Neural Copula: A unified framework for estimating generic high-dimensional Copula functions

The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on simplified assumptions or on complicating recursive decompositions. Therefore, people still hope to obtain a generic Copula estimation method with both universality and simplicity. To reach this goal, a novel neural network-based method (named Neural Copula) is proposed in this paper. In this method, a hierarchical unsupervised neural network is constructed to estimate the marginal distribution function and the Copula function by solving differential equations. In the training program, various constraints are imposed on both the neural network and its derivatives. The Copula estimated by the proposed method is smooth and has an analytic expression. The effectiveness of the proposed method is evaluated on both real-world datasets and complex numerical simulations. Experimental results show that Neural Copula's fitting quality for complex distributions is much better than classical methods. The relevant code for the experiments is available on GitHub. (We encourage the reader to run the program for a better understanding of the proposed method)

A copula-based quantified airworthiness modelling for civil aircraft engines

The aircraft engine serves as the core system of an aircraft and operates under extreme conditions, requiring high reliability and absolute safety. The design, manufacturing, and after-sales services of aircraft engines are complex processes. To ensure safety and performance, maintenance checks are performed periodically and hierarchically throughout the engine’s life-cycle. Among these checks, shop visit (SV) heavy maintenance checks play a crucial role but are also costly, especially when they occur unexpectedly and unplanned. Analysis of the maintenance logbook, recording aviation operations, reveals a significant occurrence of unplanned SVs, which may be attributed to the existing maintenance policy based on a single time-definition. To address this issue, this paper seeks to establish a novel approach to quantifying airworthiness through copula modeling, which combines two time-definitions: the flying hour (FH) and the flying cycle (FC). This approach is unique in the aviation industry. By employing the Gumbel copula with the generalized extreme value (GEV) distribution as the marginal distribution, and utilizing non-parametric association measurement parameter estimation, the quantified airworthiness of civil aircraft engine fleets across multiple product lines can be effectively modeled. This research provides valuable insights into optimizing maintenance policies and enhancing the reliability and safety of aircraft engines