A new architecture for large-scale system design optimization

A large-scale finite element model-based design optimization algorithm is developed for improving the drive-cycle efficiency of permanent magnet (PM) synchronous machines with wide operating ranges such as those used in traction propulsion motors. The load operating cycle is efficiently modeled by using a systematic k -means clustering method to identify the operating points representing the high-energy-throughput zones in the torque–speed plane. The machine performance is evaluated over these cyclic representative points using a recently introduced computationally efficient finite element analysis, which is upgraded to include both constant torque and field-weakening operations in the evaluation of the machine performance metrics. In contrast with the common practice, which aims at enhancing the rated performance, the entire range of operation is considered in the present design optimization method. Practical operational constraints imposed by the voltage and current limits of the motor-drive system, excessive PM demagnetization, and torque ripple are accounted for during the optimization process. The convergence to the optimal design solutions is expedited by utilizing a new stochastic optimizer. The developed design algorithm is applicable to any configuration of sinewave-drive PM and synchronous reluctance motors over any conceivable load profile. Its effectiveness is demonstrated by optimizing the well-established benchmark design represented by the Toyota Prius Gen. 2 interior PM motor configuration over a compound operating cycle consisting of common U.S. driving schedules. Multiphysics electromagnetic, thermal, and mechanical performance of the optimized design solutions is discussed in a postdesign optimization stage.

This paper describes the development of a geographic independent virtual design environment for large-scale Multidisciplinary Design Optimization (MDO) problems. The environment described provides a designer with the ability to see and interact with a 3-D Virtual Reality (VR) representation of the design or a representation of a subset of the design space. The designer can make graphical alterations to the design and see the effects in real-time. The environment supports multiple users to be logged on at the same time and to see the desired design changes and effects hi real time or near real time made by other designers. The designers have several means of communication available involving words, pictures, and text to communicate their ideas and concepts.

Next-generation additive manufacturing technologies will enable novel, low-weight, highperformance aircraft structures. Topology optimization techniques can be used to obtain unconventional internal aircraft wing structures that can be manufactured using additive methods which depart significantly from conventional rib-spar wing constructions. However, there are significant issues that must be overcome when applying traditional topology optimization techniques to the design of aerospace structures. These challenges include efficiently solving large-scale design problems, and applying buckling criteria within a topology optimization design formulation. In this paper, we seek to address these issues by applying a scalable topology optimization method to the undeformed Common Research Model (uCRM) wing with buckling constraints applied to the skins of the wingbox. The proposed approach uses a multigrid-preconditioned Krylov method to solve the large-scale finite element analysis problem, coupled with a parallel interior-point optimizer to solve the largescale constrained design optimization problem. This proposed method is applied to two different optimization problems: mass-constrained compliance minimization, and mass-constrained bucklingload maximization. In addition, we apply a segment-wise topology optimization design strategy to the uCRM wingbox.

Aircraft conceptual design is a high-dimensional optimization problem, involving up to hundreds of continuous design variables and constraints. The design of novel aircraft concepts such as electric vertical takeoff and landing (eVTOL) vehicles can benefit from the systematic exploration of the design space through the use of gradient-based optimization. In this paper, we demonstrate the application of large-scale multidisciplinary design optimization (MDO) to NASA's lift-plus-cruise electric air taxi concept, using low and mid-fidelity physics-based simulations to model the aircraft. We improve the modeling fidelity from our previous work on the same air taxi concept through refined rotor-aerodynamic and aeroacoustic models as well as in-the-loop structural analysis. In addition, we expand the scope of the analysis to include several steady design conditions, a quasi-steady transition maneuver, structural sizing conditions, as well as one-engine-inoperative (OEI) scenarios, amounting to 18 design conditions. To perform the analysis and optimization, we use a newly developed software library called the Comprehensive Aircraft high-Dimensional Design Environment (CADDEE), which facilitates the integration of all discipline models. We solve a gross weight minimization problem with over 300 design variables and over 200 constraints, spanning all modeled disciplines. Results show a decrease in gross weight of 10% after a total optimization time of about 17 hours. These results demonstrate the effectiveness of applying of large-scale MDO to the aircraft conceptual design problem.

Automatic generation of global shell-element meshes for large-scale structural design optimization

The process of constructing computationally benign approximations of expensive computer simulation codes, or metamodeling, is a critical component of several large-scale Multidisciplinary Design Optimization approaches. Such applications typically involve complex models, such as finite elements, computational fluid dynamics, or chemical processes. The decision regarding the most appropriate metamodeling approach usually depends on the type of application. However, several newly-proposed kernel-based metamodeling approaches can provide consistently accurate performance for a wide variety of applications. The authors recently proposed one such novel and effective metamodeling approach — the Extended Radial Basis Function approach — and reported encouraging results. To further understand the advantages and limitations of this new approach, we compare its performance to that of the typical radial basis function approach, and another closely related method — kriging. Several test functions with varying problem dimensions and degrees of nonlinearity are used to compare the accuracies of the metamodels using these metamodeling approaches. We consider several performance criteria, such as metamodel accuracy. effect of sampling technique, effect of problem dimension, and computational complexity. The results suggest that the E-RBF approach is a potentially powerful metamodeling approach for MDO-based applications.

Through a systematic optimization study using high-fidelity finite-element (FE) models, torque capability of three common synchronous machine technologies, namely a permanent magnet (PM) synchronous machine (PMSM) with V-shaped rare-earth (RE) rotor magnets, a PMSM with deep V-shaped ferrite rotor magnets, and a synchronous reluctance machine (SynRM) with four layers of conforming flux barriers are compared for an application in a 48-V mild hybrid electric car. The optimization of the deep V-shaped ferrite PMSM automatically resulted in a spoke-type PM layout for maximum torque production. Yet, an optimized SynRM with conforming flux barriers was achieved that could produce a higher torque than ferrite PMSM. One machine technology is selected and is subsequently subjected to a large-scale FE model-based drive-cycle design optimization. Various pole-slot combinations are methodically compared in terms of drive-cycle losses, active material cost, torque ripple, and PM demagnetization level. More than 20,000 designs were analyzed over ten energy-centric torque-speed points to identify an optimal design solution. The results of multi-physics analysis incorporating electromagnetics, computational fluid dynamics (CFD), and structural analyses are provided, including a study on two different water jacket concepts. A final design is prototyped and initial experimental results are provided.

Aircraft conceptual design is a high-dimensional, multidisciplinary design optimization (MDO) problem. It involves a large number of design variables (~10-1000s), multiple disciplines, and diverse operating conditions, including nominal on-design and off-design scenarios such as structural sizing and system failure modes. Recent advancements in modeling and adjoint-based sensitivity analysis have facilitated the use of low- to mid-fidelity physics-based models to achieve computationally efficient solutions for this complex, large-scale MDO problem. However, employing higher-fidelity simulations, such as CFD-based aerodynamic analysis, for large-scale MDO of aircraft concepts remains challenging. This is largely due to the high computational cost and the complex mesh movement requirements associated with significant design geometry changes, particularly at the conceptual design stage. In this paper, we propose initial steps toward a mesh movement algorithm designed to bridge the gap between high-fidelity aerodynamic analysis and large-scale MDO of aircraft concepts using mixed-fidelity system models. The algorithm minimizes the projection error volume between the mesh and the central geometry while incorporating a non-uniformity penalty to maintain mesh quality. Additionally, it computes intersection curves between intersecting geometries, ensuring that the mesh conforms to the outer hull of the geometry. We demonstrate the proposed algorithm on a simple test case involving a wing and fuselage configuration.

Actuator saturation is a common nonlinearity. In wave energy conversion, force saturation conveniently limits drivetrain size and cost with minimal impact on energy generation. However, such nonlinear dynamics typically demand numerical simulation, which increases computational cost and diminishes intuition. This paper instead uses describing functions to approximate a force saturation nonlinearity as a linear impedance mismatch. In the frequency domain, the impact of controller impedance mismatch (such as force limit, finite bandwidth, or parameter error) on electrical power production is shown analytically and graphically for a generic nondimensionalized single degree of freedom wave energy converter in regular waves. Results are visualized with Smith charts. Notably, systems with a specific ratio of reactive to real mechanical impedance are least sensitive to force limits, a criteria which conflicts with resonance and bandwidth considerations. The describing function method shows promise to enable future studies such as large-scale design optimization and co-design.

A large-scale continuous optimization benchmark suite with versatile coupled heterogeneous modules

New processes for the design of dependable systems must address both cost and dependability concerns. They should also maximize the potential for automation to address the problem of increasing technological complexity and the potentially immense design spaces that need to be explored. In this paper we show a design process that integrates system modelling, automated dependability analysis and evolutionary optimization techniques to achieve the optimization of designs with respect to dependability and cost from the early stages. Computerized support is provided for difficult aspects of fault tolerant design, such as decision making on the type and location of fault detection and fault tolerant strategies. The process is supported by HiP‐HOPS, a scalable automated dependability analysis and optimization tool. The process was applied to a Pre‐collision system for vehicles at an early stage of its design. The study shows that HiP‐HOPS can overcome the limitations of earlier work based on Reliability Block Diagrams by enabling dependability analysis and optimization of architectures that may have a network topology and exhibit multiple failure modes. Copyright © 2011 John Wiley & Sons, Ltd.

As part of H2020 EU project AGILE, A Collaborative System of Systems Multidisciplinary Design Optimization research approach is presented in this paper. This approach relies on physics-based analysis to evaluate the correlations between the airframe design, as well as propulsion, aircraft systems, aerodynamics, structures and emission, from the early design process, and to exploit the synergies within a simultaneous optimization process. Further, the disciplinary analysis modules from multiple organizations, involved in the optimization are integrated within a distributed framework. The disciplinary analysis tools are not shared, but only the data are distributed among partners through a secured network of framework. In order to enable and to accelerate the deployment of collaborative, large scale design and optimization frameworks, the Paradigm, a novel methodology, has been formulated during the project. The main elements composing the AGILE Paradigm are the Knowledge Architecture (KA), and the Collaborative Architecture (CA). The first formalizes the overall product development process in a multi-level structure. The latter formalizes the collaborative process within the entire supply chain, and defines how the multiple stakeholders interact with each other.The current paper is focused on the application of using the AGILE Paradigm to solve system of stystems MDO on a regional jet transport aircraft. The focus of the current research paper is: 1) Creation of a system of systems frame work using AGILE Paradigm to support multidisciplinary distributive analysis capability. The framework involves physics based modules such as : Airframe synthesis, aerodynamics, structures, aircraft systems , propulsion system design, nacelle design, nacelle airframe integration, aircraft mission simulation,costs and emissions. 2) Validate the frame work with case study of a regional jet reference aircraft. 3) Assess the sensitivity and coupling of design parameters, local disciplinary optimizataion and its effect on global optimization objectives or constraints. The effects of varying Bypass Ratio (BPR) of engine, offtake effects due to degree of electrification and nacelle effects are propagated through the AGILE MDO framework and presented.

A methodology for optimizing transit networks based on both passenger and operator costs is presented. Given information on transit demand, street network, and a set of feasibility constraints of a transit service area, the methodology searches for the transit network that best fits design goals through the minimization of a total cost objective function. The goal is to provide an effective mathematical solution procedure with minimal reliance on heuristics to solve large-scale transit network optimization problems. The methodology consists of a representation of transient route network and headway search spaces; a normalized, dimensionless total cost function; and a stochastic global search scheme that combines simulated annealing, tabu, greedy, and bisection search methods. The methodology has been tested with published benchmark problems and applied to a large-scale realistic network optimization problem. The results show that the methodology is capable of producing improved solutions to large-scale transit network design problems with reasonable computing resources.

We develop new fast and efficient algorithms for designing single or multiple unimodular waveforms with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding problems can quickly grow to a large scale with increasing the code length and the number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are nonconvex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as nonconvex quartic optimization problems in frequency domain, and then simplify them into quadratic problems via majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or nonconvex optimization problems. While designing our fast algorithms, we explore and use the inherent algebraic structures in objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form that allows us to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.

The demand for large-scale design optimization and probability-based analysis is constantly increasing. In design optimization and stochastic analysis, repeated analyses are required, which impede computational efficiency. Several effective reanalysis techniques using the Sherman–Morrison–Woodbury (SMW) formula have been formulated for application to static analysis. However, it is difficult to directly apply the SMW formula for dynamic reanalysis, and, consequently, substructuring techniques are frequently employed for the dynamic reanalysis. The existing dynamic substructuring finite element techniques require recalculations for all the substructures, including changed elements, even when only a single element is changed; thus, the accuracy is reduced owing to the interface assumption. Therefore, to apply the SMW formula to the dynamic reanalysis, an approach is employed in which, using dynamic condensation, the dynamic problem is transformed into a problem where the SMW formula can be employed. Furthermore, to improve the speed of convergence in the condensation method, the proposed method reuses the condensed matrices calculated in the previous analysis. Thus, the proposed method precisely updates and recalculates only the elements of interest, thus increasing the computation efficiency and accuracy. Several numerical examples are presented to verify the efficiency and accuracy of the proposed method.