scholarly journals Reliability analysis of the uncertain fractional‐order dynamic system with state constraint

2021 ◽  
Author(s):  
Ting Jin ◽  
Hongxuan Xia ◽  
Shangce Gao
Keyword(s):  
Dynamic System ◽  
Reliability Analysis ◽  
Fractional Order ◽  
State Constraint

scholarly journals RELIABILITY ANALYSIS OF THE UNCERTAIN FRACTIONAL-ORDER DYNAMIC SYSTEM WITH STATE CONSTRAINT

2021 ◽  
Author(s):  
Ting Jin ◽  
Hongxuan Xia ◽  
Shangce Gao
Keyword(s):  
Dynamic System ◽  
Reliability Analysis ◽  
Fractional Order ◽  
Uncertain System ◽  
State Constraint ◽  
Barrier Option ◽  
Initial State ◽  
Expected Time ◽  
Liu Process ◽  
Predictor Corrector

Uncertain fractional-order differential equations driven by Liu process are of significance to depict the heredity and memory features of uncertain dynamical systems. This paper primarily investigates the reliability analysis of the uncertain fractional-order dynamic system with a state constraint. On the basis of the first-hitting time (FHT), a novel uncertain fractional-order dynamic system considering a state constraint is proposed. Secondly, in view of the relation between the initial state and the required standard, such uncertain fractional-order dynamic systems are subdivided into four types. The concept of reliability of proposed uncertain system with a state constraint is presented innovatively. Corresponding reliability indexes are ulteriorly formulated via FHT theorems. Lastly, the uncertain fractional-order dynamic system with a state constraint is applied to different physical and financial dynamical models. The analytic expression of the reliability index is derived to demonstrate the reasonableness of our model. Meanwhile, expected time response and American barrier option prices are calculated by using the predictor-corrector scheme. A sensitivity analysis is also illustrated with respect to various conditions.

scholarly journals Reliability Analysis of a Filtering Reducer under the Discrete Space Environmental Shocks

2014 ◽  
Vol 6 ◽  
pp. 921720 ◽  
Author(s):  
Jing Lu ◽  
Zhonglai Wang ◽  
Wei Chen ◽  
Xuefei Zhang ◽  
Hao Liu
Keyword(s):  
Differential Equations ◽  
Dynamic System ◽  
Mechanism Design ◽  
Reliability Analysis ◽  
Dynamic Model ◽  
Space Environment ◽  
Newmark Method ◽  
Lumped Mass ◽  
Dynamic Reliability ◽  
Environmental Shocks

Dynamic reliability analysis of a filtering reducer is performed by accounting for discrete shocks from the space environment. Gears are considered as the lumped mass and meanwhile the meshing between different gears is equivalent to a dynamic system consisting of springs and dampers during construction of the dynamic model. The Newmark method is employed to resolve differential equations, and then the additional acceleration could be obtained, caused by shocks to the filtering reducer. Dynamic reliability analysis is conducted with the help of the Simulink tool for the outputs. The results are hopefully useful for spacecraft mechanism design.

Stochastic Model Bias Correction of Dynamic System Responses for Simulation-Based Reliability Analysis

2015 ◽  
Author(s):  
Zhimin Xi ◽  
Hao Pan ◽  
Ren-Jye Yang
Keyword(s):  
Stochastic Model ◽  
Dynamic System ◽  
Simulation Model ◽  
Reliability Analysis ◽  
Dynamic Model ◽  
Bias Correction ◽  
Simulation Models ◽  
Model Bias ◽  
Thermal Problem ◽  
Simulation Based

Reliability analysis based on the simulation model could be wrong if the simulation model were not validated. Various model bias correction approaches have been developed to improve the model credibility by adding the identified model bias to the baseline simulation model. However, little research has been conducted for simulation models with dynamic system responses. This paper presents such a framework for model bias correction of dynamic system responses for reliability analysis by addressing three technical components including: i) a validation metric for dynamic system responses, ii) an effective approach for dynamic model bias calibration and approximation, and iii) reliability analysis considering the dynamic model bias. Two case studies including a thermal problem and a corroded beam problem are employed to demonstrate the proposed approaches for simulation-based reliability analysis.

A Reliability-Based Formulation for Simulation-Based Control Co-design Using Generalized Polynomial Chaos Expansion

2021 ◽  
pp. 1-15
Author(s):  
Mohammad Behtash ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Dynamic System ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Polynomial Chaos ◽  
Probabilistic Constraints ◽  
Stochastic Dynamic ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
And Control ◽  
Stochastic Dynamic Systems

Abstract Combined plant and control design (control co-design, or CCD) methods are often used during product development to address the synergistic coupling between the plant and control parts of a dynamic system. Recently, a few studies have started applying CCD to stochastic dynamic systems. In their most rigorous approach, reliability-based design optimization (RBDO) principles have been used to ensure solution feasibility under uncertainty. However, since existing reliability-based CCD (RBCCD) algorithms use all-at-once (AAO) formulations, only most-probable-point (MPP) methods can be used as reliability analysis techniques. Though effective for linear/quadratic RBCCD problems, the use of such methods for highly nonlinear RBCCD problems introduces solution error that could lead to system failure. A multidisciplinary feasible (MDF) formulation for RBCCD problems would eliminate this issue by removing the dynamic equality constraints and instead enforcing them through forward simulation. Since the RBCCD problem structure would be similar to traditional RBDO problems, any of the well-established reliability analysis methods could be used. Therefore, in this work, a novel reliability-based MDF formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) has been proposed for RBCCD. To quantify the uncertainty propagated by the random decision variables, Monte Carlo simulation has been applied to the generalized polynomial chaos (gPC) expansion of the probabilistic constraints. The proposed formulation is applied to two engineering test problems, with the results indicating the effectiveness of both the overall formulation as well as the reliability analysis technique for RBCCD.

scholarly journals Parametric Identification of Nonlinear Fractional Hammerstein Models

2019 ◽  
Vol 4 (1) ◽  
pp. 2
Author(s):  
Vineet Prasad ◽  
Kajal Kothari ◽  
Utkal Mehta
Keyword(s):  
Dynamic System ◽  
Fractional Order ◽  
Operational Matrix ◽  
Parametric Identification ◽  
Linear Dynamic System ◽  
Order Linear ◽  
Linear Dynamic ◽  
Block Pulse Functions ◽  
Hammerstein Models ◽  
Nonlinear Static

In this paper, a system identification method for continuous fractional-order Hammerstein models is proposed. A block structured nonlinear system constituting a static nonlinear block followed by a fractional-order linear dynamic system is considered. The fractional differential operator is represented through the generalized operational matrix of block pulse functions to reduce computational complexity. A special test signal is developed to isolate the identification of the nonlinear static function from that of the fractional-order linear dynamic system. The merit of the proposed technique is indicated by concurrent identification of the fractional order with linear system coefficients, algebraic representation of the immeasurable nonlinear static function output, and permitting use of non-iterative procedures for identification of the nonlinearity. The efficacy of the proposed method is exhibited through simulation at various signal-to-noise ratios.

Sign in / Sign up

Export Citation Format

Share Document