A new reliability analysis method based on the conjugate gradient direction
- Authors: Ezzati, Ghasem , Mammadov, Musa , Kulkarni, Siddhivinayak
- Date: 2015
- Type: Text , Journal article
- Relation: Structural and Multidisciplinary Optimization Vol. 51, no. 1 (2015), p. 89-98
- Full Text: false
- Reviewed:
- Description: Reliability-based design optimization (RBDO) is an important area in structural optimization. A principal step of the RBDO process is to solve a reliability analysis problem. This problem has been considered in inner loop of double-loop RBDO approaches. Although many algorithms have been developed for solving this problem, there are still some challenges. Existing algorithms do not have good convergence rates and often diverge. There is a need to develop more efficient and stable algorithms that can be used for evaluating all performance functions sufficiently. In this paper, a new method, called “Conjugate Gradient Analysis (CGA) Method”, is proposed to apply in the reliability analysis problems. This method is based on the conjugate gradient method. Some mathematical problems are provided in order to demonstrate the advantages of the proposed method compared with the existing methods. © 2014, Springer-Verlag Berlin Heidelberg.
A reliability-based design optimization model for electricity power networks
- Authors: Ezzati, Ghasem
- Date: 2015
- Type: Text , Journal article
- Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 22, no. 5 (2015), p. 339-357
- Full Text: false
- Reviewed:
- Description: Significant attentions have recently been attracted by electricity power net- works where many optimization models are applied to optimize distributed power. Many optimization models are available for electricity networks that mainly take into accoun- t total cost. Reliability related issues of electricity networks are also considered in the literature. However, there is a lack to formulate a reliability-based design optimization (RBDO) model of these networks. An RBDO model is introduced in this paper to deal with probabilistic constraints in an optimization model for electricity networks. In our suggested approach, an optimization problem is firstly solved to find optimal parameters of the network. Then, the optimal solution is adjusted using an RBDO problem. Our main aim is to minimize an extra cost that is experienced by considering reliability. It is expected to have a higher extra cost for a lower failure probability. © 2015 Watam Press.
Reliability-based design optimisation methods in large scale systems
- Authors: Ezzati, Ghasem
- Date: 2015
- Type: Text , Thesis , PhD
- Full Text:
- Description: Doctor of Philosophy
- Description: Structural optimisation is an important field of applied mathematics, which has proved useful in engineering projects. Reliability-based design optimisation (RBDO) can be considered a branch of structural optimisation. Different RBDO approaches have been applied in real world problems (e.g. vehicle side impact model, short column design, etc.). Double-loop, single-loop, and decoupled approaches are three categories in RBDO. This research focuses on double-loop approaches, which consider reliability analysis problems in their inner loops and design optimisation calculations in their outer loops. In recent decades, double-loop approaches have been studied and modified in order to improve their stability and efficiency, but many shortcomings still remain, particularly regarding reliability analysis methods. This thesis will concentrate on development of new reliability analysis methods that can be applied to solve RBDO problems. As a local optimisation algorithm, the conjugate gradient method will be adopted. Furthermore, a new method will be introduced to solve a reliability analysis problem in the polar space. The reliability analysis problem must be transformed into an unconstrained optimisation problem before solving in the polar space. Two methods will be introduced here and their stability and efficiency will be compared with the existing methods via numerical experiments. Next, we consider applications of RBDO models to electricity networks. Most of the current optimisation models of these networks are categorised as deterministic design optimisation models. A probabilistic constraint is introduced in this thesis for electricity networks. For this purpose, a performance function must be defined for a network in order to define safety and failure conditions. Then, new non-deterministic design optimisation models will be formulated for electricity networks by using the mentioned probabilistic constraint. These models are designed to keep failure probability of the network below a predetermined and accepted safety level.