Iterative Pinch Analysis to address non-linearity in a stochastic Pinch problem

摘要

Pinch Analysis is a widely used technique for resource conservation. It minimizes the requirement of the external resource through efficient use of internally available sources. These networks are designed based on the flow and quality parameters of internal sources and demands. However, Pinch Analysis is applicable only for the linear problems and fails if the problem becomes non-linear under certain conditions. The uncertainty in the quality parameter of sources in a resource allocation problem is one such situation where the problem becomes non-linear. The quality parameter is considered to be normally distributed with known mean and standard deviation to incorporate uncertainty. In such a case, the quality load constraint is probabilistic, which on conversion to its deterministic equivalent using chance-constrained programming, becomes non-linear. The previous works adopted a conservative approach to linearize the constraint and to solve it using Pinch Analysis. This leads to a higher value of resource requirement than resource targeted using non-linear formulation. This difference in the resource requirements, obtained from the two formulations, can be extremely high in certain cases. In this work, an iterative Pinch Analysis methodology is proposed to bridge this gap between the two formulations that helps in reducing the resource requirement while maintaining the desired demand reliability. An approximated Pinch problem is solved in each iteration to reach the optimal resource. This work extends the applicability of Pinch Analysis to the source-sink problems with non-linear constraints. The applicability of the methodology has been demonstrated through three different examples. (C) 2019 Elsevier Ltd. All rights reserved.