Due to the inner deteriorating mechanism or the mutant environmental stress, the degradation systems with multi-phase features have frequently been encountered in engineering practice. The key issue for prognostics of such systems is to account for the impact of the changing-point variability and the associated degradation state at this point on the progression of the degradation process. However, current studies usually treat the degradation state at the change point as a fixed value rather a random variable. Thus, it is still challenging to predict the lifetime of such multi-phase degrading systems. To this end, we first formulate a general degradation modeling framework based on a two-phase Wiener process. In prognostics, we take into full account the uncertainty of the degradation state at the changing point and then derive the analytical expressions of the lifetime and remaining useful life under the concept of the first passage time. The derived results are distinguished from existing results limited to the fixed state at the changing point. Furthermore, we extend our approach and results to cases with unit-to-unit variability and multiple phases. To facilitate the model implementation, we propose both offline and online methods for parameter identification, which make full use of the historical data and the in-service data. Finally, a numerical simulation and a practical case study are provided for illustration.

The high thermopower characteristics of ionic thermoelectric cells (ITECs) significantly improve the efficiency of environmental heat and energy collection and utilization. Herein, based on the low thermal conductivity of biomass materials, we propose a novel strategy on structural design and component modulation for full component utilization and synergistic enhancement of thermodiffusion and thermogalvanic effects of single electrolytes to achieve high thermopower and output energy density. Grafting guanidinium salt ions in the chitosan gel can facilitate the selective separation of positive and negative ions of the FeCl_3/2 electrolyte and enhance the thermodiffusion effect. Meanwhile, introduction of melamine in the chitosan gel enables the selective complexation/desorption of Fe³⁺ at cold and hot ends, which enlarges the concentration and entropy difference of redox pairs in electrolyte ions. Significant magnification of the thermocouple effect is observed, resulting in 700% increase in thermopower (−1.04 to −7.24 mV K⁻¹). Particularly, the 90-min output energy density of the ITECs reaches 17.93 kJ m⁻² at ΔT of 25 K, which is a record-breaking result among the reported quasi-solid-state ITECs. This study provides a new design pathway for development and application of high-performance ITECs.