Evaluation of a Product Development Process through Uncertainty Analysis Techniques

For any product development process, limited time and resources are always a focus for the engineer. However, will the overall program goals be achieved with the provided time and resources? Uncertainty analysis is a tool that is capable of providing the answer to that question. Product development process uncertainty analysis employs previous knowledge in modeling, experimentation, and manufacturing in an innovative approach for analyzing the entire process. This research was initiated with a pilot project, a four-bar-slider mechanism, and an uncertainty analysis was completed for each individual product development step. The uncertainty of the final product was then determined by combining uncertainties from the individual steps. The uncertainty percentage contributions of each term to the uncertainty of the final product were also calculated. The combination of uncertainties in the individual steps and calculation of the percentage contributions of the terms have not been done in the past. New techniques were developed to evaluate the entire product development process in an uncertainty sense. The techniques developed in this work will be extended to other processes in future work

Emulating dynamic non-linear simulators using Gaussian processes

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate or the functioning of the human brain. The models we are interested in are highly non-linear and exhibit tipping points, bifurcations and chaotic behaviour. However, each simulation run could be too time-consuming to perform analyses that require many runs, including quantifying the variation in model output with respect to changes in the inputs. Therefore, Gaussian process emulators are used to approximate the output of the code. To do this, the flow map of the system under study is emulated over a short time period. Then, it is used in an iterative way to predict the whole time series. A number of ways are proposed to take into account the uncertainty of inputs to the emulators, after fixed initial conditions, and the correlation between them through the time series. The methodology is illustrated with two examples: the highly non-linear dynamical systems described by the Lorenz and Van der Pol equations. In both cases, the predictive performance is relatively high and the measure of uncertainty provided by the method reflects the extent of predictability in each system

Some Remarks about the Complexity of Epidemics Management

Recent outbreaks of Ebola, H1N1 and other infectious diseases have shown that the assumptions underlying the established theory of epidemics management are too idealistic. For an improvement of procedures and organizations involved in fighting epidemics, extended models of epidemics management are required. The necessary extensions consist in a representation of the management loop and the potential frictions influencing the loop. The effects of the non-deterministic frictions can be taken into account by including the measures of robustness and risk in the assessment of management options. Thus, besides of the increased structural complexity resulting from the model extensions, the computational complexity of the task of epidemics management - interpreted as an optimization problem - is increased as well. This is a serious obstacle for analyzing the model and may require an additional pre-processing enabling a simplification of the analysis process. The paper closes with an outlook discussing some forthcoming problems

Multifidelity approaches for optimization under uncertainty

It is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low-fidelity models to provide approximate information about the expensive, high-fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high-fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem.United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Uncertainty Quantification Grant FA9550-09-0613

Review of optimal design of composite structures under uncertainty

This study represents optimization of hollow circular, rectangular and airfoil composite beam by using sub problem approximation method in ANSYS. A three dimensional static analysis of large displacement type has been carried out for hollow circular, rectangular and airfoil composite beams. Weight of beam was objective function, material parameter, geometrical, ply thickness, ply angles and load. In order to validate the results, one loop of simulation is benchmarked from results in literature. Ultimately, best set of optimized design variable is proposed to reduce weight under static loading condition