Proper orthogonal decomposition and smooth orthogonal decomposition approaches for pattern recognition: Application to a gas turbine rub-impact fault

Abstract

This paper aims to investigate the rub-impact fault of a gas turbine using the proper orthogonal decomposition (POD) and the smooth orthogonal decomposition (SOD). It is an attempt to combine POD and SOD for pattern recognition. First, simulated data are generated to investigate the sensitivity of POD and SOD to pattern changes. After that, field data from a gas turbine are presented. We consider two data sets: one related to the standard operation, and another to the rub-impact fault. The results show that POD and SOD can recognize the pattern changes, and identify the rub-impact fault. Moreover, the present work demonstrates that POD and SOD can complement each other. The proposed methodology offers the possibility to monitor the evolution of modal component patterns and might support the plant engineers to make decisions.

Introduction

Gas turbine faults are responsible for losses in energy production and plant reliability. In this regard, Condition Based Maintenance (CBM) methods extend the durability of the equipment and reduce costs since it guarantees that no early interventions are made unnecessarily [1]. Because of its complexity, the rub-impact phenomenon is still a matter of discussion and interest [2], [3], [4], especially with technological advances, where the efficiency of gas turbines is getting higher, but at the cost of reducing the clearance between rotating and stationary components [5].

A technique of particular interest is the Proper Orthogonal Decomposition (POD), or Karhunen Loève Decomposition [6], which is the continuous version of the Principal Component Analysis (PCA) [7], [8]. PCA was first introduced by Pearson [7] and applied by Hotelling [9], with significant contributions in the 1960s [10], [11], [12]. The method gained importance after the growth of computational capacity, and, in the 1990s, many areas of science employed it [8]. The idea is to perform an orthogonal transformation to the collected data, converting the original correlated variables into new uncorrelated variables and look for patterns.

Batailly et al. [5] used PCA to recognize fault patterns of an industrial pump, where the components with the highest energy presented the evolution of a malfunction and enabled the fault pattern to be detected. Jing and Hou [13] discussed Support Vector Machine (SVM) and PCA to classify faults in complicated industrial processes. The comparisons between SVM and PCA demonstrated that PCA provides sound results with less computational effort. Portnoy et al. [14] developed a new weighted adaptive PCA-based technique to reduce false alarm rates in the monitoring process. Yang et al. [15] used PCA to extract features of time and frequency domains to characterize faulted gears. Together with an artificial neural network, the authors classified different types of malfunctions. Bonniard et al. [16] employed Karhunen–Loève decomposition to identify faults in pumps. Finally, Reddy et al. [17] applied PCA for fault detection of magnetic bearings.

Chelidze and Zhou [18] developed a more recent technique called Smooth Orthogonal Decomposition (SOD). In the SOD approach, both displacement and velocity are evaluated to obtain the principal components. Farooq and Feeny [19] showed that, under certain conditions, SOD could identify the modal parameters of a structure excited by a random force. This technique was employed to evaluate dynamic systems subjected to damage evolution [20], aiming to identify feature changes in the subspace corresponding to the modified operating conditions. Kuehl et al. [21] applied SOD to an oceanographic data set and observed that this decomposition presented better results than POD. As a final note, one can use POD and SOD for constructing reduced-order models [22], [23], [24], [25].

In this context, the present work proposes to employ POD and SOD to analyze a faulty gas turbine. The fault under consideration is the rub-impact between the last stage of compressor blades and the turbine housing. Field data, such as vibration amplitudes and temperature, are presented. The analyzed event was observed after a maintenance stop where vibration levels increased at high frequencies, which were directly related to the number of blades available at the last stage of the compressor section. This diagnostic was confirmed after a frequency analysis and borescope inspection.

To the best of the authors’ knowledge, no article in the literature investigates the rub-impact fault of a rotating machine with POD or SOD. The contributions of the present article are twofold. First, POD and SOD are investigated (and compared) to recognize patterns in rotating machines. Second, field data (vibration, temperature, and pressure) of a faulty (rub-impact) gas turbine is analyzed with POD and SOD. Gas turbines and other industrial equipment have monitoring systems with low or high-frequency data acquisition. The latter has a higher implementation cost. The idea of the current investigation is to improve the diagnosis tools considering data with low-frequency acquisition rate from various sources (vibration, temperature, pressure). It is especially relevant for turbines with no advanced vibration tools.

The idea of applying POD and SOD is new in this context. Another novelty is related to the way the problem is presented and explored. A detailed analysis is done to evaluate the empirical modes’ components under different conditions related to typical machine signals.

This article is organized as follows. The first section describes the POD and SOD methods. The second section applies the presented techniques to the analysis of a simulated data set to unveil the properties of these methods. The field data are presented and analyzed in section three, and, finally, in the last section, the concluding remarks are made.