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The Constraint Function Response Shifting Scalar-Based Optimization Method for the Reliability-Based Dynamic Optimization Problem.

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Title: The Constraint Function Response Shifting Scalar-Based Optimization Method for the Reliability-Based Dynamic Optimization Problem.
Authors: Qiao, Ping, Zhang, Qi, Wu, Yizhong
Source: Mathematics (2227-7390); Feb2025, Vol. 13 Issue 4, p567, 25p
Subject Terms: PROBABILITY density function, DYNAMICAL systems, RANDOM variables, FUNCTION spaces, ORBITS (Astronomy)
Abstract: This work aims to improve the reliability of dynamic systems by eliminating the effect of random control variables. At first, the reliability-based dynamic optimization problem (RB-DOP) is introduced and defined to account for dynamic systems with uncertainty associated with random control variables. Whereafter, in order to solve RB-DOP efficiently, the constraint function response shift scalar (CFRSS)-based RB-DOP optimization method is proposed, in which the nested RB-DOP is decoupled into an equivalent deterministic DOP and a CFRSS search problem, and the two problems are addressed iteratively until the control law converges. Specifically, the shift scalar CFRSS is calculated by the probability density function of the constraint function response and deducted for probabilistic constraints in the constraint function response space to move the violated constraints toward the reliable region, avoiding solving large-scale optimization problems in the control variable space. Finally, two numerical examples and a low-thrust orbit transfer problem are investigated to demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]
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Database: Complementary Index
Description
Abstract:This work aims to improve the reliability of dynamic systems by eliminating the effect of random control variables. At first, the reliability-based dynamic optimization problem (RB-DOP) is introduced and defined to account for dynamic systems with uncertainty associated with random control variables. Whereafter, in order to solve RB-DOP efficiently, the constraint function response shift scalar (CFRSS)-based RB-DOP optimization method is proposed, in which the nested RB-DOP is decoupled into an equivalent deterministic DOP and a CFRSS search problem, and the two problems are addressed iteratively until the control law converges. Specifically, the shift scalar CFRSS is calculated by the probability density function of the constraint function response and deducted for probabilistic constraints in the constraint function response space to move the violated constraints toward the reliable region, avoiding solving large-scale optimization problems in the control variable space. Finally, two numerical examples and a low-thrust orbit transfer problem are investigated to demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]
ISSN:22277390
DOI:10.3390/math13040567