Prognostics and Health Management (PHM) attracts increasing interest of many researchers due to its potentially important applications in diverse disciplines and industries. In general, PHM systems... Show morePrognostics and Health Management (PHM) attracts increasing interest of many researchers due to its potentially important applications in diverse disciplines and industries. In general, PHM systems use real-time and historical state information of subsystems and components of the operating systems to provide actionable information, enabling intelligent decision-making for improved performance, safety, reliability, and maintainability. Every year, a substantial number of papers in this area including theory and practical applications, appear in academic journals, conference proceedings and technical reports. This paper aims to summarize and review researches, developments and recent contributions in PHM for automotive- and aerospace industries. It can also be considered as the starting point for researchers and practitioners in general to assist them through PHM implementation and help them to accomplish their work more easily. Show less
The Expected Hypervolume Improvement (EHVI) is a frequently used infill criterion in Multi-Objective Bayesian Global Optimization (MOBGO), due to its good ability to lead the exploration. Recently,... Show moreThe Expected Hypervolume Improvement (EHVI) is a frequently used infill criterion in Multi-Objective Bayesian Global Optimization (MOBGO), due to its good ability to lead the exploration. Recently, the computational complexity of EHVI calculation is reduced to O(n log n) for both 2-D and 3-D cases. However, the optimizer in MOBGO still requires a significant amount of time, because the calculation of EHVI is carried out in each iteration and usually tens of thousands of the EHVI calculations are required. This paper derives a formula for the Expected Hypervolume Improvement Gradient (EHVIG) and proposes an efficient algorithm to calculate EHVIG. The new criterion (EHVIG) is utilized by two different strategies to improve the efficiency of the optimizer discussed in this paper. Firstly, it enables gradient ascent methods to be used in MOBGO. Moreover, since the EHVIG of an optimal solution should be a zero vector, it can be regarded as a stopping criterion in global optimization, e.g., in Evolution Strategies. Empirical experiments are performed on seven benchmark problems. The experimental results show that the second proposed strategy, using EHVIG as a stopping criterion for local search, can outperform the normal MOBGO on problems where the optimal solutions are located in the interior of the search space. For the ZDT series test problems, EHVIG still can perform better when gradient projection is applied. Show less
