Fault diagnosis using Interpolated Kernel Density Estimate

Fault detection and diagnosis (FDD) methods often face the challenge that there is no prior knowledge about the distribution of the monitored variables and features. Data-driven methods based on statistics often incorporate a simplifying assumption that the data can be described by a Gaussian distribution. Such a simplification might cause deterioration in the accuracy of fault detection. Kernel Density Estimation is a powerful non-parametric method. Its main advantage lies in the fact that no prior assumption is necessary about the distribution of the data, and that it is able to handle multimodal distributions in an effective way. However, it is very computationally expensive. In this paper, Interpolated Kernel Density Estimate (IKDE) is proposed to reduce the computational cost and improve processing times. IKDE is based on interpolated KDE functions using Chebyshev polynomials and the barycentric formula to obtain the posterior probabilities. The method is used with a Naive Bayes classifier for fault detection for a non-Gaussian distributed, multimodal induction motor dataset. The performance and computational cost compared with the standard KDE implementation show the superiority of IKDE, making it suitable for online FDD problems where reduced computational costs are highly beneficial. The main advantage of this approach is the reduction in the stored data as well as the reduced number of multiplications needed for a single evaluation.

Automated summary

Interpolated Kernel Density Estimate (IKDE) method reduces computational cost and improves processing times by using Chebyshev polynomials and the barycentric formula, making it suitable for fault detection in non-Gaussian distributed, multimodal datasets.