Abstract The identification of dynamic loads on structures relies on an accurate finite element model. For structures under certain complex working conditions, it is difficult to determine the specific structural constraints, posing challenges to the study of the structure’s dynamic characteristics. To accurately conduct dynamic load identification research on structures under such conditions, a high-precision finite element model is required. This paper introduces existing finite element model correction methods, as well as the current status of dynamic load identification research, and proposes a model correction method based on sensitivity correction to adjust finite element models of structures with unknown constraint conditions. The constraint stiffness of the model is set as a design parameter, and adjusting the constraint stiffness is used to modify the model’s modal frequencies and frequency response functions. The errors in the first two modal frequencies after correction are 0.2%. Dynamic load identification studies are conducted on the corrected model and structure under typical loads, such as concentrated loads. The experimental identification results meet the working condition standards, with errors all below 10%. After the model correction, the dynamic load identification results are more accurate.

Accurate and efficient identification of distributed dynamic loads is a critical task in inverse dynamics and structural vibration analysis. However, online identification in continuous structures remains challenging when the initial conditions of each identification window are unknown, since inaccurate initial-state estimation may introduce significant boundary errors in segment-wise time-domain reconstruction. This paper proposes a finite-memory time-domain method for online identification of distributed dynamic loads in continuous structures under unknown initial conditions. Based on the Newmark- integration scheme, the mapping relationship between structural responses and modal loads is established in the time domain. Unlike conventional segment-wise identification methods, the proposed approach truncates the historical memory of the dynamic system to a finite length, thereby replacing the explicit contribution of the unknown initial state in each sliding window with an equivalent finite-history load contribution. This strategy effectively alleviates the adverse influence of unknown initial conditions and enables sliding-window-based online identification. To reduce the dimensionality of the inverse problem, the distributed dynamic load is represented by Legendre orthogonal polynomials. A generalized Tikhonov regularization scheme with temporal difference constraints is further introduced to enhance the stability and noise robustness of the inverse solution. Numerical simulations on a simply supported beam and a simply supported plate are conducted under distributed periodic, impact, and random loads. The results demonstrate that the proposed method can accurately reconstruct distributed dynamic loads under different noise levels, while the computational time remains considerably shorter than the identification duration. Compared with the standard Newmark-β method, the proposed method exhibits a significant accuracy advantage in the presence of nonzero initial conditions. Experimental validation on a cantilever plate subjected to a loudspeaker-induced sinusoidal distributed load further confirms the accuracy, efficiency, and engineering applicability of the proposed method.

Distributed dynamic load identification is a technique used to identify dynamic loads applied to structures through dynamic responses, and it is a typical inverse problem. Current research mainly focuses on identification methods, with little attention given to the selection of observation positions during the measurement of dynamic responses. The difficulty in analyzing the impact of observation positions on the identification results lies in the fact that the regularization methods and the inherent randomness of noise must also be considered during the identification process, making it challenging to draw sufficient theoretical conclusions. This work theoretically derives the impact of observation positions on the upper bound of identification result errors, under the premise of a fixed number of observation positions. Based on this, an observation position selection model aimed at minimizing identification errors is proposed. Finally, the effectiveness of this model in reducing identification errors is verified through simulations and experiments. Experimental results show that the proposed observation position selection model reduced the mean identification error by 37.12 % and the maximum error by 10.56 %.

In distributed dynamic load identification, loads are inferred from the response-load relationship based on measurements taken at multiple positions. Therefore, the selection of measurement positions is crucial. This work investigates the impact of measurement positions on identification results, assuming a fixed number of measurement positions, and proposes an optimization method aimed at improving identification stability. Two key challenges are addressed in this context. The first is that measurement positions act as a hyperparameter in the response-load relationship, making it difficult to directly assess their influence on the identification results. The second challenge is the need to consider the effect of measurement positions across different identification methods. This work provides solutions to both issues. To tackle the first challenge, it is demonstrated for the first time that, in methods based on generalized orthogonal base functions, the effects of measurement positions and the choice of base functions on identification results are independent. Regarding the second challenge, it is shown that any valid identification method is an approximation of the correct response-load relationship, meaning that it suffices to study the impact of measurement positions in a single method. Based on these findings, an optimization method for measurement positions is proposed to enhance identification stability. Fast optimization methods for one-dimensional structures and more general optimization methods for complex structures are proposed. Experimental results demonstrate that optimizing measurement positions reduces identification errors by 20.5%, significantly improving stability.

As the second inverse problem in structural dynamics, dynamic load identification is highly dependent on the system’s intrinsic properties. For distributed loads, establishing an accurate mapping between structural responses and the underlying dynamic excitations remains particularly challenging, and the ill-posed nature of the problem further amplifies measurement noise, leading to significant identification errors. To overcome these difficulties, this study proposes a novel distributed dynamic load identification framework based on a Transformer architecture that directly learns the inverse dynamic relationship without requiring explicit system parameter estimation. Specifically, Legendre orthogonal polynomial decomposition is first employed to transform the load identification task into the estimation of a finite set of orthogonal polynomial coefficients. Building upon this framework, innovative architectural optimizations are introduced by embedding physical constraints into attention computation and linear prediction, leveraging the temporal causality of dynamic responses. These enhancements improve model interpretability and substantially reduce training difficulty. Numerical simulations demonstrate that the proposed method can accurately identify sinusoidal, impact, and random loads under various noise levels. Furthermore, a distributed load identification experiment on a cantilever beam is carried out, validating the practical applicability of the approach. Finally, the selection of model hyperparameters is discussed based on fitting and generalization performance, and a comparative study with traditional dynamic calibration methods was conducted in an experimental setting, further demonstrating the superior accuracy, noise robustness, and practical reliability of the proposed framework.

This systematic review evaluates the paradigm shift in airfield pavement deterioration modelling over the past fifteen years, tracing the transition from empirical deterministic formulations to advanced Artificial Intelligence (AI) and Machine Learning (ML) architectures. A bibliometric analysis of 64 Scopus-indexed publications confirms a decisive move towards computational intelligence: 23 studies utilize AI/ML and 14 employ hybrid models, collectively outpacing traditional deterministic (20) and probabilistic (5) approaches. Research activity has accelerated significantly, reaching a peak during the 2023–2024 period. Artificial Neural Networks have emerged as the dominant algorithmic framework, particularly for structural performance evaluation and image-based distress analysis. However, a critical bifurcation persists in the literature: research remains heavily concentrated on either load-bearing capacity (54.7%) or functional metrics such as the Pavement Condition Index (32.8%), yet these domains remain largely siloed. Crucially, only a marginal fraction of studies (4.7%) utilize integrated datasets that combine structural and functional parameters. The review is distinctive in linking bibliometric trends with a technical diagnosis of the structural–functional divide that limits operational deployment of airfield pavement prediction models. This paper identifies this lack of holistic integration as a primary systemic gap and suggests that the advancement of hybrid ML architectures is essential to meet the resilience and efficiency demands of increasing global air traffic.

Phononic crystals offer new insights for reducing vibration and noise. The bandgaps of traditional phononic crystals are challenging to balance between low frequency and broadband. Achieving subwavelength vibration suppression has always been a challenge, in particular, tunability without introducing additional weight has attracted great attention. Here, we utilized oblique springs to construct a quasi-zero stiffness (QZS) mechanism, which harnesses geometric nonlinearity to achieve tunability of the bandgap within the ultralow-frequency range. We have evaluated the dispersion relations of this system using both linearized model and perturbation methods. The results indicate that the introduction of the QZS mechanism can generate zero-frequency bandgap and critical wavenumber. The proposed structure offers two types of band gap tunability-variation amplitude and changes in the length of the oblique springs. To support these findings, numerical simulation was carried out, and provides strong support for our theoretical results. We expect that this research offers a new perspective for low-frequency vibration reduction.

As an essential component of dynamic loads, traditional time-domain identification methods exhibit notably insufficient accuracy when dealing with distributed dynamic load identification under unknown initial conditions. This paper explores a novel and effective methodology, utilizing the Bayesian framework and orthogonal polynomials fitting, to reconstruct the distributed dynamic loads of thin plate structures over any arbitrary time period under unknown initial conditions. The forced vibration under the orthogonal basis function loads and the free decay vibration after the removal of basis function loads are used to characterize the forced vibration induced by the identified distributed dynamic load and the decay vibration caused by unknown initial conditions, respectively. By integrating structural dynamic responses within a multi-layer Bayesian framework, the time history and spatial distribution of the load over any arbitrary time period are identified. The innovation of this methodology is that the contribution of the initial conditions to the response is independently characterized by the free decay response caused by the removal of the basis function loads, which effectively resolves the issue of insufficient identification accuracy in existing traditional time-domain methods due to unknown initial conditions. Consequently, the accuracy and reliability of the distributed dynamic load identification is significantly enhanced, which provides a new solution for distributed dynamic load identification under unknown initial conditions. Additionally, simulation cases involving various load conditions and noise levels are discussed under unknown initial conditions over arbitrary time periods. The results demonstrate that the proposed method achieves favorable identification accuracy and robustness under unknown initial conditions.

To address the challenge of accurately applying distributed dynamic loads in experiments, a method is proposed whereby concentrated dynamic loads are applied at Gauss points to achieve an equivalent effect. This approach utilizes modal truncation in the modal space, discretizes the distributed dynamic load through a modal force equivalence method, and calculates the coefficients of the concentrated dynamic loads using the Gauss-Legendre quadrature formula. In numerical simulations, dynamic responses of a cantilever beam and a simply supported plate under both distributed and equivalent concentrated dynamic loads are analyzed, with the modal superposition method used to evaluate the dynamics of the beam and plate. Results indicate that the acceleration response error under distributed and equivalent concentrated loads does not exceed 4. 5% , and the displacement response error does not exceed 4. 2% . Additionally, the variation of equivalent results under noise in the concentrated loads is examined. The simulation results validate the accuracy and applicability of this equivalent method for distributed dynamic loads.

Uncertainties in practical engineering structures can significantly affect the accuracy of load identification. This paper investigates the identification of random loads in structures with uncertain parameters, marking the first attempt to identify the power spectral density of random loads using second-order Taylor series expansion. Initially, the midpoint of the random load is identified. To reduce the ill-posedness of the inverse problem, a novel adaptive regularization method is proposed. Unlike traditional regularization methods, this method employs a variable-parameter regularization scheme and introduces a correction factor based on the condition number of the frequency response normal matrix to achieve adaptive regularization. Subsequently, the interval radius of the random load is determined. A new second-order interval optimization method is developed, which accounts for the possibility of extreme points within the interior of the interval model. This method formulates and solves a constrained nonlinear optimization problem to determine the load interval radius. Finally, the effectiveness and feasibility of the proposed methods are validated through three numerical examples and one experimental case. The results indicate that the proposed methods significantly improve identification accuracy, and the second-order interval optimization method exhibits strong robustness to structural uncertainty.

This work focuses on the dynamic load identification motivated by Newmark-(3 Method and regularization strategy. Given the ill-posed nature of load identification, an improved hybrid LSQR regularization strategy is proposed, which incorporates an adaptive correction mechanism by iteratively comparing the computed response with the measured response. For load identification problems with prior conditions, an augmented hybrid LSQR regularization strategy is further developed, which expands the Krylov subspace with prior information and combines the improved hybrid LSQR regularization strategies to ensure stable iteration. Simulation examples using a simply supported beam as a representative structure of continuous systems, involving different load types and noise levels, validate the stability and accuracy of the two methods. The results show that the improved hybrid LSQR algorithm exhibits superior stability and accuracy compared to the conventional LSQR algorithm and yields relatively favorable identification results. Moreover, the superposition load identification simulation indicates that the augmented hybrid LSQR algorithm further improves the accuracy of load identification when prior knowledge of the load is available.

Dynamic load identification is an inverse problem in structural dynamics aimed at recovering the loads acting on a structure. Determining sensor locations to ensure stable and accurate identification has long been an important research topic. Kalman-filter-based methods can identify dynamic loads while simultaneously estimating the state vector, enabling online identification from multiple types of sensor measurements. Although these methods offer clear advantages over traditional approaches, they also place stricter demands on algorithmic stability-a fundamental requirement for reliable performance. However, the algorithmic stability from the perspective of sensor placement has not been systematically investigated. This paper presents a theoretical derivation of practical and easy-to-implement stability criteria in both the physical and modal state-space frameworks. Then, an optimal sensor placement (OSP) strategy is proposed, which explicit clarifies the different roles of sensor types in the adopted estimation algorithm. Infeasible sensor configurations are first excluded according to the invertibility and stability requirements, and the optimal configuration is then selected from the remaining feasible candidates by minimizing the trace of the input covariance matrix. Simulation studies verify that the proposed OSP strategy can determine the optimal sensor layout under single-point excitation, multi-point excitation, and complex structural systems, while exhibits a certain degree of robustness. Finally, dynamic load identification experiments on a simply supported beam are conducted, and the accurate identification results further demonstrate the effectiveness of the proposed OSP strategy.

Accurate localization and reconstruction of dynamic loads are critical tasks in the analysis of engineering structures subject to vibration. However, the rapid identification of multiple dynamic loads in continuous systems remains challenging due to the strong coupling of their effects in the measured response. This paper proposes a novel and efficient method for the simultaneous localization and time history reconstruction of multiple dynamic loads in continuous structures. Through numerical integration, the mapping relationship between structural responses and modal loads is established, facilitating the identification of modal loads across various orders. Unlike conventional methods, the proposed approach applies Fast Independent Component Analysis (FastICA) for the first time to this problem, leveraging the statistical independence of typical load signals to decouple the modal load components in the time domain. This information-theoretic strategy allows for the use of only response signals to isolate individual load contributions. Subsequently, the modal shape comparison method is applied to accurately localize load locations and determine their magnitudes. The computational efficiency of the proposed framework is further analyzed to theoretically demonstrate its performance advantage. Simulation studies on a simply supported beam and a complex wing model confirm that the method can accurately localize loads and reconstruct their time histories under various loading conditions. The method also exhibits strong robustness to measurement noise and model errors. Furthermore, the assumption of statistical independence among load signals is analyzed and confirmed. To validate practical applicability, experimental studies on a simply supported beam are conducted, further confirming the method's accuracy and reliability.

This paper presents a method for dynamic load positioning and identification in linear time-varying (TV) continuous beam structures. The technique enhances the inverse Wentzel-Kramers-Brillouin (IWKB) approach by transforming the step parameters from implicit to explicit formulas and integrating the calculation process of step parameters to minimize rounding errors in the iterative process of dynamic load identification. Additionally, based on the properties of time-varying structural mode shape functions, an iterative function for load position was constructed, achieving non-global traversal method (NTM) for the fast positioning of dynamic loads. Simulation examples verify the algorithm's effectiveness and speed under noise-free and noisy conditions. Simulation examples were utilized to study the impact of time steps on the efficiency and accuracy of dynamic load position and amplitude identification, recommending suitable time steps. Compared to the inverse Wilson-theta method with the exhaustive localization method (IW-ELM), the method proposed in this paper achieves higher identification accuracy. It enhances position identification efficiency by more than 80% when a suitable time step is selected. Experiments with water-filled beams of varying mass further validate that this method has excellent accuracy and high efficiency in practical applications.

This paper focuses on the anti-resonance vibration isolation system. In response to the limitation of the narrow effective vibration isolation bandwidth in traditional anti-resonance vibration isolation, a more effective vibration isolator is proposed. This study designs an anti-resonance vibration isolation system with a tunable anti-resonance frequency by imbedding a movable mass block into the resonant beam based on the SARIB system. Additionally, by employing a multi-BP neural network algorithm, frequency-following control of the mass block based on the external excitation frequency is achieved, reducing the displacement of the mass block and enhancing the response speed of vibration isolation. The effectiveness of the proposed model and control strategy was validated through vibration-damping tests under varying excitation frequencies. Within the experimental frequency range, compared to the vibration isolation efficiency at the initial position of the mass block, the system’s vibration isolation efficiency improved by 70

Distributed dynamic loads are commonly encountered in engineering applications. The identification of such loads, especially time-space coupled distributed dynamic loads, is an emerging area of research. Accurately representing these loads requires capturing the load’s time history across all degrees of freedom of the structure, which can be an extremely labor-intensive task. To address this challenge, this paper proposes a novel method for dimensionality reduction of time-space coupled distributed dynamic loads using Principal Component Analysis (PCA), where the load is represented as the sum of several load principal components. The identification process begins with the application of the Algorithm for Multiple Unknown Signal Extraction (AMUSE) to extract the load distribution matrix. An improved Kalman filter algorithm is then employed for the online identification of the time functions corresponding to the principal components. Sparse regularization is applied to obtain the spatial functions of these components. Finally, the distributed dynamic load is reconstructed by combining the time and spatial functions. In addition, the necessary conditions, computational complexity, and other characteristics of the proposed method are discussed in detail. Numerical results show that the method can accurately identify distributed dynamic load even under noise interference. For complex loading scenarios, the method is still able to produce accurate equivalent loads that replicate the structural response of the actual loads.

This paper proposes a novel dynamic response reconstruction method based on the Kalman filter which can simultaneously identifies external excitation and reconstructs dynamic responses at unmeasured positions. The weighted least squares method determines the load weighting matrix for excitation identification, while minimum variance unbiased estimation determines the Kalman filter gain. The excitation prediction Kalman filter is constructed through time, excitation, and measurement updates. Subsequently, the response at the target point is reconstructed using the state vector, observation matrix, and excitation influence matrix obtained through the excitation prediction Kalman filter algorithm. An algorithm for reconstructing responses in Continuous System using the excitation prediction Kalman filtering algorithm in modal space is derived. The proposed structural dynamic response reconstruction method evaluates response reconstruction and load identification performance under various load types and errors through simulation examples. Finally, a test system for structural dynamic response reconstruction on simply supported beams is constructed and tested. Results demonstrate accurate excitation identification under different load conditions and simultaneous reconstruction of target point responses, verifying the feasibility and reliability of the method.

Distributed dynamic load identification plays a crucial role in structural vibration reduction, noise attenuation, optimization design, fatigue analysis, as well as intelligent and adaptive control. Non-rectangular plates are commonly encountered in practical applications. This paper firstly addresses the challenges involved in extending the method for identifying distributed dynamic loads on rectangular plates to non-rectangular plates. Secondly, coordinate transformation approach is introduced to establish a relationship between non-rectangular and rectangular plates, leading to the proposal of a novel method for identifying distributed dynamic loads on non-rectangular plates. Finally, the effectiveness of the proposed method is validated through both simulations and experiments. The results show an amplitude identification error of 8.6% and a phase identification error of 9.3%, confirming the method's reliability.

Accurately determining the location and magnitude of dynamic loads on a structure is crucial for solving or optimizing vibration issues. However, identifying the source of vibration through direct measurement is extremely challenging. Therefore, developing a rapid and accurate method for dynamic load location identification is essential. However, achieving rapid localization of multi-point excitation in continuous systems has been challenging due to the coupling relationship of their contributions to the response. This paper presents a novel method that can simultaneously identify the location and magnitude of dynamic loads acting on the structure under multi-point excitation. A "Modal-based Dynamic Load Location Identification" framework is proposed, analyzing the influence of dynamic load locations on the structural dynamic response. The relationship between system acceleration response and modal loads is constructed using numerical integration through the Newmark explicit method, thereby determining the modal loads of various orders in the vibration system. By converting the relationship between physical space loads and modal loads, a modal load residual fitness function is established. The fitness function is iteratively optimized using genetic algorithm to determine the load location, achieving rapid localization of dynamic loads under multi-point excitation. Subsequently, the computational efficiency of dynamic load identification is analyzed. Simulation results indicate that this method reduces the identification time of dynamic loads under the condition of unknown load locations to the same order of magnitude as when the load location is known, significantly improving the computational efficiency of load location identification. Moreover, it can be effectively applied to various types of load conditions, demonstrating high accuracy and excellent robustness to noise. To further verify the performance of the algorithm in practical engineering, experimental studies on dynamic load identification were conducted on a simply supported beam system, and the results confirm that the algorithm is effective. Additionally, the influence of measurement locations and Newmark parameters on the identification accuracy is discussed.

Distributed dynamic loads, which is regarded as an essential component of the dynamic loads, occupy a very important role in practical engineering. This paper explores a novel and effective methodology, utilizing the Gaussian prior model and the orthogonal polynomials, to reconstruct the distributed dynamic load loads varying with the distribution of spatial and temporal history in time domain. The unknown orthogonal polynomial coefficients and the measurement are considered as the random vectors to determine the corresponding probability density distribution functions using Bayesian framework. Thus, the posterior density function of the unknown parameters is obtained through the Bayesian formulation. Then, the unknown parameters are identified using the Maximum A Posteriori estimator and the numerical iteration to further reconstruct the distributed loads. Especially, the hyper-parameters of the load identification model based on the Gaussian prior model are also regarded as the random vectors to decrease the impact of imprecise estimation of these hyper-parameters on the load reconstruction. From this perspective, the prior probability distributions of the hyper-parameters are determined to further obtain the joint posterior probability density function of the distributed dynamic load identification problem. The innovation of this methodology is that the Bayesian framework on the basis of Gaussian prior is first applied to the time-domain distributed dynamic loads reconstruction from the perspective of randomness, which decreases the ill-posedness and adaptively determines the hyper parameters, overcoming the disadvantage in selecting optimal regularization parameters of traditional regularization. In addition, concerning the discretization representation of distributed dynamic loads, the method to determine the coupling truncation orders of time-spatial domain is also explored. Additionally, an array of numerical examples are discussed to reveal the reasonability, accuracy and the operation efficiency in the case of various loading conditions. Simultaneously, the noise resistance is discussed in terms of different noise levels contrasted with the Tikhonov method. The results highlight the effectiveness of the discussed approach in different structures and loading conditions.