Dynamic Load Identification Research Articles

Low-resource dynamic loading identification of nonlinear system using pretraining

To address the challenge of load identification in nonlinear systems, an audio neural network-based method called WaveNet is proposed that leverages its capability to capture long-term dependencies in mechanical systems, enabling accurate load identification. Unlike traditional dynamic load identification methods that often encounter difficulties with matrix solutions, this approach takes advantage of WaveNet’s capabilities, enhancing both accuracy and efficiency. We integrate pre-training and transfer learning techniques to address the data scarcity challenges often encountered in real-world engineering applications. By transferring features across distributed datasets, this method reduces the dependency on single-task data, thereby improving model robustness. The performance of the WaveNet method is rigorously evaluated against traditional benchmarks such as Multilayer Perceptron (MLP) and Convolutional Neural Network (CNN) benchmarks under random load conditions applied to a complex structural framework. The proposed method achieves a root mean squared error (RMSE) of 1.521 and a determination coefficient (R²) of 0.996 in the random load case, demonstrating superior accuracy compared to other approaches. Moreover, its applicability is verified through simulations of both impact load and harmonic load scenarios, showcasing the effectiveness of transfer learning in overcoming domain discrepancies. Finally, the method is tested in random experiments to validate its engineering applicability. The results highlight the significant accuracy improvement in low-resource tasks achieved through pre-training, showcasing the potential and value of the proposed method.

Research on improved dynamic load identification method based on Kalman filter under noise interference

As a mathematical approach for solving inverse problems, the dynamic load identification method is particularly useful when directly measuring the load acting on a structure is challenging. The Kalman filter (KF) algorithm is commonly employed for dynamic load identification. However, in practice, measurement noise can significantly affect the accuracy of the KF algorithm's results. In this study, we investigate the impact of response noise on the accuracy of load identification results using the KF algorithm. To eliminate the influence of measurement noise on identification accuracy, we propose an improved dynamic load identification method. This method incorporates adaptive techniques to assess varying levels of response noise and improve the load identification accuracy. Notably, this method is applicable in both physical and modal domains. We conduct numerical simulations using a 5-DOF system under different noise conditions. Compared to traditional dynamic load identification method based on KF algorithm, the improved method consistently achieves superior accuracy in load identification across various noise levels. Moreover, an experiment is conducted to further validate the feasibility of the proposed method. The results showed that the proposed method is effective and can achieve high-precision identification of unknown loads.

A distributed dynamic load identification approach for thin plates based on inverse Finite Element Method and radial basis function fitting via strain response

Dynamic load identification is crucial for structural design and health monitoring. Traditional methods for distributed dynamic loads (DDLs) typically involve establishing a transfer matrix, which often leads to ill-posed problems. In this paper, a novel method based on the inverse Finite Element Method (iFEM) and radial basis function (RBF) fitting was proposed to identify DDLs from measured strain responses. The method begins with the reconstruction of the displacement field from discrete strain data using iFEM, followed by applying RBF fitting to obtain a continuous displacement field. To enhance the performance of the RBF fitting, a constrained matrix for force boundary conditions is introduced, along with a selection rule for the RBF shape parameter. The identified loads are subsequently determined by incorporating the well-fitted RBFs into the motion equations of thin plates. This approach eliminates the need for a transfer matrix, thereby avoiding ill-posedness, and enables the simultaneous identification of the spatial distribution and time history of the loads. Three numerical examples for the identification of concentrated loads, uniformly distributed loads, and globally distributed loads demonstrate the method's effectiveness, accuracy, and noise resistance, with additional validation provided through a comparison with the classic time-domain method.

Deep recurrent-convolutional neural network learning and physics Kalman filtering comparison in dynamic load identification

Deep recurrent-convolutional neural network learning and physics Kalman filtering comparison in dynamic load identification

Dynamic Load Identification at Natural Frequencies for Aircraft via Attention Based 1D-CNN

Since the frequency response function is ill-conditioned at the natural frequency of the system, the traditional load identification method based on the system parameters is no longer applicable. Aiming at the difficulty of dynamic load identification at the natural frequency of the structural system, a dynamic load identification method at the natural frequency of the structure based on one-dimensional convolutional neural network(1D-CNN) with attention mechanism is proposed. Specifically, the high-level features in the vibration response signal are first extracted through the convolution layer. Then the weight matrix of the network is updated by backpropagation algorithm, which represents the importance of different features. The mapping relationship between response and load is established to realize the task of load identification. From the trained data, the attention module learns the contribution of features according to the different contribution of different features to load prediction. The important components in the response signal are highlighted and noise pollution is suppressed. Excitation and response signals at the natural frequency of the system were acquired using exciters and an accelerometer mounted on the GARTEUR aircraft model. Excitation and response signals at the natural frequencies of the system are obtained by an exciter and accelerometer mounted on the GARTEUR aircraft model. The responses of the model at the first three natural frequencies of 6.4Hz,35.8Hz and 48.5Hz were obtained respectively. Experimental results show that compared with the traditional TSVD load identification method, the maximum error of this method is only 3.19%. Compared with the 1D-CNN method, the proposed method has stronger robustness under 20%, 50% and 80% noise levels.

Identification of Wind Load Exerted on the Jacket Wind Turbines from Optimally Placed Strain Gauges Using C-Optimal Design and Mathematical Model Reduction

Wind turbine towers experience complex dynamic loads during actual operation, and these loads are difficult to accurately predict in advance, which may lead to inaccurate structural fatigue and strength assessment during the structural design phase, thereby posing safety risks to the wind turbine tower. However, online monitoring of wind loads has become possible with the development of load identification technology. Therefore, an identification method for wind load exerted on wind turbine towers was developed in this study to estimate the wind loads using structural strain, which can be used for online monitoring of wind loads. The wind loads exerted on the wind turbine tower were simplified into six equivalent concentrated forces on the topside of the tower, and the initial mathematical model for wind load identification was established based on dynamic load identification theory in the frequency domain, in which many candidate sensor locations and directions were considered. Then, the initial mathematical model was expressed as a linear system of equations. A numerical example was used to verify the accuracy and stability of the initial mathematical model for the wind load identification, and the identification results indicate that the initial mathematical model combined with the Moore–Penrose inverse algorithm can provide stable and accurate reconstruction results. However, the initial mathematical model uses too many sensors, which is not conducive to engineering applications. Therefore, D-optimal and C-optimal design methods were used to reduce the dimension of the initial mathematical model and determine the location and direction of strain gauges. The C-optimal design method adopts a direct optimisation search strategy, while the D-optimal design method adopts an indirect optimisation search strategy. Then, four numerical examples of wind load identification show that dimensionality reduction of the mathematical model leads to high accuracy, in which the C-optimal design algorithm provides more robust identification results. Moreover, the fatigue damage calculated based on the load identification wind loads closely approximates that derived from finite element simulation wind load, with a relative error within 6%. Therefore, the load identification method developed in this study offers a pragmatic solution for the accurate acquisition of the actual wind load of a wind turbine tower.

A deep learning method for heavy vehicle load identification using structural dynamic response

The identification of dynamic vehicle loads is crucial for bridge health monitoring. Currently, bridge weigh-in-motion (BWIM) system and image recognition methods are extensively used for vehicle load identification. However, BWIM systems are costly, while single image recognition methods struggle to accurately identify vehicle weight. Hence, an improved approach is proposed to address the above issues, which employs a Bidirectional Long Short-Term Memory (BiLSTM) network model to establish the mapping relationship between vertical deflection of bridges and vehicle loads. Firstly, based on practical engineering, the Grey Wolf Optimization-Variational Mode Decomposition (GWO-VMD) method is employed to address the influence of temperature effects on deflection response data. Then, through a time matching algorithm, the sliced deflection data and the corresponding BWIM system vehicle load information are paired to form the dataset for the deep learning models. The results of the models demonstrate that the optimal BiLSTM model exhibits better robustness and generalization performance. It achieves high accuracy of 97.9% in load identification. The method significantly reduces the economic cost and improves the accuracy of vehicle load identification.

Impact load identification of high-speed train scale carbody based on multi-objective optimisation and TwIST sparse regularisation

ABSTRACT Effective identification of dynamic loads on vehicle systems is crucial for evaluating the structural integrity of railway vehicles. The inverse problem method has been proposed for dynamic load identification to determine the impact load on the carbody. Due to the sparse nature of the impact load, the combination of the l 1-norm and TwIST (two-step iterative threshold shrinkage method) methods is used to reconstruct the impact load, taking into account the influence of sensor placement on the identification results. The MOHBA (Multi-objective Optimisation Honey Badger Algorithm) was proposed to simultaneously select the regularisation and iteration parameters. This algorithm aims to improve the accuracy of subsequence load reconstruction by considering the influence of noise levels when selecting the measured data. The impact load experiment was conducted on the scale carbody, and the single-point impact load and multi-point impact load matched well with the actual load. Satisfactory load identification results can still be achieved when the noise level is within 15%. When arranging measurement points on the boundary of the vehicle body, satisfactory load identification results can also be achieved.

A Non-Global Traversal Method for Dynamic Load Rapid Localization and Identification

Dynamic load localization and identification technology is very important in the structural design and optimization of aircraft. This paper proposes a non-global traversal method (NTM) for the fast positioning and recognition of dynamic loads on continuous beams. This method separates the load’s position and amplitude information in the modal space. Then, it constructs an interpolation function about position information, and converts load positioning to solving the zero point of the interpolation function. After determining the position of the dynamic load, the amplitude of the dynamic load is recognized. This method does not need to traverse all the position points globally, thereby greatly improving the efficiency of load positioning. Numerical simulations and experiments show that compared with the original variable separation fast positioning method (VSRPM), this method improves the calculation efficiency by more than 80% while maintaining the same recognition accuracy. NTM is a new method of great application value.

Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

A novel dynamic load identification method based on improved basis functions and implicit Newmark-[formula omitted] for continuous system with unknown initial conditions

For structural design and optimization, precise knowledge of dynamic load on structures is essential. However, load identification can be sensitive to the initial conditions, and even small variations can lead to inaccurate results. The existing load identification methods always assume that the structure’s initial condition is zero, which is not the case in real engineering problems where structures are already in a state of vibration before load identification implementation. In this work, we propose a novel dynamic load identification method that takes into account unknown initial conditions of structures which is based on the improved basis functions and implicit Newmark-β method. The real vibration response is decomposed into forced vibration caused by dynamic load and free vibration caused by initial condition, which are characterized by the coefficients of undetermined orthogonal polynomials. Moreover, to overcome the ill-posedness problem arising from factors such as response noise and model error, we introduce the L1 regularization method. To validate the performance of the proposed method, numerical simulations and tests of load identification are conducted on simply supported beam. The effects of noise and model error on the load identification results are analyzed. Finally, we discuss the impact of modal truncation order and the effect of measurement points on load identification.

Research on the prediction method of string-supported dome cable force based on digital twin technology

Abstract To improve the accuracy of rope force prediction and the safety of the construction process. In this paper, based on digital twin technology in the design process, digital twins of physical entities in virtual space are constructed using digital to achieve digital control and optimization of physical entities. The structural response information collected by sensors is brought into the dynamic load identification method by calculating the solution method of the dynamic load of the digital twin technology. The damping effect is considered in the load vector. The displacement is eliminated by constructing an average loss function to disperse the motion time to solve for the dynamic load imposed on the structure and obtain the load-bearing state of the structure for dome cable force prediction. To verify the feasibility of the model, the results of the cable force prediction analysis show that the overall displacement of the mesh shell displacement nodes at the bishop number 200-400 has a more uniform step distribution, and the cable force of the internal and external radial cables has a small change in the predicted structural cable force at the position of 40° angle with the long axis. Thus, it can be seen that the cable force prediction of a circular chord-supported dome with digital twin technology can break the tradition and further improve structural safety and implementability.

An accurate method for identifying hub dynamic loads by condition number of measured FRF matrix on helicopter fuselage

AbstractIt is a simple method to identify the hub dynamic loads of rotor by measuring the vibration responses on helicopter fuselage. However, the identification accuracy of the hub dynamic loads is related to the layout or placement of measuring points on the fuselage. The identification will be inaccurate if the layout of measuring points on the fuselage is unreasonable to result in the “ill-conditioned” frequency response function (FRF) matrix measured on the fuselage. In order to avoid the inaccurate identification due to the “ill-conditioned” measured FRF matrix, an accurate method for identifying the hub dynamic loads of rotor by vibration measurement on helicopter fuselage is proposed in this paper. In the proposed method, the reasonable layout of the measuring points on the fuselage for the “well-conditioned” measured FRF matrix can be obtained according to the condition number of the measured FRF matrix on the fuselage, and then the hub dynamic loads of rotor can be accurately identified. The simulation and experiment of the identification of the hub dynamic loads on a dynamically similar frame structure of a helicopter cockpit floor have verified the effectiveness and accuracy of the proposed method.

Method for Dynamic Load Location Identification Based on FRF Decomposition

The location identification of dynamic load is an important part of load-identification technology. Traditional methods are mostly aimed at the identification of dynamic load’s amplitude and phase. A new method for dynamic load location identification is proposed in this paper. An amplitude ratio or a phase difference between structural dynamic response signals is only related to the frequency response function (FRF), which is a complex-valued function that implies the location information of the load to be identified. In this method, the amplitude and phase variables of the excitation can be eliminated with symbolic calculations, and the location variables can be extracted from the FRF in a complex-number field. An excitation location can be identified quickly with parameter optimization using a Genetic Algorithm (GA), avoiding the ill-posed problem caused by matrix inversion. Numerical simulations and experiments demonstrate that this method can realize the fast recognition of several excitation positions, and has a high recognition accuracy, a short calculation time and a strong anti-noise ability.

Advances in dynamic load identification based on data-driven techniques

Dynamic loads on engineering structures are often difficult to measure directly. Therefore, indirect identification methods based on dynamic responses are commonly used. However, this approach is often influenced by ill-conditioned matrices, noise interference, unknown structural and/or material parameters, and difficulty of constructing transfer functions when the traditional physics-based model is used. To address these issues, significant strides have been made in data-driven identification of dynamic loads, which are model-free and independent of structural characteristics. This paper tries to present a comprehensive review of dynamic load identification methods based on data-driven techniques, covering two aspects: load localization and load reconstruction. Features of the widely used data-driven techniques such as the geometric method, reference database method, machine learning methods including SVM-based methods and ANN-based methods and deep learning methods are discussed in detail. Additionally, this paper offers insight into the challenges and prospects of the data-driven techniques for dynamic load identification. The review aims to provide valuable insights for identifying dynamic loads in complex structures based on data-driven techniques and suggests future research directions.

Multi-type dynamic load identification algorithm in continuous system: A numerical and experimental study based on SSM-Newmark-β

Dynamic load identification based on structural responses is an important problem in the field of engineering and plays an important role in the condition assessment of mechanical structures. Current popular load identification methods such as the state-space method (SSM) and the Green's kernel function method (GKFM) are implemented on discrete systems with outstanding performance, but when dealing with complex continuous systems, there are some limitations such as low efficiency and inaccuracy. In this paper, a continuous system load identification algorithm based on SSM and Newmark-β is proposed for the first time. Using modal coordinate transformation and modal truncation methods, the number of infinite vibration differential equations of a continuous system in physical space are converted to a finite number of vibration differential equations in modal space, where the modal truncation order and the optimal layout of the sensors are combined by modal strain energy. The Newmark-β method in modal space is derived and thus combined with SSM to obtain a load identification model Y=HF called SSM-Newmark-β method, which reduces the size of the transfer matrix H. The solution time of the proposed algorithm is 0.38 s for continuous systems, which is rather shorter than that for discrete systems. Furthermore, the simulations show that it has better accuracy and noise immunity than SSM and GKFM in the identification of sinusoidal load, impact load, and random load. The effect of time step is also discussed which reveals that the larger time step has less effect on the proposed algorithm. An experimental study is carried out on a cantilever beam system. The result verifies that the SSM-Newmark-β algorithm has better accuracy in load identification for the continuous system. This research provides a new sight for the real-time identification of dynamic loads for complex structures.

An improved homotopy perturbation method for dynamic force reconstruction

In many engineering application, it is still a challenge in directly obtaining external force acting on structures. Moreover, many researchers attach more attention to indirect measurement technology using some response signals. This paper presents an improved homotopy perturbation method (IHPM) for dynamic load identification. This method can identify multi-source dynamic sine and triangle force. Firstly, the present method is proposed based on improved homotopy operator. Secondly, the sequence that the present method generates is proved to be a Cauchy sequence when ‖Aeα−I‖<1. Finally, the proposed method is applied to the dynamic load identification of hanging basket structure. Numerical simulations verify the stability and effectiveness of the newly developed method, and also validate that it is superior to the traditional homotopy perturbation method (HPM) and Tikhonov regularization method.

The Least Squares Time Element Method Based on Wavelet Approximation for Structural Dynamic Load Identification

Dynamic load identification is a commonly used and quite important approach to obtain the excitation loads of structures in engineering practice. In this paper, a novel dynamic load identification method combining the least squares time element method (LSTEM), wavelet scaling function and regularization method is proposed, which performs a better accuracy and a stronger anti-noise ability. It decomposes the time history of dynamic load into a series of time elements, and approximates the load profile at each time element using wavelet scaling functions. In order to balance the accuracy and efficiency for load identification, an optimal wavelet resolution is then determined. Simultaneously, the least squares time element model is derived which establishes the forward model for computing the wavelet coefficient. Finally, the wavelet coefficients for dynamic load identification are accurately and stably solved by implementing regularization. By this method, on the one hand, the wavelet scaling function and LSTEM improve the identification accuracy, and on the other hand, the integral process in the least squares operation gains the anti-noise ability for the load identification. A numerical example of a roof structure and an experiment of a composite laminate are studied and verify the effectiveness of the proposed method.

Dynamic Force Reconstruction for Structural Support Platforms Based on the Combined Strategy of Experiment and Simulation

Dynamic force reconstruction theory has been developed for many years, generating numerous effective methods. However, the applications of engineering structures are relatively rare, owing to the difficult experiment, low accuracy and noise disturbance, among others. Aiming at the support platform structure commonly used in engineering, we propose the complete dynamic force reconstruction process based on the direct inversion method in frequency domain. The dynamic calibration methods of experiment and simulation are both analyzed in this case. In order to improve identification accuracy, the Tikhonov regularization is introduced. The results validate the reliability of our proposed method in real scenarios and the necessity of regularization method. Moreover, dynamic load identification method of structural variable stiffness is derived by the four-terminal parameter method. This work provides engineering application–a reference for the engineering of dynamic load identification technology.

Study of dynamic load identification under unknown initial conditions

Dynamic load identification belongs to the second inverse problem of structural dynamics, i.e. the inversion of the load history in the real state by collecting the measured data of structural vibration. Some traditional dynamic load identification methods do not consider the initial conditions, i.e. the initial conditions of the structure are assumed to be zero, however, the structure is not always at rest during the process of collecting the vibration response, which leads to a large error between the identified force and the actual force using traditional methods. Since the measurement of initial conditions is very difficult, in order to solve the influence brought by the initial conditions to the dynamic load identification process, this paper proposes a method based on sparse regularization to identify the load history under unknown initial conditions. Firstly, the unknown force is represented using basis functions, and the vibration response of the structure is divided into two parts: forced vibration caused by the force and free vibration under the initial conditions, and finally sparse regularization is used to solve the ill-conditioned equation. The experimental and simulation results also further verify the applicability and robustness of the method proposed in this paper in dealing with the load identification problem under unknown initial conditions.