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.
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 [
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 [
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 [
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 [
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
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
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) [
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 [
The use of techniques for prognosis of bearing degradation should be divided into two parts: data acquisition and the data processing [
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 [
The power unit shaft’s mechanical vibration usually presents two signal sources, orthogonally installed, as shown in Figure
Sensors displacement and measurements.
Vibration monitoring systems installed in power plants usually use inductive proximity sensors to measure the distance between probe tips and the shaft surface [
Technical issues related to data acquisition require signal processing using filtering techniques for better understanding of transient and steady state vibration waveforms.
The technical limitations of vibration monitoring systems directly impact the precision and accuracy of orbit curve calculation. Hence, proper filtering tools must be applied to acquired waveforms. The signal processing depends on the correct mathematical approach given to each data characteristic, operation state, sensor accuracy, associated errors of analogue-to-digital converters, frequency sampling, SNR, noise distribution, and window lengths. Figure
Orbit curve formation for different inputs quality.
Frequency spectrum analysis is applied before choosing filtering tools in order to better understand the signal behavior and how its processing will be properly performed. This preliminary mathematical feature indicates the signal content and which harmonic components are the most important [
Specifically, the transient vibration signals acquired during machine start-ups present a nonstationary characteristic; that is, the frequency spectrum is not constant in the whole window analysis. This condition demands more general time and frequency-domain analysis such as short-time Fourier transform (STFT) [
Using the time and frequency excursion of the STFT it is possible to infer a diverse frequency content of the AC component and also a DC level. The DC level content indicates the sensor setup before the data acquisition. The intrinsic differences between the original AC and DC vibration components require different mathematical tools to properly filter them.
Orbit curve calculation necessarily uses peak-to-peak vibration values. Otherwise they would be shifted from the origin of the Cartesian plane and the waveform would be distorted, as can be inferred by (
There are many techniques that can filter the DC component such as digital FIR or IIR high pass filtering [
The vibration measurement during the runner start-up tends to assume nonstationary behavior, as can also be inferred using (
After the signal processing, the vibration data and the shaft replacement are ready to be statistically analyzed.
According to ISO 7919-5, there is a relationship between
The association of a discrete nominal scale represented by linguistic expressions like “small deterioration” with a continuous degradation process is a fertile field for errors of judgment. Since
Markov chains are stochastic processes in which the progression to the next state depends exclusively on the previous one [
Emitted and observable states in HMM.
The elements
It can be observed that
Methodology flowchart.
The method presented in the previous section is applied as a case study to a power unit of Corumbá IV, which is a medium-sized hydro power plant located in Brazil. Its main technical characteristics are reported in Table
Corumbá IV HPP main technical characteristics.
Number of power units | 2 |
Rated turbine power | 64.8 MW |
Turbine diameter | 3287 mm |
Rated turbine speed | 200 RPM |
Net head | 65 m |
Reservoir capacity | 3.8 billion m3 |
From August 2016 to May 2017, 14 measurements were acquired by the vibration monitoring system during the runner start-up. The method depicted in Figure
It is strongly recommended to acquire the start-up vibration measurement from stand still until the no-load speed condition, to assure complete acquisition of vibration data. The process takes approximately five minutes. According to the technical data sheet of the vibration monitoring system [
Applying (
Short term Fourier transform of a transient state vibration.
The normalized absolute value given by its image presents clear nonstationary behavior due to its nonconstant frequency arrangement. The hill over low frequencies presents decay up to 10 Hz, suggesting an intense flicker noise content due to the signal’s low sampling frequency [
The DC filtering techniques discussed in Section
DC filtering techniques result.
Acquisition | Mean value | FIR filter | Difference |
---|---|---|---|
16/04/2017 | 1089.76 [ | 1087.34 [ | 0.22 [%] |
02/05/2017 | 1023.05 [ | 1022.54 [ | 0.05 [%] |
20/03/2017 | 1018.53 [ | 1018.09 [ | 0.04 [%] |
23/05/2017 | 1035.73 [ | 1036.67 [ | 0.09 [%] |
09/09/2016 | 1063.90 [ | 1063.50 [ | 0.04 [%] |
17/04/2017 | 1064.40 [ | 1063.52 [ | 0.08 [%] |
Figure
SNR comparison.
Harmonic | Frequency [Hz] | SNR before | SNR after |
---|---|---|---|
0 | 0 | 37.39 | 317.62 |
1 | 3.33 | 35.68 | 304.38 |
3 | 10 | 25.99 | 205.45 |
6 | 20 | 17.77 | 191.3 |
8 | 26.66 | 15.16 | 132.9 |
Comparison between original and filtered signals.
The maximum displacement evolution over the operating time fits an exponential function nicely, as depicted in Figure
Acquisition | | | |
---|---|---|---|
09/09/2016 | 149.92 | 147.71 | 146.59 |
19/12/2016 | 166.45 | 163.65 | 158.91 |
06/01/2017 | 169.22 | 161.93 | 156.87 |
19/01/2017 | 171.97 | 170.36 | 166.24 |
20/02/2017 | 178.09 | 175.69 | 170.64 |
21/02/2017 | 176.28 | 174.07 | 170.95 |
20/03/2017 | 183.35 | 180.22 | 174.52 |
05/04/2017 | 186.39 | 183.62 | 179.97 |
16/04/2017 | 188.74 | 181.79 | 177.00 |
17/04/2017 | 185.51 | 182.72 | 177.15 |
24/04/2017 | 190.84 | 183.91 | 178.70 |
02/05/2017 | 191.62 | 183.55 | 176.31 |
23/05/2017 | 196.98 | 191.45 | 184.93 |
30/05/2017 | 197.68 | 189.71 | 180.82 |
Exponential adherence between
The runner nominal speed is 200 RPM, and according to [
State | Maximum displacement [ |
---|---|
A | |
B | 82 ≤ |
C | 136 ≤ |
D | |
Guide bearing overview.
The deterioration process often accelerates as the operating time increases until reaching the remaining useful life. The expectation of the distribution of states in degradation prediction models presents features similar to those of exponential distributions [
To simulate how the transitions states will evolve, an exponential curve is plotted, supported by the exponential behavior observed through the measurements. This exponential curve, shown in (
After calculating the sojourn times and knowing that on average Corumbá IV HPP operates 80.48 hours per start-stop cycle, it is possible to determine how many start-stop cycles, here called
In this case study, the estimated values for
The plant’s maintenance records showed that when the power unit operating time reached 24,000 hours, it underwent preventive maintenance. On this occasion, no anomaly was identified in the guide bearing and therefore this was judged subjectively by the technicians as if it still remained in operating condition. However, after operating 36,000 hours, the power unit underwent new preventive maintenance, when severe scratching of the coating metal was detected. As a result, the guide bearing was identified as being in a state of high deterioration and likely to compromise the regular operating condition of the power unit. The guide bearing was thus replaced and the equipment was classified as good as new again. This information about the guide bearing degradation identified in the 24,000 and 36,000 hour inspections was used to validate the model parameterization.
Due to the characteristic of
Table
Posteriori probabilities.
| | | ||||||
---|---|---|---|---|---|---|---|---|
State | ||||||||
19 | 20 | 21 | 22 | 19 | 20 | 21 | 22 | |
253–262 | 24% | 76% | 0 | 0 | 0 | 93% | 7% | 0 |
262–271 | 0 | 27% | 73% | 0 | 0 | 0 | 93% | 7% |
| 0 | 0 | 79% | 21% | 0 | 0 | 71% | 29% |
The signal processing methods applied in this article, such as mean DC level and wavelet packet, presented fair performance in handling nonstationary data. Flicker and thermal noise were attenuated and the obtained signals presented high SNR. The resulting vibration values and the maximum axis displacement were consistent for use as inputs for the proposed stochastic model. The proposed method has some important aspects. First, the vibration readings are acquired in a real operational environment, which means application of standard vibration monitoring systems. While on the one hand this method has the downside of reading imprecision, on the other it enables the operator himself to collect the signals without external assistance. The adoption of HMM has two aspects, both important features of the proposed method. First, it is related to the main aspect of a Markov technique that allows the operator to carry out the guide bearing diagnosis without the need of putting the runner on hold to perform inspections. The second is concerned with the possibility of modeling guide bearing diagnosis by means of corrective maintenance records, therefore based on past experience. In the case of Corumbá IV HPP, the filtering and HMM parameters are adapted to a routine diagnosis system. In this case, the plant operator simply acquires the axial vibration signals during the runner start-up and feeds the model with such raw data. The automated routine calculates the probabilities of the guide bearing being at certain stages of degradation. Therefore, the proposed method has substantial advantages by reducing failure risk and maintenance costs.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors would like to acknowledge Corumbá Concessões S/A and ANEEL for their financial and operational support to this R&D project.