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.
Skip Nav Destination
Article navigation
August 2018
Research-Article
A Frequency Domain Method for Calculating the Failure Probability of Nonlinear Systems With Random Uncertainty
Haitao Liao,
Haitao Liao
Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China
Beijing Institute of Technology,
Beijing 100081, China
Search for other works by this author on:
Wenwang Wu
Wenwang Wu
Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: ht0819@163.com
Beijing Institute of Technology,
Beijing 100081, China
e-mail: ht0819@163.com
Search for other works by this author on:
Haitao Liao
Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China
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
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. Aug 2018, 140(4): 041019 (9 pages)
Published Online: March 30, 2018
Article history
Received:
October 13, 2017
Revised:
January 24, 2018
Citation
Liao, H., and Wu, W. (March 30, 2018). "A Frequency Domain Method for Calculating the Failure Probability of Nonlinear Systems With Random Uncertainty." ASME. J. Vib. Acoust. August 2018; 140(4): 041019. https://doi.org/10.1115/1.4039405
Download citation file:
Get Email Alerts
Cited By
Primary Resonance in a Weakly Forced Oscillator With Both Parametric Damping and Stiffness
J. Vib. Acoust (February 2024)
Reduced-Order Modeling in Rotordynamics and Its Robustness to Random Matrix Perturbation
J. Vib. Acoust (February 2024)
Reviewer's Recognition
J. Vib. Acoust (February 2024)
Related Articles
An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems
J. Appl. Mech (October,2015)
Using Constrained Bilinear Quadratic Regulator for the Optimal Semi-Active Control Problem
J. Dyn. Sys., Meas., Control (November,2017)
Nonlinear Stochastic Dynamics, Chaos, and Reliability Analysis for a Single Degree of Freedom Model of a Rotor Blade
J. Eng. Gas Turbines Power (January,2009)
Uncertainty of Integral System Safety in Engineering
ASME J. Risk Uncertainty Part B (June,2022)
Related Proceedings Papers
Related Chapters
Establishing Unmanning Criteria for a Jacket Structure on the NCS
Ageing and Life Extension of Offshore Facilities
PSA Level 2 — NPP Ringhals 2 (PSAM-0156)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
A PSA Update to Reflect Procedural Changes (PSAM-0217)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)