A Probabilistic Approach to Multivariate Constrained Robust Design Simulation

Several approaches to robust design have been proposed in the past. Only few acknowledged the paradigm shift from performance based design to design for cost. The incorporation of economics in the design process, however, makes a probabilistic approach to design necessary, due to the inherent ambiguity of assumptions and requirements as well as the operating environment of future aircraft. The approach previously proposed by the authors, linking Response Surface Methodology with Monte Carlo Simulations, has revealed itself to be cumbersome and at times impractical for multiconstraint, multi-objective problems. In addition, prediction accuracy problems were observed for certain scenarios that could not easily be resolved. Hence, this paper proposes an alternate approach to probabilistic design, which is based on a Fast Probability Integration technique. The paper critically reviews the combined Response Surface Equation/ Monte Carlo Simulation methodology and compares it against the Advanced Mean Value (AMV) method, one of several Fast Probability Integration techniques. Both methods are used to generate cumulative distribution functions, which are being compared in an example case study, employing a High Speed Civil Transport concept. Based on the outcome of this study, an assessment and comparison of the analysis effort and time necessary for both methods is performed. The Advanced Mean Value method shows significant time savings over the Response Surface Equation/Monte Carlo Simulation method, and generally yields more accurate CDF distributions. The paper also illustrates how by using the AMV method for distribution generation, robust design solutions to multivariate constrained problems may be obtained. These robust solutions are optimizing the objective function for a given level of risk the decision maker is willing to take. INTRODUCTION Systems design, in particular as applied to aerospace vehicles, has experienced a paradigm shift from emphasizing performance to maximizing affordability.[1, 2] The resulting new ‘design for affordability’ requires the addition of cost estimation as a new discipline to systems design. But since most of the economic assumptions and ground rules, such as number of paying passengers, fluctuations in fuel price, travel distance, etc.[1, 3], are inherently uncertain, more emphasis has been put on replacing "point" by probabilistic estimates that quantify the uncertainty of the predicted outcome. This new way of thinking has shifted the design focus from optimizing to ‘compromising’, where compromising describes a decision process that yields a robust solution[2, 4], i.e. a design that is insensitive to the variation of those economic parameters that are difficult or impossible to control. Such a design might be preferable to a true optimum which exhibits low confidence of achieving that optimum consistently. In order to quantify and minimize the uncertainty of a design outcome, a methodology called Robust Design Simulation (RDS) has been introduced.[5, 6, 7, 8] It is based on a Concurrent Engineering (CE)/Integrated Product and Process Development (IPPD) approach and opens up the traditional deterministic to a probabilistic approach to systems design. The methodology treats the cost parameters as random variables and models their variation with probability distributions. The paper critically reviews two approaches to probabilistic robust systems design, that allow for random changes in the assumptions made in the design process and aircraft operating environment. ROBUST DESIGN SIMULATION An aircraft synthesis and sizing process, utilizing appropriate analytical tools, evaluates the system value to the customer for each aircraft configuration through selected objectives such as performance, cost, profit, quality, or reliability. Regardless of the defined objective, customer satisfaction can be achieved only if all system design and environmental constraints are met. This algorithm is displayed in Figure 1, depicting the dependence of the objective on economic and discipline uncertainties as well as technological and schedule risk. Objectives: Optimum Performance Lower Acquisition Cost Higher Profit Higher Quality Increase Reliability Reduced O&S Cost Customer Satisfaction Design & Environmental Constraints Synthesis & Sizing Technology Infusion Product Characteristics (disciplines) Process Characteristics (Producibility, Supportability, Subject to Economic & Discipline Uncertainties Technological & Schedule Risk Robust Solutions Robust Design Simulation Business Practices Reduced Variability