The novelty of the project lies in combining state of the art methodologies for cost-optimal reliability-based design (COPRD) with actual production optimization. To achieve the COPRD beyond state of the art multi-physical modeling concepts were developed and validated for significantly improved understanding of the production and operation of SOFC stacks. The most critical failure modes for stack operation were identified in order to align the experimental investigations to generate suitable data for modelling these failures. The multi-physics model allows a probabilistic approach to consider statistical variations in production, material and operating parameters for the optimization phase. The project provides a methodology for 3D description of spatial distribution of material properties based on a random field models. The key for the whole methodology are validating experiments, homogenized models on multiple levels of the SOFC system (cell, interconnect, sealings) and introduction of extensive test programs specified by the COPRD methodology. The probabilistic models were related to the experimentally obtained properties of base materials to establish a statistical relationship between the material properties and the most relevant load effects in view of potential damage/failure based on multi-physics simulation can be established. Software algorithms for meta models that allow the detection of relationships between input parameters (materials, loading, etc.) and output parameters and to perform a sensitivity analysis were developed and implemented. The capabilities of the methodology for COPRD being developed is illustrated on two practical cases.

A procedure based on meta models has been developed to estimate elastic, primary and secondary creep model parameters from 4-point bending tests. The goal is to (i) account for the effects of the friction between the sample and the rollers, anticlastic curvature, contact point shift and large deflection, which can affect the accuracy of the measurements, and (ii) measure properties which cannot be obtained using closed-form analytical solutions. This could be achieved by model-based parameter estimation with a 3-D continuum finite-element (FE) model, at the cost of very high running time. The proposed approach is computationally much more efficient. It starts with a sensitivity analysis to generate distributed meta models of the displacement at the inner rollers during loading-unloading cycles and creep measurements simulated by the 3-D FE model. The optimization problem for parameter estimation is then solved using the meta models. The accuracy of the approach was tested using a set of numerical experiments and comparison with results from 3-D imaging and computational homogenization. The experiments on Ni-YSZ samples were then analyzed.

For the stochastic investigation of the thermo-electrochemical behavior of the stack a multi-physics stack model implemented in gPROMS and Fluent was linked and controlled automatically by optiSlang to perform a sensitivity analysis. The outcome is (i) the identification of the most relevant production and operating parameters which can have a significant impact on the stack lifetime and (ii) meta models of the efficiency and of the 3-D temperature distribution generated in the view of optimization. The tests show for instance that the accuracy of the 3-D meta model of the temperature distribution is sufficient to identify the minimum of variations in the spatial distribution of the temperature during cycling between full and part load by using sets of operating conditions for optimization.