Shock and Vibration

Volume 2018, Article ID 5981089, 12 pages

https://doi.org/10.1155/2018/5981089

## Bearing Diagnostics of Hydro Power Plants Using Wavelet Packet Transform and a Hidden Markov Model with Orbit Curves

Correspondence should be addressed to Gabriel Pino; rb.psu@onip.leirbag

Received 15 August 2017; Revised 23 November 2017; Accepted 11 December 2017; Published 2 January 2018

Academic Editor: Marc Thomas

Copyright © 2018 Gabriel Pino et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The contribution of a medium-sized hydro power plant to the power grid can be either at base load or at peak load. When the latter is the most common operation mode, it increases the start and stop frequency, intensifying the hydro turbine components’ degradation, such as the guide bearings. This happens due to more frequent operation in transient states, which means being outside the service point of the machines’ nominal condition, consisting of speed, flow, and gross head. Such transient state operation increases the runner bearings’ mechanical vibration. The readings are acquired during the runner start-ups and filtered by a DC component mean value and a wavelet packet transform. The filtered series are used to estimate the relationship between the maximum orbit curve displacement and the accumulated operating hours. The estimated equation associated with the ISO 7919-5 vibration standards establishes the sojourn times of the degradation states, sufficient to obtain the transition probability distribution. Thereafter, a triangular probability function is used to determine the observation probability distribution in each state. Both matrices are inputs required by a hidden Markov model aiming to simulate the equipment deterioration process, given a sequence of maximum orbit curve displacements.

#### 1. Introduction

Hydro power plants (HPPs) are generally expected to run either at base load or at peak load. The former condition means they should operate uninterruptedly, irrespective of the interconnected grid’s instantaneous demand variation, due to their lower marginal costs. Most electricity flowing in national interconnected grid (NIG) is generated by large HPPs. In addition, peak demand is usually supplied by thermal power plants (TPPs) and small HPPs, due to their higher marginal costs and lower energy efficiency. In theory, HPPs should only perform a normal shutdown during planned maintenance and for reservoir water level control. The continuous operation of large HPPs near the best efficiency point (BEP) demands low intermittency, which in turn depends on the reservoir gross head constancy, regular rainfall periods, and rigorous maintenance plans [1]. The national system operator (NSO) forces all Brazilian HPPs to start, shut down, or change their generated power to attend the grid’s instantaneous requirements. During a system demand variation, runners can assume different operation states: static, start-up, no-load, low-load, nominal-load, and shut down. Start-up is one of the most damaging states regarding runner operating condition [2, 3].

Depending on the HPP’s operation regime, its power unit components can be subject to greater degradation. A stressful start-stop cycle makes the runner operate in transient state many times, increasing degeneration of mechanical elements. Off-design conditions, such as unit start-stop, switching between operation regimes, load rejection, and out-of-phase synchronization, can influence rotors’ transient operations [4, 5]. The aging generated by electrical, thermal, and environmental stress due to excessive starts and stops can be compared with the years of operation and the estimated annual equivalent cost of reduced remaining lifetime [6]. There are four main failure modes related to volatile HPP conditions: cavitation, erosion, material defects, and fatigue [7]. For instance, pressure fluctuation due to rotor-stator interaction and occurrence of vortex rope in the draft tube at partial load operation are hydrodynamic effects addressed by researchers [8].

Orbit curve diagrams have been used in condition-based maintenance (CBM) studies. They are included among the instruments used for vibration measurement and signal processing techniques for condition monitoring of machine tools in manufacturing operations [9, 10]. For instance, orbit curves were used in the evaluation of the dynamic behavior of power units affected by steam-whirl instability, a common phenomenon in steam turbines caused by a rise of the steam flow and pressure [11, 12].

It is important to predict degradation of HPP’s components before they reach failure limits. It is also valuable to know how the system operation and the degradation process are related. This paper focuses on one of the most important rotating machinery components, the turbine guide bearing [13]. During start-ups, they are submitted to hydraulic transient state [14]. This phenomenon is associated with mechanical vibrations that lead to a higher shaft surface displacement and a likely guide bearing trimming process. Continuous start-stop cycles cause progressive degradation of rotating elements. Shaft vibration measurement is essential to understand and quantify the entire process, so vibration monitoring systems are commonly installed in power units’ bearings. These systems usually have limited resources regarding digital-to-analogue sampling frequency, memory buffer register and offset error induction. This lowers the quality measurements due to the presence of noise in a significant part of the information. More details are given in Section 3.2 and described in [15–18].

The acquired transient vibration waveforms are nonstationary and present low signal-to-noise ratio (SNR). These original noisy signals are unsuitable to analyze and design orbit curves, mainly for two reasons: high DC levels distort the orbit curve formation from the origin of the Cartesian plane; and low SNR signals do not properly represent the axis displacement due to vibration sparks and undesired harmonic content. Section 3.1 shows the difference of applying filtering techniques to better interpret the transient vibration behavior. The nonstationary waveforms require sophisticated filtering tools to handle time and frequency dependent data [19, 20]. There are several mathematical methods to deal with vibration signals. They have chronologically evolved from frequency-domain analysis regarding digital filters [21] to wavelet transform denoising [22]. The wavelet transform method, applied in this paper, has the mathematical mechanisms to properly denoise and process the primary data acquired.

The filtered vibration database is accurate to develop a statistical method to predict and track the bearing degradation process. The signal processing applied to the database results in higher SNR and better represents the axis displacements as described in Section 4.1. The stochastic phenomenon evolves from “good as new” to “imminent failure.” The state progression moves through adjacent states, in such way that the next state only depends on the current one, characterizing a Markov process. Markovian models are suitable for dividing equipment conditions into any meaningful state, facilitating general understanding of the specification of the process model [23]. Furthermore, they can characterize the stochastic relationship between the features extracted from condition monitoring data and the actual health states of the equipment [24].

Nevertheless, most of the time the bearing degradation state is not detectable because it is not possible to perform inspections during the HPP operation. So, the degradation process cannot be followed directly, meaning evolution is hidden. To overcome this limitation, vibration measurements are used as an observable variable indicating the degradation states of the bearing. The entire process can be statistically better represented as a hidden Markov model (HMM) [25–28]. Besides the proposed purpose, HMM has other successful applications in speech recognition [29–31], monitoring of machine conditions, and fault diagnosis [32, 33].

This paper develops a procedure that does not require extensive historical vibration data to perform statistical assessment. The model also incorporates previous technical experiences acquired during preventive and corrective maintenance performed at the power plants and these parameters determine the decision model for maintenance based on the condition-based maintenance (CBM) of the equipment. It is possible to ascertain the guide bearing deterioration condition, for instance, based on available measurements and the proportional vibration limits established in ISO 7919-5 [34, 35]. After the theoretical background presented in Section 2 and the technical development in Section 3 regarding vibration and stochastic methods, Section 4 discusses and applies the proposed method to measurements obtained from generating unit 1 (GU-1) of Corumbá IV HPP, located in Brazil, and finally Section 5 presents the conclusion.

#### 2. Theoretical Background

The use of techniques for prognosis of bearing degradation should be divided into two parts: data acquisition and the data processing [36]. When considering data acquisition, this study performs a nonstationary signal analysis for bearing fault diagnosis. Feng et al. [37] classified the various time-frequency analysis methods applied to machinery fault diagnosis into four categories: linear and bilinear time-frequency representations (e.g., wavelet transform); adaptive parametric time-frequency analysis; adaptive nonparametric time-frequency analysis (e.g., Hilbert-Huang transform) [38]; and time varying higher order spectra. Various methods adapted to specific conditions have been used since then. The nuisance attribute projection (NAP) is introduced in the bearing performance degradation assessment to mitigate the influence of problems irrelevant to the degradation state introduced by operation conditions [25]. The Rényi entropy based features exploit the idea that a progressing fault implies rising dissimilarity in the distribution of energies across the vibrational spectral band sensitive to the bearing faults [39]. Envelope analysis has been applied to overcome the constraint of constant operating speed of the rolling element bearing. The squared envelope spectrum has been extended to cases in which small speed fluctuations occur [40, 41]. The spectral kurtosis technique adopts the concept of kurtosis to capture the impulsiveness of a signal. It uses a combination of short-time Fourier transform-based SK, kurtogram, adaptive SK, and protrugram [42]. However, despite such specific situations, the wavelet transform has been the most popular denoising technique for the extraction of the defect vibratory signature from the measured signal in which the random noise and other parameters of the bearing are immersed [43–45]. With respect to data processing, the stochastic process inherent to bearing wear can be classified as a single component which depends on the nature of the degradation state: discrete or continuous [46]. When the technical condition of a bearing cannot be described by a continuous, measurable value, its deterioration is often assessed by visual inspections or by other methods that only lead to qualitative results. As an alternative to continuous measures, several discrete deterioration states can be defined [47]. Markov processes are used in such cases when measurement of discrete degradation states is not precise.

#### 3. Materials and Methods

The reasons why a guide bearing degradation increases are strongly related to the shaft’s axial displacement. This leads to possible relationship between the shaft vibration intensity and the deterioration caused by mechanical contact of rotating and static elements. Vibration measurements and degradation status are so closely related that many power plants have installed vibration monitoring systems to detect its evolution [48]. This type of system records a substantial increase of vibration level during hydro power units’ start-up, which takes approximately five minutes, depending on speed governor parameterization [49]. The vibration data acquired during these events are crucial to understand its consequences to the whole rotating group, including the evolution of the guide bearings’ degradation.

##### 3.1. Data Acquisition

The power unit shaft’s mechanical vibration usually presents two signal sources, orthogonally installed, as shown in Figure 1. The configuration of both signals permits parameterizing them so as to describe the external profile of the shaft. The graph of the signal parameterization and composition that suppresses the time dependency is generally called a Lissajous curve [50], and specifically for shaft surface displacement it is called an orbit curve [51, 52]. This curve is fundamental to infer how much the shaft perimeter is displaced from its center line. This particular measurement, called , is the maximum axis vector distance and its measurement is also used as an indicator for technical standards [34]. It is calculated as in where is the rated turbine speed in revolutions per minute. This article considers a collusion variable of the entire vibration phenomenon per machine revolution in transient and steady states operation, so it is stored in a database for stochastic analysis.