Multi-objective robust design optimization of an engine mounting system

International audienceThis paper introduces a new method to support designers to find optimal and robust solutions of engine mounting system. The mounting system design is a compromise between isolation of the vehicle from engine vibration and constraining the motion of the powertrain within vehicle packaging. Based on the classical pendulum mounting system of a front wheel drive vehicle with a transversely four-cylinder engine, this study deals with the definition of a new global engine mounting concept for the NVH (Noise Vibration and Harshness) improvement of the vehicle characteristics at idle speed. The practical application of the numerical optimization is complicated by the fact that engine mounting system is a stochastic system. Its characteristics have a probabilistic nature. Multi-Objective Genetic Algorithm (MOGA), i.e. Pareto-optimization, is taken as the appropriate framework for the definition and the solution of the addressed multi-objective robust optimization problem. An experimental correlation analysis has been conducted on a Pareto-optimal solution to show the model accuracy

Multidisciplinary Multiobjective Optimal Design for Turbomachinery Using Evolutionary Algorithm

This report summarizes Dr. Lian s efforts toward developing a robust and efficient tool for multidisciplinary and multi-objective optimal design for turbomachinery using evolutionary algorithms. This work consisted of two stages. The first stage (from July 2003 to June 2004) Dr. Lian focused on building essential capabilities required for the project. More specifically, Dr. Lian worked on two subjects: an enhanced genetic algorithm (GA) and an integrated optimization system with a GA and a surrogate model. The second stage (from July 2004 to February 2005) Dr. Lian formulated aerodynamic optimization and structural optimization into a multi-objective optimization problem and performed multidisciplinary and multi-objective optimizations on a transonic compressor blade based on the proposed model. Dr. Lian s numerical results showed that the proposed approach can effectively reduce the blade weight and increase the stage pressure ratio in an efficient manner. In addition, the new design was structurally safer than the original design. Five conference papers and three journal papers were published on this topic by Dr. Lian

A Novel Design Approach to X-Band Minkowski Reflectarray Antennas using the Full-Wave EM Simulation-based Complete Neural Model with a Hybrid GA-NM Algorithm

In this work, a novel multi-objective design optimization procedure is presented for the Minkowski Reflectarray RAs using a complete 3-D CST Microwave Studio MWS-based Multilayer Perceptron Neural Network MLP NN model including the substrate constant εr with a hybrid Genetic GA and Nelder-Mead NM algorithm. The MLP NN model provides an accurate and fast model and establishes the reflection phase of a unit Minkowski RA element as a continuous function within the input domain including the substrate 1 ≤ εr ≤ 6; 0.5mm ≤ h ≤ 3mm in the frequency between 8GHz ≤ f ≤ 12GHz. This design procedure enables a designer to obtain not only the most optimum Minkowski RA design all throughout the X- band, at the same time the optimum Minkowski RAs on the selected substrates. Moreover a design of a fully optimized X-band 15×15 Minkowski RA antenna is given as a worked example with together the tolerance analysis and its performance is also compared with those of the optimized RAs on the selected traditional substrates. Finally it may be concluded that the presented robust and systematic multi-objective design procedure is conveniently applied to the Microstrip Reflectarray RAs constructed from the advanced patches

Robust multi-objective design of suspension systems

This thesis presents a robust multi-objective optimal design of four-degree-of-freedom passive and semi-active suspension systems. The passive suspension system is used in a racing car and the semi-active suspension is implemented on a passenger car. Mathematical models of the commercial and racing vehicle suspension systems are used in the computer simulations. A robust multi-objective design of the suspension systems is carried out by considering the minimization of three objectives: passenger’s head acceleration (HA), suspension deflection (SD), and tire deflection (TD). The first objective is concerned with the passenger’s health and comfort. The suspension stroke is described by SD and the tire holding is characterized by TD. The optimal design of the passive suspension involves tuning the coefficients of the sprung spring and damper, tire stiffness, and inertance of the inerter. Suspension systems’ parametric variations are very common and cannot be avoided in practice. To this end, a robust multi-objective optimization method that takes into consideration small changes in the design parameters should be considered. Unlike traditional multi-objective optimization problems where the focus is placed on finding the global Pareto-optimal solutions which express the optimal trade-offs among design objectives, the robust multi-objective optimization algorithms are concerned with robust solutions that are less sensitive to perturbations of decision variables. As a result, the mean effective values of the fitness functions are used as design objectives. Constraints on the design parameters and goals are applied. Numerical simulations show that the robust multi-objective design (RMOD) is very effective and guarantees a robust behavior as compared to that of the classical multi-objective design (MOD). The results also show that the robust region is inside the feasible search space and avoids all of its boundaries. The decision parameter space of the semi-active suspension includes both passive and active components. The passive components include the stiffness of the sprung spring, damping coefficient of the shock absorber, and stiffness of the tire. The active elements are the design details of the LQR algorithm. During the design, global sensitivity analysis is conducted to determine the elements of the suspension system that have high impact on the design objectives. The mass of the passenger’s head and upper body, the mass of the passenger’s lower body and cushion, passenger and cushion’s elastic properties, and the sprung mass of the vehicle are selected for the sensitivity analysis. Results show that the design goals are more sensitive to the variations in the sprung mass than the other parameters. As a result, parametric variations in the sprung mass of the vehicle and passive elements of the suspension system are considered. Similar to the design of the passive suspension, the mean effective values of SD, TD, and HA are used as design objectives. Also, constraints are applied on the objectives in compliance with the requirements of ISO 2631-1 on the design of car suspension systems. The optimization problem is solved by the NSGA-II (non-dominated sorting genetic algorithm) and robust Pareto front and set are obtained

Multidisciplinary and Multi-Objective Optimal Design of a Cascade Control System for a Flexible Wing with Embedded Control Surfaces Having Actuator Dynamics

A multidisciplinary and multi-objective optimization approach that integrates the design of the control surfaces’ sizes, active control systems, and estimator for an aircraft’s wing with three control surfaces is developed. Due to its attractive stability robustness properties, a control system based on the LQR (Linear Quadratic Regulator) is built for each control surface. The geometrical parameters of the control surfaces such as the span wise and chord lengths, the design details of the LQR penalty matrices, and the locations of the estimator poles are tuned by a widely used multi-objective optimization algorithm called NSGA-II (Non-dominated Sorting Genetic Algorithm). Four objectives are considered: minimizing impacts of external gust loads, maximizing stability robustness and extending flutter boundaries, reducing control energy consumption, and minimizing the Frobenius norm of the estimator gains. The solution of the multi-objective optimization problem is a set called Pareto set and the set of the corresponding function evaluation is called Pareto front. The solution set contains various geometrical configurations of the control surfaces with different feedback gains, which represent different degrees of optimal compromises among the design objectives. The optimization results demonstrate the competing relationship between the design objectives and necessity of handling the design problem in a multidisciplinary and multi-objective context. Three major results are obtained from inspecting the profiles of the closed-loop eigenvalues at various airspeeds 1) a unique control gain can be designed for the entire flight envelope, 2) the flutter boundaries can be infinitely extended, and 3) a unique observer gain can be designed for the entire flight envelope. The third chapter of this thesis presents a multi-objective and multidisciplinary optimal design of a cascade control system for an aircraft wing with four aerodynamic ailerons actuated by four identical brushless DC motors. The design of the control system is broken into a secondary and primary control algorithm. The primary control algorithm is designed based on the concept of LQR and then applied to mathematical model of the wing and its control surfaces to calculate their required deflections. The output of the primary controller serves as set-point for the secondary control loop which consists of the dynamic of the DC motor and Proportional Velocity (PV) based controller. Then, an optimal design of the control algorithms is carried out in multi-objective and multidisciplinary settings. Three objectives are considered: 1) the speed of response of the secondary controlled system must be faster than that of the primary one, 2) the controlled system must be robust against external disturbances affecting both control layers, and 3) optimal energy consumption. The decision variables of the primary as well as secondary control algorithms and the sizing elements of the control surfaces form the design parameter space of the optimization problem. Both geometrical and dynamic constraints are applied on the setup parameters. The multi-objective optimization problem (MOP) is solved by NSGA-II, which is one of the popular algorithms in solving MOPs. The solution of the MOP is a set of optimal control algorithms that represent the conflicts among the design objectives. Numerical simulations show that the design goals are achieved, the secondary control is always fast enough to prevent the propagation of disturbances to the primary loop, the inner and outer control algorithms are robust against disturbance inputs, and the primary control loop stays stable when the air stream velocity varies from 80 to 1000 (⁄) even at its worst relative stability value. The presented study may become the basis for multi-objective and multidisciplinary optimal design for aeroelastic structure having actuator dynamics

Multi-Objective Optimization in CFD by Genetic Algorithms

This report approaches the question of multi-objective optimization for optimum shape design in aerodynamics. The employed optimizer is a semi-stochas- tic method, more precisely a Genetic Algorithm (GA). GAs are very robust optimization algorithms particularly well suited for problems in which (1) the initialization is not intuitive, (2) the parameters to be optimized are not all of the same type (boolean, integer, real, functionnal), (3) the cost functional may present several local minima, (4) several criteria should be accounted for simultaneously (multiphysics, efficiency, cost, quality, ...). In a multi-objective optimization problem, there is no unique optimal solution but a whole set of potential solutions since in general no solution is optimal w.r.t. all criteria simultaneously ; instead, one identifies a set of non-dominated solutions, referred to as the Pareto optimal front. After making these concepts precise, genetic algorithms are implemented and first tested on academic examples ; then a numerical experimentation is conducted to solve a multi-objective shape optimization problem for the design of an airfoil in Eulerian flow

Robust Optimization and Sensitivity Analysis with Multi-Objective Genetic Algorithms: Single- and Multi-Disciplinary Applications

Uncertainty is inevitable in engineering design optimization and can significantly degrade the performance of an optimized design solution and/or even change feasibility by making a feasible solution infeasible. The problem with uncertainty can be exacerbated in multi-disciplinary optimization whereby the models for several disciplines are coupled and the propagation of uncertainty has to be accounted for within and across disciplines. It is important to determine which ranges of parameter uncertainty are most important or how to best allocate investments to partially or fully reduce uncertainty under a limited budget. To address these issues, this dissertation concentrates on a new robust optimization approach and a new sensitivity analysis approach for multi-objective and multi-disciplinary design optimization problems that have parameters with interval uncertainty. The dissertation presents models and approaches under four research thrusts. In the first thrust, an approach is presented to obtain robustly optimal solutions which are as best as possible, in a multi-objective sense, and at the same time their sensitivity of objective and/or constraint functions is within an acceptable range. In the second thrust, the robust optimization approach in the first thrust is extended to design optimization problems which are decomposed into multiple subproblems, each with multiple objectives and constraints. In the third thrust, a new approach for multi-objective sensitivity analysis and uncertainty reduction is presented. And in the final research thrust, a metamodel embedded Multi-Objective Genetic Algorithm (MOGA) for solution of design optimization problems is presented. Numerous numerical and engineering examples are used to explore and demonstrate the applicability and performance of the robust optimization, sensitivity analysis and MOGA techniques developed in this dissertation. It is shown that the obtained robust optimal solutions for the test examples are conservative compared to their corresponding optimal solutions in the deterministic case. For the sensitivity analysis, it is demonstrated that the proposed method identifies parameters whose uncertainty reduction or elimination produces the largest payoffs for any given investment. Finally, it is shown that the new MOGA requires a significantly fewer number of simulation calls, when used to solve multi-objective design optimization problems, compared to previously developed MOGA methods while obtaining comparable solutions

Enhancing optimization capabilities using the AGILE collaborative MDO framework with application to wing and nacelle design

This paper presents methodological investigations performed in research activities in the field of Multi-disciplinary Design and Optimization (MDO) for overall aircraft design in the EU funded research project AGILE (2015–2018). In the AGILE project a team of 19 industrial, research and academic partners from Europe, Canada and Russia are working together to develop the next generation of MDO environment that targets significant reductions in aircraft development costs and time to market, leading to cheaper and greener aircraft. The paper introduces the AGILE project structure and describes the achievements of the 1st year that led to a reference distributed MDO system. A focus is then made on different novel optimization techniques studied during the 2nd year, all aiming at easing the optimization of complex workflows that are characterized by a high number of discipline interdependencies and a large number of design variables in the context of multi-level processes and multi-partner collaborative engineering projects. Three optimization strategies are introduced and validated for a conventional aircraft. First, a multi-objective technique based on Nash Games and Genetic Algorithm is used on a wing design problem. Then a zoom is made on the nacelle design where a surrogate-based optimizer is used to solve a mono-objective problem. Finally a robust approach is adopted to study the effects of uncertainty in parameters on the nacelle design process. These new capabilities have been integrated in the AGILE collaborative framework that in the future will be used to study and optimize novel unconventional aircraft configurations

Optimal Design of Switched Reluctance Motor Using Genetic Algorithm

Switched reluctance motor (SRM) is gaining more interest in both research and industry. Its simple structure without windings or permanent magnets on the rotor makes the motor robust and reliable with reduced manufacturing cost. The SRM also provides high starting torque and high efficiency over a wide range of speeds, which is strongly desired for electric vehicles’ applications. However, these advantages of switched reluctance motors come with some challenges. Torque ripples, low power density, and temperature rise are common questions about SRM. This paper utilizes multi-objective optimization of SRM design to get most of the SRM desired characteristics with minimization of the machine’s common drawbacks. The optimization process has considered twelve variables and five objective functions. These functions include average torque, efficiency, iron weight, torque-ripples, and maximum temperature rise. The electromagnetic analysis of each candidate is performed by the finite elements method (FEA). The performance indices of SRM are calculated based on FEA analysis results via calculations that compensate for accuracy and computation time. The multi-objective genetic algorithm technique (MOGA) combines the objective functions into a single objective function. Verifying the optimal design comprises generating the efficiency map, torque profile, and dynamic simulation of the motor. This paper mainly focuses on the design and optimization of SRM to fulfill the general requirements of electric vehicle applications

Optimal Design of Switched Reluctance Motor Using Genetic Algorithm

Switched reluctance motor (SRM) is gaining more interest in both research and industry. Its simple structure without windings or permanent magnets on the rotor makes the motor robust and reliable with reduced manufacturing cost. The SRM also provides high starting torque and high efficiency over a wide range of speeds, which is strongly desired for electric vehicles’ applications. However, these advantages of switched reluctance motors come with some challenges. Torque ripples, low power density, and temperature rise are common questions about SRM. This paper utilizes multi-objective optimization of SRM design to get most of the SRM desired characteristics with minimization of the machine’s common drawbacks. The optimization process has considered twelve variables and five objective functions. These functions include average torque, efficiency, iron weight, torque-ripples, and maximum temperature rise. The electromagnetic analysis of each candidate is performed by the finite elements method (FEA). The performance indices of SRM are calculated based on FEA analysis results via calculations that compensate for accuracy and computation time. The multi-objective genetic algorithm technique (MOGA) combines the objective functions into a single objective function. Verifying the optimal design comprises generating the efficiency map, torque profile, and dynamic simulation of the motor. This paper mainly focuses on the design and optimization of SRM to fulfill the general requirements of electric vehicle applications