Solution of an inverse dynamics problem using an eigenvalue reduction technique

Busby, Henry R.; Trujillo, David

doi:10.1016/0045-7949(87)90222-7

Cited by 49 publications

(24 citation statements)

References 13 publications

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“…The storage requirements of the dynamic programming routine for system of Equations (1) are very expensive, and some technique is necessary to reduce the dimension of the system. An eigenvalue reduction technique is employed for this purpose [24,33]. It is assumed that the displacements vector, {y}, can be replaced with an equivalent vector of modal coordinates, {z}, through Equation (2).…”

Section: Inverse Model and State Space Equationsmentioning

confidence: 99%

A general solution to the identification of moving vehicle forces on a bridge

González

Rowley

O’Brien

2008

Numerical Meth Engineering

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Magnetic nickel shells can be grown on gold nanorods with platinum tips by reduction of Ni2+ with hydrazine in aqueous cetyl‐trimethylammonium bromide (CTAB) solution, using Pt tips as catalysts. The plasmon absorption of the starting gold nanorods can be totally quenched by the metallic layer of nickel, while the magnetic character of these anisotropic, hybrid nanocrystals is demonstrated through alignment under an external magnetic field. Quasi‐epitaxial growth is demonstrated by HRTEM and electron diffraction (see figure).

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Section: Inverse Model and State Space Equationsmentioning

confidence: 99%

A general solution to the identification of moving vehicle forces on a bridge

González

Rowley

O’Brien

2008

Numerical Meth Engineering

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“…The MFI algorithm implemented here was developed by the authors [3][4][5], and is an extension of the one-dimensional algorithm by Law and Fang [6] to two dimensions. The mathematics behind general inverse theory is available in the literature [7][8][9][10][11]. The MFI algorithm requires a finite element (FE) mathematical model that accurately represents the static and dynamic behavior of the bridge structure.…”

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confidence: 99%

Experimental Testing of a Moving Force Identification Bridge Weigh-in-Motion Algorithm

et al. 2008

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Bridge weigh-in-motion systems are based on the measurement of strain on a bridge and the use of the measurements to estimate the static weights of passing traffic loads. Traditionally, commercial systems employ a static algorithm and use the bridge influence line to infer static axle weights. This paper describes the experimental testing of an algorithm based on moving force identification theory. In this approach the bridge is dynamically modeled using the finite element method and an eigenvalue reduction technique is employed to reduce the dimension of the system. The inverse problem of finding the applied forces from measured responses is then formulated as a least squares problem with Tikhonov regularization. The optimal regularization parameter is solved using the Lcurve method. Finally, the static axle loads, impact factors and truck frequencies are obtained from a complete time history of the identified moving forces.Keywords: Bridge, Weigh-in-motion, Force identification, Regularization, Dynamic programming, Traffic loads Moving Force Identification Bridge Weigh-in-Motion AlgorithmThe traditional static bridge weigh-in-motion (B-WIM) algorithm provides static axle weights from minimizing the sum of squares of differences between measured total bridge strain and theoretical static strain [1]. Although the deviations with respect to the static response that vehicle and bridge dynamics introduce in the measured response tend to be averaged out during the minimization process, they remain a significant source of inaccuracy [2]. This paper proposes an alternative B-WIM algorithm that calculates the time history of moving forces as they cross the bridge, based on moving force identification (MFI) theory. The MFI algorithm implemented here was developed by the authors [3][4][5], and is an extension of the one-dimensional algorithm by Law and Fang [6] to two dimensions. The mathematics behind general inverse theory is available in the literature [7][8][9][10][11]. The MFI algorithm requires a finite element (FE) mathematical model that accurately represents the static and dynamic behavior of the bridge structure. The method of dynamic programming requires that the equilibrium equation of motion be converted to a discrete time integration scheme. In this case the equilibrium equation of motion is reduced to an equation in modal coordinates defined by:where [Φ] is the modal matrix of normalized eigenvectors and n z is the number of modes to be used in the inverse analysis.[Ω] is a diagonal matrix containing the natural frequencies and ζ is the percentage damping. [L(t)] is a time varying location matrix relating the n g applied vehicle forces of the vector g(t) to the degrees of freedom, n dof , of the original FE model. Tikhonov regularization [12] is applied to provide a bound to the error and 'smoother' solutions to the ill-conditioning nature of the MFI problem [13,14]. The final part of the solution lies in the calculation of the optimal regularization parameter; the L-curve has been chosen to obtain...

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“…The manipulation of Equation 1 to produce the final equation in state space includes an eigenvalue reduction technique [18] which reduces the computational demands of the calculations. In state space, the equation becomes:…”

Section: State Space Equations and Dynamic Programmingmentioning

confidence: 99%

“…This method utilises dynamic programming in combination with first order regularisation and the eigenvalue reduction technique, which reduces the order of the system [18], to calculate the history of a number of vehicle forces from multiple strain measurements on the bridge. An unresolved problem for MFI algorithms in Bridge WIM is the MFI based algorithm's requirement for an accurate Finite Element (FE) model of the bridge.…”

Section: Introductionmentioning

confidence: 99%

Adaptation of Cross Entropy optimisation to a dynamic Bridge WIM calibration problem

Dowling

O’Brien

González

2012

Engineering Structures

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Publication information Engineering Structures, 44 (44): 13-22Publisher Elsevier Item record/more information http://hdl.handle.net/10197/4858 Publisher's statementThis is the author's version of a work that was accepted for publication in Engineering Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Engineering Structures (44, , (2012) AbstractMoving Force Identification (MFI) theory can be used to create an algorithm for a Bridge Weigh-in-Motion (WIM) system that can produce complete force histories of the loads that have traversed a bridge structure. MFI is based on general inverse theory, however, and calibration of such a system requires a complete Finite Element (FE) model of the bridge to be available for implementation in the field. This is something that is often infeasible in practice as FE models created using theoretical values for material properties bear a poor relation to reality. The Cross-Entropy optimisation method has been adapted here to address this calibration problem. The general system FE global mass and stiffness matrices of the bridge FE model are found by best fit optimisation to match field measurements. In this fashion a fully automated calibration procedure is developed for an MFI algorithm. This system is tested theoretically using three different FE plate models, coupled with a threedimensional vehicle model, allowing for Vehicle Bridge Interaction (VBI).

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Solution of an inverse dynamics problem using an eigenvalue reduction technique

Cited by 49 publications

References 13 publications

A general solution to the identification of moving vehicle forces on a bridge

A general solution to the identification of moving vehicle forces on a bridge

Experimental Testing of a Moving Force Identification Bridge Weigh-in-Motion Algorithm

Adaptation of Cross Entropy optimisation to a dynamic Bridge WIM calibration problem

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