Multi-objective Robust Design Research Articles

Improving the potential of fifth-generation district heating and cooling networks through robust design and operational optimization under future energy market and demand uncertainties

Improving the potential of fifth-generation district heating and cooling networks through robust design and operational optimization under future energy market and demand uncertainties

Multi-Objective Robust Design Optimization for Crashworthiness Enhancement of Hybrid 2D Triaxially Braided Composite Tube Using Evolutionary Algorithms.

An innovative optimal design framework is developed aiming at enhancing the crashworthiness while ensuring the lightweight design of a hybrid two-dimensional triaxial braided composite (2DTBC) tube, drawing insights from the mesostructure of the composite material. To achieve these goals, we first compile the essential mechanical properties of the 2DTBC using a concentric cylinder model (CCM) and an analytical laminate model. Subsequently, a kriging surrogate model to elucidate the intricate relationship between design variables and macroscopic crashworthiness is developed and validated. Finally, employing multi-objective evolutionary optimization, we identify Pareto optimal solutions, highlighting that reducing the total fiber volume and increasing the glass fiber content in the total fiber volume are crucial for optimal crashworthiness and the lightweight design of the hybrid 2DTBC tube. By integrating advanced predictive modeling techniques with multi-objective evolutionary optimization, the proposed approach not only sheds light on the fundamental principles governing the crashworthiness of hybrid 2DTBC but also provides valuable insights for the design of robust and lightweight composite structures.

Multi-objective robust optimization design framework for low-pollution emission burners

Multi-objective robust optimization design framework for low-pollution emission burners

Bi-level game theoretic approach for robust design: A case study of path-generating four-bar

Bi-level game theoretic approach for robust design: A case study of path-generating four-bar

Multi-Objective Robust Trajectory Design for Powered Descent and Landing

A robust trajectory optimization approach for guidance algorithm gain and target vector selection for powered descent and landing is developed. A genetic algorithm is used to determine optimized guidance algorithm parameters to minimize the impact of initial condition, environment, navigation, and vehicle property uncertainty on flight performance for a given sensor suite. Vehicle state uncertainties are computed efficiently using linear covariance analysis techniques. When implemented in the guidance algorithm, the optimized gains and target vectors shape a trajectory that has more favorable conditions for a given navigation sensor suite, resulting in improved flight performance. As a demonstration of this method, the optimized guidance parameters are found for a multiphase trajectory from powered descent initiation to touchdown for a robotic lunar landing mission. Single-objective optimization results demonstrate a reduction in uncertainty and an improvement in nominal performance. Multi-objective optimization results showing the tradeoff between terminal position uncertainty and total propellant usage are presented for multiple sensor suite compositions. Further, guidance parameters selected using the developed robust trajectory design approach may enable acceptable flight performance with fewer and/or lower-quality sensors. The resulting Pareto fronts present the optimal trade space early in the mission design process to enable informed decision-making.

Robust design optimization of a multi-body system with aleatory and epistemic uncertainty

Robust design optimization of a multi-body system with aleatory and epistemic uncertainty

Probabilistički višekriterijumski robustni dizajn i njegova primena u sečenju metala

Introduction/purpose: Cutting is a typical material process. However, an appropriate solution for simultaneous optimization of material machinability and tool life in material cutting processes has not been obtained yet. In this article, probabilistic multi-objective robust design (PMORD) is expounded and the robust design problem in the simultaneous optimization of material machinability and tool life is analyzed by taking the machining of ferrite-bainite dual-phase steel as an example. Methods: According to PMORD, the arithmetic mean and its deviation of various performance and utility indexes of alternative schemes are evaluated as twin independent responses, which respectively contribute a part of the partial preferable probability to the performance indexes. In the evaluation, the arithmetic average of the utility index is taken as the representative of the utility attribute, and the evaluation is made in accordance with the function or preference of the utility index. However, the deviation term is generally used as an unbeneficial type of the index (that is, the smaller the better) to participate in the evaluation. The product of the two parts of partial preferable probability is the actual partial preferable probability of the corresponding performance index. The product of the partial preferable probability of all performance utility indexes gives the total preferable probability of the corresponding scheme, which is the only index for each scheme to participate in the competition in robust design. Results: The optimization result of this example is that the tool life is 1297.3333 s (standard deviation is 2.0817 s) and the surface roughness is 2.22mm (standard deviation is 0.2mm), while the corresponding working conditions are that the heat treatment temperature of the material is 790°C, the cutting speed is 150m/min, the feed speed is 0.15mm/rev, and the cutting depth is 0.2mm. Conclusion: The example of the parameter optimization of cutting of ferrite-bainite dual-phase steel by means of PMORD indicates the rationality of the appropriate solution.

Multi-objective topology optimization design of truss structures based on evidence theory under limited information

Uncertainty information is often limited and has great discreteness, how to ensure the structure having good robustness under epistemic uncertainty becomes a technical problem for multi-objective topology optimization design. In this paper, the evidence theory is used to quantify the epistemic uncertainty; the plausibility measurement expressing upper limit of failure probability is applied to be a new evaluation of reliability. The total weight and the reliability of structures are taken as the optimization objectives, and a multi-objective robust topology optimization design model based on evidence theory is proposed. Parallelization technique based differential evolution for multi-objective optimization (DEMO) is preferable to search above robust Pareto front due to its merits of non-requirement of any gradient and superior mechanisms of non-dominate strategy. In order to verify the effectiveness of the proposed method, the multi-objective reliability optimization of a wood truss structure is implemented with considering elastic modulus and structural load as uncertain variables. According to the optimization results, six same truss specimens are made for the static random loading test. The failure probability of the truss structure is judged by the stress and node displacement obtained from the test, so as to verify the feasibility of the reliability optimization method based on evidence theory. The experimental results also indicate that the proposed method can avoid the deviation of the optimization results caused by the fluctuation of epistemic uncertainty, and provide a new method for designers to make the optimization results robust even when the data information is insufficient and the cognitive level is limited.

Robust Optimization Design of the Aerodynamic Shape and External Ballistics of a Pulse Trajectory Correction Projectile

To improve the tactical and technical performance of pulse correction projectiles while maintaining stability in uncertain conditions and considering practical engineering constraints, this study performs a multi-objective robust optimization design of the aerodynamic shape and external ballistics of a projectile. The study utilizes an aerodynamic force engineering algorithm and numerical trajectory calculations to obtain the projectile’s performance responses within the Latin hypercube design space. To enhance optimization efficiency, a stochastic Kriging surrogate model is established to capture the inherent uncertainty of limited input data. Ultimately, a Pareto optimal solution for the projectile is obtained using a non-dominated sorting multi-objective sparrow search algorithm. The results of this study demonstrate that the consideration of design uncertainty in the robust optimization of pulse correction projectiles leads to significant enhancements in both lateral correction ability and range while satisfying flight stability requirements. Moreover, when compared to deterministic optimization, the performance variability of the design is markedly improved. This research methodology provides valuable insights for optimizing the performance of pulse correction projectiles.

Parameter uncertainty modeling for multiobjective robust control design. Application to a temperature control system in a proton exchange membrane fuel cell

Parameter uncertainty modeling for multiobjective robust control design. Application to a temperature control system in a proton exchange membrane fuel cell

Robust Multi-Objective Design Optimization of Water Distribution System under Uncertainty

The multi-objective design optimization of water distribution systems (WDS) is to find the Pareto front of optimal designs of WDS for two or more conflicting design objectives. The most popular conflicting objectives considered for the design of WDS are minimization of cost and maximization of resilience index which are considered for the current study. Robust multi-objective optimization is to find the optimal set of the Pareto front considering demand is uncertain. The robustness is controlled by a single parameter that defines the size of the uncertainty set it can vary. The study explores ellipsoidal uncertainty set with different sizes and co-variance matrices. A combined simulation–optimization framework with a combination of self-adaptive multi-objective cuckoo search (SAMOCSA) and the fmincon optimization algorithm is proposed to solve the robust multi-objective design problem. The proposed algorithm is applied to medium and large WDS. The main contribution of this paper is to study the effect of demand uncertainty and the correlation on the WDS designs in a multi-objective framework. The study shows that the inclusion of correlation into the multi-objective design framework can significantly affect the optimal designs.

Undeterministic analysis and process optimization for short-fiber composite injection molding

When designing vehicle parts, reliability is required to be insensitive to the change of design parameters, so as to improve product safety and robustness. The traditional design method mainly considers the deterministic model and ignores the influence of noise factors. Based on deterministic optimization, a multi-objective robust design model with multi-quality characteristics is proposed in this paper. The response surface model (RSM) of controllable factors, noise factors and quality objectives is established. Then based on the RSM model, it is applied to do robust optimization design with undeterministic analysis method, 6 Sigma optimization design and NSGA-II optimization algorithm. Taking the optimization design of the vehicle navigation fixed base as an example, the feasibility and effectiveness of the optimization method are verified by numerical simulation and actual injection molding experiment respectively.The results show that the 6 Sigma robust design achieves the minimum mean square error and improves the robustness of the optimized solution, compared to the deterministic optimization. • The traditional design method ignores the influence of noise factors. • A multi-objective robust design model with multi-quality characteristics is proposed. • The response surface model of controllable factors, noise factors and quality objectives is established. • Do robust optimization design with undeterministic analysis method and NSGA-II optimization algorithm.

An interval-based multi-objective robust design optimization for vehicle dynamics

This study presents an Interval-based Multi-objective Robust Design Optimization (IB-MORDO) algorithm applied to a vehicle dynamic problem. The proposed algorithm optimizes a full 15 degrees-of-freedom (15-DOF) vehicle model, subjected to a double-lane change (DLC) maneuver under random road profiles, to attain driver comfort and safety. This study does not make assumptions about uncertain parameter statistics; instead, the uncertainties are quantified using a non-probabilistic α-cut level interval analysis. These uncertainties are applied to the system parameters and design variables to ensure robust results. After the optimization process, the root mean square (RMS) vertical acceleration at the driver’s seat resulted in a robust solution of 1.041 m/s2 and a parameter interval radius (IR) equals to 0.631 m/s2, whereas the RMS lateral acceleration at the driver’s seat resulted in a solution of 1.908 m/s2 with an interval radius of 0.168 m/s2. Unlike the Robust Optimization, the algorithm proposed herein considers uncertainties at system parameters and design variables without assuming any statistical data. HIGHLIGHTS An Interval-based Robust Multi-objective Optimization procedure is proposed and tested on a 15-DOF vehicle model. Αn α-cut level methodology is used to deal with the uncertainty propagation. Resulted optimal suspension parameters minimize center and interval radius of driver’s vertical and lateral accelerations.

Multi-Objective and Robust Design of a Semi-Active Suspension System

This paper presents a robust multi-objective optimal design (RMOP) of a passenger car with a semi-active suspension system. The mean-effective values of the root mean square of the passenger’s head acceleration, suspension travel, and tire deflection are considered as design objectives. The passive components of the suspension and the design details of the Linear Quadratic Regulator (LQR) algorithm are used as design parameters. During the design, global sensitivity analysis is carried out using the Fourier Amplitude Sensitivity Test (FAST) to specify the elements of the model that can highly alter 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 criteria are very sensitive to the variations in the sprung mass of the vehicle as compared to the other parameters. As a result, the variations in this parameter and passive elements of the suspension system are considered. 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 II) and robust Pareto front and set are obtained. The Pareto set includes multiple design options from which the decision-maker can choose to implement. Responses of the passenger’s head acceleration, suspension travel, and tire deflection show that the robust multi-objective design algorithm (RMOA) is very effective and guarantees less sensitivity to the suspension passive elements.

Adaptive Optimal Multi-Surface Back-Stepping Sliding Mode Control Design for the Takagi-Sugeno Fuzzy Model of Uncertain Nonlinear System With External Disturbance

This paper proposes a novel scheme of the multi-objective robust control design for a class of uncertain nonlinear systems in strict-feedback-form based on Takagi–Sugeno fuzzy model (TSFM). The nonlinear system contains both the matched and the unmatched uncertainties and also subjected to the external disturbances. The TSFM provides the generalization of the linear systems concepts to the nonlinear systems field in a convex framework. First, a new sliding surface is defined using a convex combination of the surfaces which are defined for each fuzzy rule consequence local linear subsystems. Then, their gains are designed optimally via a generalized eigenvalue problem (GEVP). Also, the upper-bounds of the matched and unmatched uncertainties are estimated using the adaptive update laws. The multi-objective control aims not only to satisfy the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization performance, but also, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability region is formulated to improve the transient response performance. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization characterization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability design conditions are derived in terms of new linear matrix inequalities (LMIs) conditions. Finally, the effectiveness of the proposed approach is demonstrated by considering a comparative practical example.

Multi-objective robust design approach usage in integration of bond graph and genetic programming

ABSTRACT In this paper, a new hybrid algorithm, based on multi-objective genetic programming and bond graphs in combination with Monte Carlo simulation, is proposed for Pareto optimal robust design of dynamical systems. For this purpose, first, an embryo model is considered for a dynamical system. Then, genetic programming is used to help this embryo model evolve through generations and achieve an optimum model. It is clear that without considering the uncertain parameters of the designing system, unwanted behaviors could occur. To overcome this, Monte Carlo simulation has been used to minimize the variations of objective functions by generating some samples around the nominal values of the uncertain parameters. In other words, the mean and variance of the objective function are minimized simultaneously through sampling, generated by Monte Carlo simulation, to reach a robust behavior. The proposed algorithm has been employed for robust design of two case studies, namely a closed-loop typewriter drive system and an optimum controller for quarter-car suspension system. A comparison between the results obtained using the proposed algorithm and those obtained through other approaches in the literature shows that more robust behavior in the presence of uncertainties can be observed in the proposed method.

Multi-objective robust optimization of a solar power tower plant under uncertainty

The optimal design of a molten salt solar power tower (SPT) plant is sensitive to the variations of uncertainties, such as solar radiation, which result in dispersion of the model output. To mitigate the impacts of uncertainties on the thermo-economic performance of SPT plant, this study develops an uncertainty-based multi-objective robust optimization design method for the case of a SPT plant in Sevilla with the expected value (i.e. the average energy cost) and the standard deviation (i.e. the dispersion of the model output) of the levelized cost of energy (LCOE) as the objectives. The Monte Carlo (MC) simulation and simulated annealing (SA) algorithm are combined to solve the robust optimization problem. The results of Pareto frontier indicate that a trade-off is needed through decision-making. The final optimal solution is determined with expectation of LCOE of 23.09 c/kWhe and standard deviation of LCOE of 1.25 c/kWhe. Compared with the deterministic optimal design, the standard deviation of LCOE of the multi-objective robust optimum is reduced by 17.22 %, which turns out to be less sensitive to the uncertainties. Moreover, the Sobol’ global sensitivity analysis results show that the direct solar radiation, heliostat field cost and receiver cost are the most sensitive to LCOE.

Bayesian optimization for robust design of steel frames with joint and individual probabilistic constraints

• Bayesian optimization handles probabilistic constrained robust optimization problems. • Two new acquisition functions guide Bayesian optimization toward better solutions. • Solving the maximization of the acquisition functions using a novel random search. This work proposes a Bayesian optimization (BO) method for solving multi-objective robust design optimization (RDO) problems of steel frames under aleatory uncertainty in external loads and material properties. Joint and individual probabilistic constrained RDO problems are formulated to consider two different ways the frame reaches its collapse state. Each problem involves three conflicting objective functions, namely, the total mass of the frame, the mean and variance of the maximum inter-story drift. Since the uncertain objective and probabilistic constraint functions of both problems are implicit within a finite element analysis program and the computation of the probabilistic constraints is an NP-hard problem, BO is used to guide the optimization process toward better solutions after it completes an iteration and offers a set of near Pareto-optimal solutions when it terminates. Specifically, Bayesian regression models called Gaussian processes (GPs) serve as surrogates for the structural responses. Two acquisition functions are then developed for the two RDO problems and a maximization problem of these functions is formulated as a mixed-integer nonlinear programming (MINLP) problem. A new random search coupled with simulated annealing is devised to solve the MINLP problem, thereby locating the most promising point in the input variable space at which the current solutions maximize their chance to be improved and the GP models are refined before the BO starts a new iteration. A test problem and two design examples show that exact or good Pareto-optimal solutions to the RDO problems can be found by the proposed method with 20 iterations.

Multi-objectives robust optimization based on Grey-Taguchi method for the electric vehicle frame collision

The proportion of electric vehicles in vehicle manufacturing is increasing, but with the endurance mileage of the battery improved, the collision safety problem of electric vehicles is becoming more prominent. To solve a multi-objective robust design problem with discrete variables for vehicle collision design, we propose the Grey-Taguchi robust optimization method. The Grey-Taguchi method transforms the multi-objective functions into a single grey relation grade sequence instead of the signal-noises ratio used in Taguchi and selects the optimal combination of design variables predicted by the minimum design of experimental and the analysis of means. For the vehicle crashworthiness problem, the Grey-Taguchi method can converge to the Pareto front with several iterations. The mass of frame, maximum lateral intrusion, and peak deceleration after the optimization are decreased 14.5 %, 32.3 %, and 17.8 %, respectively. The Grey-Taguchi robust optimization method can not only enhance the robustness of the optimization design but also improve the lightweight design performance and crashworthiness. The proposed method is considered promising for complex engineering design problems with multi-objectives and discrete design variables.

Hybrid multi-objective robust design optimization of a truck cab considering fatigue life

Abstract Fatigue performance optimization without considering uncertainties of design variables can be problematic or even dangerous in real life. In this paper, a hybrid multi-objective robust design optimization methodology is proposed to make a proper tradeoff between the lightweight and fatigue durability for the design of a truck cab. However, the uncertainties, in reality, could lead to the optimized design unstable or even useless; this situation can be more serious in non-deterministic optimization. The Taguchi robust parametric design technique is adopted to refine the intervals of design variables for the subsequent optimization based on the validated simulation model against fatigue tests. Three types of dual surrogate models, namely the dual polynomial response surface, dual Kriging, and dual radial basis function methods are compared, and the dual Kriging is selected to model the mean and standard deviation of the mass and fatigue life for its high accuracy. The multi-objective particle swarm optimization algorithm is utilized to perform robust design. The Pareto fronts with different weight factors are analyzed to provide some insightful information on optimum designs. The robust optimization results demonstrate that the optimized design improves the fatigue life and reduces the mass of the truck cab significantly and becomes less sensitive to uncertainty. Different optimums can be obtained based on three different normalization techniques (Linear, vector, and LMM) and three MCDM methods (TOPSIS, WPM, and WSM) from the same Pareto front. The comparison analysis emphasizes the importance of normalization and MCDM method selection in the optimal design selection process.