Robust multidisciplinary UAS design optimisation

There are many applications in aeronautical/aerospace engineering where some values of the design parameters/states cannot be provided or determined accurately. These values can be related to the geometry (wingspan, length, angles) and or to operational flight conditions that vary due to the presence of uncertainty parameters (Mach, angle of attack, air density and temperature, etc.). These uncertainty design parameters cannot be ignored in engineering design and must be taken into the optimisation task to produce more realistic and reliable solutions. In this paper, a robust/uncertainty design method with statistical constraints is introduced to produce a set of reliable solutions which have high performance and low sensitivity. Robust design concept coupled with Multi-Objective Evolutionary Algorithms (MOEAs) is defined by applying two statistical sampling formulas; mean and variance/standard deviation associated with the optimisation fitness/objective functions. The methodology is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing and asynchronous evaluation. It is implemented for two practical Unmanned Aerial System (UAS) design problems; the first case considers robust multi-objective (single-disciplinary: aerodynamics) design optimisation and the second considers a robust multidisciplinary (aero-structures) design optimisation. Numerical results show that the solutions obtained by the robust design method with statistical constraints have a more reliable performance and sensitivity in both aerodynamics and structures when compared to the baseline design.     

Multidisciplinary design optimisation and robust design approaches applied to concurrent design

The increasing economic competition of all industrial markets and growing complexity of engineering problems lead to a progressive specialisation and distribution of expertise, tools and work sites. Most industrial sectors manage this fragmentation using the concurrent engineering approach, which is based on tools integration and shared databases and requires significant investments in design and work organisation. Besides, the multidisciplinary design optimisation (MDO) is more and more used as a method for optimal solutions search with regard to multiple coupled disciplines. The paper describes a quite innovative multidisciplinary optimisation method based on robust design techniques: MORDACE (multidisciplinary optimisation and robust design approaches applied to concurrent engineering). Managing uncertainty due to design teams collaboration, our automatic optimisation strategy allows concurrently designing different aspects or parts of a complex product. The method assures effective design work distribution and high optimisation results, containing the CPU time. In addition, our strategy is suited to the early stages of the design cycle, where evolutions of design goals and constraints are possible and exhaustive information about the design space is necessary. A roll stabiliser fin optimisation is presented as an example of this method applied to an industrial design problem.     

The generation of hierarchic structures via robust 3D topology optimisation

Commonly used building structures often show a hierarchic layout of structural elements. It can be questioned whether such a layout originates from practical considerations, e.g. related to its construction, or that it is (relatively) optimal from a structural point of view. This paper investigates this question by using topology optimisation in an attempt to generate hierarchical structures. As an arbitrarily standard design case, the principle of a traditional timber floor that spans in one direction is used. The optimisation problem is first solved using classical sensitivity and density filtering. This leads indeed to solutions with a hierarchic layout, but they are practically unusable as the floor boarding is absent. A Heaviside projection is therefore considered next, but this does not solve the problem. Finally, a robust approach is followed, and this does result in a design similar to floor boarding supported by timber joists. The robust approach is then followed to study a floor with an opening, two floors that span in two directions, and an eight-level concrete building. It can be concluded that a hierarchic layout of structural elements likely originates from being optimal from a structural point of view. Also clear is that this conclusion cannot be obtained by means of standard topology optimisation based on sensitivity or density filtering (as often found in commercial finite element codes); robust 3D optimisation is required to obtain a usable, constructible (or in the future: 3D printable) structural design, with a crisp black-and-white density distribution.     

Robust design optimisation using multi-objective evolutionary algorithms

In this paper, a new robust design method is investigated with a hierarchical asynchronous parallel multi-objective evolutionary algorithms in an optimisation framework environment to solve single and multi-point design optimisation problems in aerodynamics. The single design techniques produce solutions that perform well for the selected design point but have poor off-design performance. Here, it is shown how the approach can provide robust solutions using game theory in the sense that they are less sensitive to little changes of input parameters. Starting from a statistical definition of stability, the method captures, simultaneously Pareto non-dominated solutions with respect to performance and stability criteria, offering alternative choices to the designer.     

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.     

Shape optimisation for crashworthiness followed by a robustness analysis with respect to shape variables

This paper presents the results of a study on shape optimisation for crashworthiness design of passenger cars based on the software SFE CONCEPT. In contrast to classical morphing approaches, SFE CONCEPT allows for larger geometrical modifications via an implicit parameterisation technique. This is advantageous in particular in the early design phases where different design alternatives are investigated and the optimal and robust geometry needs to be identified. As a first example, the front rail of a standard passenger car is optimised here. This is – as one of the main parts of the body in white – an appropriate example for exploration of optimisation methods. The performance of a classical optimisation approach is analysed and complemented by a robustness analysis where uncertainties in shape parameters are considered.     

Tail mean and related robust solution concepts

Robust optimisation might be viewed as a multicriteria optimisation problem where objectives correspond to the scenarios although their probabilities are unknown or imprecise. The simplest robust solution concept represents a conservative approach focused on the worst-case scenario results optimisation. A softer concept allows one to optimise the tail mean thus combining performances under multiple worst scenarios. We show that while considering robust models allowing the probabilities to vary only within given intervals, the tail mean represents the robust solution for only upper bounded probabilities. For any arbitrary intervals of probabilities the corresponding robust solution may be expressed by the optimisation of appropriately combined mean and tail mean criteria thus remaining easily implementable with auxiliary linear inequalities. Moreover, we use the tail mean concept to develope linear programming implementable robust solution concepts related to risk averse optimisation criteria.     

Continuation methods for robust controller design for plants with operating-point-dependent behaviour

The design of robust controllers for processes with operating-point-dependent behaviour is a minimax optimisation problem which can, in general, e.g. for given controller structures or for practical relevant performance functionals, only be solved by numerical minimisation. The convergence of the minimisation algorithm is only ensured if the initial point needed to start the optimisation is in the neighbourhood of the local minimum. This makes the design difficult for the engineer because there is no systematic way to find an initial point. The paper presents a contribution to overcome this difficulty by using continuation methods.     

Realization of robust nonlinear model predictive control by offline optimisation

This paper describes a new method for increasing the computational efficiency of nonlinear robust model-based predictive control. It is based on the application of neuro-fuzzy networks and improves the computation efficiency by arranging the online optimisation to be done offline. The offline optimisation is realized by offline training a neuro-fuzzy network, consisting of zero-order T–S fuzzy rules, which is designed to approximate the input–output relationship of a robust model-based predictive controller. The design and the training of the neuro-fuzzy network are described, and the corresponding control algorithm is developed. Experiment results performed on the temperature control loop of an experimental air-handling unit (AHU) demonstrate the effectiveness of this approach.     

Evolutionary algorithms in control systems engineering: a survey

Challenging optimisation problems, which elude acceptable solution via conventional methods, arise regularly in control systems engineering. Evolutionary algorithms (EAs) permit flexible representation of decision variables and performance evaluation and are robust to difficult search environments, leading to their widespread uptake in the control community. Significant applications are discussed in parameter and structure optimisation for controller design and model identification, in addition to fault diagnosis, reliable systems, robustness analysis, and robot control. Hybrid neural and fuzzy control schemes are also described. The important role of EAs in multiobjective optimisation is highlighted. Evolutionary advances in adaptive control and multidisciplinary design are predicted.     

Die shape optimisation for net-shape accuracy in metal forming using direct search and localised response surface methods

In this paper, three direct search algorithms, i.e. a modified simplex, random direction search and enhanced Powell’s methods together with a new localised response surface method are presented and applied to solve die shape optimisation problems for achieving net-shape accuracy in metal forming processes. The main motivation is to develop efficient and easy to implement optimisation algorithms in metal forming simulations which often involve complex tool and workpiece interaction and coupled thermal and mechanical analysis. Three case studies are presented including a simple upsetting, a 2D blade forging and a forward extrusion problem. In all cases, the objective was to achieve net-shape accuracy of the formed parts, one important criterion for precision forming. C+ + programs were developed to implement these algorithms and to automatically integrate optimisation computation and forging simulation. The optimisation results from the three case problems show that direct search based methods especially the modified simplex and the localised response surface methods are computationally efficient and robust for net-shape forging and extrusion optimisation problems. It is also suggested that these methods can be used in more complex forging problems where die shape design and optimisation are essential for achieving net-shape accuracy.     

Design of robust H ∞ controller for a half-vehicle active suspension system with input delay

This article is concerned with the problem of robust H _∞ control for a half-vehicle active suspension system with input delay. The delay is assumed to be interval time-varying delay with unknown derivative. The vehicle front sprung mass and the rear unsprung mass are assumed to be varying due to vehicle load variation and may result in parameter uncertainties being modelled by polytopic uncertainty. First of all, regarding the heave and pitch accelerations as the optimisation objectives, and suspension deflection and relative tire load constraints as the output constraints, we build the corresponding suspension systems. Then, by constructing a novel Lyapunov functional involved with the lower and upper bounds of the delay, sufficient condition for the existence of robust H _∞ controller is given to ensure robust asymptotical stability of the closed-loop system and also guarantee the constrained performance. The condition can be converted into convex optimisation problem and verified easily by means of standard software. Finally, a design example is exploited to demonstrate the effectiveness of the proposed design method.     

A Flexible Evolutionary Agent: cooperation and competition among real-coded evolutionary operators

Since it has currently became essential to design more efficient and robust alternative techniques to solve hard optimisation problems in industry or science, and of easy use for practitioners, here a new way of developing simple Artificial Intelligence based Evolutionary Algorithms will be introduced. Our evolutionary computational implementation is a new idea in optimisation. Any evolutionary operators and their associated parameters from well-established evolutionary methods can be considered in such a way that the entire algorithm or intelligent agent-based software performs with very high efficiency without a prior need to investigate which method will be the best for a given optimisation problem.The implementation presented, named Flexible Evolution (FE), has capacity to adapt the operators, the parameters and the algorithm to the circumstances faced at each step of every optimisation run and is able to take into account lessons learned by different research works in the adaptation of operators and parameters. The FE uses Artificial Intelligence concepts to manage internal procedures to adopt decisions and correct the wrong ones. Our aim in this paper will be to give the keys to design these types of procedures, and more specifically, to find the way of achieving an optimum performance of the operators involved in the search, in our case by means of a function included in our algorithm called Sampling Engine. An early implementation has been already developed and tested in our previous works [66–68], so in this paper, new results of a second software implementation are presented comparing the results with those obtained by other methods, using well-known hard test functions.     

A robust optimisation framework in composite generation and transmission expansion planning considering inherent uncertainties

Abstract

This paper presents a robust optimisation framework for long-term composite generation and transmission expansion planning problem which considers inherent uncertainties such as load growth, fuel cost and renewable energy output uncertainties. In this paper, a bi-level robust optimisation framework is proposed to accommodate wind output uncertainty in line with the uncertain demanded loads and uncertain fuel cost. The addressed optimisation problem is modelled as a mixed-integer optimisation framework with the objective of providing a robust expansion plan while maintaining the minimum cost expansion. In order to evaluate the robustness of each plan, an off-line Lattice Monte Carlo simulation technique is adopted in this study. The validity of the proposed method is examined on a simple six-bus and modified IEEE 118-bus test system as a large-scale case study. The simulation results show that the presented method is both satisfactory and consistent with expectation.     

Robust H ∞ control for a class of uncertain mechanical systems

In this article, the problem of H _∞ control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass, damping and stiffness matrices. Two approaches, norm-bounded and linear fractional transformation (LFT) uncertainty formulations, are considered. By using a new Lyapunov–Krasovskii functional approach, combined with the advanced techniques for achieving delay dependence, improved robust H _∞ state-feedback controller design methods are developed. The existence condition for admissible controllers is formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimisation problem subject to LMI constraints. If the optimisation problem is solvable, a desired controller can be readily constructed. The result for the norm-bounded uncertainty case improves the existing ones in terms of design conservatism, and that for the LFT uncertainty case represents the first attempt in this direction. An illustrative example is provided to show the effectiveness and advantage of the proposed controller design methodologies.     

Quantised and sampled output feedback for nonlinear systems

In this paper we consider the analysis and design of an output feedback controller for a perturbed nonlinear system in which the output is sampled and quantised. Using the attractive ellipsoid method, which is based on Lyapunov analysis techniques, together with the relaxation of a nonlinear optimisation problem, sufficient conditions for the design of a robust control law are obtained. Since the original conditions result in nonlinear matrix inequalities, a numerical algorithm to obtain the solution is presented. The obtained control ensures that the trajectories of the closed-loop system will converge to a minimal (in a sense to be made specific) ellipsoidal region. Finally, numerical examples are presented in order to illustrate the applicability of the proposed design method.     

Dominant pole and eigenstructure assignment for positive systems with state feedback

In this paper, the dominant pole assignment problem, the dominant eigenstructure assignment problem and the robust dominant pole assignment problem for linear time-invariant positive systems with state feedback are considered. The dominant pole assignment problem is formulated as a linear programming problem, and the dominant eigenstructure problem is formulated as a quasiconvex optimisation problem with linear constraints. The robust dominant pole assignment problem is formulated as a non-convex optimisation problem with non-linear constraints which is solved using particle swarm optimisation (PSO) with an efficient scheme which employs the dominant eigenstructure assignment technique to accelerate the convergence of the PSO procedure. Each of the three problems can be further constrained by requiring that the controller has a pre-specified structure, or the gain matrix have both elementwise upper and lower bounds. These constraints can be incorporated into the proposed scheme without increasing the complexity of the algorithms. Both the continuous-time case and the discrete-time case are treated in the paper.     

A robust optimisation model and cutting planes for the planning of energy-efficient wireless networks

In this paper, we present an optimisation model for the energy-efficient planning of future wireless networks. By applying robust optimisation, we extend this model to a robust formulation which considers demand uncertainties. The computability of the resulting model is moderate. Hence, we apply three different cutting plane approaches for an improvement. Furthermore, an extensive case study is performed to examine the price of robustness, to compare the robust solution to conventional planning, and to explore the performance of the cutting planes.     

Parameter free shape and thickness optimisation considering stress response

In the parameter free approach, FE-based data are used as design variables, such as nodal coordinates and nodal thickness. During shape and thickness optimisation, this approach provides much design freedom for a limited modelling effort. Stress results are, however, very sensitive to the local shape changes that can occur during parameter free optimisation. When stress results are used as response function, this irregularity can complicate the optimisation. As a solution, the Kreisselmeier-Steinhauser function for the stresses is introduced as a response function for parameter free shape optimisation. In this function, the local stress results are aggregated to obtain a global measure of stress in a structure. This measure can be used as an objective to reduce the overall stress in the structure or as a constraint to limit the stress in the structure to a maximum allowable value. As a result, the optimal structures are smooth and material efficient. Several examples are presented in this paper to illustrate the use of the parameter free design approach in combination with the stress response function.