Research Papers

L-Curve Based Tikhonov’s Regularization Method for Determining Relaxation Modulus From Creep Test

[+] Author and Article Information
Yaoting Zhu

School of Transportation, Southeast University, No. 2 Sipailou, Nanjing 210096, China

Lu Sun1

School of Transportation, Southeast University, No. 2 Sipailou, Nanjing 210096, China; Department of Civil Engineering, Catholic University of America, Pangborn Hall, 620 Michigan Avenue Northeast, Washington, DC 20064

Huilin Xu

Department of Mathematics, Southeast University, No. 2 Sipailou, Nanjing 210096, China


Corresponding author.

J. Appl. Mech 78(3), 031002 (Feb 01, 2011) (7 pages) doi:10.1115/1.4002843 History: Received July 31, 2008; Revised January 08, 2010; Posted October 22, 2010; Published February 01, 2011; Online February 01, 2011

A numerical method for directly obtaining discrete relaxation modulus from static creep tests data is developed for linear viscoelastic asphalt mixtures. To overcome the ill-posedness of interconversion between creep compliance and relaxation modulus, Volterra integral equations of the second kind and L-curve based Tikhonov’s regularization method are used to construct the computational scheme of parameter estimation. A numerical case study is presented to demonstrate the efficiency of the regularization method, which takes into account different step lengths and noise levels. It indicates that the computed results are accurate and robust at different noise levels. Compared with other existing methods, the L-curve based Tikhonov’s regularization method provides the best parameter estimates in dealing with both the numerical case study and the experiment data. The method can be used to extract viscoelastic parameters of asphalt mixtures from creep tests effectively and robustly.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

A typical L-curve for Tikhonov regularization

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Figure 2

Exact data and noisy data with SNR=30 dB

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Figure 3

The relative error and computing time for different step length

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Figure 4

Exact solution and computed results with different noise levels

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Figure 5

Choice of regularization parameters with SNR=30 dB

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Figure 6

Computed results compared with different methods

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Figure 7

Results of different collocation for relaxation times

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Figure 8

Gradation curves of asphalt mixtures

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Figure 9

Calculated relaxation modulus of asphalt mixture




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