Dynamic Load Identification Research Articles

A new regularization method for dynamic load identification.

Dynamic forces are very important boundary conditions in practical engineering applications, such as structural strength analysis, health monitoring and fault diagnosis, and vibration isolation. Moreover, there are many applications in which we have found it very difficult to directly obtain the expected dynamic load which acts on a structure. Some traditional indirect inverse analysis techniques are developed for load identification by measured responses. These inverse problems about load identification mentioned above are complex and inherently ill-posed, while regularization methods can deal with this kind of problem. However, most of regularization methods are only limited to solve the pure mathematical numerical examples without application to practical engineering problems, and they should be improved to exclude jamming of noises in engineering. In order to solve these problems, a new regularization method is presented in this article to investigate the minimum of this minimization problem, and applied to reconstructing multi-source dynamic loads on the frame structure of hydrogenerator by its steady-state responses. Numerical simulations of the inverse analysis show that the proposed method is more effective and accurate than the famous Tikhonov regularization method. The proposed regularization method in this article is powerful in solving the dyanmic load identification problems.

An efficient inverse algorithm for load identification of stochastic structures

Force identification of stochastic structures is very important in science and engineering, which also leads to the challenges in the field of computational mechanics. Monte-Carlo simulation (MCS) method is a robust and effective random simulation technique for the dynamic load identification problem of the stochastic structure. However, the MCS method needs large computational cost and is also inefficient for practical engineering applications because of the requirement of a large quantity of samples. In this paper, in order to improve computational efficiency of MCS, a novel algorithm is proposed based on the modified conjugate gradient method and matrix perturbation method. First, the new developed algorithm exploits matrix perturbation method to transform dynamic load identification problems for stochastic structures into equivalent deterministic dynamic load identification problems. Then the dynamic load identification can be realized using modified conjugate gradient method. Finally, the statistical characteristics of identified force are analyzed. The accuracy and efficiency of the newly developed computational method are demonstrated by several numerical examples. It has been found that the newly proposed algorithm can significantly improve the computational efficiency of MCS and it is believed to be a powerful tool for solving the dynamic load identification for stochastic structures.

A non-iterative identification method of dynamic loads for different structures

In order to identify quickly and accurately the load state of structures in some complex environments, a non-iterative inversion method based on finite element method and Newmark method is proposed. By exploring the relationship between measurement data and loads that need to be identified, the error function is established. Based on the least square method and the matrix decomposition scheme, the formulas are derived without iteration process. To improve the inversion accuracy and efficiency in the identification of dynamic loads, the basis function expansion and the singular value decomposition method are adopted. Several different structures are considered to verify the influence of some factors on the inversion results, such as the basis function expansion, the computational time, the measurement noise, the number of measurement points and the location of measurement points. Numerical examples show that the present method can obtain the stable and accurate identifying results.

Dynamic load identification for interval structures under a presupposition of ‘being included prior to being measured’

Influences of structural uncertainties in the dynamic load identification are always significant and need to be quantified. In case of insufficient information available, intervals are favorable for modelling uncertainties. To perform the interval propagation in an inverse problem, this paper develops a sequential dual-stage interval identification method under a presupposition that each noisy response, which is an accomplished measurement for reconstructing unknown loads, should be included in the corresponding interval response of the structure exerted by interval loads to be identified. The proposed method transforms the interval identification problem into a classical one at the midpoint of interval parameters and an optimization model for minimizing the radius of each interval load. The effectiveness of the proposed method is validated by a spatial truss subjected to multiple forces due to the inclusion of each unknown load in the corresponding load. Besides, regularized solutions without exact knowledge of the accuracy loss are recommended to be used as few as possible in the interval identification of unknown loads.

A novel method of distributed dynamic load identification for aircraft structure considering multi-source uncertainties

A series of work for distributed dynamic load identification is investigated in this paper considering unknown-but-bounded uncertainties in the aircraft structure. To facilitate the analysis, the complicated rudder structure is simplified to a plate structure based on the robust equivalence principle of mechanical property under multi-cases of flight environments. Aiming at the plate structure, a time domain–based model for distributed dynamic load identification is established through the acceleration response measured by sensors. Among them, the spatial distributed load is approximated by Chebyshev orthogonal polynomials at each sampling time, and load boundaries can be calculated by the Taylor-expansion-based uncertain propagation analysis. As keys to improve the reliability of recognition results, the optimization process for sensor placement is constructed by the particle swarm optimization algorithm, taking the robustness evaluation index and sensor distribution index into consideration. The validity and the feasibility of the proposed methodology are demonstrated by several numerical examples, and the results reveal that designer can make a rational tradeoff choice among the cost of sensor placement and the performance of load identification in a systematic framework.

A Quotient Function Method for Selecting Adaptive Dynamic Load Identification Optimal Regularization Parameter

A Quotient Function Method for Selecting Adaptive Dynamic Load Identification Optimal Regularization Parameter

Identification of dynamic loads on structural component with artificial neural networks

Enhancing structural components by implementing sensors offers great potential regarding condition monitoring for lifetime analysis, predictive maintenance and automatic adaptation to environmental conditions. This article describes an approach to determining the operational forces applied to the front suspension arm of a car using strain gauges. Since suspension arms are components with free-form surfaces, an analytical calculation of applied forces by means of measured strains is not feasible. Hence, artificial neural networks are applied to approximate the functional relationship. The results reveal how artificial neural networks can be applied to identify load conditions on structural components and, therefore, deliver essential data for condition monitoring.

Online identification of impact loads of multi-degree-of-freedom system based on Kalman filter

Dynamic load identification is the second kind of inverse problem in structural dynamics. It is a process of reconstructing load applied to structure in case of structural dynamic model and information of structural response. Online identification is one of the frontier problems in dynamic load identification, which has high difficulty and broad application prospects. In this paper, an online identification of dynamic load of the multi-degree-of-freedom system based on Kalman filter in modal space is proposed. Since the Kalman filter has excellent real-time performance and robustness, it is possible to be used in dynamic load online identification. We start from the theoretical derivation in detail for the multi-degree-of-freedom system, then the feasibility and effectiveness of the method is verified by numerical simulation of three-degree-of-freedom system with the single impact load and continuous multiple impact load.

Dynamic Load Identification of a Nonlinear System Based on Newmark-β Method

Dynamic Load Identification of a Nonlinear System Based on Newmark-β Method

Fuzzy identification of dynamic loads in presence of structural epistemic uncertainties

The interval identification of dynamic loads for uncertain structures was performed primarily by the interval perturbation method (IPM). Influences of structural epistemic uncertainties on unknown loads cannot be effectively quantified for now and the interval inversion needs to be furtherly investigated. In this paper, Tikhonov regularized technique for the inverse analysis is integrated into a non-intrusive de/re-uncertainty procedure, i.e. the dimension-wise analysis, to reconstruct unknown loads under structural epistemic uncertainties. The proposed method transforms the interval identification model at zero-cut of fuzzy inputs into a finite number of classical ones with crisp parameters, regularized solutions to which are adopted to construct a polynomial approximation of each slice of the unknown load. The extreme point set of each approximation at zero-cut is derived to calculate its minimum/maximum (min/max) points at any alpha-cut with respect to the corresponding uncertain parameter, from which the min/max input vectors of the unknown load are assembled in a dimension-wise manner. Subsequently, the interval bounds of the unknown load at each alpha-cut can thus be evaluated by Tikhonov regularized inversion, based on which the fuzzy description is obtained. The effectiveness of the proposed method is validated by the inclusion of the unknown load in the identified result and a tighter identified interval suggests its accuracy advantage over the IPM if the same regularization method is adopted.

Dynamic load identification of stochastic structures based on unscented transformation

In view of some unknown parameters in structures, which are described by the Gaussian distribution model in this paper, a new dynamic load identification method for stochastic structures is proposed based on unscented transformation (UT). Firstly, the convolution equation for solving structural response is discretized, and the sampling points, namely, sigma points of stochastic parameters are calculated according to the unscented transformation. Then, when the stochastic parameters take each sigma point, the dynamic load is calculated by the direct inversion method combined with the regularization method. Finally, the mean value and standard deviation of the identified load are obtained, and the coefficient of variation and the upper and low bounds of the identified load are defined. The result of an example shows that compared with the Monte Carlo simulation (MCS) and perturbation method (PM), the proposed method has higher computational efficiency and accuracy.

Dynamic load identification algorithm based on Newmark-β and self-filtering

In this paper, a dynamic load identification iteration algorithm based on Newmark -β is proposed. Aiming at the problem of excessive iteration error in the process of calculation, a self-filtering algorithm is proposed and added to the load identification algorithm. After adding the self-filtering algorithm, the recognition accuracy of the algorithm has been improved significantly. The recognition result of the proposed method and explicit Newmark- β method is compared by simulations and experiment. The results show that the recognition precision and calculation efficiency of this algorithm are higher, especially in the aspect of calculation efficiency, the proposed method has obvious advantages. Under the same conditions, the proposed method can save a lot of computation time.

Thirteenth International Conference on Recent Advances in Structural Dynamics (RASD)

RASD2019: Recent Advances in Structural DynamicsPrefaceThis volume contains the papers presented at the Thirteenth International Conference on Recent Advances in Structural Dynamics (RASD). The twelve previous RASD conferences have been held every three years or so since 1980, primarily in Southampton, UK.This conference was devoted to theoretical, numerical and experimental developments in structural dynamics and their application to all types of structures and dynamical systems. The conference reflected the state-of-the-art structural dynamics and dynamical systems in science and engineering practice and it was an opportunity to exchange scientific, technical and experimental ideas.The Conference Proceedings included papers by authors from over twenty four countries, twenty one technical sessions and five plenary presentations. The five invited speakers were Professor Li Cheng (Hong Kong Polytechnic University, Hong Kong) presenting “Structural Wave Manipulation through Acoustic Black Holes”, Dr Alain Berry (Université de Sherbrooke, Canada) presenting “Time-space identification of dynamic transverse loads on plane elastic structures”, Professor Gaetan Kerschen (University of Liège, Belgium,) presenting “Dynamic vibration absorbers: revisiting classical results and introducing new tuning strategies”, Professor Domingos A. Rade (Aeronautics Institute of Technology, Brazil) presenting “Dynamic modeling of advanced composite materials”, and Dr John Macdonald (University of Bristol, UK) presenting “Human-structure interaction: modelling, experiments and full-scale measurements”.I would like to thank members of the Organising Committee for their help, over the last year or so, in shaping the conference and for their invaluable assistance in the paper review process. In particular, I would like to thank the hosting Chairs, Quentin Leclère and Nicolas Totaro from the Laboratory of Vibration and Acoustics of INSA Lyon. I would also like to thank the conference secretary, Harriet Gemmell, without whom there would be no conference. Lastly, I would like to thank all delegates for supporting the conference.Emiliano RustighiLyon, France15-17 April 2019List of Chairs, Organising Committee and Proceedings Editors and Conference Secretariat are available in this PDF.

Stochastic Dynamic Load Identification on an Uncertain Structure With Correlated System Parameters

Abstract A stochastic dynamic load identification algorithm is proposed for an uncertain dynamic system with correlated random system parameters. The stochastic Green's function is adopted to establish the relationship between the Gaussian excitation and the response. The Green's function is approximated by the second-order perturbation method, and orthogonal polynomial chaos bases are adopted to replace the corresponding bases in the Tayler series. The stochastic system responses and the stochastic forces are then represented by the polynomial chaos expansion (PCE) and the Karhunen–Loève expansion (KLE), respectively. A unified probabilistic framework for the stochastic dynamic problem is formulated based on the PCE. The stochastic load identification problem of an uncertain dynamic system is then transformed into a stochastic load identification problem of an equivalent deterministic system with the orthogonality of the PCE. Numerical simulations and experimental studies with a cantilever beam under a concentrate stochastic force are conducted to estimate the statistical characteristics of the stochastic load from the stochastic structural response samples. Results show that the proposed method has good accuracy in the identification of force's statistics when the level of uncertainty in the system parameters is not small. Large errors in the identified statistics may occur when the correlation in the random system parameters is neglected. Different correlation lengths for the random system parameters are investigated to show the effectiveness and accuracy of the proposed method.

Time-space identification of mechanical impacts and distributed random excitations on plates and membranes

The identification of dynamic loads acting on structures is a key aspect of several engineering domains involving structure-borne sound and vibration problems, stress analysis, or even the study of fatigue-induced structural damages. This work is concerned with the reconstruction of localized transient and distributed random excitations on plates and membranes from their measured vibration response. In previous investigations by the authors, the virtual fields method, an identification approach based on the principle of virtual work, was employed to identify mechanical and acoustic loadings applied to a bending panel. However, vibration data were obtained using scanning laser Doppler vibrometry, which limits the application of the virtual fields method to stationary excitations in both space and frequency. In contrast, the deflectometry technique used here is an optical method that directly provides a full-field measurement of local slopes. With the addition of a high-speed camera, the measurements are resolved in both space and time, enabling the study of nonstationary excitations. Moreover, since the acquisition time is independent of the number of measurement points, high spatial density measurements can be performed in seconds. This paper reviews the principles of the virtual fields method for nonstationary excitations on plates and membranes. The deflectometry technique is then demonstrated and experimental reconstruction results on an aluminum panel are presented for two different load cases: impacting metal marbles (multiple unknown transient excitations) and a diffuse acoustic field excitation. Finally, the identification of acoustic and aerodynamic (turbulent boundary layer) excitations is considered using a membrane as the receiving structure.

An inverse method for distributed dynamic load identification of structures with interval uncertainties

A time-domain based method for distributed dynamic load identification is proposed in this study considering unknown-but-bounded uncertainties in structural systems. The spatiotemporal dynamic load is further approximated by Chebyshev orthogonal polynomial in time history. Thus, the problem of distributed load reconstruction may be converted into the issue of polynomial coefficient calculation at each sampling time by utilizing a series of dynamic analysis. In accordance with the practical engineering, the acceleration response is used as the system input. In terms of the uncertainty quantification problems, the interval analysis method based on Taylor expansion (IAMBTE) is systematically developed to accomplish the envelope interval of identified load. To facilitate the analysis, two kinds of load are required to be identified, among which the nominal value of the identified load may be straightforwardly achieved through the inverse system, whereas the interval boundaries should be settled by the interval propagation analysis. Eventually, two numerical examples are investigated to demonstrate the efficiency and precision of the developed methodology.

Frequency Response-Based Indirect Load Identification Using Optimum Placement of Strain Gages and Accelerometers

This paper presents an approach for indirect identification of dynamic loads acting on a structure through measurement of structural response at a finite number of optimally selected locations. Using the concept of frequency response function (FRF), the structure itself is considered as a load transducer. Two different types of sensors are investigated to measure the structural response. These include a use of accelerometers that leads to the identification of the displacement mode shapes. The second measurement approach involves a use of strain gages since strain measurements are directly related to imposed loads. A use of mixed strain-acceleration measurements is also considered in this work. Optimum sensor locations are determined herein using the D-optimal design algorithm that provides most precise load estimates. The concepts of indirect load identification, strain frequency response function (SFRF), displacement frequency response function (DFRF), along with the optimal locations for sensors are used in this paper. The fundamental theory for strain-based modal analysis is applied to help estimate imposed harmonic loads. The similarities and differences between acceleration-based load identification and strain-based load identification are discussed through numerical examples.

Dynamic Load Identification and Displacement Prediction Based on FBG for a Cantilever Beam

To identify load and predict displacement of the cantilever beam, a dynamic strain measurement method based on distributed fiber Bragg grating (FBG) sensor network is proposed. The applied inverse algorithm contains two parts: Kalman filter (KF) without input items and a load estimator. Firstly, structure’s state equations are established using finite element method (FEM). Secondly, noise is suppressed and the displacement of cantilever beam is predicted through KF. Finally, the load is identified through the corresponding matrixes generated by KF. For the simulations of the sinusoidal load, rectangular load and triangular load, the mean errors of load identification are less than 0.058%, 0.273%, and 0.09%, respectively. The RMSE values of load identification are less than 0.283, 0.781 and 1.374, respectively. Under the above conditions, the mean errors of displacement prediction at the end node are less than 0.003%, 0.00012%, and 0.00016%, respectively. The RMSE values of displacement prediction at the end node are less than 0.025, 0.00034 and 0.00018, respectively. Both the results of simulation and experiment indicate that the method is feasible, and its performance is excellent.

A Novel Improved Maximum Entropy Regularization Technique and Application to Identification of Dynamic Loads on the Coal Rock

A new signal processing algorithm was proposed to identify the dynamic load acting on the coal-rock structure. First, the identification model for dynamic load is established through the relationship between the uncertain load vector, and the assembly matrix of the responses was measured by the machinery dynamic system. Then, the entropy item of maximum entropy regularization (MER) is redesigned using the robust estimation method, and the elongated penalty function according to the ill-posedness characteristics of load identification, which was named as a novel improved maximum entropy regularization (IMER) technique, was proposed to process the dynamic load signals. Finally, the load identification problem is transformed into an unconstrained optimization problem and an improved Newton iteration algorithm was proposed to solve the objective function. The result of IMER technique is compared with MER technique, and it is found that IMER technique is available for analyzing the dynamic load signals due to higher signal-noise ratio, lower restoration time, and fewer iterative steps. Experiments were performed to investigate the effect on the performance of dynamic load signals identification by different regularization parameters and calculation parameters, pi, respectively. Experimental results show that the identified dynamic load signals are closed to the actual load signals using IMER technique combined with the proposed PSO-L regularization parameter selection method. Selecting optimal calculated parameters pi is helpful to overcome the ill-condition of dynamic load signals identification and to obtain the stable and approximate solutions of inverse problems in practical engineering. Meanwhile, the proposed IMER technique can also play a guiding role for the coal-rock interface identification.

Research on Dynamic Load Identification Based on Explicit Wilson‐θ and Improved Regularization Algorithm

In the research of dynamic load identification, the method of obtaining kernel function matrix is usually rather cumbersome. To solve this problem, an explicit dynamic load identification algorithm based on the Wilson‐θ (DLIAEW) method is proposed to easily obtain the kernel function matrix as long as the parameters of the system are known. To aim at the ill‐posed problem in the inverse problem, this paper improves the Tikhonov regularization, proposes an improved regularization algorithm (IRA), and introduces the U‐curve method to determine the regularization parameters. In the numeric simulation investigation of a four dofs vibrating system, effects of the sampling frequency and the noise level on the regularization parameters and the identification errors of impact and harmonic loads for the IRA are discussed in comparison with the Tikhonov regularization. Finally, the experiments of a cantilever beam excited by impact and harmonic loads are carried out to verify the advantages of the IRA.