A new time domain method is presented to identify moving loads on a bridge deck based on the measured responses. The bridge deck is modeled as an orthotropic plate and the loads are modeled as a group of four loads moving on top of the bridge deck at fixed distance apart. Dynamic behavior of the bridge deck is analyzed by the orthotropic plate theory and mode superposition technique. Like all inverse problems, this identification is an ill-conditioned problem, and a regularization technique is employed to stabilize the computations. The identified loads moving at different eccentricities are presented. Laboratory work on the force identification is also presented. The effect of incomplete measured modes in the responses is discussed, and an underestimation in the loads may result if the number of vibration mode for identification is larger than that in the responses. Computational simulations and laboratory tests show that the method is effective and practical for identification of individual wheel loads on bridge decks.

1.

Yen

,

C.-S.

, and

Wu

,

E.

,

1995

, "

On the Inverse Problem of Rectangular Plates Subjected to Elastic Impact, Part I: Method Development and Numerical Verification

,"

ASME J. Appl. Mech.

,

62

(

3

), pp.

692

698

.

2.

Yen

,

C.-S.

, and

Wu

,

E.

,

1995

, "

On the Inverse Problem of Rectangular Plates Subjected to Elastic Impact, Part II: Experimental Verification and Further Application

,"

ASME J. Appl. Mech.

,

62

(

3

), pp.

699

705

.

3.

Choi

,

K. Y.

, and

Chang

,

F.-K.

,

1996

, "

Identification of Impact Force and Location Using Distributed Sensors

,"

AIAA J.

,

34

(

1

), pp.

136

142

.

4.

Moller

,

P. W.

,

1999

, "

Load Identification Through Structural Modification

,"

ASME J. Appl. Mech.

,

66

(

1

), pp.

236

241

.

5.

Rao

,

Z.-S.

,

Shi

,

Q.-Z.

, and

Hagiwara

,

I.

,

1999

, "

Optimal Estimation of Dynamic Loads for Multiple-Input System

,"

ASME J. Vibr. Acoust.

,

121

(

3

), pp.

397

401

.

6.

Lee

,

H.

, and

Park

,

Y. S.

,

1995

, "

Error Analysis of Indirect Force Determination and A Regularization Method to Reduce Force Determination Error

,"

Mech. Syst. Signal Process.

,

9

(

6

), pp.

615

633

.

7.

Busby

,

H. R.

, and

Trujillo

,

D. M.

,

1987

, "

Solution of An Inverse Dynamics Problem Using an Eigenvalue Reduction Technique

,"

Comput. Struct.

,

25

(

1

), pp.

107

117

.

8.

Busby

,

H. R.

, and

Trujillo

,

D. M.

,

1997

, "

Optimal Regularization of Inverse Dynamics Problem.

"

Comput. Struct.

,

63

(

2

), pp.

243

248

.

9.

Hansen

,

P. C.

,

1992

, "

Analysis of Discrete Ill-Posed Problems by Means of the L-Curve

,"

SIAM Rev.

,

34

(

4

), pp.

561

580

.

10.

Golub

,

G. H.

,

Heath

,

M.

, and

Wahaba

,

G.

,

1979

, "

Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter

,"

Technometrics

,

21

(

2

), pp.

215

223

.

11.

Kammer

,

D. C.

,

1998

, "

Input Force Reconstruction Using A Time Domain Technique

,"

ASME J. Vibr. Acoust.

,

120

(

4

), pp.

868

874

.

12.

O'Connor

,

C.

, and

Chan

,

T. H. T.

,

1988

, "

Dynamic Wheel Loads from Bridge Strains

,"

J. Struct. Div. ASCE

,

114

(

8

), pp.

1703

1723

.

13.

Chan

,

T. H. T.

, and

Yung

,

T. H.

,

2000

, "

A Theoretical Study of Force Identification Using Prestressed Concrete Bridge

,"

Eng. Struct.

,

23

(

12

), pp.

1529

1537

.

14.

Chan

,

T. H. T.

,

Law

,

S. S.

,

Yung

,

T. H.

, and

Yuan

,

X. R.

,

1999

, "

An Interpretive Method for Moving Force Identification

,"

J. Sound Vib.

,

219

(

3

), pp.

503

524

.

15.

Law

,

S. S.

,

Chan

,

T. H. T.

, and

Zeng

,

Q. H.

,

1997

, "

Moving Force Identification: A Time Domain Method

,"

J. Sound Vib.

,

201

(

1

), pp.

1

22

.

16.

Chan

,

T. H. T.

,

Law

,

S. S.

, and

Yung

,

T. H.

,

2000

, "

Moving Force Identification Using Existing Prestressed Concrete Bridge

,"

Eng. Struct.

,

22

(

10

), pp.

1261

1270

.

17.

Law

,

S. S.

,

Chan

,

T. H. T.

, and

Zeng

,

Q. H.

,

1999

, "

Moving Force Identification: A Frequency and Time Domain Analysis

,"

ASME J. Dyn. Syst., Meas., Control

,

121

(

3

), pp.

394

401

.

18.

Zhu

,

X. Q.

, and

Law

,

S. S.

,

1999

, "

Moving Forces Identification on A Multi-Span Continuous Bridge

,"

J. Sound Vib.

,

228

(

2

), pp.

377

396

.

19.

Zhu

,

X. Q.

, and

Law

,

S. S.

,

2000

, "

Identification of Vehicle Axle Loads from Bridge Responses

,"

J. Sound Vib.

,

236

(

4

), pp.

705

724

.

20.

Trujillo

,

D. M.

, and

Busby

,

H. R.

,

1983

, "

Investigation of a Technique for the Differentiation of Empirical Data

,"

ASME J. Dyn. Syst., Meas., Control

,

105

(

3

), pp.

200

202

.

21.

Law

,

S. S.

, and

Zhu

,

X. Q.

,

2000

, "

Study on Different Beam Models in Moving Force Identification

,"

J. Sound Vib.

,

234

(

4

), pp.

661

679

.

22.

Santantamarina, J. C., and Fratta, D., 1998, Introduction to Discrete Signals and Inverse Problems in Civil Engineering, ASCE Press.

23.

Fafard, M., and Mallikarjuna, Savard M., 1993, "Dynamics of Bridge-Vehicle Interaction," Structural Dynamics, Proc. EURODYN'93, pp. 951–960.

24.

Bakht, B., and Jaeger, L. G., 1985, Bridge Analysis Simplified, McGraw-Hill.

25.

The American Association of State Highway and Transportation Officials, 1996, Standard Specifications for Highway Bridges, Washington, D. C., U.S.A.

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