Gerd Bramerdorfer

Hybridization of multi-objective evolutionary algorithms and artificial neural networks for optimizing the performance of electrical drives

Performance optimization of electrical drives implies a lot of degrees of freedom in the variation of design parameters, which in turn makes the process overly complex and sometimes impossible to handle for classical analytical optimization approaches. This, and the fact that multiple non-independent design parameter have to be optimized synchronously, makes a soft computing approach based on multi-objective evolutionary algorithms (MOEAs) a feasible alternative. In this paper, we describe the application of the well known Non-dominated Sorting Genetic Algorithm II (NSGA-II) in order to obtain high-quality Pareto-optimal solutions for three optimization scenarios. The nature of these scenarios requires the usage of fitness evaluation functions that rely on very time-intensive finite element (FE) simulations. The key and novel aspect of our optimization procedure is the on-the-fly automated creation of highly accurate and stable surrogate fitness functions based on artificial neural networks (ANNs). We employ these surrogate fitness functions in the middle and end parts of the NSGA-II run (->hybridization) in order to significantly reduce the very high computational effort required by the optimization process. The results show that by using this hybrid optimization procedure, the computation time of a single optimization run can be reduced by 46-72% while achieving Pareto-optimal solution sets with similar, or even slightly better, quality as those obtained when conducting NSGA-II runs that use FE simulations over the whole run-time of the optimization process.

DECMO2: a robust hybrid and adaptive multi-objective evolutionary algorithm

We describe a hybrid and adaptive coevolutionary optimization method that can efficiently solve a wide range of multi-objective optimization problems (MOOPs) as it successfully combines positive traits from three main classes of multi-objective evolutionary algorithms (MOEAs): classical approaches that use Pareto-based selection for survival criteria, approaches that rely on differential evolution, and decomposition-based strategies. A key part of our hybrid evolutionary approach lies in the proposed fitness sharing mechanism that is able to smoothly transfer information between the coevolved subpopulations without negatively impacting the specific evolutionary process behavior that characterizes each subpopulation. The proposed MOEA also features an adaptive allocation of fitness evaluations between the coevolved populations to increase robustness and favor the evolutionary search strategy that proves more successful for solving the MOOP at hand. Apart from the new evolutionary algorithm, this paper also contains the description of a new hypervolume and racing-based methodology aimed at providing practitioners from the field of multi-objective optimization with a simple means of analyzing/reporting the general comparative run-time performance of multi-objective optimization algorithms over large problem sets.

A flux-based PMSM motor model using RBF interpolation for time-stepping simulations

This paper describes an advanced method of modeling synchronous machines, in particular interior permanent magnet (IPM) motors. The dynamic motor model considers magnetic saturation and the dependence of electrical, magnetic and mechanical quantities on the rotation angle, and can be integrated into multidisciplinary system simulations. A set of magnetic finite element method (FEM) solutions is used to set up the model based on radial basis function (RBF) interpolation. The presented motor model can be used to simulate any time-stepping cases, such as studies of field weakening control, sensorless motor control algorithms or short circuit behavior. No magnetic FEM simulation is needed at runtime. We demonstrate the functionality of our method using the example of a BLDC motor simulation with voltage block commutation. The model derivated results are in good accordance with our measurements.

Using FE Calculations and Data-Based System Identification Techniques to Model the Nonlinear Behavior of PMSMs

This paper investigates the modeling of brushless permanent-magnet synchronous machines (PMSMs). The focus is on deriving an automatable process for obtaining dynamic motor models that take nonlinear effects, such as saturation, into account. The modeling is based on finite element (FE) simulations for different current vectors in the

Coupled optimization in MagOpt

dq plane over a full electrical period. The parameters obtained are the stator flux in terms of the direct and quadrature components and the air-gap torque, both modeled as functions of the rotor angle and the current vector. The data are preprocessed according to theoretical results on potential harmonics in the targets as functions of the rotor angle. A variety of modeling strategies were explored: linear regression, support vector machines, symbolic regression using genetic programming, random forests, and artificial neural networks. The motor models were optimized for each training technique, and their accuracy was then compared based on the initially available FE data and further FE simulations for additional current vectors. Artificial neural networks and symbolic regression using genetic programming achieved the highest accuracy, particularly with additional test data.

Combined Analytical–Numerical Noise Calculation of Electrical Machines Considering Nonsinusoidal Mode Shapes

Optimizing mechatronic components is of increasing importance, e.g. for minimizing energy consumption and the use of rare materials. MagOpt is a modular software tool for the simulation and optimization of mechatronic components. Parametric design optimization can be carried out with various different optimization strategies like gradient-based methods or multi-objective evolutionary or genetic algorithms. MagOpt features a flexible structure for the storage of complex data and an open and modular interface to existing third-party programs. One such third-party program which can be used by MagOpt for the optimization of mechanic components is the multi-body software HOTINT. This article describes MagOpt and how it was coupled with HOTINT to optimize a rotor geometry.

Identification of a nonlinear PMSM model using symbolic regression and its application to current optimization scenarios

This paper describes a calculation method for the electromagnetically excited noise of different types of rotating electrical machines. A numerically gained modal matrix of the stator is used for the analytical calculation of the surfaces deflection and thus combines short calculation times of analytical methods with the accuracy of numerical calculations. Considering elliptic deformations due to nonsymmetrical pairs of eigenvectors, as especially occurring for small machines with few teeth, a time-stepping algorithm allows the examination of noncircular spatial harmonics of the deformation. An adapted analytical sound pressure calculation is appended. Finally, a comparison with a measurement of the surface oscillation validates the improved calculation method.

A Hybrid Soft Computing Approach for Optimizing Design Parameters of Electrical Drives

This article presents the nonlinear modeling of the torque of brushless PMSMs by using symbolic regression. It is still popular to characterize the operational behavior of electrical machines by employing linear models. However, nowadays most PMSMs are highly utilized and thus a linear motor model does not give an adequate accuracy for subsequently derived analyses, e.g., for the calculation of the maximum torque per ampere (MTPA) trajectory. This article focuses on modeling PMSMs by nonlinear white-box models derived by symbolic regression methods. An optimized algebraic equation for modeling the machine behavior is derived using genetic programming. By using a Fourier series representation of the motor torque a simple to handle model with high accuracy can be derived. A case study is provided for a given motor design and the motor model obtained is used for deriving the MTPA-trajectory for sinusoidal phase currents. The model is further applied for determining optimized phase current waveforms ensuring zero torque ripple.

Possibilities for Speeding Up the FE-Based Optimization of Electrical Machines—A Case Study

In this paper, we are applying a hybrid soft computing approach for optimizing the performance of electrical drives where many degrees of freedom are allowed in the variation of design parameters. The hybrid nature of our approach originates from the application of multi-objective evolutionary algorithms (MOEAs) to solve the complex optimization problems combined with the integration of non-linear mappings between design and target parameters. These mappings are based on artificial neural networks (ANNs) and they are used for the fitness evaluation of individuals (design parameter vectors). The mappings substitute very time-intensive finite element simulations during a large part of the optimization run. Empirical results show that this approach finally reduces the computation time for single runs from a few days to several hours while achieving Pareto fronts with a similar high quality.

Speed improvements for the optimization of electrical machines — A survey

This paper deals with accelerating typical optimization scenarios for electrical machine designs. Besides the advantage of a reduced computation time, this leads to a reduction in computational power and thus to a lower power consumption when running the optimization. If machines of high power density are required, usually highly utilized assemblies that feature nonlinear characteristics are obtained. Optimization scenarios are considered where the evaluation of a potential design requires computationally expensive nonlinear finite element (FE) simulations. Improving the speed of optimization runs takes top priority and various measures can be considered. This paper is about basic and easily achievable measures, and techniques for a time-wise and computationally efficient exploration of the design space. Suggested improvements comprise sophisticated emerging techniques for modeling machine characteristics by paring the number of required FE simulations down to the minimum and nonlinear modeling of the targets of the optimization scenario as functions of the design parameters to further reduce the number of FE evaluations. In the case study, the analysis of a typical optimization task is given, and achievable speed improvements as well as still present issues are discussed.