Prognostics and remaining useful life (RUL) estimation for lithium-ion batteries play an important role in intelligent battery management systems (BMS). The capacity is often used as the fade indicator for estimating the remaining cycle life of a lithium-ion battery. For spacecraft requiring high reliability and long lifetime, in-orbit RUL estimation and reliability verification on ground should be carefully addressed. However, it is quite challenging to monitor and estimate the capacity of a lithium-ion battery on-line in satellite applications. In this work, a novel health indicator (HI) is extracted from the operating parameters of a lithium-ion battery to quantify battery degradation. Moreover, the Grey Correlation Analysis (GCA) is utilized to evaluate the similarities between the extracted HI and the battery’s capacity. The result illustrates the effectiveness of using this new HI for fading indication. Furthermore, we propose an optimized ensemble monotonic echo state networks (En_MONESN) algorithm, in which the monotonic constraint is introduced to improve the adaptivity of degradation trend estimation, and ensemble learning is integrated to achieve high stability and precision of RUL prediction. Experiments with actual testing data show the efficiency of our proposed method in RUL estimation and degradation modeling for the satellite lithium-ion battery application.

Estimating lithium-ion battery remaining useful life (RUL) is a key issue in an intelligent battery management system. This paper presents an integrated prognostic approach that unifies two types of health indices (HIs), battery capacity and time interval of equal discharging voltage difference series, to perform direct and indirect RUL estimation for lithium-ion battery. To satisfy different practical requirements, a data-driven monotonic echo state networks (MONESNs) algorithm is adopted to track the nonlinear patterns of battery degradation. The main contributions of this paper are: 1) to enhance the predictive capability of each HI and identify its failure threshold by implementing an HI correlation model and cycle life threshold transformation and 2) to increase the computational stability of the proposed approach through the ensemble of MONESN submodels that can also describe the prognostic uncertainty. Essentially, this approach constitutes a probabilistic integration and data-driven prognostic framework with uncertainty management capability. Two sets of industrial lithium-ion battery data are used to show the capability of the proposed approach. It is expected that this approach can be broadly applied to other application areas, where data-driven prognostic approaches are needed.

This article presents an integrated model to estimate the gross profit for a new durable product to be sold in a fixed sales period at a fixed price. It is assumed that the sales over time can be characterized by a stochastic Bass model in the form of a nonhomogeneous Poisson process and the production system is a make-to-order type of system. An approximate yet accurate approach is developed to quantify the expected total cost of production involving a learning effect. Moreover, a non-renewable free minimal-repair warranty and non-free post-warranty service are considered for the repair service offered by the manufacturer. To quantify the related costs and profit, the fact that customers may not always request warranty and/or post-warranty repairs is explicitly addressed and modeled. A numerical example is provided to illustrate the effects of some key parameters, including the product reliability, price elasticity, and warranty period elasticity, on the optimal settings of the price, warranty period, and post-warranty charge. The saturation effect of sales process on achieving the optimal gross profit is also discussed.