While integrated physical and control system co-design has been demonstrated successfully on several engineering system design applications, it has been primarily applied in a deterministic manner without considering uncertainties. An opportunity exists to study non-deterministic co-design strategies, taking into account various uncertainties in an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to ensure an optimized system design being obtained that satisfies all reliability constraints considering particular system uncertainties. While significant advancements have been made in co-design and RBDO separately, little is known about methods where reliability-based dynamic system design and control design optimization are considered jointly. In this article, a comparative study of the formulations and algorithms for reliability-based co-design is conducted, where the co-design problem is integrated with the RBDO framework to yield solutions consisting of an optimal system design and the corresponding control trajectory that satisfy all reliability constraints in the presence of parameter uncertainties. The presented study aims to lay the groundwork for the reliability-based co-design problem by providing a comparison of potential design formulations and problem–solving strategies. Specific problem formulations and probability analysis algorithms are compared using two numerical examples. In addition, the practical efficacy of the reliability-based co-design methodology is demonstrated via a horizontal-axis wind turbine structure and control design problem.

Solid oxide fuel cell (SOFC) with high energy conversion efficiency, low pollutant emission, and good fuel adaptability has witnessed rapid development in recent years. However, the commercialization of SOFC remains limited by constraints of performance and stability. Electrochemical impedance spectroscopy (EIS) can distinguish ohmic impedance caused by ion transport from polarization impedance related to electrode reaction; it has been widely used in the research of performance and stability as an efficient on-line characterization technology. The physical/chemical processes involved in EIS overlap significantly and can be decomposed by the distribution of relaxation times (DRT) method which does not depend on prior assumptions. Since industrial large-size SOFC is vulnerable to the influence of inductance and disturbance when testing EIS, its EIS analysis is rarely studied and mostly based on the research results of cells with smaller electrode active area. To further elucidate the impedance spectrum of industrial large-size SOFC under actual working conditions, the EIS of industrial-size (10 cm × 10 cm) anode-supported planar SOFC was systematically tested over a broad temperature and anode/cathode gas composition range. First, the quality of the impedance data was examined by performing a Kramers-Kronig test. The residuals of real and imaginary data were within the range of ±1%, indicating good data quality. Then, the DRT method was adopted to parse the EIS data. By comparing and analyzing the DRT results under different conditions, the corresponding relationships between each characteristic peak in the DRT results and the specific electrode process in the SOFC were revealed. The characteristic frequencies were separated into 0.5-1, 1-30, 10-30, 1 × 10 2 -1 × 10 3 , and 1 × 10 4 -3 × 10 4 Hz regions, corresponding to gas conversion within the anode, gas diffusion within the anode, oxygen surface exchange reaction within the cathode, charge-transfer reaction within the anode, and oxygen ionic transport process, respectively. In this study, the identification of each electrode process in industrial large-size SOFC is realized, indicate that the gas conversion process in large-size SOFC with larger active area and smaller flows cannot be ignored compared with the cells with smaller electrode active area. The method followed and the results obtained have a universal quality and can be applied to the in situ characterization, online monitoring, and degradation mechanism research of SOFC, thus laying a foundation for the optimization of the performance and stability.

Anode oxidation is a damaging fault in SOFC that may happen at high fuel utilization. To avoid anode oxidation, a 1D polarization and impedance model was developed for large planar SOFC, in order to reveal the critical operating condition. The model was validated with both experimentally measured j-V curve and impedance. The overpotential and impedance at each locality of the planar cell is predicted by a lumped-parameter model calibrated with button cell experimental data, with an RMS relative voltage error of 2.3%. The predicted operating voltage of a planar cell at given total current agrees well with measured data, with an RMS relative voltage error of 3.0%. At 750°C, the critical operating voltage increases up to 0.73 V as the fuel flow rate decreases. Further work is ongoing on a 2D spatially resolved model accounting for temperature distribution for more accurate prediction of anode-oxidizing operating conditions.

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