With this work, we present a novel derivative-free global optimisation approach for finite element model updating. The aim is to localise structural damage in a wind turbine rotor blade. For this purpose, we create a reference finite element model of the blade as well as a model with a fictitious damage. To validate the approach, we use a model updating scheme to locate the artificially induced damage. This scheme employs numerical optimisation using the parameterised finite element model and an objective function based on modal parameters. Metaheuristic algorithms are the predominant class of optimisers for global optimisation problems. With this work, we show that deterministic approaches are competitive for engineering problems such as model updating. The proposed optimisation algorithm is deterministic and a generalisation of the pattern search algorithm. It picks up features known from local deterministic algorithms and transfers them to a global algorithm. We demonstrate the convergence, discuss the numerical performance of the proposed optimiser with respect to several analytical test problems and propose a possible trade-off between parallelisation and convergence rate. Additionally, we compare the numerical performance of the proposed deterministic algorithm concerning the model updating problem to the performance of well-established metaheuristic and local optimisation algorithms. The introduced algorithm converges quickly on test functions as well as on the model updating problem. In some cases, the deterministic algorithm outperforms metaheuristic algorithms. We conclude that deterministic optimisation algorithms should receive more attention in the field of engineering optimisation.

Introduction

For optimisation tasks considering non-linear problems, derivativefree global algorithms are particularly suited. Objective functions of such problems often involve transient numerical simulations or discrete and non-linear evaluations. This is why it is usually not possible to find a direct solution for the derivative of such objective functions. We concentrate on derivative-free algorithms, since obtaining derivatives in a numerically complex design variable space is challenging. Indeed, derivatives can easily be obtained numerically by using singlesided or symmetric sampling around a base point. The Hessian matrix needed for sequential quadratic programming [1] is commonly obtained by this method. However, numerical noise and the difficulty to receive an appropriate value for the step size necessitate some numerical experiments to yield a stable optimisation. Derivative-free methods are thus desirable due to the numerical robustness they provide. Most commonly used derivative-free algorithms are metaheuristic. This means that they rely on pseudo-random numbers in order to stochastically explore the design variable space of the underlying problem. Examples of this class of algorithms are genetic algorithms [2], particle swarm optimisation [3] or harmony search [4]. More recent contributions also include algorithms inspired by biological phenomena and swarm intelligence like whale optimisation [5], bacterial foraging optimisation [6], anarchic society optimisation [7] or social-spider optimisation [8].