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A moving force identification technique based on a statistical system model is developed in this paper. Karhunen–Loéve expansion is employed to represent both the random forces and system parameters which are assumed to be Gaussian distributed with the bridge–vehicle system as the background of study. Road surface roughness is a main contributor to...
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... Step 1, 500 sample sets of seven nodal displacements evenly distributed along the structure are obtained from simulation using the proposed method described in Section 3 which is noted as the K-L method and the Latin Hypercube Sampling (LHS) technique. The covariance kernel of the response is shown in Fig. ...
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... For each given sampling frequency, four different values of vehicle speed were randomly generated from the set[5,10,20,40] m/s. ...
This study proposes a novel moving force neural identifier (MFNI), a deep neural network designed for accurately estimating dynamic vehicular axle loads without knowing the vehicle speed and axle configurations (i.e., axle number and spacing). The MFNI architecture comprises a multi-time resolution encoder/decoder (MRED) and a dynamic moving force correction block (DMF-corr block). Firstly, the MRED with hierarchical resolution is developed to adapt to the complex dynamic inverse problem-solving. It can capture the multi-time resolution features of bridge responses and dynamic moving forces, and perform stably under various lengths of identification sampling windows. Then, the DMF-corr block limits the range of identified values by assuming that the vehicular excitation on the bridge is unidirectional, which enables the MFNI model to better determine the axle number, vehicle speed, as well as whether the axle is acting on the bridge. Numerical studies are implemented to confirm the accuracy and efficiency of the proposed MFNI approach, and a parametric sensitivity analysis is conducted to evaluate the robustness of the approach. Finally, a laboratory experiment confirms the practicability of the MFNI in detecting vehicular moving forces with a limited number of sensors and training samples. Both numerical and experimental results demonstrate the potential of the proposed method to serve as a nothing-on-road bridge weigh-in-motion system in practical engineering.
... Many scholars have researched force identification problems with structural uncertainties based on interval models [20][21][22], fuzzy sets [23], and probabilistic models [24][25][26][27][28]. When the distribution intervals of the random structural variables are known, the interval perturbation method (IPM) can be used to identify the upper and lower bounds of the forces applied to the structure. ...
... Xu et al. [23] concluded that the IPM could not effectively quantify the effect of structural epistemic uncertainties on unknown forces and proposed a non-intrusive dynamic force fuzzy identification method to obtain a fuzzy description of the forces. With a known probability distribution of the random structural parameters, Wu and Law [24] used the Karhunen-Loève expansion to represent the moving forces and structural parameters to identify the mean and variance of the forces. Liu et al. [25] identified statistical properties of forces by approximating the stochastic structural parameters with the λ-probability density function (PDF) or their derivative PDFs based on the Gegenbauer polynomial expansion theory. ...
... [22][23][24] deal with moving load identification for continuous systems using modal superposition and a convolution integral. Concerning discretized systems and moving load identification, Ref. [25] solves a problem based on a stochastic FE model, while Ref. [26] formulates an explicit form of the Newmark-β method with numerical and experimental load identification assessment. Mostly, the literature on moving load identification is related to bridge structures. ...
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4634868
... In this paper, Moving Force Identification (MFI) theory [5] is used to calculate an equivalent deflection, defined as the imposed deflection signal at a point which would generate the measured acceleration. Conventional MFI [6][7][8] calculates the force signal corresponding to a measured acceleration and the principle is similar. ...
... Secondly, the purpose of structural dynamic analysis mainly focuses on formulating a function that can be used for expressing the relationship between dynamic force and structural responses. In some existing publications, the relationship between input and output can be expressed as a function of random variables [8,9]. As a result, some methodologies of force identification developed from the above relationship are always categorized as probabilistic/statistical methods [5]. ...
... ɑ is a coefficient vector including the information of dynamic forces. Herein, Eq. (8) is not normalized using the structural responses as one have done in Ref. [15]. In this way, we can ensure that different transfer matrices obtained from different time segment with (4) y Ni + 2 i iẏNi + 2 i y Ni = 0 , i = 1, 2, … , l, ...
... Firstly, we define a representative value R V as where N c represents the column number of matrix H f . Then an adjusted matrix ̄ y corresponding to initial condition is formulated, in which all the columns are calculated as According to Eqs. (8) and (10), the relationship between input and structural responses can be rewritten as where A = [H f , H̄y] is a system matrix corresponding to forces and initial condition. β = [ɑ T , Y T new ] T is a vector representing the excitation sources, in which Y new is a novel representation of initial condition. ...
Rapid identification of dynamic forces is an important research subject. To reduce the computing time, a parallel computing-oriented method is proposed in this study for dealing with a long-time duration problem of force identification. The proposed method is implemented via three continues steps, i.e., partition of parallel computing tasks, solution of parallel computing tasks and fusion of the identified results. In the first step, moving time window is applied for splitting an original problem into several sub-problems in time domain. Then the next step focuses on solving the sub-problems which can be executed in parallel. Herein, influences of unknown initial conditions are considered. Sparse regularization such as weighted l1-norm regularization method is introduced for ensuring that the identified result is sparse and stable. In the last step, the identified results calculated from all the sub-problems are fused via a weighted average method. Numerical simulations are carried out on a frame structure and a truss structure, respectively. A cluster constructed from three personal computers is used for implementation of the proposed method. Illustrated results show that the proposed method can be used for identifying the dynamic forces in long-time duration and saving the computing time. Some related issues are discussed as well.
... Generally, dynamic load identification methods can be divided into two categories: frequency-domain methods [6,7] and time-domain methods [8,9]. The spectrum of dynamic load is estimated from the spectrum of structural responses in frequency-domain methods, which are more suitable for stationary dynamic load identification. ...
Distributed load information is essential for the design and monitoring of aerospace structures. A frequency domain method for the identification of correlated random fluctuating pressure is proposed in which structural responses acquired from limited strain sensors are used. The spatially-correlated power spectral density function of the random fluctuating pressure on the structure is firstly represented by Legendre polynomials w.r.t. the spatial distance multiplying their corresponding frequency-dependent coefficients. Secondly, the transfer matrix is obtained by the stochastic response analysis using distributed load in the form of Legendre polynomials. Then, the coefficients in the power spectral density function model of the pressure are identified by inversion of the transfer matrix together with a modified regularization technique. Finally, the random fluctuating pressure load is reconstructed by the superposition of the identified coefficients multiplying with Legendre polynomials. Numerical simulations on a simply-supported plate subjected to correlated stochastic distributed loads are conducted to verify the proposed method. Factors that may influence the accuracy of identification results are also discussed. To test the performance of the proposed method on complex structures, the gust-induced pressure load on a 3D wing structure is further identified using the proposed method. Results show that the proposed method is capable of identifying the correlated random fluctuating pressure on aircraft structures.
... To find a method that can directly use acceleration and estimate GVW with good accuracy, an MFI algorithm is chosen. MFI has been proposed as a method of BWIM that potentially can give more accurate and more detailed results than the traditional approach [18][19][20]. Several forms of the MFI algorithm exist but all derive axle force histories from the equations of motion [21][22][23][24][25]. ...
... This paper presents a newly developed acceleration-based MFI (A-MFI) algorithm, that reformulates existing MFI theory to allow, for the first time, directly measured acceleration data to be used (refer to Equations (19) and (20)). This reformulation of the underlying MFI equations allows the new A-MFI algorithm to be directly applied to acceleration data, which is damage sensitive. ...
This paper presents a new moving force identification (MFI) algorithm that uses measured accelerations to infer applied vehicle forces on bridges. Previous MFI algorithms use strain or deflection measurements. Statistics of the inferred forces are used in turn as indicators of global bridge damage. The new acceleration-based MFI algorithm (A-MFI) is validated through numerical simulations with a coupled vehicle-bridge dynamic interaction model programmed in MATLAB. A focussed sensitivity study suggests that results are sensitive to the accuracy of the vehicle velocity data. The inferred Gross Vehicle Weight (GVW), calculated by A-MFI, is proposed as the bridge damage indicator. A real weigh-in-motion database is used with a simulation of vehicle/bridge interaction, to validate the concept. Results show that the standard deviation of inferred GVWs has a good correlation with the global bridge damage level.
... Numerous dynamic load identification methods have been developed in the past decades and can mainly be divided into two categories: frequency-domain methods [12,13] and time-domain methods [14][15][16][17]. In frequency-domain methods, frequency spectra of the structural responses are used to estimate the corresponding spectra of external forces. ...
... Because the modified Green's function G is usually ill posed and the measured structural responses always contain noise in engineering practice, the Tikhonov regularization technique [37] is adopted for solving Eq. (15). The purpose of Tikhonov regularization is to find a stability solution by minimizing the weighted combination of the residual norm and the solution norm, which can be transformed into the optimization problem ...
... By calculating the transient responses at all measuring points subject to the unit distributed pulse load on each domain, the modi- Article in Advance / ZHENG, WU, AND FEI fied Green's function matrix G in Eq. (14) can be assembled. The force vector P can further be estimated from the vector Y by solving Eq. (15) or Eq. (18). ...
Spatially distributed load on aircraft structures is difficult to obtain due to the limitation of measurement technology, the complexity of load and the external environment of the aircraft during flight, etc. A load identification method based on a subregion interpolation technique is proposed to indirectly estimate the distributed dynamic load from measured strain data on planar structures. The load distribution area is discretized into several subregions and the load distribution function in each subregion is represented by a set of local interpolation functions multiplied by their corresponding coefficients. A modified Green's function matrix is formulated to establish the relationship between the local distributed dynamic load in the domain composed of the subregions sharing the same node and the structural response data. Hence, both the load's distribution and time histories can be identified from structural response by solving the new formulated inverse problem. Numerical simulations on a flat cantilever plate and a planar structure with irregular geometry are conducted to show the effectiveness of the proposed method. Results show that the proposed method has better adaptability on the types of load distribution and structural configurations than the existing methods. Nomenclature a = coefficient of interpolation function C = matrix connecting distributed dynamic load and node forces f = distribution function of distributed dynamic load, Pa G = Green's function matrix G = modified Green's function matrix g = Green's function L = number of time steps N e k;r = shape functions of finite element N = interpolation function for load subregion, Pa P = vector of discretized distributed dynamic load p = distributed dynamic load, Pa Q = global nodal force vector, N q = nodal force of finite element, N q k;r = nodal force vector, N s = time history of distributed dynamic load, s t = time variable, s x = spatial coordinate at x direction, m Y = structural response vector y = spatial coordinate at y direction, m β = transformation matrix between elemental coordinate and global coordinate ζ, η = local coordinates in finite element
... Two methods have been proposed. The first one is a non-intrusive method by modelling stochastic system using independent realizations, then the SLI on uncertain structures can be transformed to the SLI on a set of deterministic structures [25]; The second one is an intrusive method based on the stochastic finite element model [26], the uncertainty in structural response due to stochastic system parameters is firstly removed by the proposed algorithm, and then the statistics of stochastic forces can be identified from the covariance kernel of structural response only due to the stochastic excitations. Another kind of method to identify stochastic dynamic load on uncertain structure is based on Bayesian method [27,28], in which Bayesian credible intervals of the force are 4 built from its posterior probability density function by taking into account the quantified model uncertainty and measurement noise. ...
... The non-intrusive SLI method considering system uncertainty is generally time consuming; on the other hand, the intrusive SLI method based on the stochastic finite element model is usually only suitable very simple uncertain structures, e.g. a beam structure [26]. This paper aims to propose an intrusive SLI algorithm suitable for complex uncertain structures. ...
... Based on the definition of stochastic Green's function, when a stochastic dynamical system modeled by stochastic finite element method [26] subjects to a unit pulse force (t), we have ...
... Liu and Han [21] applied both dynamic Green's function [56] and the response function of Heaviside step excitation of the composite laminate to identify the concentrated and distributed dynamic loads. Chan et al. [22][23][24] investigated the identification of moving forces exciting on a bridge-vehicle system and developed several approaches. Noting that there are slowly-varying harmonic and impact signals contained in moving forces because of bridge vibration and bumps on a bridge deck, Pan and Yu et al. [25] developed a new method for moving force identification by adopting redundant concatenated dictionary and weighted L 1 -norm regularization method. ...
Based on the thought of Green’s kernel function method (GKFM), an improved time-domain load identification method using moving weighted least square technique (MWLST) which can accurately fit dynamic load is proposed. Better than the traditional shape function method using moving least square fitting (SFM_MLSF), the proposed method considers continuity and correlation of dynamic load between two adjacent sampling points, and involves the weighted contribution of sampling points to the fitting point. In numerical examples, Gauss, Cubic and Quartic spline weight functions are utilized in the proposed method to realize the reconstruction of kernel matrix. It is found that the accuracies of load identification are almost same when their optimum supported domain radii are adopted. Furthermore, the numerical results illustrate that the proposed method can identify dynamic load more accurately and smoothly than GKFM and SFM_MLSF significantly by the same regularization method for ill-posedness, and the proposed method has excellent stability and robustness. Additionally, a special technique combining both the whole identification and the truncated-processing identification is proposed to identify external dynamic loads during hoisting process, which solves the oscillation problem caused by using inversing methods directly.
