Optimising linear regression for modelling the dynamic thermal behaviour of electrical machines using NSGA-II, NSGA-III and MOEA/D.

For engineers to create durable and effective electrical assemblies, modelling and controlling heat transfer in rotating electrical machines (such as motors) is crucial. In this paper, we compare the performance of three multi-objective evolutionary algorithms, namely NSGA-II, NSGA-III, and MOEA/D in finding the best trade-offs between data collection costs/effort and expected modelling errors when creating low-complexity Linear Regression (LR) models that can accurately estimate key motor component temperatures under various operational scenarios. The algorithms are integrated into a multi-objective thermal modelling strategy that aims to guide the discovery of models that are suitable for microcontroller deployment. Our findings show that while NSGA-II and NSGA-III yield comparably good optimisation outcomes, with a slight, but statistically significant edge for NSGA-II, the results achieved by MOEA/D for this use case are below par

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 multi-objective evolutionary approach to discover explainability trade-offs when using linear regression to effectively model the dynamic thermal behaviour of electrical machines.

Modelling and controlling heat transfer in rotating electrical machines is very important as it enables the design of assemblies (e.g., motors) that are efficient and durable under multiple operational scenarios. To address the challenge of deriving accurate data-driven estimators of key motor temperatures, we propose a multi-objective strategy for creating Linear Regression (LR) models that integrate optimised synthetic features. The main strength of our approach is that it provides decision makers with a clear overview of the optimal trade-offs between data collection costs, the expected modelling errors and the overall explainability of the generated thermal models. Moreover, as parsimonious models are required for both microcontroller deployment and domain expert interpretation, our modelling strategy contains a simple but effective step-wise regularisation technique that can be applied to outline domain-relevant mappings between LR variables and thermal profiling capabilities. Results indicate that our approach can generate accurate LR-based dynamic thermal models when training on data associated with a limited set of load points within the safe operating area of the electrical machine under study

On the Use of the Cumulative Distribution Function for Large-Scale Tolerance Analyses Applied to Electric Machine Design

In the field of electrical machine design, excellent performance for multiple objectives, like efficiency or torque density, can be reached by using contemporary optimization techniques. Unfortunately, highly optimized designs are prone to be rather sensitive regarding uncertainties in the design parameters. This paper introduces an approach to rate the sensitivity of designs with a large number of tolerance-affected parameters using cumulative distribution functions (CDFs) based on finite element analysis results. The accuracy of the CDFs is estimated using the Dvoretzky–Kiefer–Wolfowitz inequality, as well as the bootstrapping method. The advantage of the presented technique is that computational time can be kept low, even for complex problems. As a demanding test case, the effect of imperfect permanent magnets on the cogging torque of a Vernier machine with 192 tolerance-affected parameters is investigated. Results reveal that for this problem, a reliable statement about the robustness can already be made with 1000 finite element calculations

Impact of IM pole count on material cost increase for achieving mandatory efficiency requirements

This paper presents a study about cost-optimal induction machines fulfilling particular efficiency requirements. As an increase of efficiency inevitably causes higher material costs, the tradeoff for these two conflicting objectives is analyzed in particular. Optimization scenarios comprising crucial design parameters are investigated and evolutionary algorithms are employed to reduce the overall computational cost. To obtain results in satisfactory time, the performance of machine designs is determined by means of an analytic approach. A case study for rated power of 11kW is presented. All number of poles and efficiency classes considered in corresponding regulations are investigated. This allows a comparison of the relative cost increase with regard to mandatory efficiency requirements, starting from IE1 up to the IE4 class. The results further provide interesting insights into optimal length to diameter ratios, air gap flux densities, and stato

Cost-optimal machine designs fulfilling efficiency requirements: A comparison of IMs and PMSMs

This article presents a study about cost-optimal machine designs fulfilling mandatory efficiency requirements. A case study for a rated power of 3kW and speed of 1500rpm is considered and the tradeoff material costs vs. efficiency are optimized. A comparison is made for induction machines and permanent magnet synchronous machines. As in the past the price for Neodymium-Iron-Boron magnets was volatile, two different scenarios regarding the material costs of the permanent magnets are evaluated. The cost-optimal machine designs for both topologies are further analyzed regarding thermal indices, power density, and optimal ratios of geometric dimensions. The results shall provide valuable insights and serve as a guidance for both people from academia and industry involved in the process of future machine design

Optimization of Electric Machine Designs-Part I

As the electric machine is the backbone of any electric drive, maximizing their performance takes top priority. Advances and trends in mathematical modeling and computer simulation, together with the availability of sophisticated optimization techniques, have opened the way to a new approach for electrical machine design. The already-proven reliability of the today's optimization strategies allows speed up of the final product definition, reducing the prototyping needs for project validations, and minimizing development and manufacturing cost. The potentialities offered by the modern optimization techniques are grown of interest for industry year after year, giving the reason for their massive penetration into the design chain. Due to the intrinsic multiphysics nature of electrical machines, as well as the multiple requirements imposed on their characteristics, electrical engineers usually face complex multiobjective optimization problems. The vastness of the cases, both in terms of possible electromagnetic structures, materials properties, and specific applications, pushed the Guest Editors to propose this "Special Section on Optimization of ElectricMachine Designs" to the Editors of the IEEE Transactions on Industrial Electronics. This Special Section received strong interest and feedback from designers and researchers involved on the topic: interest that is proved by the initially submitted contributions (134) and the 44 papers published in Part I and Part II. These papers illustrate the current state of the art, latest advances, and future trends of electrical machines design by using optimization methodologies. The Guest Editors are pleased to briefly sum up the first 24 papers included in Part I of this Special Section