Modeling of stress spectrum using long-term monitoring data and finite mixture distributions

Yiqing Ni, X. W. Ye, J. M. Ko

Research output: Journal article publicationJournal articleAcademic researchpeer-review

85 Citations (Scopus)


This study focuses on how to exploit long-term monitoring data of structural strain for analytical modeling of multimodal rainflow-counted stress spectra by use of the method of finite mixture distributions in conjunction with a hybrid mixture parameter estimation algorithm. The long-term strain data acquired from an instrumented bridge carrying both highway and railway traffic is used to verify the procedure. A wavelet-based filtering technique is first applied to eliminate the temperature effect inherent in the measured strain data. The stress spectrum is obtained by extracting the stress range and mean stress from the stress time histories with the aid of a rainflow counting algorithm. By synthesizing the features captured from daily stress spectra, a representative sample of stress spectrum accounting for multiple loading effects is derived. Then, the modeling of the multimodal stress range is performed by use of finite mixed normal, lognormal, and Weibull distributions, with the best mixed distribution being determined by the Akaike's information criterion (AIC). The joint probability density function (PDF) of the stress range and the mean stress is also estimated by means of a mixture of multivariate distributions. It turns out that the obtained PDFs favorably fit the measurement data and reflect the multimodal property fairly well. The analytical expressions of PDFs resulting from this study would greatly facilitate the monitoring-based fatigue reliability assessment of steel bridges instrumented with structural health monitoring (SHM) system.
Original languageEnglish
Pages (from-to)175-183
Number of pages9
JournalJournal of Engineering Mechanics
Issue number2
Publication statusPublished - 3 Aug 2011


  • Fatigue assessment
  • Probability density functions
  • Probability distribution
  • Steel bridges
  • Stress
  • Structural health monitoring

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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