A Preliminary Fault Detection Methodology for Abnormal Distillation Column Operations Using Acoustic Signals

Abstract

The fault detection of the chemical equipment operation process is an effective means to ensure safe production. In this study, an acoustic signal processing technique and a k-nearest neighbor (k-NN) classification algorithm were combined to identify the running states of the distillation columns. This method can accurately identify various fluid flow states in distillation columns, including normal and flooding states. First, the acoustic signals were collected under normal and abnormal states in an experimental distillation column. Then, the method of dual-domain feature extraction was used to extract the features such as the energy ratio and linear prediction coefficient (LPC). Moreover, the extracted feature parameters were analyzed and compared in a general way. Finally, the k-NN model was used to classify the acoustic signals. The results show that this method had high identification accuracy and provided an important reference for further research.

1. Introduction

The distillation column is characterized by a large scale, continuity and multiple variables. It is widely used in chemical production and separation processes [1,2]. Many control parameters must be regulated in order to maintain the balance of the operation process [3,4,5,6,7]. When the operating parameters change or malfunction occurs, the distillation column loses its original balance and enters an abnormal operation state [8], which threatens the safety of the chemical production process if it is not solved in time. Therefore, it is important to develop quick fault diagnosis method of fluid flow in columns to reduce the probability of accidents [9].

At present, the monitoring methods of chemical equipment mainly include ray scanning and ultrasound techniques [10,11]. However, these methods are not the ideal choices for column operation monitoring because of their high cost of operation and restrictions on application conditions. Recently, the rapid development of processing technology has promoted the application of acoustic signal in various fields [12,13,14]. As a new technology, acoustic detection technology has been successful in the detection of chemical dynamic equipment [15,16].

Compared to the obvious mechanical acoustics of dynamic equipment, as static equipment, the distillation column has less obvious acoustics. The acoustics of fluid flows in sieve tray distillation columns are affected by numerous factors, such as the gas–liquid two phase interaction, and fluid interaction with the column wall [17,18]. These interactions are the main source of acoustics from the operation of the distillation column. Different operating states correspond to various acoustic characteristics. The feature database can be constructed by extracting acoustic features in different flow states. Based on the database, the unknown states can be recognized by a machine learning classification algorithm.

In this work, the microphone array was installed on the outer wall of the sieve tray distillation column to collect the acoustic signals of different flow states. Then, the acoustic signals were preprocessed [19] and the characteristic parameters of the acoustic signals were extracted [20]. Next, the acoustic feature database containing the flow states label was constructed. Finally, the acoustic method based on the k-NN algorithm was used to identify the fluid flow states. The acoustic method could judge the operation states, which provided a strong guarantee for the safe operation of the distillation column.

This paper is divided into six sections. Section 2 introduces the initial state and text process of the experiment and test equipment. Section 3 presents the feature extraction method of an acoustic signal. Section 4 describes the theory of the k-NN algorithm and the selection process of the k value. Section 5 shows the experimental process and analyzes the experimental data. Section 6 offers a synthesis of the objective and importance of this work.

2. Experiment and Test Device

The diameter of the distillation column is 50 mm, the number of trays is 9, the system is 15% ethanol- water solution, and the total reflux operation is carried out. The condensing capacity is sufficient for the system to achieve the apparent flooding operation by adjusting the amount of heating steam. The experimental device and acoustic measuring element are shown in Figure 1. The geometrical parameters of the sieve tray distillation columns and operational parameters are shown in

Table 1. The geometrical parameters of the sieve tray distillation columns and operational parameters.

Specification	Value
Column height	2230 mm
Type of tray	Sieve tray
Tray spacing	100 mm
Number of trays	9
Column diameter	50 mm
Diameter of sieve pore	2 mm
Opening rate	8.7%
Operation state	Total reflux
Reboiler duty	3.19 kW
Gas flow velocity	3.0–4.6 m/s
Top temperature	81.5 °C
Bottom temperature	93.4 °C

.

Acoustic signal acquisition process: Place the recording pen vertically on the outer wall of the column insulation layer. The hand-held acoustic meter should be close to the two-layer tray. When the distillation column is fully refluxed to the state of flooding, recording begins; the same position is recorded and saved many times. The acoustic signal sampling frequency is 8000, and the sample quantity includes 45 normal data and 55 abnormal data.

3. Feature Extraction of Acoustic Signal

3.1. Double-Domain Feature Extraction Method

The original acoustic signal has many characteristics. Dual-domain feature extraction is used to select suitable features for research and classification. First, the energy ratio of the acoustic signals is judged based on the time domain characteristics. Then, the sixth-order linear prediction coefficient (LPC) of the acoustic signal is obtained based on the frequency domain characteristics.

3.1.1. Analysis of Sectional Energy Ratio

This paper studied the energy ratio of an acoustic signal produced by different attenuation speeds. Since the acoustic signal is a slow-changing short-time stable signal, the energy ratio at different time periods should be different. In order to improve the total energy ratio which could not be better used for comparison, a segmented energy ratio was adopted [21]. First, the acoustic signal of the column was divided into three parts and the energy of each part was calculated. Then, the energy ratio could be obtained by comparing the total energy of the acoustic signal with the total energy of the column. The expression is as follows:

$$k_i=\frac{E_i}{E}$$

(1)

where $E$ is the total energy of the input signal. The three sections of energy are represented by $E_1$, $E_2$ and $E_3$, respectively. The energy proportion of each segment is $k_1$, $k_2$ and $k_3$.

3.1.2. LPC

LPC is a parameter model based on acoustic synthesis. The purpose of linear prediction is to predict the present or future sample values. Therefore, the current sampling value of the input signal is calculated by the relationship between the past sampling value, the current sampling value and the future sampling value [22]. In this paper, the relationship between the two was closer so that the error was also reduced to a minimum. Finally, a unique set of sixth-order linear prediction coefficients is obtained [23].

For the sampled acoustic signal $s(n)$ at a given time, the linear combination of the preceding $p$ samples can be used for prediction. The expression is as follows:

$$s(n)=a_{1}s(n-1)+a_{2}s(n-2)+\dots +a_{p}s(n-p)+u(n)$$

(2)

where $a_1$, $a_2$, …$a_p$ is the linear prediction coefficient of the previous $p$ samples, and $u(n)$ is the prediction error. Z transforms $s(n)$ to obtain $S(z)$.

$$S(z)={\displaystyle \sum _{k=1}^p{a}_k{z}^{-k}S(z)+U(z)}$$

(3)

The transfer function of the linear predictive synthetic filter system can be written as

$$H(z)=\frac{S(z)}{U(z)}=\frac{1}{1-{\displaystyle \sum _{k=1}^p{a}_k{z}^{-k}}}$$

(4)

3.2. Analysis and Comparison of Characteristic Parameters

The acoustic signals of different parts of the column were extracted; for example, the acoustic signals of the normal operation of the upper layer of the tray tower, the overflow of the upper layer and the overflow of the lower part of the tray tower were extracted, respectively. The dual-domain feature extraction method was used to judge the energy ratio of the acoustic signal from the perspective of the time domain, and then to process the feature of the acoustic signal according to the sixth-order LPC based on the frequency domain characteristics. This method can realize the feature extraction of all acoustic signals through nine feature vector parameters. The acoustic signals in different states can be distinguished according to these eigenvector parameters.

4. k-NN Algorithm

4.1. Basic Process of the k-NN Algorithm

The k-NN algorithm is a non-parametric regression classification algorithm, which means that the category of any sample can be judged by its adjacent k samples. First, the algorithm selects a feature as the similarity measure and specifies the distance rule. Next, the k adjacent samples are found by calculating the similarity between the test sample and the training set sample to form a neighborhood of the samples to be tested. Finally, the classification of the test samples is determined by the category proportion of the most training samples in the neighborhood.

In this experiment, k-NN was realized through three steps. The first step was to calculate the distance d between the acoustic signal to be measured and the acoustic signal of each sample. Specifically, the center of the acoustic signal to be measured was used to find the k neighboring points around it. The Euclidean distance between two sampling points was calculated, as shown in the equation below.

$$\mathrm{dist}(x_i,y_i)=\sqrt{{\displaystyle \sum _{i=1}^n{(x_i-y_i)}^2}}$$

(5)

where $(x_i,y_i)$ are the coordinates of its reference point. In addition, the signals are arranged in order of distance from small to large.

The second step is to arrange the signals in order of distance from the smallest to the largest. Then, the k points closest to the acoustic signal to be measured are selected as the reference points.

In the last step, the number of classes to which the k reference points belong is compared. According to the principle of maximum winning, the test samples are classified into the winning category. The adjacent points are divided into two types: normal acoustic signal and fault acoustic signal, as indicated in Equation (6).

$$C_X=\underset{j\in l}{\mathrm{argmax}}{\displaystyle \sum _{y\in X_k}I(C_y=j)}$$

(6)

$X_k$ is the k-NN including y, and C is the label. When the label of y is j, the return value is 1 and the value of $I(\cdot )$ is “true”. Otherwise, $I(\cdot )=0$ [24].

4.2. The Value of k

The k is the proximity number. The category of the acoustic signal to be measured is determined by selecting the k adjacent points.

Selection of the k value is very important. If the value of k is very small, the noise will have a great impact on the prediction results. The reduction in the k value is easy to overfit, which increases the complexity of the classification model. If the value of k is large, it is equivalent to using the acoustic signal in the larger neighborhood to predict the target point, which will increase the error.

The common method is to use the test set to estimate the classifier error rate from k = 1, repeat the process and increase k by 1 each time. The k value that produces the minimum error rate should be selected. Generally, the value of k does not exceed 20 and the upper limit is the root of N. With the increase in the data set, the value of k also increases.

4.3. K-Fold Cross-Validation Method

K-fold cross-validation was used to randomly divide data set A into k packets, one of which was used as a test set, and the remaining (k − 1) packets were used as a training set.

The specific operation process of the K-fold cross-validation method is as follows.

• Data set D is split by k packets, and the process of splitting is random.
• One of the k packets is used as the test set, and the remaining (k − 1) packets are used as the training set. The data set is divided into feature (train_ x), training set label (train_ y) and test set feature (test_ x). The k-NN model is trained by train_ x and train_ y, and then the trained model is used to predict train_ x.
• The average of k times classification rate is the real classification rate of the model (hypothesis function).

Figure 2 shows the prediction probability corresponding to different k values. We found that when the k value was 5, the maximum prediction probability was 88.2353%; therefore, we chose the k value as 5.

5. Experimental Data Analysis

5.1. Experimental Process

First, the acoustic signals obtained from the distillation column of Hebei University of Technology were used to establish a characteristic acoustic parameter database and verify the acoustic recognition method. The following steps were performed, as shown in Figure 3.

• For acoustic signals, 100 acoustic signals in two operating states (normal and flooding) were recorded, respectively.
• MATLAB was used to convert all analog signals into digital signals to achieve A/D conversion.
• The characteristic information of the acoustic signal was extracted from the time domain and frequency domain.
• The characteristic parameter data of 100 acoustic signals were divided into a training set and test set. The ratio of training set to test set was 7:3. Each group included the characteristic value of the signal and the corresponding operation state. The training set was used as the signal feature database.
• The k-NN was constructed by using the signal characteristic database of three flow states. Then, the characteristic parameters of the test set were input into the algorithm to predict the operation state of the distillation column. The precision of k-NN was calculated according to the matching degree between the predicted state and the actual state.

5.2. Experimental Result

Three kinds of acoustic signals of different parts and different operating states of the column were extracted and divided into two angles. First, from the perspective of the time domain, the energy ratio of the acoustic signal was used to judge. Then, from the perspective of the frequency domain, the acoustic signal was processed according to the sixth-order LPC. The characteristic vector parameters of the distillation column’s acoustic signal under different operating conditions are shown in

Table 2. The characteristic vector parameters of acoustic signal of tray column under different operating conditions.

Characteristic Vector Parameters	Normal Operation of the Upper Layer	Flooding of the Upper Layer	Flooding of the Lower Layer
Sectional energy ratio	0.3403	0.1252	0.5526
	0.3362	0.5126	0.2338
	0.3234	0.3622	0.2137
Sixth-order LPC	−0.0109	−0.1563	−0.2805
	−0.1616	−0.0894	−0.0781
	−0.1427	−0.0249	0.4036
	0.1167	−0.0671	0.0163
	0.0752	0.0792	0.2537
	−0.0706	−0.0881	0.1217

. The waveform of the original acoustic signal and the spectrum of linear prediction are shown in Figure 4. Figure 4a shows the waveform of the original acoustic signal and the linear prediction spectrum of the upper layer’s normal operation; Figure 4b shows the waveform of the original acoustic signal and the linear prediction spectrum of the flooding of the upper layer; Figure 4c shows the waveform of the original acoustic signal and the linear prediction spectrum of the flooding of the lower layer.

Table 2 shows that the sectional energy ratio of the acoustic of ‘Flooding of the upper layer’ increased first and then decreased, and its attenuation degree was convex. There was no large change in the section energy ratio of ‘normal operation of the upper layer’, as the section energy ratio represents the attenuation speed of the acoustic signal. The attenuation speed of the acoustic signal of the ‘normal operation of the upper layer‘ was very slow, while the section energy ratio of the ‘Flooding of the lower part’ accounted for 55.26% in the first section. Therefore, the two types of acoustic can be distinguished according to the segmented energy ratio.

The double-domain feature extraction method was analyzed taking the distillation column as an example. The nine feature vector parameters were applied to the feature extraction of the column’s acoustic signal.

5.3. Analysis of Test and Simulation Results

5.3.1. Testing of Simulation Results

Ten independent experiments were conducted on 70 types of acoustics, and the experimental results were the same. As shown in

Table 3. Prediction result of acoustic signal to be measured.

Prediction Outcomes	Normal	Abnormal
Abnormal data	5	35
Normal data	27	3

, among the 70 groups of acoustic signals to be measured, five groups of abnormal signals were wrongly judged as normal signals, three groups of normal signals were wrongly judged as abnormal signals, and the prediction results of the remaining 62 groups were correct, so the accuracy of the simulation experiment was 88.57%.

5.3.2. Error Analysis of Test Simulation Experiment Results

Three typical acoustic signals were selected from the test data set for a comparative analysis. ‘Signal a’ and ‘Signal b’ were signals when the upper layer was seriously flooded, and ‘Signal c’ was the test signal when the column was in normal operation at the same position. The time–frequency domain characteristics comparison diagram of three test signals is shown in Figure 5. Figure 5a is composed of three subgraphs showing the waveform, linear prediction and spectrum of the ‘Signal a’ original acoustic signal from left to right; Figure 5b shows the waveform, linear prediction and spectrum diagram of the ‘Signal b’ original acoustic signal; and Figure 5c shows the waveform, linear prediction and spectrum of the ‘Signal c’ original acoustic signal. The time domain characteristic parameter used in the experiment was the sectional energy ratio, and the frequency domain characteristic parameter was the sixth-order LPC. The characteristic parameters of the three test signals are shown in

Table 4. Characteristic vector of ‘Signal a’, ‘Signal b’ and ‘Signal c’.

Characteristic Vector Parameters	Signal a	Signal b	Signal c
Sectional energy ratio	0.3528	0.3511	0.3403
	0.3256	0.2978	0.3362
	0.3216	0.3511	0.3234
Sixth-order LPC	0.2286	−0.0179	−0.0109
	0.0070	−0.3010	−0.1616
	−0.1259	−0.3978	−0.1427
	0.3901	0.3375	0.1167
	0.1045	0.0704	0.0752
	0.2355	0.2038	−0.0706

. The actual experimental result shows that ‘Signal b’ was judged as flooding, which is correct; however, ‘Signal a’ was incorrectly judged to be in a normal operation state.

In Table 4, the sectional energy ratio of ’Signal a’ decreases in turn, and the gap is very small, which is highly similar to the ’Signal c’ sectional energy ratio, while the sectional energy ratio of ’Signal b’ is larger at both ends and smaller in the middle, which is the first reason for miscalculation. In Figure 5, the linear prediction spectrum of ’Signal a’ has two peaks (4.5, 1.60) (17.4, 2.69), while the linear prediction spectrum of ’Signal b’ has two peaks (3.1, 2.31) (17.1, 2.43), and the peak value of ’Signal c’ is (15.2, 1.30), which is the second reason for miscalculation. The spectrum shows that the components of ’Signal a’ were concentrated in the low frequency and high frequency parts, while ’Signal b’ was concentrated in a small number of high frequency parts, which is the third reason for miscalculation.

6. Conclusions

This paper proposed a fault detection methodology for abnormal distillation column operations using acoustic signals. The k-NN classification algorithm based on the sectional energy ratio and LPC fusion feature vector proved to have high recognition accuracy (88.57%). In addition, the feasibility of acoustic signals monitoring in static equipment operation was demonstrated.

Based on the acoustic signals of a chemical column under different operating conditions, this study mainly monitored and classified the plate tower under normal and flooding operating conditions and demonstrated the feasibility of monitoring the operating conditions of the chemical column based on acoustic signals. In addition to the flooding mentioned in this paper, the chemical column also had many abnormal operating conditions, such as liquid leakage, downcomer blockage, plate hole abnormality, entrainment of mist, etc. The accurate classification of different types of chemical column under various abnormal operating conditions will be the focus of our next research work.

In the future, acoustic signal detection technology can be widely used in the chemical equipment of operation states identification and fault diagnosis, which is of great importance for safe chemical production.