Research Papers

A Frequency Domain Method for Calculating the Failure Probability of Nonlinear Systems With Random Uncertainty

[+] Author and Article Information
Haitao Liao

Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China

Wenwang Wu

Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: ht0819@163.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 13, 2017; final manuscript received January 24, 2018; published online March 30, 2018. Assoc. Editor: Maurizio Porfiri.

J. Vib. Acoust 140(4), 041019 (Mar 30, 2018) (9 pages) Paper No: VIB-17-1456; doi: 10.1115/1.4039405 History: Received October 13, 2017; Revised January 24, 2018

A hybrid approach is proposed to evaluate the probability of unacceptable performance with respect to uncertain parameters. The evaluation of structural reliability and the solution of maximum vibration response are performed simultaneously. A constrained optimization problem is deduced for which several techniques have been developed to obtain the reliability index. The nonlinear equality constraints of the optimization problem are constructed based on the harmonic balance equations, the optimality condition of the maximum vibration response with respect to the vibration frequency and the limit state failure function. With the nonlinear equality constraints imposed on the harmonic balance equations and the derivative of the maximum vibration response with respect to the vibration frequency, the inner loop for solving the maximum vibration response is avoided. The sensitivity gradients are derived by virtue of the adjoint method. The original optimization formulation is then solved by means of the sequential quadratic programming method (SQP) method. Finally, the developed approach has been verified by comparison with reference values from Monte Carlo simulation (MCS). Numerical results reveal that the proposed method is capable of predicting the failure probability of nonlinear structures with random uncertainty.

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Grahic Jump Location
Fig. 1

Schematic illustration of a two-dimensional LSF



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