We study the reliability of stochastically excited and controlled single first-integral systems and present an approximate analytical solution for the first-passage rate (FPR). By introducing the stochastic averaging method (SAM), we reduce the dimension of the original system to an averaged one-dimensional controlled Ito^ differential equation. We then modify the classic Laplace integral method (LIM) and apply it to deal with the arduous integrals in the expression of reliability function. The procedure of acquiring the analytical solution for the reliability is illuminated in detail as well. In addition, we provide two controlled single first-integral nonlinear vibration systems, namely, the classical bistable model and the two coupled nonlinear oscillators, as examples. By comparing the results obtained from the modified Laplace integral method (MLIM) to Monte Carlo simulations (MCS), we verify the effectiveness and exactness of the proposed procedure. We identified two properties in the obtained analytical solution: One is that the solutions are independent of the initial system state. The other is that they are only effective in the high passage threshold range. Finally, a reasonable explanation has been given to explain these two properties.
Skip Nav Destination
Article navigation
June 2019
Research-Article
Approximate Analytical Solutions of Reliability for Controlled Single First-Integral Nonlinear Stochastic Systems
Shenlong Wang,
Shenlong Wang
School of Mechanical Engineering,
University of Shanghai for Science
and Technology,
Shanghai 200093, China
e-mail: shenlongwang@usst.edu.cn
University of Shanghai for Science
and Technology,
Shanghai 200093, China
e-mail: shenlongwang@usst.edu.cn
Search for other works by this author on:
Shilun Zhao
Shilun Zhao
School of Mechanical Engineering,
University of Shanghai for Science
and Technology,
Shanghai 200093, China
e-mail: zhaoshilun@st.usst.edu.cn
University of Shanghai for Science
and Technology,
Shanghai 200093, China
e-mail: zhaoshilun@st.usst.edu.cn
Search for other works by this author on:
Shenlong Wang
School of Mechanical Engineering,
University of Shanghai for Science
and Technology,
Shanghai 200093, China
e-mail: shenlongwang@usst.edu.cn
University of Shanghai for Science
and Technology,
Shanghai 200093, China
e-mail: shenlongwang@usst.edu.cn
Maolin Deng
Shilun Zhao
School of Mechanical Engineering,
University of Shanghai for Science
and Technology,
Shanghai 200093, China
e-mail: zhaoshilun@st.usst.edu.cn
University of Shanghai for Science
and Technology,
Shanghai 200093, China
e-mail: zhaoshilun@st.usst.edu.cn
1Corresponding author.
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 10, 2018; final manuscript received November 29, 2018; published online February 5, 2019. Assoc. Editor: Maurizio Porfiri.
J. Vib. Acoust. Jun 2019, 141(3): 031009 (9 pages)
Published Online: February 5, 2019
Article history
Received:
June 10, 2018
Revised:
November 29, 2018
Citation
Wang, S., Deng, M., and Zhao, S. (February 5, 2019). "Approximate Analytical Solutions of Reliability for Controlled Single First-Integral Nonlinear Stochastic Systems." ASME. J. Vib. Acoust. June 2019; 141(3): 031009. https://doi.org/10.1115/1.4042277
Download citation file:
Get Email Alerts
Cited By
Designing Topological Acoustic Lattices via Electroacoustic Analogies
J. Vib. Acoust (October 2023)
On the Feasibility of Dynamic Substructuring for Hybrid Testing of Vibrating Structures
J. Vib. Acoust (August 2023)
Related Articles
Probabilistic Control for Uncertain Systems
J. Dyn. Sys., Meas., Control (March,2012)
Nonlinear Stochastic Dynamics and Control in Hamiltonian
Formulation
Appl. Mech. Rev (July,2006)
Approximating
Markov Chain Approach to Optimal Feedback Control of a Flexible
Needle
J. Dyn. Sys., Meas., Control (November,2016)
Optimal Control Strategies for Robust Certification
J. Comput. Nonlinear Dynam (July,2010)
Related Proceedings Papers
Related Chapters
Stability for a Class of Infinite Dimension Stochastic Systems with Delay
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)
Establishing Unmanning Criteria for a Jacket Structure on the NCS
Ageing and Life Extension of Offshore Facilities
A PSA Update to Reflect Procedural Changes (PSAM-0217)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)