Palaniappan Ramu

Normal transformations are often used in reliability analysis. A Third order Polynomial Normal Transformation (TPNT) approach is used in this work. The underlying idea is to approximate the Cumulative Distribution Function (CDF) of the response in probit space using a third order polynomial while imposing monotonicity constraints. The current work proposes to apply log transformation to the ordinate of the transformed CDF and hence names the approach Log-TPNT. The log transformed data assists in improved fitting to the tails of the distribution resulting in better predictions of extreme values. Log-TPNT is demonstrated on a suite of statistical distributions covering all types of tails and analytical examples that cover aspects of high dimensions, non-linearity and system reliability. Results reveal that Log-TPNT can predict the response values corresponding to high reliability, with samples as scarce as 9. Finally, the variations associated with the response estimates are quantified using bootstrap.

The paper presents a methodology to synthesis simple planar linkage mechanism involving a multi objective optimization model considering cost associated with mechanical tolerances and the reliability based robustness of generating the intended path. An adapted probabilistic model for the deviation of the actual path generated by a coupler point from the desired one, by considering the structural and mechanical errors due to tolerances and clearances is considered. A synthesis procedure of the linkages is formulated as a multi objective non-linear optimization problem with robustness subject to a reliability level and cost as objectives. The reliability index of the mechanism is based on the probability with which a linkage will generate its intended design motion with specified precision. The robustness is based on the ratio of the mean to standard deviation of the error in the traced path with respect to the target. The cost index is based on manufacturing and assembly cost, which are functions of tolerances and clearances in joints. Multi objective genetic algorithm (Moga) is employed as the search tool. A Four-bar path generating mechanism is selected for numerical illustration.

Treatment of uncertainties in structural design involves identifying the boundaries of the failure domain to estimate reliability. When the structural responses are discontinuous or highly nonlinear, the failure regions tend to be an island in the design space. The boundaries of these islands are to be approximated to estimate reliability and perform optimization. This work proposes Alpha (α) shapes, a computational geometry technique to approximate such boundaries. The α shapes are simple to construct and only require Delaunay Tessellation. Once the boundaries are approximated based on responses sampled in a design space, a computationally efficient ray shooting algorithm is used to estimate the reliability without any additional simulations. The proposed approach is successfully used to decompose the design space and perform Reliability based Design Optimization of a tube impacting a rigid wall and a tuned mass damper.

The performance of a path generating linkage is measured in terms of the error in the generated path. The probability of producing its intended path is its reliability. Tighter tolerances in link lengths and joint clearances result in higher reliability but incur more costs. Therefore, it is desirable to understand the trade-off relationship between the costs and reliability. In the current work, a genetic algorithm is used to construct the Pareto trade-off front between cost and reliability by solving a bi-criterion optimisation problem. Statistical moments required to estimate reliability are computed by combining an approximate cumulative density function of error and a 3-point approximation technique. This approach uses a fraction of the samples compared to crude Monte Carlo simulation. The proposed approach is demonstrated on a four bar mechanism tracing a straight line and a closed path. It is observed that the Pareto front generated using the proposed approach with fewer samples compares well with the one generated with crude Monte Carlo simulation with a large sample set, thus offering enormous gains in computational efficiency.