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

Abstract

a b s t r a c tAn inverse problem is solved for estimating fuel cell operating parameters such as current density, pressure and fuel flow rate (FFR) separately and then simultaneously two parameters in an internal reforming solid oxide fuel cell (IRSOFC). Initially, a mathematical model for the forward problem is developed to simulate the IRSOFC steady state operation and its performance in terms of power output and then an inverse problem is solved for recovering the above parameters using a simplex search minimization algorithm. The objective function (IRSOFC power) and the estimation accuracy are studied for the effects of initial guess values of the operating parameters and the number of iterations required for retrieval of these parameters. The objective function is represented by the sum of square of the error between a given IRSOFC power and the power evaluated based on some arbitrary guessed values of the unknowns which is then regularized in an iterative manner for solution of the inverse fuel cell problem. The study reveals that a multiple combinations of parameters (current density, operating pressure and FFR) exist which provides guidelines for selecting feasible combinations of these parameters required for meeting a given power requirement. The results show relatively good agreement between the inverse and exact solutions.

Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem

“…First, let us show that φ 0 (z) ∈ C[0, T ]. Using integration by parts, it easy to see that using (17), the assumptions (A 1 ), (A 2 ) and first condition of (A 3 ), we have…”

“…The estimations of h(t) and q(t), as minimizers of (10), can be achieved either by gradient-free heuristic techniques, such as evolutionary optimization algorithms [9][10][11]17], or by gradient-based methods. Gradient-free methods can be applied to problems where the objective function is not differentiable, but if this is not the case, gradientbased deterministic techniques are preferred due to their higher efficiency.…”

Estimation of operating parameters of a reheat regenerative power cycle using simplex search and differential evolution based inverse methods

“…(15), n corresponds to the molar coefficients of products (P) and reactants (R) per 100 kg of fuel. h 0 d is the standard molar specific enthalpy of devaluation, its value for various substances are known and available in [32,35].…”

“…In such cases, the unknown operating parameters can be predicted through inverse analysis. Inverse analysis is however computationally expensive and mathematically more complicated compared to its forward counterpart due to ill posed and iterative nature of the problem [14][15][16] and many a times multiple combinations of parameters are obtained that satisfy the same given reference output. This is one of the unique features of inverse analysis due to which it has become very popular and successfully applied in many engineering problems in the last decade [17][18][19][20][21][22][23][24][25][26][27][28].…”