Influence line extraction by deconvolution in the frequency domain

Abstract This paper proposes a new method for extracting static influence lines from measurements on bridges. The response of a structure is the convolution of the load and the influence line. Previous research has not embraced the fact that convolution is very efficiently handled in the frequency domain. The new method is based on the Fourier transform, which reduces the computational complexity of influence line extraction by several orders of magnitude compared to the conventional matrix method. The method can therefore be used to extract influence lines in near real time when implemented in low-powered devices, high-sensor-count systems, under high sampling rates and/or long signal sizes. It is shown that the inverse approach is ill-posed for certain vehicle configurations. A regularization technique for the ill-posed inverse problem is provided by a stabilizing filter. A numerical example is used to validate the regularization technique. The feasibility of the proposed method on real-world applications is demonstrated by a case study. The method is relevant to applications of and research on B-WIM algorithms, damage detection in structural health monitoring applications as well as model validation and model updating in the model-based evaluation of bridges.

[1]  Arturo González,et al.  Wavelet domain analysis for identification of vehicle axles from bridge measurements , 2006 .

[2]  Raid Karoumi,et al.  Implementing bridge weigh-in-motion for railway traffic , 2007 .

[3]  Nasim Uddin,et al.  Field-calibrated influence lines for improved axle weight identification with a bridge weigh-in-motion system , 2015 .

[4]  Moshe Livneh,et al.  Optimal Quality Characteristic Evaluation for Asphalt Mixing Plants , 2003 .

[5]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[6]  C. S. Cai,et al.  State-of-the-art review on bridge weigh-in-motion technology , 2016 .

[7]  Dan M. Frangopol,et al.  Influence line- model correction approach for the assessment of engineering structures using novel monitoring techniques , 2012 .

[8]  Y. L. Xu,et al.  Multiscale Modeling and Model Updating of a Cable-Stayed Bridge. II: Model Updating Using Modal Frequencies and Influence Lines , 2015 .

[9]  Gene H. Golub,et al.  Matrix computations , 1983 .

[10]  Eugene J. O'Brien,et al.  Calculating an influence line from direct measurements , 2006 .

[11]  Ian F. C. Smith,et al.  Damage detection using data-driven methods applied to moving-load responses , 2013 .

[12]  B. R. Hunt,et al.  The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer , 1973, IEEE Transactions on Computers.

[13]  Fred Moses,et al.  Weigh-In-Motion System Using Instrumented Bridges , 1979 .

[14]  You-Lin Xu,et al.  Damage Detection in Long Suspension Bridges Using Stress Influence Lines , 2015 .

[15]  James Demmel,et al.  LAPACK Users' Guide, Third Edition , 1999, Software, Environments and Tools.

[16]  Myra Lydon,et al.  Recent developments in bridge weigh in motion (B-WIM) , 2016 .

[17]  Eiki Yamaguchi,et al.  Bridge-Weigh-In-Motion by Two-Span Continuous Bridge with Skew and Heavy-Truck Flow in Fukuoka Area, Japan , 2009 .

[18]  E. Kreyszig,et al.  Advanced Engineering Mathematics. , 1974 .

[19]  ProblemsPer Christian HansenDepartment.  The L-curve and its use in the numerical treatment of inverse problems , 2000 .

[20]  Huijuan Zhao,et al.  Application of Fourier-wavelet regularized deconvolution for improving image quality of free space propagation x-ray phase contrast imaging , 2012, Physics in medicine and biology.

[21]  P. Hansen.  Discrete Inverse Problems: Insight and Algorithms , 2010 .

[22]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[23]  Arturo González,et al.  The Virtual Axle concept for detection of localised damage using Bridge Weigh-in-Motion data , 2015 .

[24]  Maja Kreslin,et al.  Railway Bridge Weigh-in-Motion System , 2016 .

[25]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[26]  R Zaurin,et al.  Integration of computer imaging and sensor data for structural health monitoring of bridges , 2009 .

[27]  Álvaro Cunha,et al.  Weigh-in-motion implementation in an old metallic railway bridge , 2016 .

[28]  Arturo González,et al.  A filtered measured influence line approach to bridge weigh-in-motion , 2010 .

[29]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[30]  Mark F. Green,et al.  A regularised solution to the bridge weigh-in-motion equations , 2009 .

[31]  Steven W. Smith,et al.  The Scientist and Engineer's Guide to Digital Signal Processing , 1997 .

[32]  Eugene J. O'Brien,et al.  Testing of bridge weigh-in-motion system in a sub-arctic climate , 2003 .