AGMC method in terms of impact force reconstruction and localization, particularly in the presence of noise. Results demonstrate that the proposed AGMC method achieves faster convergence and provides more accurate and sparse reconstruction and localization of impact forces compared to other state-of-the-art sparse regularization methods.

Simultaneous identification of impact force and structural local damage under pre-segmentation of structural elements

Identifying dynamic force and structural damage is often mathematically treated as an optimization problem. The number of optimization variables is closely related to the complexity and calculation amount of the identified problem. To reduce the number of optimization variables during the solution process and emphasize the localized characteristics of structural damage, a novel output-only method is proposed to address the problem of simultaneous identification under a pre-assumption of structural damage locations. The main idea is to decompose the identified problem into a series of subtasks. For each task, only part of a structure rather than the whole will be updated to reduce the discrepancy between the calculated responses and the measured ones. To realize this idea, the structure is simulated via a finite element (FE) model, and then the structural elements are divided into several groups. Each group is used to generate one identified task, in which the identified problem is formulated as a constrained optimization problem. Stiffness reduction coefficients of the elements, which are contained in the corresponding element group, are regarded as the optimization variables, while the impact force reconstructed via sparse regularization is mathematically formulated as a constraint for the optimization problem. The gradient descent method combined with a greedy strategy is introduced for solving the optimization problem of each task. The identified results obtained from all the tasks are regarded as candidates for a final one. To comprehensively consider the residual errors of structural responses and the sparsity of identified results, the Bayesian information criterion (BIC) is introduced for determining the final identified result. Numerical simulations and experimental studies are carried out. The illustrated results demonstrate that the proposed method is capable of simultaneously identifying the impact force and structural local damage, even though it still has shortcomings such as relatively poor robustness of identified damage and great subjectivity of group division for structural elements. Some relative issues are discussed as well.

Non-convex sparse optimization-based impact force identification with limited vibration measurements

Non-convex sparse optimization-based impact force identification with limited vibration measurements

Group sparsity extension of “Non-convex sparse regularization via convex optimization for impact force identification”

We recently proposed a non-convex sparse regularization method in the ADMM framework to reconstruct and localize unknown impact forces. This method surpasses the convex ℓ1 regularization not only in inducing sparsity but also in avoiding the high-amplitude underestimation of solutions. In this work, we aim to improve the identification performance and enable the monitoring of unknown impact forces with fewer sensors by incorporating prior information in the form of natural grouping of the solution components. To achieve this, we extend our previous work on non-convex sparse regularization by incorporating group information into the method. The resulting group sparsity problem is challenging to solve due to the mixed structure and possible grouping irregularity. To address this, we develop an efficient ADMM solver in a grouped manner, featuring a novel shrinkage operator. We validate our approach both numerically and experimentally on aircraft-like composite laminated plates. Our case studies demonstrate that the proposed method achieves high accuracy and strong robustness in impact localization and time–history reconstruction from single-sensor-based measurements.

Impact force reconstruction and localization using Distance-assisted Graph Neural Network

In this paper, a novel impact force identification method named Distance-assisted Graph Neural Network (DAGNN) is proposed for simultaneous force localization and force history reconstruction. The DAGNN model is a graph-based supervised learning method. A graph is formed by treating the sensors as nodes and the connections between them as edges. The relationships of the nodes and edges contained in the graph are mathematically characterized into two matrices, an adjacency matrix and a degree matrix, that form the basis of the Graph Neural Network (GNN). Meanwhile, in order to improve the learning of the DAGNN model and realize impact force localization, physical distances between the position of the impact force and sensors are infused into the training process as physics-informed constraints. An experiment on a metal plate is conducted to verify the effectiveness and practicability of DAGNN. A sparse grid is arranged on the plate to collect the force and response signals to form a dataset for the DAGNN model. The results indicate that the accuracy of time history reconstruction of DAGNN is higher than a conventional GNN model, a typical Graph Convolutional Network (GCN) model and an ANN model, and also remain high accuracy with different locations of impact. In addition, due to the infused distance information, a simple relation regarding the distances between the impact location and the sensor location can be constructed to realize localization of the impact with good accuracy.

Impact force identification on composite panels using fully overlapping group sparsity based on Lp-norm regularization

Impact force identification is of great importance for composite structural health monitoring due to the poor impact resistance of composite materials. Convex sparse regularization method based on L1-norm tends to underestimate the amplitude of the impact force. This paper proposes a novel method using fully overlapping group sparsity based on Lp-norm regularization (FOGSLp) for impact force identification, which can localize the impact force and reconstruct its time history simultaneously with limited measurements in under-determined cases. The FOGSLp method takes more sparse prior information into account by combining the non-convex Lp-norm () and fully overlapping group sparsity to promote sparse solutions, thus improving the accuracy of the reconstructed impact force. An accelerated grouped shrinkage-thresholding algorithm is employed to solve the non-convex optimization problem under the majorization-minimization framework. The Nesterov’s acceleration strategy is modified to accommodate the requirements of non-convex optimization. Simulations and experiments are conducted on composite panels to validate the effectiveness of the FOGSLp method. Results demonstrate the efficiency and robustness of the FOGSLp method to localize the impact force and reconstruct its time history simultaneously while 25 potential impact points are monitored using two sensors. Compared with L1-norm, Lp-norm, and L2,1-norm regularization methods, the proposed method performs best in both simulations and experiments.

Randomized Kaczmarz and Landweber algorithms for impact force identification on a composite panel

Randomized Kaczmarz and Landweber algorithms for impact force identification on a composite panel

A Force Identification Method for Geometric Nonlinear Structures

Excitation identification for nonlinear structures is still a challenging problem due to the convergence and accuracy in this process. In this study, a load estimation method is proposed with orthogonal decomposition, the order for which can be fairly accurately determined by a regression. In this process, the force time history is represented by the orthogonal basis and the coefficients of the orthogonal decomposition are taken as unknowns and augmented to the state variable, which can be identified recursively in state space. A general energy-conserving method is selected to a step-by-step integration to guarantee the convergence of this integration. The proposed method is first validated by numerical simulation studies of a truss structure considering its geometric property. The identification results of the numerical studies demonstrate that the proposed excitation identification method and the orthogonal decomposition order determination method work well for nonlinear structures. The laboratory work of a 7-story frame is investigated to consider the geometric nonlinearity in impact force identification. The results of experimental studies show that uncertainties such as measurement noise and model error are included in the investigation of the accuracy and robustness of the proposed force identification method, while the time history of external forces could be identified with promising results.

Non-convex sparse regularization via convex optimization for impact force identification

Instead of traditional Tikhonov regularization, sparse regularization methods like ℓ1 regularization have been a popular choice for impact force identification because it can encode sparse prior information into the inverse problem solving. However, ℓ1 regularization tends to have a limited ability to promote sparsity and underestimate high-amplitude components in the solution. Non-convex regularization holds the potential to promote sparsity more efficiently, and then further improves the accuracy of solutions. In this paper, we consider a family of non-convex regularizers with convexity-preserving characteristics to promote sparsity. By virtue of the non-convex regularizers, we propose a non-convex sparse regularization method to simultaneously localize and reconstruct impact events with a highly under-determined sensor setting. To avoid the inherent difficulties concerning non-convex optimization, we turn to the Alternating Direction Method of Multipliers(ADMM) algorithm. ADMM helps separate the primal non-convex problem into a sequence of convex sub-problems, each of which is easy-to-solve. The non-convex exponential penalty is chosen as the representative of this class of regularizers through theoretical analysis. Several simulations and experiments are conducted on a stiffened composite laminated panel to validate the proposed method. The proposed method outperforms the standard ℓ1 regularization in both localization accuracy and time-history reconstruction accuracy.