Development of a Multi-Objective Genetic Algorithm for the Design of Offshore Renewable Energy Systems

This is the author accepted manuscript. The final version is available from the publisher via the URL in this record.Optimization algorithms have been deployed for a range of renewable energy problems and can successfully be applied to aid in the design of devices, farms, control strategies, and operations and maintenance strategies. Building on this, the present work makes use of a multi-objective genetic algorithm (GA) in order to develop a framework that can further aid in the design and development of offshore renewable energy systems by explicitly taking into account reliability considerations. Though the reliability-based design optimization approach has previously been used in offshore renewable energy applications and multi-objective optimization applications, it has not previously been applied to multi-objective offshore renewable energy design optimization. As the offshore renewable energy sectors grows it is important for the industry to explore more sophisticated methods of designing devices in order to ensure that the device reliability and lifetime can be maximized while downtime and cost are minimized. This paper describes the development of a framework using a GA in order to aid in the design of a mooring system for offshore renewable energy devices. This framework couples numerical models of the mooring system and structural response to both stress-life cumulative damage models and cost models in order for the GA to effectively operate considering the multiple objectives. The use of this multi-objective optimization approach allows multiple design objectives such as system lifetime and cost to be satisfied simultaneously using an automated mathematical approach. From the outputs of this approach, a designer can then select a solution which appropriately balances the different objectives. The developed framework will be applicable to any offshore technology subsystem allowing multi-objective optimization and reliability to be considered from the design stage in order to improve the design efficiency and aid the industry in using more systematic design approaches.This work is funded by the EPSRC (UK) grant for the SuperGen United Kingdom Centre for Marine Energy Research (UKCMER) [grant number: EP/P008682/1]

Reliability-based optimization for multiple constraints with evolutionary algorithms

In this paper, we combine reliability-based optimization with a multi-objective evolutionary algorithm for handling uncertainty in decision variables and parameters. This work is an extension to a previous study by the second author and his research group to more accurately compute a multi-constraint reliability. This means that the overall reliability of a solution regarding all constraints is examined, instead of a reliability computation of only one critical constraint. First, we present a brief introduction into this so-called 'structural reliability' aspects. Thereafter, we introduce a method for identifying inactive constraints according to the reliability evaluation. With this method, we show that with less number of constraint evaluations, an identical solution can be achieved. Furthermore, we apply our approach to a number of problems including a real-world car side impact design problem to illustrate our method

Multi-objective reliability based design of complex engineering structures using response surface methods

Extensive research contributions have been carried out in the field of Reliability-Based Design Optimisation (RBDO). Traditional RBDO methods deal with a single objective optimisation problem subject to probabilistic constraints. However, realistic problems in engineering practice require a multi-criteria perspective where two or more conflicting objectives need to be optimised. These type of problems are solved with multi-objective optimization methods, known as Multi-Objective Reliability Based Design Optimization (MORBDO) methods. Usually, significant computational efforts are required to solve these types of problems due to the huge number of complex finite element model evaluations. This paper proposes a practical and efficient approach based for talking this challenge. A multiobjective evolutionary algorithms (MOEAs) is combined with response surface method to obtain efficiently, accurate and uniformly distributed Pareto front. The proposed approach has been implemented into the OpenCossan software. Two examples are presented to show the applicability of the approach: an analytical problem where one of the objectives is the system reliability and the classic 25 bars transmission tower

A simulation-based multi-criteria management system for optimal water supply under uncertainty

For cost and reliability efficiency, optimal design and operation of pressurized water distribution networks is highly important. However, optimizing such networks is still a challenge since it requires an appropriate determination of: (1) dimension of pipe / pump / tank - decision variables (2) cost / network reliability - objective functions and (3) limits or restrictions within which the network must operate - a given set of constraints. The costs mentioned here consist in general of capital, construction, and operation costs. The reliability of a network mainly refers to the intrinsic capability of providing water with adequate volume and a certain pressure to consumers under normal and extreme conditions. These contradicting objective functions are functions of network configuration regarding component sizes and network layout. Because considerable uncertainties finally render the overall task to a highly complex problem, most recent approaches mainly focus only on finding a trade-off between minimizing cost and maximizing network reliability. To overcome these limitations, a novel model system that simultaneously considers network configuration, its operation and the relevant uncertainties is proposed in this study. For solving this multi-objective design problem, a simulation-based optimization approach has been developed and applied. The approach couples a hydraulic model (Epanet) with the covariance matrix adaptation evolution strategy (CMA-ES) and can be operated in two different modes. These modes are (1) simulation–based Single-objective optimization and (2) simulation-based multi-objective optimization. Single-objective optimization yields the single best solution with respect to cost or network reliability, whereas multi-objective optimization produces a set of non-dominated solutions called Pareto optimal solutions which are trade-offs between cost and reliability. In addition, to prevent a seriously under-designed network, demand uncertainties was also taken into account through a so called “robustness probability” of the network. This consideration may become useful for a more reliable water distribution network. In order to verify the performance of the proposed approach, it was systematically tested on a number of different benchmark water distribution networks ranging from simple to complex. These benchmark networks are either gravity-fed or pumped networks which need to be optimally designed to supply urban or irrigation water demand under specific constraints. The results show that the new approach is able: • to solve optimization problems of pressurized water distribution network design and operation regarding cost and network reliability; • to directly determine the pumping discharge and head, thus allowing to select pumps more adequately; • to simulate time series of tank water level; • to eliminate redundant pipes and pumps to generate an optimal network layout; • to respond well to complex networks other than only to simple networks; • to perform with multiple demand loading; • to produce reliable Pareto optimal solutions regarding multi-objective optimization. In conclusion, the new technique can be successfully applied for optimization problems in pressurized water distribution network design and operation. The new approach has been demonstrated to be a powerful tool for optimal network design not only for irrigation but also for an urban water supply

Structural Optimization for Reliability Using Nonlinear Goal Programming

This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem

Multi-Objective Optimization of Mooring Systems for Offshore Renewable Energy

This is the author accepted manuscript. The final version is available from EWTEC via the link in this record.This paper presents a method for the optimization of mooring systems in offshore renewable energy systems. This methodology considers the location of anchors as well as the length, material, and diameter of the mooring lines in order to simultaneously minimize the tension in the lines, the cost of the mooring system, and the fatigue damage in the system. By considering these three objectives using a multi-objective approach rather than reduction to a single objective optimization problem allows a Pareto hull of solutions to be obtained representing a range of solutions which balance the three objectives. From this, a system designer can select the design which appropriately balances the trade-off between the competing objectives. In this work, a set of mooring designs that represent efficient solutions for the constraints are found and presented considering the OC4 DeepCWind semi-submersible at Wave Hub. This reliability-based design optimization approach will be applicable to other offshore technology subsystems allowing reliability to be considered in a multi-objective optimization from the design phase.This work is funded by the EPSRC (UK) grant for the United Kingdom Centre for Marine Energy Research (UKCMER) [grant number: EP/P008682/1]

Integrated reliable and robust design

The objective of this research is to develop an integrated design methodology for reliability and robustness. Reliability-based design (RBD) and robust design (RD) are important to obtain optimal design characterized by low probability of failure and minimum performance variations respectively. But performing both RBD and RD in a product design may be conflicting and time consuming. An integrated design model is needed to achieve both reliability and robustness simultaneously. The purpose of this thesis is to integrate reliability and robustness. To achieve this objective, we first study the general relationship between reliability and robustness. Then we perform a numerical study on the relationship between reliability and robustness, by combining the reliability based design, robust design, multi objective optimization and Taguchi\u27s quality loss function to formulate an integrated design model. This integrated model gives reliable and robust optimum design values by minimizing the probability of failure and quality loss function of the design simultaneously. Based on the results from the numerical study, we propose a generalized quality loss function that considers both the safe region and the failure region. Taguchi\u27s quality loss function defines quality loss in the safe design region and risk function defines quality loss in the failure region. This integrated model achieves reliability and robustness by minimizing the general quality loss function of the design. Example problems show that this methodology is computationally efficient compared to the other optimization models. Results from the various examples suggest that this method can be efficiently used to minimize the probability of failure and the total quality loss of a design simultaneously --Abstract, page iii

Efficiently Estimating Survival Signature and Two-Terminal Reliability of Heterogeneous Networks through Multi-Objective Optimization

The two-terminal reliability problem is a classical reliability problem with applications in wired and wireless communication networks, electronic circuit design, computer networks, and electrical power distribution, among other systems. However, the two-terminal reliability problem is among the hardest combinatorial problems and is intractable for large, complex networks. Several exact methods to solve the two-terminal reliability problem have been proposed since the 1960s, but they have exponential time complexity in general. Hence, practical studies involving large network-type systems resort to approximation methods to estimate the system\u27s reliability. One attractive approach for quantifying the reliability of complex systems is to use signatures, but even signature-based approaches in computing exact network reliability may become computationally prohibitive as the number of components grows, and simulation-based approximations, such as Monte Carlo algorithms, are generally required. Nonetheless, the computation of the network\u27s signature poses a majorchallenge in terms of computational time, especially when considering large, heterogeneous networks. Motivated by this, we propose a MC-survival signature based method to estimate two-terminal reliability for heterogeneous networks through multi-objective optimization. We formulate the problem of estimating the multi-dimensional survival signature of a network with heterogeneous components as a repeated multi-objective maximum capacity path problem and we present a fast and memory-efficient, Dijkstra-like algorithm to solve it. To the best of our knowledge, this is the first work to point out the relationship between the multi-dimensional survival signature computation and a multi-objective optimization problem. We empirically validate our method and perform computational experiments to compare its performance against two other approaches. The results of the experiments shows that our method is much faster than the other two approaches and can be used with a larger number of replications so to improve the accuracy of the reliability estimation

Application of derivative-free multi-objective algorithms to reliability-based robust design optimization of a high-speed catamaran in real ocean environment

A reliability-based robust design optimization (RBRDO) for ship hulls is presented. A real ocean environment is considered, including stochastic sea state and speed. The optimization problem has two objectives: (a) the reduction of the expected value of the total resistance in waves and (b) the increase of the ship operability (reliability). Analysis tools include a URANS solver, uncertainty quantification methods and metamodels, developed and validated in earlier research. The design space is defined by an orthogonal four-dimensional representation of shape modifications, based on the Karhunen-Loeve expansion of free-form deformations of the original hull. The objective of the present paper is the assessment of deterministic derivative-free multi-objective optimization algorithms for the solution of the RBRDO problem, with focus on multi-objective extensions of the deterministic particle swarm optimization (DPSO) algorithm. Three evaluation metrics provide the assessment of the proximity of the solutions to a reference Pareto front and their wideness.A Reliability-Based Robust Design Optimization (RBRDO) for ship hulls is presented. A real ocean environment is considered, including stochastic sea state and speed. The optimization problem has two objectives: (a) the reduction of the expected value of the total resistance in waves and (b) the increase of the ship operability (reliability). Analysis tools include a URANS solver, uncertainty quantification methods and metamodels, developed and validated in earlier research. The design space is defined by an orthogonal four-dimensional representation of shape modifications, based on the Karhunen-Loève expansion of free-form deformations of the original hull. The objective of the present paper is the assessment of deterministic derivativefree multi-objective optimization algorithms for the solution of the RBRDO problem, with focus on multiobjective extensions of the Deterministic Particle Swarm Optimization (DPSO) algorithm. Three evaluation metrics provide the assessment of the proximity of the solutions to a reference Pareto front and their wideness