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Efficient fault detection and diagnosis of distillation column using gamma scanning

  • Zeinab F. Elsharkawy
  • Mohammed E. Hammad
Article
  • 68 Downloads

Abstract

This paper presents an efficient approach for automated fault detection and diagnosis of the distillation column by analyzing the gamma intensity variations. Gamma-ray scanning is one of the most common techniques that is used in industrial radioisotopes applications. It is used to get signals that reflect the inner details of a distillation column. These signals are gamma intensity variation that comes from material density variation in the column. In the proposed approach, the signals of each distillation column are divided into frames. Each frame contains the signal of just one column tray. Therefore, the position of the defected tray can be determined exactly in the column. Discrete wavelet transform, power density spectrum, higher order statistics (HOS), area under the curve (AUC) and correlation between signals are features that are extracted to be used in artificial neural network. The proposed results prove that the selection of HOS with correlation and AUC effectively achieves the fault detection and diagnosis approach in different high noise environments.

Keywords

Distillation column faults Gamma scanning Higher order statistics Bispectrum Power density spectrum Artificial neural network 

Introduction

Distillation columns are important elements in the chemical and petroleum industries. They guarantee the accuracy of the production of the plant. Distillation columns faults cause major losses in production and financial issues. These faults can also lead to fire hazards and atmospheric pollution [1]. Gamma scanning is a non-intrusive, efficient, convenient, fast, and cost-effective technique for examining the distillation column internal details, during its operation [2]. Hence it is used for forthcoming maintenance and troubleshooting of the working columns. The early identification and correction of the problem reduce the losses and the cost of the repair. Many techniques are used to see these internal details as X-ray imaging, tomography, and gamma scanning (GS) [1, 2, 3, 4].

GS has been used for distillation column malfunction detection in [1, 2, 3, 4, 5, 6]. GS is used to measure the packet column water distribution using Co-60, I-131 and Tc-99m radioactive sources [5]. In [6], Co-60 source and nucleonic meter with scintillation detector have been used to scan distillation column and identify the problem area. For nonlinear distillation column, the multivariable online identification approach is applied and its effectiveness is approved in [7], where the adaptive Takagi–Sugeno fuzzy model was used. The features are extracted using principal component analysis (PCA) and are fed into multiple adaptive neuro-fuzzy [8], to identify the different distillation column malfunctions, and it is modified and applied on a distillation column benchmark in [9]. For a steady-state nonlinear procedure, the fuzzy c-means clustering method can be used instead of feature extraction to identify normal and abnormal operation of the column [10]. Indiscernibility dynamic kernel principal component analysis (I-DKPCA) has been applied to distillation column in [11] and higher detection accuracy has been obtained compared to kernel principal component analysis (KPCA) and dynamic kernel principal component analysis (DPCA). Multiscale partial least squares (MSPLS) models and generalized likelihood ratio (GLR) has been used distillation column simulated data for fault detection in processes [12].

Multi-rate adaptive model predictive control model was developed to achieve satisfactory performance when the moderate purity region is shifted to the high purity region in the distillation column operation [13]. To improve distillation column working conditions, a mathematical model has been used for behavior prediction [14]. Improved KPCA has been used in [15] to improve the prediction of the column process failure. In [16], the HOS (bispectrum and trispectrum) and matched filter are used as features to classify distillation column malfunctions. The Bispectrum HOS using indirect method results in highest identification rate [16, 17].

Most previously published researches are interested in monitoring of distillation columns and classifying only its normal and abnormal operation. Only, few of them consider one or more of distillation column faults with low detection accuracy in the presence of noise. In this paper, an efficient approach for automatic detection of distillation columns malfunctions is proposed. The normal operation and five faults’ signals are tested and classified. Discrete wavelet transform (DWT) [18, 19, 20, 21], power density spectrum (PDS) [21, 22, 23, 24], HOS [16, 17, 25], correlation between signals (Corr) [26, 27], AUC [28] and a hybrid of some of them are features that are extracted and selected to feed artificial neural network (ANN) [21, 22, 23, 24]. Higher detection accuracy is obtained compared to other previous methods.

The organization of the paper as follows. First section is the “Introduction”. The second section presents the principle of gamma ray scanning. The proposed detection approach is presented in the third section. The experimental work is investigated in the fourth section. Results and discussions are explained in the fifth section. Finally, the conclusion is illustrated in the sixth section.

Scanning of distillation column with gamma rays

The emitted gamma rays from the radioactive sealed source and a scintillation detector are used for scanning the distillation columns. The source and the detector are installed on distillation column opposite sides as shown in Fig. 1 and are incrementally moved down concurrently along its length, so the scan position is relative to the top of the distillation column. The absorbed or transmitted gamma ray intensity indicates the real quantity and nature of the material, which exists between the detector and the source. The relation that describes the gamma rays transmitted through a material [2, 4] is:
$$ A = A_{0} e^{( - \mu \rho x)} $$
(1)
where A is the transmitted radiation intensity through the material, A0 the incident radiation intensity, ρ is the absorbing material density, μ is the material absorption coefficient and x is the path length of the transmitted radiation.
Fig. 1

Distillation column scanning with gamma rays

By using constant distance between the source and the detector during the scanning process, the measured radiation intensity will vary only when the internal material density changes, where the relation between the radiation intensity and the absorber material density is inversely proportional. The intensity of transmitted radiation is stored graphically on a computer through a data acquisition system (DAS). The DAS converts the detected radiation to pulses and their counts per second (CPS) is an indicator of the radiation intensity as shown in Fig. 2 and the distance is measured from the top of the distillation column at the beginning of scanning process. The detected gamma rays intensity varies according to the column in-between material density variation. Hence, the distillation column malfunction detection can be done by examining this intensity variation.
Fig. 2

Normal and faults signals of distillation column a normal, foaming and weeping signals, b damage, collapse and flooding signals

As shown in Fig. 2, the gamma scanning pulses consist of many minima points that indicate the distillation column trays positions which carry the liquid over it. While the high radiation intensity regions represent the vapor regions between trays.

The common distillation column faults that considered in this paper are weeping, foaming, column tray collapse, column tray damage, and flooding as shown in Fig. 2. The normal scanning signals without any processing problems are shown in the first five trays in the signal shown in Fig. 2a. Foaming malfunction is shown in the sixth tray, which results from the passing gas or vapor reduction, which leads to liquid expansion. Hence, the radiation intensity above the tray is not correct and there is a gradual increase in it above the tray towards the vapor line. The weeping malfunction also appeared in this figure at the eighth tray. Insufficient vapor or liquid sealing, an ineffective working of contactors and higher liquid flow rate are the reason for weeping. Tray damage, tray collapse, and tray flooding are shown in Fig. 2b over tray number one, four and eight respectively. Tray damage is a partially damaged tray. The main reasons of this fault are the susceptible tray vibration, which can be attributed to missing valves, large holes in trays from corrosion, missing tray panels, heavily fouled (dirty) trays due to deposits, coking, debris, and long-term fatigue fosters failures. The tray has collapsed when the tray is full damage. This refers to the absence of absorption material in this area, so this fault appears as high-transmitted radiation intensity at its position in a signal. Tray flooding resulting from the excessive amount of liquid on a tray. Tray flooding undermines good vapor or liquid disengagement between trays. Flooding can also due to a blockage on a tray or in its down comer, poor vapor or liquid disengagement and high difference of pressure over the column.

The experimental signal obtained from gamma scanning of a distillation column will not be smooth as the signal discussed above; instead, it will have some noises due to the variation of sealed source radiation as it is not uniformly radiate its rays and due to the field and environmental noises. Figure 3 shows a real signal obtained by scanning a 7-m top portion of a distillation column using a 95 mCi 60Co radioactive sealed source and ALTAIX Colscan MKINIBRAS System [17].
Fig. 3

Example of real scanning signal of distillation column

This figure illustrates the existence of flooding on tray number 14, which may be caused, by the existence of blockage on that tray or in its down comers. This blockage leads to an excessive amount of liquid over that tray which leads to filling the regions of vapor with the liquid and hence it yields the density profile shown.

The paper proposes the detection approach of distillation column faults on simulated data generated using ALTAIX Colscan MKINIBRAS system software. The normal signal and all faults’ signals are considered in the used database. A sample of this database signals are shown in Fig. 2. These data are used for scientific studies, but the proposed approach can be applied in the practical application. The database consists of 105 different distillation column scanning signals, 20 signals of them represent foaming type fault, 20 signals represent damage type fault, 20 signals represent weeping type fault, 9 signals represent flooded tray fault, 18 signals represent collapsed tray, and 18 signals represents the normal signals of the distillation column. These signals are then degraded with Gaussian, Rayleigh and Rician noise to be similar to real faults’ signals and used for testing process.

The proposed detection approach of distillation column faults

The fault detection of distillation column signal obtained by gamma scanning is so difficult as it is contaminated by different type of noise and usually needs an expert for the interpretation of that data. Therefore, this paper presents an efficient approach for automatic detection the type and position of the distillation column faults. Figure 4 shows the configuration of the proposed approach as it consists of a training phase and testing phase. The segmentation of signal into frames is the first stage in training and testing phases. Each frame contains just a signal of one column tray only. The intensity profile signal of column consists of many minimum points, each represents the tray position. Some faults appear in the column signal above its tray as foamed and flooded trays while other faults appear below the tray as weep trays, so after determining the position of trays, the segmentation should be done as indicated in Fig. 5.
Fig. 4

Distillation column faults detection approach

Fig. 5

Distillation column signal segmentation

The second stage is feature extraction using DWT, PDS (periodogram) and HOS (bispectrum) followed by frequency cepstral coefficients (MFCC) and polynomial coefficient. Correlation between signals and AUC are also used in this stage. To achieve higher detection accuracy, all these features are used to reduce the noise effect.

Discrete wavelet transform

Wavelet transform is recently a very popular transform used for analysis, denoising, compression and feature extraction of signals and images. DWT is used to decompose signal into different scales that represent various frequency bands. The position of signal’s instantaneous structures can be determined at each scale approximately.

This property can be used for denoising. The wavelet coefficients \( W_{F} (b,\varvec{\eta}) \) can effectively reconstruct the original signal when the family of shifted and scaled mother wavelets of the selected b and η comprise a complete and orthogonal basis, where b and η are scale and translation parameters, respectively. The DWT of a signal I(n) is calculated by passing it through a series of filters. Firstly, the samples are passed through a low-pass filter with impulse response Hlow resulting in Y(n) which is a convolution (*) of the signal I(n) and the impulse response of the filter Hlow(n) as in Eq. (2) [12, 13, 14, 15]:
$$ Y(n) = I(n)\,*\,H_{\text{low}} (n) = \mathop \sum \limits_{k = - \infty }^{\infty } I(k)H_{\text{low}} (n - k) $$
(2)
The signal is decomposed also using a high-pass filter with impulse response Hhigh. The high-pass filter output is the detail coefficients while the approximation coefficients is the output of low-pass filter. It is important that the two filters are related to each other to allow a perfect reconstruction. The half of the samples (signal frequencies) are discarded according to Nyquist’s rule. So, the filter outputs are subsampled by 2 as follows
$$ Y_{\text{low}} (n) = \sum\limits_{k = 0}^{{L_{f} }} {I(k)\,H_{\text{low}} (2n - k)} $$
(3)
$$ Y_{\text{high}} (n) = \sum\limits_{k = 0}^{{L_{\text{f}} }} {I(k)\,H_{\text{high}} (2n - k)} $$
(4)
where Lf is the length of the filter.

Power density spectrum

PDS is the corresponding frequency domain representation of auto-correlation. The function of auto-correlation is to describe a random process. This function characterize the time-correlation between a random process samples. The average time of the autocorrelation and the power density are estimated and the limit of the average autocorrelation or average power density is used to estimate the actual values of the PDS [16, 17, 18]. For a signal, I(n) with length Ms, the periodogram of the signal is obtained using the following equation
$$ P_{\text{e}}^{\text{Per}} \left( f \right) = \frac{1}{{M_{\text{s}} }}\left| {\mathop \sum \limits_{m = 0}^{{M_{\text{s}} - 1}} I(n)e^{ - j2\pi fn} } \right|^{2} $$
(5)
The advantages of this method are its simplicity and the ability to be computed directly by the Fourier transform of the signal that may be interpreted as a measure of the correlation of the signal I(n) and the complex sinusoid ej2πfn, where j refers to complex and f is the fundamental frequency.

Higher order statistics

HOS is an extension of second order measure of power spectrum and is defined in terms of moments and cumulants. HOS is used as a preprocessing step of the column data before classification step to suppress all additive colored Gaussian noises of the unknown power spectrum obtained during gamma scanning of the column. Suppression of such noises will make the process of classification so easy for the classifiers and will be not affected by the noise level. The HOS of third order (bispectrum) can also suppress non-Gaussian noises that have a symmetrical probability density function [10, 19]. The cumulants and moments of order n of real stationary discrete time signal x(k) can be defined as
$$ m_{n}^{x} \left( {\tau_{1} ,\tau_{2} , \ldots ,\tau_{n - 1} } \right) = E(x(k)x\left( {k + \tau_{1} } \right), \ldots ,x(k)x(k + \tau_{n - 1} )) $$
(6)
It depends on the time differences τ1τ2, …, τn−1. E(x) is the expected value of x. The cumulants and moments relationship is defined as
$$ C_{n}^{x} \left( {\tau_{1} ,\tau_{2} , \ldots ,\tau_{n - 1} } \right) = m_{n}^{x} \left( {\tau_{1} ,\tau_{2} , \ldots ,\tau_{n - 1} } \right) - m_{n}^{G} \left( {\tau_{1} ,\tau_{2} , \ldots ,\tau_{n - 1} } \right) $$
(7)
where m n x (τ1τ2, …, τn−1) is the nth order moment function of x(k) and m n G (τ1τ2, …, τn−1) is nth order moment function of an equivalent Gaussian signal that has the same mean value and autocorrelation function of the same signal.

Estimation of HOS is a problem in the practical case where due to the finite length of the collected data. HOS can be estimated by two fundamental approaches; the parametric approach and conventional nonparametric method that is classified into two classes, indirect and direct methods. Estimation of HOS 3rd order using conventional indirect estimator is used in this paper, which achieves highest recognition rate in [10].

The correlation between signals

The cross correlation between signals can be used as discriminant feature for distillation column signals [20, 21]. The similarity between two signals x(t) and y(t) can be measured by correlation and it is given by this formula.
$$ \int\limits_{ - \infty }^{\infty } {x(t)y(t - \tau ){\text{d}}t} $$
(8)
Correlation between normal column signal and other fault signals can be effectively used in this paper. The correlation coefficients of two normal signals are very high and these coefficients are degraded as the similarities between these signals are decreased. Hence, the correlation coefficient of normal and foaming or weeping or flooding signal is different from each other. So, the correlation feature can be used to discriminate between different column signals.

Area under the curve

The AUC of the continuous function I(n) on the closed measurement interval [a, b] of a column tray is given by:
$$ {\text{AUC}} = \int\limits_{a}^{b} {I(n){\text{d}}n} $$
(9)

As shown in Fig. 5, the AUC of each signal has different value depending on the fault type, which can be used as a discrementing feature.

Mel-frequency cepstral coefficients (MFCCs) and polynomial coefficients are applied after DWT, PSD and HOS estimation to reduce the amount of data introduced by these estimations while keeping the distinctive information. The MFCCs are sensible to time shifts and mismatches between testing and training data, which are followed by Polynomial coefficients to increase the similarity between the testing and training signals [16, 23, 24, 29]. The Mel-scale is a mapping between the perceived frequency scale in Mels and the real frequency scale in Hz and it is given by the following equation
$$ f_{\text{Mel}} = 2.595\log \left( {1 + \frac{{f_{\text{linear}} }}{700}} \right) $$
(10)

Estimation of the MFCCs can be obtained by windowing the signal and then the discrete Fourier transform (DFT) and Mel filter bank, the log of the spectrum, and the DCT are applied sequentially.

Many features are estimated in the proposed approach. So, the feature selection is very important stage in this approach. In this stage, many trails have been done. In each trail, one or more features have been used to train and test the classifier. This is done to obtain the best features that result in the highest classification accuracy.

The classification process is the last stage in the proposed approach, in which the selected features are fed to the ANN classifier in order to match each signal to its related fault type. In this paper, multi-layer perceptrons (MLPs) neural networks are used. They consist of three different layers. The first, is the input layer which consists of neurons that has the same size as the input feature vector of each distillation column signals. The second, is the hidden layer and the last one is the output layer that consists of six neurons as the number of different types of distillation column tray signals. The training algorithm of ANN adapts its weights by trying to minimize the sum square error between the desired output Rout and actual output Aout of the output neurons of the kth output neurons [16, 17, 18] and it was given by
$$ E_{o} = \frac{1}{2}\sum\limits_{k = 0}^{{K_{\text{out}} }} {\left( {R_{\text{out}} - A_{\text{out}} } \right)^{2} } $$
(11)
where Kout is the number of output neurons. Each weight in the different layers of the neural network is adapted by the addition of an increment to reduce the error Eo rapidly as possible.

Experimental work

The distillation column is connected to motors and furnace to separate chemical mixture depending on their boiling points and the vapor from a boiling solution is passed upwards along a column. So, the column signals are scanned at very high noisy environment and they are contaminated with very high and different noise types. Hence, it is important to highlight the approaches that achieve better detection accuracy at high noise level.

The proposed approach of fault detection of the distillation column is applied to previously explained database to be examined. The training database is constructed first from 54 signals and contains all types of distillation column tray signals, i.e., normal and faults’ signals. These signals are segmented to frames and each frame acts as just one tray, then features are extracted and selected to train ANN classifier. The testing database is built by degrading the tested data with different types of noise, i.e., Gaussian, Rayleigh and Rician noise, before testing the classifier. There is an effective parameter for each noise which can describe its effect. For example the noise power can describe the Gaussian noise level. Hence, Signal to Noise Ratio (SNR) has been used for studying the effect of that noise on the tested signals. But in Rayleigh noise, the noise variance can describe its effect. The Rayleigh distribution \( f_{Y} (y) \) can be calculated as:
$$ f_{Y} (y) = \left\{ {\begin{array}{ll} {\frac{y}{{\sigma^{2} }}\exp \left( { - \frac{{y^{2} }}{{2\sigma^{2} }}} \right),} \quad &{y \ge 0} \\ {0,} \quad &{\text{elsewhere}} \\ \end{array} } \right. $$
(12)
where \( \sigma \) is the scale parameter of the distribution and \( \sigma \sqrt {\frac{\pi }{2} } \) is the mean value. The noise variance (σ2) can be used to examine the noise effect on the tested signals as in [22, 23, 24]. The Rician distribution is the probability distribution of the magnitude of a circular bivariate normal random variable with non-zero mean and it is given by the following probability density equation.
$$ f_{R} (r) = \frac{r}{{\alpha^{2} }}\exp \left( { - \frac{{r^{2} + A^{2} }}{{2\alpha^{2} }}} \right)I_{0} \left( {\frac{rA}{{\alpha^{2} }}} \right) $$
(13)
where α is the standard deviation of the Gaussian distribution that underlies the Rician distribution noise. The parameter A2 = (A I 2  + A Q 2 ), where \( A_{I}^{2} \) and \( A_{Q}^{2} \) are the mean values of two independent Gaussian components. I0 is the modified zero-order Bessel function of the first kind. A and α are not the mean value and standard deviation for the Rician noise, when A = 0, the Rician distribution reduced to Rayleigh noise and when A is large compared with α, the noise distribution is approximately Gaussian. So, the only effective parameter that can be used here is the probability density as in [22, 23, 24]. All experiments are evaluated using the classification accuracy which is defined as:
$$ C_{\text{a}} = \frac{{S_{\text{no}} }}{{T_{\text{no}} }} $$
(14)
where Ca is classification (detection) accuracy, Sno is the number of success classifications and Tno is the total number of classifications trails.

Results and discussion

The detection accuracies of the proposed approach are illustrated in Tables 1, 2 and 3, where Table 1 clarifies the percentage detection accuracy of distillation column signals degraded by Gaussian noise for each selected feature. It is clear from the results that the Bispectrum using indirect method give high detection accuracy as expected and estimated [16]. However, higher detection accuracy can be obtained by incorporating AUC, Corr or (Corr + AUC) with HOS especially at low SNR. In comparison with the (HOS + Corr + AUC) hybrid feature, (HOS + Corr) hybrid feature provides higher performance at low SNR under 25 dB, but with lower detection accuracies at higher SNR. Also the PDS feature results in acceptable detection accuracy at low SNR. The PDS performance can be improved by incorporating the AUC or Corr or (AUC + Corr) with it, which leads to higher detection accuracy with different SNR. In low SNR the HOS hybrid features results in higher detection accuracies compared to the PDS hybrid ones, and the situation is reversed in high SNR. All other features provide good results but with lower detection accuracy at low SNR, which is the usual operation circumstances.
Table 1

Detection accuracy (%) when the signal degraded by Gaussian noise

SNR dB

DWT

Corr

AUC

Corr + AUC

PDS

PDS + AUC

PDS + Corr

PDS + Corr + AUC

HOS [16]

HOS + AUC

HOS + Corr

HOS + Corr + AUC

0

70.0529

67.7014

70.4449

69.7122

65.6085

67.9365

70.8995

72.4868

82.0106

85.2910

86.0317

86.0317

5

63.0688

75.0965

75.0525

75.0464

72.2751

71.5344

77.5661

78.6243

81.1640

83.1746

85.9259

85.9259

10

64.9735

82.0427

83.1356

82.4675

68.8889

70.2646

73.3333

78.4127

80.1052

85.7143

85.9259

85.2910

15

73.6508

89.3332

90.5395

87.1735

64.3386

69.4180

72.3810

80.2116

83.1746

84.7619

85.0794

83.4921

20

87.9365

94.1785

94.1785

94.3928

71.0053

80.4233

78.5185

85.5026

82.4675

84.1270

85.3968

83.2804

25

95.1323

97.2155

96.8800

97.2388

84.9735

87.8307

89.1005

91.1111

85.6085

86.3492

86.5608

85.0794

30

97.1429

98.2124

97.1429

98.1489

95.0265

94.4974

95.6614

94.4974

87.6190

87.6190

88.2540

89.5238

35

97.9894

98.2759

96.9490

98.2970

97.0370

95.7672

97.2487

96.4021

91.5342

87.9365

90.1587

90.8995

40

98.2011

98.2970

97.5885

98.2970

97.9894

95.7672

97.2487

97.0370

92.6984

90.8995

92.2751

93.5450

45

98.2011

98.2970

97.5885

98.2970

98.2011

96.9312

97.0370

96.8254

93.9683

91.9577

93.4392

94.6032

50

98.3069

98.2970

97.5885

98.2970

98.3069

96.1905

97.4603

97.0370

94.1785

93.5450

94.7090

96.7196

Table 2

Detection accuracy (%) when the signal degraded by Rayleigh noise

Noise variance

DWT

Corr

AUC

Corr + AUC

PDS

PDS + AUC

PDS + Corr

PDS + Corr + AUC

HOS

HOS + AUC

HOS + Corr

HOS + Corr + AUC

0

98.6179

98.2970

97.5885

98.2970

98.8360

96.8254

97.8836

97.1429

94.5284

93.8624

95.2381

96.9543

5

97.2316

93.9406

93.8771

93.9276

96.4021

94.1799

95.5556

93.9683

88.6772

84.9735

86.0317

86.1376

10

91.7836

88.7944

90.5186

87.7064

88.6772

90.1587

90.4762

91.6402

80.8466

85.8201

86.0317

86.0317

15

85.6259

83.0597

85.9431

83.8514

82.6455

84.3386

82.8571

89.6296

74.4974

86.2434

86.0317

85.6085

20

78.5955

80.4744

82.0542

80.9316

77.0370

79.6825

79.8942

87.6190

73.8624

85.9259

85.9259

85.0794

25

73.4979

76.8876

80.6947

76.0089

75.8730

75.6614

75.6614

84.6561

71.9577

86.0317

85.9259

85.5026

30

73.7850

73.7948

78.4246

73.3148

73.8624

76.2963

73.1217

84.3386

72.2751

85.9259

86.0317

86.2434

35

74.6897

73.6909

76.7130

70.1076

70.7937

71.5344

74.1799

82.8571

71.6402

85.9259

86.0317

85.8201

40

74.4721

69.5135

75.5277

69.7156

69.5238

75.2381

72.8042

82.2222

72.4868

85.7143

85.9259

85.9259

45

68.1427

67.8142

74.2268

69.7297

69.3122

69.6296

73.3333

81.4815

72.2751

85.5026

85.9259

85.3968

50

66.0345

67.4251

72.7948

66.2445

71.8519

71.2169

74.9206

79.8942

74.7090

85.1852

85.9259

85.6085

Table 3

Detection accuracy (%) when the signal degraded by Rician noise

Probability density

DWT

Corr

AUC

Corr + AUC

PDS

PDS + AUC

PDS + Corr

PDS + Corr + AUC

HOS

HOS + AUC

HOS + Corr

HOS + Corr + AUC

0

98.2723

97.2222

96.9856

97.8713

98.8360

96.8254

97.0370

97.9894

94.5284

94.0741

95.2381

95.6614

5

61.3593

53.4261

53.4261

52.5015

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

86.0317

86.0317

10

61.0180

50.3740

50.3740

52.5015

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

86.0317

86.0317

15

57.2389

49.7636

49.7636

49.2644

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

86.0317

86.0317

20

57.1446

49.6110

49.6110

49.2644

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

86.0317

86.0317

25

57.1446

49.6110

49.6110

48.6170

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

86.0317

86.0317

30

57.1409

49.6110

49.6110

48.6170

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

86.0317

86.0317

35

57.1409

49.6110

49.6110

48.6170

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

86.0317

86.0317

40

57.1409

49.6110

49.6110

48.6170

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

86.0317

86.0317

45

57.1409

49.6110

49.6110

48.6170

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

76.7196

86.0317

50

57.1409

49.6110

49.6110

48.6170

86.0317

86.0317

86.0317

86.0317

86.0317

76.8254

76.7196

86.0317

Table 2 illustrates detection accuracy versus noise variance of column signals that are contaminated with Rayleigh noise. The results illustrate that the HOS incorporated with AUC, Corr or (Corr + AUC) hybrid feature results in higher detection accuracies than HOS feature especially, at high noise variance. Also the PDS feature results in acceptable detection accuracy at high noise variance. The PDS performance also, can be improved by incorporating the (AUC + Corr) which leads to higher detection accuracy with different noise variance. In this case, the HOS hybrid features beats PDS hybrid ones at high noise variance. All other features provide good results but with lower detection accuracy at high noise variance.

Table 3 shows the detection accuracies of signal column faults when the signal is degraded by Rician noise. The results indicate that PDS and HOS are not affected by this noise. However, all other features give low results with noisy signals. The PDS and HOS with and without other selected features achieve high detection accuracies.

All previous results indicate that the extracted features from HOS incorporated with Corr and AUC of distillation column signals is the best choice for detection and diagnosis of the distillation column faults. It is clear also that the PDS hybrid features give good performance at low noise and its performance is degraded slightly at higher noise. All other features can be used for this process but with slightly lower accuracy especially at high noise level. The ability of Corr to measure the similarity between signals and the ability of AUC to calculate the net area under each signal, which depends on the column signal type, make them good discriminating features when used with other features. The reason for high results of HOS is its ability to suppress additive Gaussian colored noise and the Bispectrum can also suppress non-Gaussian noises that have the symmetrical probability density function. Generally, the results indicate that the HOS combined with Corr + AUC can be used efficiently for the detection of distillation column faults, especially when the column signals are scanned at high noise condition and contaminated with different types of noise.

Conclusion

An efficient fault detection approach of distillation column malfunctions using gamma scanning are proposed and validated in this paper. This approach not only detects the column faults but also determines the type of faults and its position. A lot of features are extracted from column signals and selected such as DWT, Corr, AUC, PDS, and HOS. Also a hybrid features are used to improve the performance. These features are fed to ANN classifier for the detection and diagnoses process. The results illustrate that the utilization of HOS Bispectrum incorporated with Corr and AUC is efficient for the distillation column faults detection in the high noisy environment and with different types of noise.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Engineering DepartmentNuclear Research Center, Atomic Energy AuthorityCairoEgypt

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