About four zetta bytes of data, which falls into the category of big data, is generated by complex manufacturing systems annually. Big data can be utilized to improve the efficiency of an aging manufacturing system, provided, several challenges are handled. In this paper, a novel methodology is presented to detect faults in manufacturing systems while overcoming some of these challenges. Specifically, a generalized distance measure is proposed in conjunction with a novel hierarchical dimension reduction (HDR) approach. It is shown that the HDR can tackle challenges that are frequently observed during distance calculation in big data scenarios, such as norm concentration, redundant dimensions, and a non-invertible correlation matrices. Subsequently, a probabilistic methodology is developed for isolation and detection of faults. Here, Edgeworth expansion based expressions are derived to approximate the density function of the data. The performance of the dimension reduction methodology is demonstrated to be efficient with simulation results involving the use of big data sets. It is shown that HDR is able to explain almost 90% of the total information. Furthermore, the proposed dimension reduction methodology is seen to outperform standard dimension reduction approaches and is able to improve the performance of standard classification methodologies in high dimensional scenarios.

每年由复杂的制造系统生成大约四个Zetta字节的数据（属于大数据）。大数据可以用来提高老化的制造系统的效率，前提是要解决一些挑战。在本文中，提出了一种新颖的方法来检测制造系统中的故障，同时克服其中的一些挑战。具体而言，提出了一种通用的距离测度，并结合了一种新颖的层次降维（HDR）方法。结果表明，HDR可以解决在大数据场景中距离计算期间经常观察到的挑战，例如范数集中，冗余维和不可逆相关矩阵。随后，开发了一种概率方法来隔离和检测故障。这里，得出基于Edgeworth展开的表达式，以近似数据的密度函数。通过涉及大数据集使用的仿真结果，证明了降维方法的性能是有效的。结果表明，HDR能够解释全部信息的近90％。此外，所提出的降维方法被认为优于标准降维方法，并且能够改善高维场景中标准分类方法的性能。结果表明，HDR能够解释全部信息的近90％。此外，所提出的降维方法被认为优于标准降维方法，并且能够改善高维场景中标准分类方法的性能。结果表明，HDR能够解释全部信息的近90％。此外，所提出的降维方法被认为优于标准降维方法，并且能够改善高维场景中标准分类方法的性能。