A simplex search method for a conductive–convective fin with variable conductivity

Inverse analysis of an internal reforming solid oxide fuel cell system using simplex search method

“…An iterative process is done for replacing the worst vertex with a new vertex. For an objective function, f(x) which needs to be minimized, if V k = (x k ), k = 1,2,3 represent the three vertices, then the ranking of vertices from best to worst is done as per the following details [33,[35][36][37][38],…”

“…(27), the value of the objective function increases from B to W. Thus, B becomes the best vertex and W becomes the worst vertex of the simplex. The value of G falls in between B and W After construction of the initial simplex, the midpoint of good side, M is found by averaging the coordinates and is given by the following equation [33,[35][36][37]39], Since, the value of the objective function decreases from W to B via G, therefore at certain point(s) on either side of B and G, the function may assume smaller values. Thus, a reflection vector R is calculated by using the following equation [33,[35][36][37]39],…”

“…If the value of the objective function at R(f(R)) is smaller than that at W(f(W)) the expansion point, E 0 is calculated by using the equation as given below [33,[35][36][37]39],…”

“…In contrast to the direct problems, the inverse problems are defined as the estimation of the operating parameters, properties of the system/material, shape of the fuel cell etc. The solution of inverse problems is much more difficult in comparison with direct problems due to instability in solution where these problems are called mathematically ill-posed [33] and sometimes multiple combinations of unknown parameters may exist, which may satisfy the same given reference output. With the improvement of computer capability, inverse techniques have become a popular means of resolving many engineering problems in the last decade.…”

Predicting multiple combination of parameters for designing a porous fin subjected to a given temperature requirement

“…Das [18] applied GA to estimate the radius ratio in a cylindrical fin using temperature data from FDM. For simultaneous estimation of two parameters, a simplex search method (SSM) was also proposed by Das [19] for a rectangular fin with variable conductivity. For estimating the thermal conductivity and heat capacity in a transient heat transfer problem, a hybrid method involving GA and Levenberg-Maquardt method was used by Liu [20].…”