4. Proposed new predictive maintenance technique

The proposed solution to described problem is based on predictive maintenance. In this research, for the last step in predictive maintenance, the condition-monitoring data approach is chosen. This approach can be divided into two main categories: model-based prognostic technique and data-driven prognostic technique. Here, data-driven technique is chosen, because condition-monitoring data were available. Model-based method requires an accurate model of the system, which is highly complex. Maffezoni presents a useful physical model of the mill, the so-called mass-balance model with 76 ordinary differential equations (ODE), better known as a knowledge-based model [21]. It is obvious that it is very hard to make accurate model of the system, so this approach was not considered. On the other hand, the experience-based prognostic approach could not be used, because of the variable data statistics and an insufficient amount of data. For all these reasons, the data-driven approach was selected.

and fall back onto the grinding table for additional grinding. Both the separator and classifier contain a significant amount of coal. These coal masses, along with the coal on the grinding table and the three recirculating loads (primary, secondary and tertiary), play a key role in the dynamic

In this research, one such system at the thermoelectric power plant 'TEKO' (Serbia) is analysed. As it is previously described, the coal inside the mill is ground by impact and friction against the grinding table that rotates around the mill centre line (CL). The only way to determine the current condition of the grinding table is to shut down the entire subsystem and open it for visual inspection. This time-based maintenance method guarantees that grinding tables will be replaced before they become dysfunctional, but at a cost of frequent shutdowns. If inspection shows that grinding table replacement is not yet necessary, then significant material losses will incur. In Figure 2, two grinding tables are shown. On the left figure is a new grinding table, immediately after replacement, and on the right figure is a worn grinding table, straight before replacement.

In practice which is common on plant A1, at thermoelectric power plant 'TEKO', Kostolac, grinding tables are replaced every 1800 h. However, it often happens that because of the increased presence of limestone, sand and other impurities in coal, grinding tables become deteriorated already after 1400 h, or even shorter. In that case, weaker effectiveness of the mill is noticeable, it is 'chocked', and serious problem with regulation occurs in an attempt to regulate the temperature of air mixture and pressure of fresh steam in front of the turbine. This appearance has for consequence significant misbalance of temperature distribution inside the firebox, which has negative influence on increased water injection in fresh steam, knockdown of coefficient of boiler efficiency and so on. In such conditions, usually, mill must be stopped unplanned for grinding table replacement and that incurs financial losses. Because of that, system which offers predictive maintenance is of great

The proposed solution to described problem is based on predictive maintenance. In this research, for the last step in predictive maintenance, the condition-monitoring data approach

4. Proposed new predictive maintenance technique

Figure 2. New grinding table (left) and worn grinding table (right).

performance of the mill [21, 22].

32 Recent Improvements of Power Plants Management and Technology

importance.

As it is described earlier, the first step in predictive maintenance programme is data acquisition. In this research, acoustic signals recorded in the vicinity of the mill were used to detect the condition of the mill. The acoustic signals were acquired from a coal mill at the 'TEKO' thermoelectric power plant, while it was operational. The main mill rotation frequency was about 12.5 Hz and the mill from which the signals were acquired had 10 impact plates.

Namely, in the literature it can be found that failure information is hidden in the spectral characteristics of vibration signals [23], but it has been demonstrated that in some cases acoustic signals are equally informative. In 2001, Baydar conducted a parallel analysis of the frequency characteristics of vibration signals and acoustic signals to detect various types of failures of rotary components, concluding that both signals can be used equally effectively [24]. The present research uses acoustic signals because they are simpler and less costly to record than vibration signals. They can also be acquired without interfering with mill operation because they are recorded externally.

The acoustic signals were acquired by means of a directional microphone at a distance of several millimetres, while the coal-grinding subsystem was operational. Recording of these signals is performed at the low altitude in thermoelectric power plant, where acoustic contamination is highly expressed. Because of that, special system for microphone fixation is projected, at a distance of several millimetres from the walls of analysed mill, so the power of useful signal could be multiple higher than the power of contaminating acoustic sources as neighbouring mills, feed pumps, surrounding valves and so on. The sampling frequency of recorded acoustic signals was 48 kHz. Data acquisition was conducted every 2 weeks on average, and it lasted for several minutes. Table 1 shows the dates of recording, the dates of grinding table replacement and the duration of each signal. For faster implementation of the algorithm, the sampling frequency was decimated from 48 to 4.8 kHz, and the duration of the analysed signals was 1 min.

We can see from Table 1 that the whole time period from the moment of grinding table replacement until the moment when grinding tables are worn is covered. After the first cycle of acoustic signal recording, three more recordings were performed after grinding table replacement. In this way, based on recorded acoustic signals, coal-grinding subsystem data are collected in different states. A large base of condition-monitoring data is obtained (without disturbing coal-grinding subsystem while it is operational) which can be further processed.

The second step in predictive maintenance is data processing. Given that collected data are acoustic signals, they are classified as waveform type of data. In order to overcome disadvantages encountered when such data are analysed in time domain and frequency domain [25], these data are analysed in time-frequency domain. A spectrogram was used to assess the acoustic signals in


Table 1. Recorded acoustic signals.

the time-frequency domain, which represented the spectral components of the signals in three dimensions very well: time information along the horizontal axis, frequency information along the vertical axis and amplitude depicted by a colour-coded scale. Colour intensity illustrated the strength of the spectral components. Figure 3 [26] shows the spectrogram of an acoustic signal recorded on 30 March 2012, 6 days after grinding table replacement.

Figure 3 clearly shows the dominant frequencies, and indicates that they are the high harmonics of the basic frequency of mill rotation, which was f<sup>0</sup> =12.5 Hz. Also, the dominant peaks in the spectrum occurred at frequencies 10f0,20f<sup>0</sup> and so on, according to the fact that there were 10 impact plates inside the mill, such that the basic frequency of grinding table travelling alongside the microphone was 10f0. Given that the microphone was positioned so as to be as close as possible to the grinding table, these spectral components were much more pronounced than the other components.

Figure 3. Spectrogram of acoustic signal.

After data acquisition, it was necessary to extract proper characteristics of the recorded acoustic signals in the frequency domain, in order to obtain vector of observations for analysis with T<sup>2</sup> control charts. As it was mentioned earlier, a spectrogram was used for acoustic signal representation. If recorded acoustic signal is denoted as y[n], the spectrogram of acoustic signal Sp is often denoted as short time fast Fourier transform (STFFT) in literature [27] and computed as fast Fourier transform (FFT) on sliding window data. The idea of STFFT is dividing of the whole signal on segments with short time window, and applying the Fourier transform on each segment. The spectrogram represents a function of time and frequency arguments, which can be written as follows:

$$\mathcal{S}\_p = STFFT\{y[n]\} = \mathcal{S}\_p[f, n] \tag{1}$$

where f denotes the frequency and n the time argument of spectrogram.

The extracted quality characteristics in the frequency domain are the values of Sp across the time at the frequencies which represents the values around the high harmonics or the high harmonics themselves. Fourteen selected frequencies are shown in the vector fp:

$$f\_p = [14 \ 18.7 \ 23.4 \ 28.1 \ 32.8 \ 60.93 \ 126.5 \ 178.1 \ 187.5 \ 262.5 \ 346.8 \ 754.6 \ 1200 \ 2025] \quad (2)$$

Accordingly, the 14-dimensional vector of observations is formed at each time point:

$$X[n] = \begin{bmatrix} \mathbf{x}\_1[n] & \mathbf{x}\_2[n] & \dots & \mathbf{x}\_{14}[n] \end{bmatrix}^T \tag{3}$$

Coordinates of the vector X[n] are calculated as follows:

the time-frequency domain, which represented the spectral components of the signals in three dimensions very well: time information along the horizontal axis, frequency information along the vertical axis and amplitude depicted by a colour-coded scale. Colour intensity illustrated the strength of the spectral components. Figure 3 [26] shows the spectrogram of an acoustic signal

Date of acquisition Signal duration Time since last maintenance

2 February 2012 10 min 51 s 14 days 24 February 2012 8 min 8 s 36 days 1 March 2012 8 min 8 s 42 days 15 March 2012 7 min 3 s 54 days 30 March 2012 6 min 6 days 5 April 2012 5 min 12 days 19 April 2012 6 min 26 days

34 Recent Improvements of Power Plants Management and Technology

Figure 3 clearly shows the dominant frequencies, and indicates that they are the high harmonics of the basic frequency of mill rotation, which was f<sup>0</sup> =12.5 Hz. Also, the dominant peaks in the spectrum occurred at frequencies 10f0,20f<sup>0</sup> and so on, according to the fact that there were 10 impact plates inside the mill, such that the basic frequency of grinding table travelling alongside the microphone was 10f0. Given that the microphone was positioned so as to be as close as possible to the grinding table, these spectral components were much more pronounced

recorded on 30 March 2012, 6 days after grinding table replacement.

than the other components.

Figure 3. Spectrogram of acoustic signal.

Table 1. Recorded acoustic signals.

$$\mathfrak{x}\_{i}[n] = \sum\_{j=n-L\_{w}}^{n} \mathbb{S}\_{p}[f\_{i^{\*}}j] \tag{4}$$

where fi represents the ith coordinate of the frequency vector fp, and Lw is the length of the window function. This is a procedure for the generation of the initial observation vector. In this way, the data-processing step and feature extraction are completed.

The last step in predictive maintenance programme is maintenance decision-making. As it is described in the beginning of this section, data-driven technique is chosen, that is, it is decided that the input of the sequence of observations be analysed with T<sup>2</sup> control charts, and then, outputs of control charts will be the input sequence for hidden Markov model (HMM). HMM should give us the information about the grinding tables condition, that is, are they worn so that their replacement is necessary. This would be the second approach in failure prognostic, because of the prediction that the system will work without failure until some future time, that is, until the next interval when inspection is needed.

After obtaining the vector of observations, T<sup>2</sup> control charts were constructed. Generally speaking, a control chart is a statistical tool used to detect failure. Control charts make a clear distinction between common causes of variations in the process and failures of the system. For a system where only common causes of variations are present, we say that such a system is under statistical control. A control chart generally has a centre line (CL), upper control limit (UCL) and lower control limit (LCL). The centre line represents the mean value of the quality characteristic of interest, detected while the process is under statistical control. The control limits are selected such that while the process is under statistical control, nearly all the points in the control chart will fall between these two lines.

The first step in constructing the control charts requires an analysis of preliminary data, which are under statistical control. This step is called Phase I, and data used in this phase are called the historical data set. In Phase II, the control chart is used to monitor the process by comparing the sample statistic for each successive sample as it is drawn from the process to the control limits established in Phase I [28, 29].

A multivariate analysis with Hotelling T<sup>2</sup> control charts was undertaken in the present research [30]. Based on observation vectors, T<sup>2</sup> sequence of values may be calculated according to the following equation:

$$\mathbf{T}^{2}[n] = (X[n] - \overline{X})^{T}\mathbf{S}^{-1}(X[n] - \overline{X})\tag{5}$$

where X and S denote the sample estimators of the mean value vector and the covariance matrix, respectively. Assuming that during the data acquisition sequence of N observations {X½0�, X½1�, …, X½N � 1�} is generated, sample estimators of vector of mean values and covariance matrix can be written as follows:

$$\overline{X} = \frac{1}{N} \sum\_{i=0}^{N-1} X[i] \tag{6}$$

$$S = \frac{1}{N-1} \sum\_{i=0}^{N-1} (X[i] - \overline{X})(X[i] - \overline{X})^T \tag{7}$$

The control limits in Phase II are

$$\text{UCL} = \chi^2\_{(a,p)^\wedge} \\ \text{LCL} = \mathbf{0} \tag{8}$$

where χ<sup>2</sup> <sup>ð</sup>α,p<sup>Þ</sup> is the upper <sup>α</sup> percentage point of the chi-squared distribution with <sup>p</sup> degrees of freedom (p represents the number of variables which is in our case 14). When the number of preliminary samples n is large (n > 100), using chi-squared control limit in Phase II is reasonable approximation [29]. In Phase I, the limits are based on beta distribution:

$$\text{LCL} = \left[ \frac{\left(n - 1\right)^2}{n} \right] \beta\_{(a; p/2, (n-p-1)/2)'} \\ \text{LCL} = 0 \tag{9}$$

where <sup>β</sup>ðα;p=2,ðn�p�1Þ=2<sup>Þ</sup> is the upper <sup>α</sup> percentile of beta distribution with parameters <sup>p</sup>/2 and ðn � p � 1Þ=2.

According to relation (5), the time sequence of T<sup>2</sup> values is formed, denoted as {T<sup>2</sup> <sup>½</sup>0�, T<sup>2</sup> ½1�, …, T2 ½n�} where n denotes the sequence number of sliding window data. In order to account for system dynamics, instead of the very last control chart sample, the last 10 samples were used for the characterization of the actual state of grinding tables. In other words, vector

$$O[n] = \begin{bmatrix} T^2[n-9] & T^2[n-8] & \dots & T^2[n] \end{bmatrix}^T \tag{10}$$

will be used for further estimation of system states. However, if this vector had been introduced as observation in HMM, it would be necessary to estimate joint probability function for this, tenth-dimensional vector. In order to avoid this complex numerical problem, it has been decided, as it is usual in the literature, to apply the procedure of vector quantization. In this purpose, the method of k-means clustering is used [31]. The result of k-means clustering is the sequence of k-cluster centres (centroids). In our case, based on try-and-error approach, it turned out that for k = 4 satisfying results are gain and cluster centres ðCi, i ¼ 1, 2, 3, 4Þ are obtained. Accordingly, the final vectors of observations <sup>O</sup>^ <sup>½</sup>n� are formed and forwarded to HMM in the following way:

$$\left\|\min\_{\{\}}\|O[n]-\mathsf{C}\_{\}\|^{2}=\|O[n]-\mathsf{C}\_{k}\|\Rightarrow\hat{O}[n]=\mathsf{C}\_{k}\tag{11}$$

After the samples were coded as described above, the next step was to construct the HMM. An HMM is a statistical model used to describe the transition of a system between states. It is an extension of the ordinary Markov chains with non-observable or partially observable states. Generally, HMM has N states S ¼ {S1, S2, …, SN} and M observation symbols V ¼ {v1, v2, …, vM}. HMM with three states is shown in Figure 4. The states are connected in such a way that it is possible to move from any one to the other. The hidden state at time t is denoted by qt, and the

Figure 4. HMM with three states.

a system where only common causes of variations are present, we say that such a system is under statistical control. A control chart generally has a centre line (CL), upper control limit (UCL) and lower control limit (LCL). The centre line represents the mean value of the quality characteristic of interest, detected while the process is under statistical control. The control limits are selected such that while the process is under statistical control, nearly all the points in

The first step in constructing the control charts requires an analysis of preliminary data, which are under statistical control. This step is called Phase I, and data used in this phase are called the historical data set. In Phase II, the control chart is used to monitor the process by comparing the sample statistic for each successive sample as it is drawn from the process to the control

A multivariate analysis with Hotelling T<sup>2</sup> control charts was undertaken in the present research [30]. Based on observation vectors, T<sup>2</sup> sequence of values may be calculated according

where X and S denote the sample estimators of the mean value vector and the covariance matrix, respectively. Assuming that during the data acquisition sequence of N observations {X½0�, X½1�, …, X½N � 1�} is generated, sample estimators of vector of mean values and covari-

TS�<sup>1</sup>

ðX½i� � XÞðX½i� � XÞ

<sup>ð</sup>α,p<sup>Þ</sup> is the upper <sup>α</sup> percentage point of the chi-squared distribution with <sup>p</sup> degrees of

freedom (p represents the number of variables which is in our case 14). When the number of preliminary samples n is large (n > 100), using chi-squared control limit in Phase II is reason-

where <sup>β</sup>ðα;p=2,ðn�p�1Þ=2<sup>Þ</sup> is the upper <sup>α</sup> percentile of beta distribution with parameters <sup>p</sup>/2 and

ðX½n� � XÞ ð5Þ

X½i� ð6Þ

<sup>ð</sup>α, <sup>p</sup>Þ, LCL <sup>¼</sup> <sup>0</sup> <sup>ð</sup>8<sup>Þ</sup>

<sup>β</sup>ðα; <sup>p</sup>=2,ðn�p�1Þ=2Þ, LCL <sup>¼</sup> <sup>0</sup> <sup>ð</sup>9<sup>Þ</sup>

<sup>T</sup> <sup>ð</sup>7<sup>Þ</sup>

½n�¼ðX½n� � XÞ

<sup>X</sup> <sup>¼</sup> <sup>1</sup> N N X�1 i¼0

N X�1 i¼0

UCL <sup>¼</sup> <sup>χ</sup><sup>2</sup>

able approximation [29]. In Phase I, the limits are based on beta distribution:

n " #

2

UCL <sup>¼</sup> <sup>ð</sup><sup>n</sup> � <sup>1</sup><sup>Þ</sup>

the control chart will fall between these two lines.

36 Recent Improvements of Power Plants Management and Technology

T2

<sup>S</sup> <sup>¼</sup> <sup>1</sup> N � 1

limits established in Phase I [28, 29].

ance matrix can be written as follows:

The control limits in Phase II are

where χ<sup>2</sup>

ðn � p � 1Þ=2.

to the following equation:

move from one state to the other is subject to Markov's rule (that state qt depends solely on state qt1). In addition to the number of states, N, and the number of observation symbols, M, several other HMM characteristics need to be defined.

The transition matrix A = {aij} represents the probability of moving from state i to state j. The coefficients aij are non-negative in the general case, and equal to zero if there is no direct switching from one state to another. The sum of probabilities in each matrix of type A needs to be equal to 1. The observation matrix (also called the emission matrix) B = {bj(k)} shows the probability that observation k was produced by the jth state.

Figure 5. Flow diagram of the proposed algorithm: offline procedure (left) and online procedure (right).

The sequence of initial states π = {πi} carries information about initial probabilities, indicating the likelihood that a new input sequence will move from a given state. Finally, the HMM can be defined by the triplet:

$$
\lambda = (\mathbf{A}\_\prime \mathbf{B}\_\prime \pi) \tag{12}
$$

There are three fundamental problems that can be solved by means of HMM. A detailed description of HMMs and the solutions to these three problems is available in Ref. [32].

Figure 5 [26] shows how the proposed algorithm for predictive maintenance is organized. For the purpose of the practical implementation of the proposed method, it should be clarified that certain activities are realized only once (like offline procedure) in order to determine the necessary statistics and HMM training. On the other hand, once the offline procedure is over, the algorithm can be implemented in real time and thus providing online monitoring of the mill-grinding plates states.

## 5. Results

move from one state to the other is subject to Markov's rule (that state qt depends solely on state qt1). In addition to the number of states, N, and the number of observation symbols, M, several

The transition matrix A = {aij} represents the probability of moving from state i to state j. The coefficients aij are non-negative in the general case, and equal to zero if there is no direct switching from one state to another. The sum of probabilities in each matrix of type A needs to be equal to 1. The observation matrix (also called the emission matrix) B = {bj(k)} shows the

Figure 5. Flow diagram of the proposed algorithm: offline procedure (left) and online procedure (right).

other HMM characteristics need to be defined.

38 Recent Improvements of Power Plants Management and Technology

probability that observation k was produced by the jth state.

In this chapter, gained results after applying the proposed technique for predictive maintenance on described problem at thermoelectric power plant will be presented. As it is previously explained, after data acquisition and feature extraction from recorded acoustic signals, T<sup>2</sup> control charts are formed.

The acoustic signal recorded on 30 March 2012 was used for X and S estimation in Eqs. (6) and (7), knowing that a new grinding table was operational. In this way, this signal was observed as historical data set. This was in effect Phase I of statistical control, where the entire coal-grinding subsystem was under statistical control. The estimated values of X and S in Phase I were to be used in Phase II of the multivariate analysis. The chi-squared control limit was taken as the UCL, as in Eq. (8). For the 14 quality characteristics, UCL = 36.12 (for the value α = 0.001) and LCL = 0. In order to justify the using of chi-squared control limit, in Figure 6, Q-Q plot [29] with T<sup>2</sup> quantiles on y-axis and chi-squared quantiles on x-axis are shown. For illustration, Q-Q plot for T<sup>2</sup> values for signals recorded on 30 March 2012 is shown, that is, for the signal recorded 6 days after grinding table replacement. During research, this check is done for all the signals in order to confirm that the choice of chi-squared control limit is justified.

From Figure 6, we can see that the values follow chi-squared distribution, that is, the figure shows approximately linear trend along the line of 45�, except the last few points which are slightly away from the projected trend line. Before T<sup>2</sup> control charts were constructed, we expected that the number of outliers will increase as grinding tables become worn out. Figure 7 [26] shows the T<sup>2</sup> control chart for the acoustic signal recorded on 2 February 2012, 2 weeks after grinding table replacement.

Figure 8 [26] shows the T<sup>2</sup> multivariate control chart for the acoustic signal recorded on 24 February 2012, 5 weeks after grinding table replacement.

Figure 6. Q-Q plot for recorded acoustic signal 6 days after grinding table replacement.

Figure 7. T<sup>2</sup> control chart for acoustic signal recorded 2 weeks after grinding table replacement.

Predictive Maintenance Based on Control Charts Applied at Thermoelectric Power Plant http://dx.doi.org/10.5772/intechopen.68685 41

Figure 8. T<sup>2</sup> control chart for acoustic signal recorded 5 weeks after grinding table replacement.

Figure 6. Q-Q plot for recorded acoustic signal 6 days after grinding table replacement.

40 Recent Improvements of Power Plants Management and Technology

Figure 7. T<sup>2</sup> control chart for acoustic signal recorded 2 weeks after grinding table replacement.

Figure 9 [26] shows the T<sup>2</sup> control chart for the acoustic signal recorded on 15 March 2012, 8 weeks after grinding table replacement.

It is apparent from Figures 7–9 that the number of points above the UCL on the T<sup>2</sup> control chart grew as the grinding table became increasingly worn. Eight weeks after replacement, nearly all the points were beyond the UCL. To confirm the results, the multivariate analysis was repeated using the signals recorded on 5 and 19 April 2012. Table 2 shows the exact number of outliers for all the recorded signals for the different values of UCL (i.e. for different values of parameter α).

The difference in the number of points above the UCL for the signals recorded on 2 February and 19 April 2012 can be explained. Namely, both signals were acquired 2 weeks after grinding table replacement, but the results are different for two reasons: (1) The signal acquisition conditions were not ideal because of noise. All the recorded signals reflect this noise, as well as other disturbances (e.g. when a large chunk of coal or stone hits the mill). The signals were not filtered, because of the possible information loss. All this could have influenced the accuracy of the results. (2) Grinding table wear depends on the quality of the coal and of the grinding table itself. It is therefore impossible to ascertain what the right time for grinding table replacement would be, unless the entire subsystem is shut down and opened for visual inspection.

According to Table 2, we can conclude that with the choice of parameter α = 0.001, 'over controlling' control chart is constructed, while with the choice of parameter α = 0.025, false alarm rate is too large. Anyway, no matter which value of UCL we have chosen, the number of outliers is larger as grinding tables are getting worn out. Namely, in the proposed method

Figure 9. T<sup>2</sup> control chart for acoustic signal recorded 8 weeks after grinding table replacement.

control charts were not used for classical fault detection, yet for forming of T<sup>2</sup> statistics that will be parameterized for making the HMM observations. The choice of the UCL does not have an influence on T<sup>2</sup> statistics value, that is, on forming of observations for HMM. Thus, the choice of parameter α, that is, making of compromise between the first type error and the second type error, does not have an influence on observation values for HMM, which is not usually the case


Table 2. Number of points above UCL.

when classical control chart needs to detect the fault and when the choice of parameter α has large influence for the correct determination of UCL.

After T<sup>2</sup> control charts were constructed, vector quantization was undertaken, as described in the previous section, in order to represent the control chart samples as a sequence of observations for the HMM. Figure 10 [26] shows the estimated probability density functions of the T<sup>2</sup> control chart samples for the signals recorded 2, 5 and 8 weeks after grinding table replacement. It is apparent that the T<sup>2</sup> statistics change over time and that they are a function of the condition of the grinding table (i.e. they change as the condition of the grinding table changes).

The final step of the proposed algorithm was to construct the HMM. The states of HMM are chosen so to represent the physical condition of mill-grinding plates. In order to illustrate the proposed method, it is assumed that HMM has three states. The first state is the condition of the grinding table immediately after replacement (i.e. that of a new grinding table). Having in mind that the average length of mill-grinding table duration is 1600 h approximately, the fact that HMM is in the first state could be interpreted as the grinding tables being in the first third of their life. The second state was the 'intermediate state', where the grinding table becomes partially worn out, but there is still time before replacement is needed. Consequently, the system staying in the second state can be interpreted as the grinding tables entering the second third of their lifetime. The third state means that the condition of the grinding table had deteriorated to the point where replacement is necessary. Namely, this research started from the assumption that HMM has only three states, but if it is needed that the grinding table

control charts were not used for classical fault detection, yet for forming of T<sup>2</sup> statistics that will be parameterized for making the HMM observations. The choice of the UCL does not have an influence on T<sup>2</sup> statistics value, that is, on forming of observations for HMM. Thus, the choice of parameter α, that is, making of compromise between the first type error and the second type error, does not have an influence on observation values for HMM, which is not usually the case

> Number of points above UCL (%), α = 0.005, UCL = 31.32

2 weeks 1.43% 2.14% 2.46% 5%

5 weeks 68.27% 79.5% 83.78% 88.41%

8 weeks 84.85% 90.91% 92.87% 95.54%

2 weeks 16.75% 27.63% 32.98% 43.14%

4 weeks 57.58% 70.05% 74.87% 81.64%

Number of points above UCL (%), α = 0.01, UCL = 29.14

Number of points above UCL (%), α = 0.025, UCL = 26.12

Figure 9. T<sup>2</sup> control chart for acoustic signal recorded 8 weeks after grinding table replacement.

42 Recent Improvements of Power Plants Management and Technology

Number of points above UCL (%), α = 0.001, UCL = 36.12

Date of recording

2 February 2012

24 February 2012

15 March 2012

05 April 2012

19 April 2012

Number of weeks after grinding table replacement

Table 2. Number of points above UCL.

Figure 10. Estimated probability density functions for signals recorded 2, 5 and 8 weeks after grinding table replacement.

conditions are characterized with greater precision, the number of states could be increased. Figure 11 [26] shows the sequence of observations and corresponding HMM states.

It is apparent from Figure 11 that the HMM provides information about a change in the condition of the grinding table. It is obvious that the time of HMM entry into the third state (worn-out grinding table) coincides with the beginning of observations that correspond to the control chart samples for the signal recorded 8 weeks after replacement.

Figure 11. HMM states.

### 6. Conclusion

Based on the presented results, we can make several conclusions. Firstly, the assumption set at the beginning of this research, that useful information from spectral components of acoustic signals can be extracted is confirmed. Based on this information, the condition of rotating elements of the mill can be recognized. As it is previously explained, in the literature there are mostly preferred vibration signals in regard to the acoustic signals, when we talk about informative content. Given that the recording of acoustic signals is much cheaper than the recording of vibration signals, and processing of acoustic signals is much simpler from vibration signals processing, confirmation about informative content of acoustic signals is very important.

conditions are characterized with greater precision, the number of states could be increased.

It is apparent from Figure 11 that the HMM provides information about a change in the condition of the grinding table. It is obvious that the time of HMM entry into the third state (worn-out grinding table) coincides with the beginning of observations that correspond to the

Based on the presented results, we can make several conclusions. Firstly, the assumption set at the beginning of this research, that useful information from spectral components of acoustic signals can be extracted is confirmed. Based on this information, the condition of rotating elements of the mill can be recognized. As it is previously explained, in the literature there are mostly preferred vibration signals in regard to the acoustic signals, when we talk about informative content. Given

Figure 11 [26] shows the sequence of observations and corresponding HMM states.

control chart samples for the signal recorded 8 weeks after replacement.

44 Recent Improvements of Power Plants Management and Technology

6. Conclusion

Figure 11. HMM states.

The originality of the proposed method is a combination of control charts and HMMs in failure prognostic, as well as in the application of control charts on extracted components from spectrogram. Namely, in the literature one can find control charts whose construction is based on spectral analysis of the signal [33]. Here, a different approach is proposed, that is, to apply the T<sup>2</sup> control charts on spectral components of the signal. Based on the results, this approach has proven to be very efficient. In the literature, one can also find the application of control charts and HMMs for degradation process diagnosis [34], as well as for fault detection [35], but in these papers standard p-charts and Hotelling T<sup>2</sup> control charts are used. Reports of other research dealing with the detection of certain types of failures at thermoelectric power plants can be found in the literature [36–38]. Also, HMM-based diagnostic models founded upon the condition of the system can be found in Refs. [39, 40]. In regard to all mentioned references, the original approach is proposed here.

As it is previously described, in the case of failure prognostic, in literature the most common approach is the first approach, that is, the estimation when the fault will occur (RUL estimation). In this research, the accent is on the second approach, that is, on the estimation of probability that the machine will work without failure until some future time (in our case, until the next interval when inspection and grinding table replacement are needed). With the proposed method, HMM gives us the information about grinding tables condition, that is, when the grinding tables are worn out, so that their replacement is needed.

The advantage of the proposed method is that it is non-invasive, because for the acquisition of condition-monitoring data it is not necessary to interrupt coal-grinding subsystem operation and shut down the whole subsystem. Another advantage is that it is based on acoustic signals processing which are simpler for processing and acquisition in regard to vibration signals. Software realization of the proposed algorithm is not too much complex and it is not time consuming when HMM is once trained.

A shortcoming of this method is the recording of acoustic signals in the presence of the unavoidable noise, which can influence on the accuracy of the results. Presented results are gathered offline, that is, HMM is trained based on the already recorded signals. For applying this method on online data, much larger amount of data are needed for adequate HMM training and more accurate determining of time moment when the grinding table replacement is needed. Anyhow, the proposed method can be applied in real time and used for higher stability and reliability of one of the most important subsystems in a thermoelectric power plant.

Further direction in this research would be the making of an adaptive system which would be adjustable to new statistics which are consequences of components ageing, not just the condition of grinding tables plates. Also, significant study could be made when condition-monitoring data would be recorded vibration signals, for comparative analysis with acoustic signals. Additional event data could upgrade the proposed method in combination with condition maintenance data. Some future research could be to make optimal maintenance policy in thermoelectric power plant, according to gain results.
