Diagnosis of defects by principal component analysis of a gas turbine

Research Article Diagnosis of defects by principal component analysis of a gas turbine Fenghour Nadir1 · Hadjadj Elias1 · Bouakkaz Messaoud1 Received: 27 September 2019 / Accepted: 18 April 2020 © Springer Nature Switzerland AG 2020 Abstract This study examines the application of the Principal Component Analysis (PCA) technique to detect the failures in complex industrial processes such as gas turbines used for electric power generation. The early detection of failures in such complex processes is indeed paramount to prevent product deterioration, performance degradation, significant property damage and human health. We identified the PCA model by determining the optimal number of principal components retained in the PCA model, then we validated the PCA model by checking the evolution of measurements and estimated the two variables X2 and X8. Thereafter, the evolution of three detection indexes is illustrated highlighting that the filtered SPE index is the best suited one for our installation, and finally, we checked the efficiency of the linear PCA method from the filtered SPE detection index using real data of defects that may occur within the gas turbine. The results obtained will aid to confirm the performance of the linear PCA method in the field of early failure detection. Thus, the PCA method appears as an efficacious tool to monitor and diagnose complex installations. Keywords Process monitoring · Fault detection · Linear principal component · Electric power production process 1 Introduction In all industrial systems, breakdowns cause considerable economic losses. It is therefore essential to implement monitoring and diagnostic systems to avoid unexpected shutdowns, increase reliability, and ensure the safety of underlying systems. In industrial diagnosis, the detection process involves merely the detection of events that affect the evolution of the systems, and the assessment consists in comparing the actual functioning systems with those under the assumption of normal operations. Originally, the diagnosis was limited to high-risk industrial applications such as nuclear or aviation domains and advanced industries such as armament and aerospace [1–5]. Over the past three decades, the diagnosis has attracted much attention both in the industrial and in the scientific research world. In the field of diagnostics, several methods based on the concept of redundancy of information have been developed. In previous works of other researchers, the PCA, PLS, kernel PCA (kPCA) and kernel PLS (kPLS)-based generalized likelihood fault detection techniques have been developed, namely PCA, PLS, kPCA and kPLS have been implemented as a modeling framework for fault detection [6–9]. Their principle is generally based on a consistency test between an observed behavior of the process provided by sensors and an expected behavior provided by a mathematical representation of the process. Analytical redundancy methods, therefore, require a model of the system to be monitored. This model includes several parameters whose values are assumed to be known during normal operation. The comparison between the actual behavior of systems and their expected behaviors given by well-developed models provides a quantity, called a residue, which will be used to determine whether the system is in a failed state or not. Multi-variable statistical methods are the most effective for treating the generation of residues. Among them, methods based on Principal Component Analysis (PCA). * Fenghour Nadir, ; Hadjadj Elias, ; Bouakkaz Messaoud, messaoud.bouakkaz@univ‑annaba.org | 1Department of Electromechanical, Badji Mokhtar University, Annaba, Algeria. SN Applied Sciences (2020) 2:980 | https://doi.org/10.1007/s42452-020-2796-y Vol.:(0123456789) Research Article SN Applied Sciences (2020) 2:980 These will be effective for highlighting significant linear correlations between the variables of processes without explicitly formulating the models of their underlying systems. Thus, all the correlations between the different variables are taken into account in the PCA models. In this paper, we study PCA models for the diagnosis (detection equipment or subassembly fault by precision) of the highly complicated system of a gas turbine [10], where the detection and localization of the fault has become a challenge requiring a profound diagnosis with specific equipment and a considerable time to determine the origin of the issue. However, with the method proposed (PCA), the issue detection will be faster and more efficient. Thus, the objective of this study is to aid in improving the diagnosis of a fault with a gas turbine by choosing the most efficient detection index for this installation, and then confirm the performance of the PCA method in this field of fault detection by the use of real data of a fault that already affected the machine during its lifetime. The plan of this article is as follows. In the first step of this study, we present the fundamental principles of the linear PCA. Secondly, we look at the existing methods of defect detection. Finally, we apply linear PCA to fault detection in an electrical energy generation process (gas turbine). 2 Principal component analysis Principal Component Analysis (PCA) is a part of the group of multidimensional descriptive methods called factorial methods. These methods, which appeared in the early 1930s, were mainly developed in France in the 1960s, in particular by Jean-Paul Benzécri, who made extensive use of geometric aspects and graphic representations. It has been adapted for the detection and isolation of defects that may occur at the system level and categorized as a multivariate data analysis technique [11, 12]. This technique is based solely on the use and analysis of system input and output measurements. A data matrix is then constructed from these measurements. By decomposing the data matrix into singular values, the PCA divides this matrix into two distinct parts, one containing the dominant singular values, representing the relevant data, and the other one including the rest of the singular values assumed to be negligible and representing the noises [13]. Several studies have recently been published in the literature dealing with the use of the PCA in the field of defect detection [14–21]. Figure 1 represents the PCA algorithm illustrating all its main steps. Vol:.(1234567890) | https://doi.org/10.1007/s42452-020-2796-y Fig. 1  PCA algorithme To find a model based on the linear PCA, a database containing variables is required to track a set of measurements performed on the normal operation of the systems. Generally, the procedure for identifying the model involves, after the standardization of the data matrix, the estimation of the parameters of the model, the selection of a fixed structure and the validation of the model. The basic idea of the PCA is to reduce the size of the data matrix. This reduction will only be possible if the i (...truncated)