A regularised solution to the bridge weigh-in-motion equations

The traditional approach to Bridge Weigh-in-Motion (WIM) developed by Moses, gives good accuracy for estimating gross vehicle weights but is less accurate for individual axle weights. In this paper, Tikhonov regularisation is applied to the original Moses' equations to reduce some of the inaccuracies inherent within the algorithm. The optimal regularisation parameter is calculated using the L-curve criterion. The new regularised solution is numerically tested using simulations of moving vehicles on a bridge. Results show that the regularised solution performs significantly better than the original approach of Moses and is insensitive to road surface roughness.

[1]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

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

[3]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[4]  Arturo González,et al.  Development of accurate methods of weighing trucks in motion , 2001 .

[5]  Kentaro Yamada,et al.  BWIM SYSTEMS USING TRUSS BRIDGES , 2000 .

[6]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[7]  R J Peters.  AXWAY - A SYSTEM TO OBTAIN VEHICLE AXLE WEIGHTS , 1984 .

[8]  David Cebon,et al.  Dynamic Response of Highway Bridges to Heavy Vehicle Loads: Theory and Experimental Validation , 1994 .

[9]  Bernard Jacob,et al.  TEST OF A MULTIPLE SENSOR AND FOUR PORTABLE WIM SYSTEMS , 2000 .

[10]  Eugene J. O'Brien,et al.  Test of WIM sensors and systems on an urban road , 2000 .

[11]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

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

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

[14]  Eugene J. O'Brien,et al.  Comparison of two independently developed bridge weigh–in–motion systems , 1999 .

[15]  R J Peters.  CULWAY, AN UNMANNED AND UNDETECTABLE HIGHWAY SPEED VEHICLE WEIGHING SYSTEM , 1986 .

[16]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

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

[18]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[19]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[20]  Donald A. Streit,et al.  Vehicle based weigh-in-motion system , 1998 .

[21]  David J. Cole,et al.  Effects of Vehicle Suspension Design on Dynamics of Highway Bridges , 1995 .

[22]  Eugene J. O'Brien,et al.  High-accuracy bridge WIM systems and future applications , 1999 .

[23]  A Znidaric,et al.  BRIDGE WEIGH-IN-MOTION SYSTEMS - AN OVERVIEW , 1998 .

[24]  Mark F. Green,et al.  Theoretical testing of a multiple-sensor bridge weigh-in-motion algorithm , 2002 .

[25]  Tommy H.T. Chan,et al.  WHEEL LOADS FROM BRIDGE STRAINS: LABORATORY STUDIES , 1988 .