A Model-Based Formulation of Robust Design

2005 ◽  
Vol 127 (3) ◽  
pp. 388-396 ◽  
Author(s):  
Khalid Al-Widyan ◽  
Jorge Angeles
Keyword(s):  
Covariance Matrix ◽  
Robust Design ◽  
Design Problem ◽  
Engineering Systems ◽  
Design Environment ◽  
Design Task ◽  
Model Based ◽  
Functional Relations ◽  
Design Variables ◽  
Environment Parameters

Laid down in this paper are the foundations on which the design of engineering systems, in the presence of an uncontrollable changing environment, can be based. The changes in environment conditions are accounted for by means of robustness. To this end, a theoretical framework as well as a general methodology for model-based robust design are proposed. Within this framework, all quantities involved in a design task are classified into three sets: the design variables (DV), grouped in vector x, which are to be assigned values as an outcome of the design task; the design-environment parameters (DEP), grouped in vector p, over which the designer has no control; and the performance functions (PF), grouped in vector f, representing the functional relations among performance, DV, and DEP. A distinction is made between global robust design and local robust design, this paper focusing on the latter. The robust design problem is formulated as the minimization of a norm of the covariance matrix of the variations in PF upon variations in the DEP, aka noise in the literature on robust design. Moreover, one pertinent concept is introduced: design isotropy. We show that isotropic designs lead to robustness, even in the absence of knowledge of the statistical properties of the variations of the DEP. To demonstrate our approach, a few examples are included.

Robustness Against Large Variations in Multi-Objective Optimization Problems

2013 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis
Keyword(s):  
Optimization Problems ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Design Environment ◽  
Multi Objective ◽  
Uncertainty Sources ◽  
Design Variables ◽  
Robustness Index ◽  
Environment Parameters

In the presence of multiple optimal solutions in multi-modal optimization problems and in multi-objective optimization problems, the designer may be interested in the robustness of those solutions to make a decision. Here, the robustness is related to the sensitivity of the performance functions to uncertainties. The uncertainty sources include the uncertainties in the design variables, in the design environment parameters, in the model of objective functions and in the designer’s preference. There exist many robustness indices in the literature that deal with small variations in the design variables and design environment parameters, but few robustness indices consider large variations. In this paper, a new robustness index is introduced to deal with large variations in the design environment parameters. The proposed index is bounded between zero and one, and measures the probability of a solution to be optimal with respect to the values of the design environment parameters. The larger the robustness index, the more robust the solution with regard to large variations in the design environment parameters. Finally, two illustrative examples are given to highlight the contributions of this paper.

Multi-Objective Robust Optimization Design of a Fixed-Speed Horizontal Axis Wind Turbine

2013 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis
Keyword(s):  
Wind Turbine ◽  
Optimization Design ◽  
Optimization Problems ◽  
Horizontal Axis ◽  
Design Environment ◽  
Horizontal Axis Wind Turbine ◽  
Multi Objective ◽  
Design Variables ◽  
Robust Optimization Design ◽  
Environment Parameters

The produced power and the thrust force exerted on the wind turbine are two conflicting objectives in the design of a floating horizontal axis wind turbine. Meanwhile, the variations in design variables and design environment parameters are unavoidable. The variations include the small variations in the design variables due to manufacturing errors, and the large variations in the wind speed. Therefore, two robustness indices are introduced in this paper. The first one characterizes the robustness of multi-objective optimization problems against small variations in the design variables and the design environment parameters. The second robustness index characterizes the robustness of multi-objective optimization problems against large variations in the design environment parameters. The robustness of the solutions based on the two robustness indices is treated as a vector defined in the robustness function space. As a result, the designer can compare the robustness of all Pareto optimal solutions and make a decision. Finally, the multi-objective robust optimization design of a fixed-speed horizontal axis wind turbine illustrates the proposed methodology.

A Comprehensive Robust Design Approach for Decision Trade-Offs in Complex Systems Design

1999 ◽  
Vol 123 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Monu Kalsi ◽  
Kurt Hacker ◽  
Kemper Lewis
Keyword(s):  
Robust Design ◽  
Systems Design ◽  
Decision Makers ◽  
Engineering Systems ◽  
Trade Offs ◽  
Design Variables ◽  
Complex Engineering ◽  
The Cost ◽  
Passenger Aircraft

In this paper we introduce a technique to reduce the effects of uncertainty and incorporate flexibility in the design of complex engineering systems involving multiple decision-makers. We focus on the uncertainty that is created when a disciplinary designer or design team must try to predict or model the behavior of other disciplinary subsystems. The design of a complex system is performed by many different designers and design teams, each of which may only have control over a portion of the total set of system design variables. Modeling the interaction among these decision-makers and reducing the effect caused by lack of global control by any one designer is the focus of this paper. We use concepts from robust design to reduce the effects of decisions made during the design of one subsystem on the performance of the rest of the system. Thus, in a situation where the cost of uncertainty is high, these tools can be used to increase the robustness, or independence, of the subsystems, enabling designers to make more effective decisions. To demonstrate the usefulness of this approach, we consider a case study involving the design of a passenger aircraft.

scholarly journals Quadrature as applied to computer models for robust design: theoretical and empirical assessment

2021 ◽  
Vol 7 ◽  
Author(s):  
Daniel D. Frey ◽  
Yiben Lin ◽  
Petra Heijnen
Keyword(s):  
Case Studies ◽  
Robust Design ◽  
Probability Model ◽  
Computer Experiments ◽  
Engineering Systems ◽  
Probability Models ◽  
Model Based ◽  
Mean And Variance ◽  
Gauss Hermite Quadrature

Abstract This paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with m noise variables, the method requires 4m + 1 function evaluations. For situations in which the polynomial response is separable, this paper proves that the method gives exact transmitted variance if the response is a fourth-order separable polynomial response. It is also proven that the relative error mean and variance of the method decrease with the dimensionality m if the response is separable. To further assess the proposed method, a probability model based on the effect hierarchy principle is used to generate sets of polynomial response functions. For typical populations of problems, it is shown that the proposed method has less than 5% error in 90% of cases. Simulations of five engineering systems were developed and, given parametric alternatives within each case study, a total of 12 case studies were conducted. A comparison is made between the cumulative density function for the hierarchical probability models and a corresponding distribution function for case studies. The data from the case-based evaluations are generally consistent with the results from the model-based evaluation.

Performance Distribution Analysis and Robust Design

2000 ◽  
Vol 123 (1) ◽  
pp. 11-17 ◽  
Author(s):  
Jianmin Zhu ◽  
Kwun-Lon Ting
Keyword(s):  
Robust Design ◽  
Robust Parameter Design ◽  
Distribution Analysis ◽  
Performance Space ◽  
Sensitivity Distribution ◽  
Performance Sensitivity ◽  
Design Variables ◽  
Robust Parameter ◽  
Performance Distribution ◽  
Feasible Space

The paper presents the theory of performance sensitivity distribution and a novel robust parameter design technique. In the theory, a Jacobian matrix describes the effect of the component tolerance to the system performance, and the performance distribution is characterized in the variation space by a set of eigenvalues and eigenvectors. Thus, the feasible performance space is depicted as an ellipsoid. The size, shape, and orientation of the ellipsoid describe the quantity as well as quality of the feasible space and, therefore, the performance sensitivity distribution against the tolerance variation. The robustness of a design is evaluated by comparing the fitness between the ellipsoid feasible space and the tolerance space, which is a block, through a set of quantitative and qualitative indexes. The robust design can then be determined. The design approach is demonstrated in a mechanism design problem. Because of the generality of the analysis theory, the method can be used in any design situation as long as the relationship between the performance and design variables can be expressed analytically.

A systematic approach to design task-specific ionic liquids and their optimal operating conditions

2016 ◽  
Vol 1 (1) ◽  
pp. 109-121 ◽  
Author(s):  
Fah Keen Chong ◽  
Dominic C. Y. Foo ◽  
Fadwa T. Eljack ◽  
Mert Atilhan ◽  
Nishanth G. Chemmangattuvalappil
Keyword(s):  
Ionic Liquid ◽  
Ionic Liquids ◽  
Design Problem ◽  
Systematic Approach ◽  
Operating Conditions ◽  
Optimal Operating ◽  
Design Task

The contribution of this work is the introduction to identification of optimal operating conditions when simultaneously solving an ionic liquid design problem.

A time-varying reliability-based robust design method considering overall efficiency of axial piston pump

2021 ◽  
pp. 1748006X2110661
Author(s):  
Zunling Du ◽  
Yimin Zhang
Keyword(s):  
Energy Conversion ◽  
Robust Design ◽  
Design Method ◽  
Design Stage ◽  
Structure Parameters ◽  
Time Varying ◽  
Design Variables ◽  
Reliability Method ◽  
Overall Efficiency ◽  
Axial Piston

Axial piston pumps (APPs) are the core energy conversion components in a hydraulic transmission system. Energy conversion efficiency is critically important for the performance and energy-saving of the pumps. In this paper, a time-varying reliability design method for the overall efficiency of APPs was established. The theoretical and practical instantaneous torque and flow rate of the whole APP were derived through comprehensive analysis of a single piston-slipper group. Moreover, as a case study, the developed model for the instantaneous overall efficiency was verified with a PPV103-10 pump from HYDAC. The time-variation of reliability for the pump was revealed by a fourth-order moment technique considering the randomness of working conditions and structure parameters, and the proposed reliability method was validated by Monte Carlo simulation. The effects of the mean values and variance sensitivity of random variables on the overall efficiency reliability were analyzed. Furthermore, the optimized time point and design variables were selected. The optimal structure parameters were obtained to meet the reliability requirement and the sensitivity of design variables was significantly reduced through the reliability-based robust design. The proposed method provides a theoretical basis for designers to improve the overall efficiency of APPs in the design stage.

scholarly journals A Nonlinear Inverse Design Problem for a Pipe Type Heat Exchanger Equipped with Internal Z-Shape Lateral Fins and Ribs

Energies ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 6424
Author(s):  
Cheng-Hung Huang ◽  
Chih-Yang Kuo
Keyword(s):  
Heat Exchanger ◽  
Thermal Performance ◽  
Design Problem ◽  
Direct Problem ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Design Variables ◽  
Non Linear ◽  
Inverse Design Problem ◽  
Η Value

A non-linear three-dimensional inverse shape design problem was investigated for a pipe type heat exchanger to estimate the design variables of continuous lateral ribs on internal Z-shape lateral fins for maximum thermal performance factor η. The design variables were considered as the positions, heights, and number of ribs while the physical properties of air were considered as a polynomial function of temperature; this makes the problem non-linear. The direct problem was solved using software package CFD-ACE+, and the Levenberg–Marquardt method (LMM) was utilized as the optimization tool because it has been proven to be a powerful algorithm for solving inverse problems. Z-shape lateral fins were found to be the best thermal performance among Z-shape, S-shape, and V-shape lateral fins. The objective of this study was to include continuous lateral ribs to Z-shape lateral fins to further improve η. Firstly, the numerical solutions of direct problem were solved using both polynomial and constant air properties and then compared with the corrected solutions to verify the necessity for using polynomial air properties. Then, four design cases, A, B, C and D, based on various design variables were conducted numerically, and the resultant η values were computed and compared. The results revealed that considering continuous lateral ribs on the surface of Z-shape lateral fins can indeed improve η value at the design working condition Re = 5000. η values of designs A, B and C were approximately 13% higher than that for Z-shape lateral fins, however, when the rib numbers were increased, i.e., design D, the value of η became only 11.5 % higher. This implies that more ribs will not guarantee higher η value.

Bayesian Surrogate Learning for Uncertainty Analysis of Coupled Multidisciplinary Systems

2021 ◽  
Vol 21 (4) ◽  
Author(s):  
Seyede Fatemeh Ghoreishi ◽  
Mahdi Imani
Keyword(s):  
Uncertainty Analysis ◽  
Closed Form ◽  
Uncertainty Propagation ◽  
Uncertainty Reduction ◽  
System Level ◽  
Engineering Systems ◽  
Sample Point ◽  
Design Variables ◽  
Multidisciplinary Systems ◽  
Stationary Behavior

Abstract Engineering systems are often composed of many subsystems that interact with each other. These subsystems, referred to as disciplines, contain many types of uncertainty and in many cases are feedback-coupled with each other. In designing these complex systems, one needs to assess the stationary behavior of these systems for the sake of stability and reliability. This requires the system level uncertainty analysis of the multidisciplinary systems, which is often computationally intractable. To overcome this issue, techniques have been developed for capturing the stationary behavior of the coupled multidisciplinary systems through available data of individual disciplines. The accuracy and convergence of the existing techniques depend on a large amount of data from all disciplines, which are not available in many practical problems. Toward this, we have developed an adaptive methodology that adds the minimum possible number of samples from individual disciplines to achieve an accurate and reliable uncertainty propagation in coupled multidisciplinary systems. The proposed method models each discipline function via Gaussian process (GP) regression to derive a closed-form policy. This policy sequentially selects a new sample point that results in the highest uncertainty reduction over the distribution of the coupling design variables. The effectiveness of the proposed method is demonstrated in the uncertainty analysis of an aerostructural system and a coupled numerical example.

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