Applying Stochastic Method in Engineering Design Under Uncertainty

Abstract

Very often design engineer uses a single-point or deterministic approach. The design modeling involves using a single “best-guess” estimate of each variable within a model to determine the model’s outcome(s). The deterministic approach often leads the engineer to make unjustified assumptions and inherent design risk decisions. To improve this design process, this paper proposes applying a stochastic method in engineering design particularly, designs under uncertainty. This paper presents three design cases of applying a stochastic method by using a Monte Carlo simulation. The first case presents a Bolted Joints (BJ) design; prediction of a bolt preload to prevent a joint of slipping investigated for a confidence of 99.97% certainty. This BJ design case demonstrates how to overcome the obstacles that exist in a deterministic Bolted Joints analysis. The variables included in this investigation are the variations of coefficient of friction, preload scatter, Bolt and the Joint geometry. The second design case investigates the angular position control of Four Bars Mechanism (FBM). In this case, the paper shows how to quantify the design risk of the real FBM angular position for a given resolution spec. Sensitivity analysis uses after each simulation to identify the driver parameters influencing the angular position of the FBM. The dominant parameters influencing the design analysis include: bars tolerance variations and an actuator driver backlash. The third case of engineering design demonstrates a stochastic optimization of a flat spring design. The goal of this stochastic optimization is to achieve the maximum spring Specific_Resilience. The optimal solution of this optimization is to select the best material of six given materials and spring geometry that fit within a given restricted envelope.