Applications of Discrete Wavelet Transform for Feature Extraction to Increase the Accuracy of Monitoring Systems of Liquid Petroleum Products

Abstract

This paper presents a methodology to monitor the liquid petroleum products which pass through transmission pipes. A simulation setup consisting of an X-ray tube, a detector, and a pipe was established using a Monte Carlo n-particle X-version transport code to investigate a two-by-two mixture of four different petroleum products, namely, ethylene glycol, crude oil, gasoline, and gasoil, in deferent volumetric ratios. After collecting the signals of each simulation, discrete wavelet transform (DWT) was applied as the feature extraction system. Then, the statistical feature, named the standard deviation, was calculated from the approximation of the fifth level, and the details of the second to fifth level provide appropriate inputs for neural network training. Three multilayer perceptron neural networks were utilized to predict the volume ratio of three types of petroleum products, and the volume ratio of the fourth product could easily be obtained from the results of the three presented networks. Finally, a root mean square error of less than 1.77 was obtained in predicting the volume ratio, which was much more accurate than in previous research. This high accuracy was due to the use of DWT for feature extraction.

1. Introduction

In the petrochemical industry, poly-pipelines are commonly used to transport oil or its derivatives to distribution centers. Using one pipeline to transport different petroleum fluids is very cost-effective, but the existence of problems, such as combinations of various petroleum fluids, shows the importance of developing a non-invasive method in controlling and detecting the interference region. For this reason, many types of research have been conducted, which are briefly reviewed. Salgado et al. developed a petrochemical product density detection system that included a Cs-137 source and a sodium iodide (NaI) detector [1]. The Monte Carlo N-Particle X-version (MCNPX) transport code was used in this study. Using an artificial neural network enabled prediction of the density of petroleum products with high accuracy, independent of fluid composition. They also performed a laboratory experiment to validate the Monte Carlo code, using a cesium source, a glass pipe, and a sodium iodide detector. Different volume percentages were simulated for both oil and water fluids. The volume percentages could be detected with an accuracy of 1% [2]. In other studies, researchers simulated two-phase [3,4,5] and three-phase [6,7,8] compositions at different volumetric percentages and different flow regimes. Various neural networks with different training algorithms, such as MLP [9,10], RBF [11,12], adaptive neuro-fuzzy inference systems [13], Jaya algorithms [14], and GMDH neural networks [15] were applied to predict volume percentages and flow regimes with high accuracy. In recent years, the use of feature extraction techniques such as time domain [16,17], frequency domain [18], and time–frequency domain [19] has been widely considered by researchers in this field. In all the above mentioned studies, the researchers presented different characteristics for distinguishing the type of flow regimes and determining the volume percentages. Sattari et al. used GMDH neural networks to recognize the type of flow regimes [20]. They simulated a structure including a Cs-137 radioisotope, a Pyrex pipe, and a NaI detector using the MCNPX transport code. They extracted the time domain characteristics of the recorded signal and considered them as neural network inputs. Estimation of volume percentages with a RMSE of less than 1.11 was the result of this investigation.

Recently, the use of X-ray tubes has been very popular with researchers because of their many benefits. The use of X-ray tubes as a source has the following advantages compared to other sources such as radioisotopes: X-ray tubes can adjust the emitted photon energy, whereas the photon emission energy is constant in radioisotopes. It should also be noted that the activity of radioisotopes decreases over time, but X-ray tubes do not follow this rule; X-ray tubes can be turned on and off. They are also easier to transport than radioisotopes. In their recent study, Roshani et al. proposed a system for monitoring fluids passing through transfer tubes [21]. Although they were able to predict the volumetric ratio of petroleum products with a MAE of less than 2.72, the use of feature extraction techniques can increase the accuracy of such systems. Much research has been conducted to measure the volume fractions of two-phase [22,23] and three-phase [24,25] flows using X-ray tubes. Researchers have claimed that the feature extraction techniques can help increase the accuracy of determining the type of flow regimes. In their study, Hosseini et al. [26] simulated a laboratory structure with an MCNP transport code in which they implemented three homogeneous, stratified, and annular regimes in different volume percentages. A cesium-137 source and a NaI detector were used in this simulation. Using the wavelet feature extraction technique combined with a neural network, they succeeded to fully recognize flow regimes and estimate volume percentages with an acceptable accuracy. In another study, Henus and colleagues implemented four flow regimes in a horizontal pipe named slug, bubble, and transitional plug–bubble flows to determine the type of flow regimes using a gamma ray absorption technique and wavelet feature extraction [27]. Further studies [28,29] have explored the applications of wavelet feature extraction in the field of radiation absorption signals.

Inspired by previous research, in this study, an attempt has been made to propose a high-precision monitoring system that can determine the volume ratio of different oil products. This article is organized as follows: first, the structure of the simulation will be explained in detail; the next section presents the discrete wavelet transform (DWT) method for extracting the received signal characteristics; in the third section, multilayer perceptron (MLP) neural networks will be discussed, and the results and accuracy of the designed networks will be shown; the last section concludes the study.

2. Simulation System

The simulation setup consisted of an X-ray tube, a pipe, and a NaI detector (Figure 1), and was performed using MCNPX [30]. A simulation of a typical industrial X-ray tube was used in this study. The real X-ray source consisted of an electron source and a tungsten target, which were mounted in an X-ray tube shield [31,32]. With the aim of reducing the simulation calculation time, a photon source inserted in the shield was regarded as a cathode–anode assembly in this investigation. The spectrum obtained from the TASMIC package [33] was also implemented to model the photon source energy. Figure 2 shows the normalized X-ray spectrum, as well as the features of X-ray peaks related to the tungsten target (Kα1, Kα2, Kβ1, and Kβ2). The circular section on the X-ray tube which was considered as the output window was 5 cm. Notably, the cylindrical form frequently shaped the X-ray tube shields, which were also made of lead or steel to prevent the emission of harmful radiation produced by X-rays.

Transmission pipes are used to transport various petroleum products, some parts of which interact with each other and are mixed together. This area is known as the interface region. In this research, four types of petroleum products—ethylene glycol, crude oil, gasoil, and gasoline—are considered as fluids passing through the pipe. By mixing all of the listed products two-by-two, six combinations were obtained. Various volume ratios from 0% to 100%, with steps of 5%, were simulated for all six different states (in this study, 118 simulations were performed in total). Data from all simulations were collected by a simulated NaI detector and used for later processing.

3. Discrete Wavelet Transform

Discrete wavelet transform (DWT) is the most commonly used method in the filtering of time–frequency [34]. The reduction of additive noises by DWT provides good resolution in the frequency and time domains. Multi-resolution analysis is enabled by the DWT method by dividing the discrete signal x(n) into low- and high-frequency components. To determine DWT, an iterative Mallat algorithm can be applied [35,36]. The low-frequency component a_j,k (approximately) and the high-frequency component d_j,k (exactly) (Figure 3) are the results of signal x(n) decomposition with multi-level filter banks:

$$a_{j,k}={\displaystyle \sum }_{l}h\left(l-2k\right)a_{j-1,m}$$

(1)

$$d_{j,k}={\displaystyle \sum }_{l}g\left(l-2k\right)a_{j-1,m}$$

(2)

where j is a parameter that affects the DWT scaling. k is related to the translation at each level of the wavelet function. l is the number of levels and is an integer scale. h(l) and g(l) are low-pass and high-pass square filters, respectively. m is utilized in the scaling function as a translation of the j scale. Daubechies, Haar, etc., are several families of wavelet functions that exist in wavelet transform. In the present study, a Daubechies 2 (db2) wavelet was selected to analyze the signals received from the scintillation detector.

The decomposition process of the signal obtained by the detector is illustrated in Figure 4. According to this figure, from the fifth stage onwards, no significant high-frequency information was obtained; thus, in this study, the signal decomposition only continued until the fifth stage. It should be noted that the details of the first stage had many fluctuations that show noisy behavior. The researchers believe that this signal is due to uncertainty problems in the MCNPX transport code. Therefore, these details were not considered for the next processing step. To provide suitable data for network inputs, the standard deviation (STD) features of a_5,1, d_5,1, d_4,1, d_3,1, and d_2,1 have been calculated. It should be noted that this statistical characteristic has been introduced in previous studies as an efficient time characteristic [16].

$$TD=\sqrt{\frac{1}{N-1}{\displaystyle \sum }_{i=1}^N{\left|x_i-\mu \right|}^2}$$

(3)

$$\mu =\frac{1}{N}{\displaystyle \sum }_{i=1}^N{x}_i$$

(4)

where $x_i$ is the primary data and N is the amount of data.

4. MLP Neural Network

In recent years, various advanced computational approaches have been applied in different fields such as chemical engineering [37,38,39,40,41,42,43,44], control and electrical engineering [45,46,47,48,49,50,51,52,53,54,55,56,57,58,59], pharmacy and medical science [60,61,62,63,64,65,66,67], industrial engineering [68,69], civil engineering [70,71,72,73], economic and business sciences, [74,75,76,77,78], mechanical engineering [79,80,81,82,83,84,85], energy engineering [86,87,88,89], computer and information technology [90,91,92,93,94,95,96,97,98,99,100,101,102], physics [103,104,105,106,107,108], mining engineering [109,110,111], petroleum engineering [112,113,114,115,116], mathematics [117,118,119,120,121,122,123,124], etc. MLP neural networks are one of the most powerful tools used in predicting, classifying, modeling, and optimizing. This network has become one of the most widely used neural networks due to the various applications for which it has been developed. This network is able to perform nonlinear mapping with high accuracy, which is what was used as the main solution in various problems. This is a feedforward network where the output is calculated directly from the input without any feedback with the backpropagation (BP) algorithm. The BP algorithm means that after determining the network’s output, first, the weights of the final layer are corrected, and then the weights of the previous layers are corrected respectively. The neuron model in the multilayer perceptron network includes a nonlinear activator function. The output of a perceptron in an MLP neural network is obtained based on Equation (6) [125,126]:

$$output=f\left({\displaystyle \sum }_{i=1}^n{x}_i{w}_i+b\right)$$

(5)

In the above equation, x represents the network inputs, w depicts the network weights, b is the bias, f is the activating function of the neurons, and n represents the number of inputs.

The perceptron implementation algorithm is the first random values assigned to weights. Perceptron is then applied to all training data. If the example is evaluated incorrectly, the values of perceptron weights are corrected. The collected data are divided into three categories: training, validation, and testing data. Training data are used to estimate network weights to create a neural network model; validation data are used to test during the training process; and test data are used to evaluate the trained network. Using these data, the ability of the designed neural network in prediction is determined. In this study, 70% of the data were used for training, 15% were allocated to the validation section, and 15% were used for network testing. In this research, to find the most optimal structure, networks with one, two, three and four layers, and with different number of neurons in each layer, have been designed, and their functions have been evaluated. MATLAB R2018b software was used to train neural networks.

5. Result and Discussion

In this study, the characteristics extracted in the previous section were considered the neural network’s inputs. Three neural networks were implemented to estimate the volume ratios of ethylene glycol, crude oil, and gasoil. By determining the volume ratio of the three mentioned products, the ratio of the fourth product, i.e., gasoline, could easily be calculated. Figure 5 and

Table 1. The specifications of the designed networks.

ANN Type	MLP
	Ethylene Glycol	Gasoil	Crude Oil
No. of input layer neurons	5	5	5
No. of 1st hidden layer neurons	12	20	16
No. of 2nd hidden layer neurons	8	10	7
No. of 3rd hidden layer neurons	4	5	3
No. of output layer neurons	1	1	1
No. of epochs	650	800	550
Activation function used for each hidden neuron	Tansig	Tansig	Tansig

show the structure of the implemented networks.

Regression and error diagrams related to training, validation, and test data can be seen in Figure 6, Figure 7 and Figure 8, presenting the accuracy of the designed networks. The most important criterion for evaluating the performance of artificial neural networks is the accuracy of prediction. Some of the most important prediction accuracy criteria calculated in this study are:

$$\mathrm{Root}\mathrm{Mean}\mathrm{Square}\mathrm{Error}\left(RMSE\right)=\frac{{{\displaystyle \sum }}_{j=1}^N{\left(e_j\right)}^2}{N}$$

(6)

$$\mathrm{Mean}\mathrm{Absolut}\mathrm{Error}\left(MAE\right)=\frac{1}{N}{\displaystyle \sum }_{j=1}^N\left|e_j\right|$$

(7)

where e is the error, y is the network output, and N represents the amount of data.

Table 2. Calculated error for the implemented networks.

	Training Data		Validation Data		Test Data
	RMSE	MAE	RMSE	MAE	RMSE	MAE
Ethylene glycol	1.42	1.28	1.76	1.54	1.49	1.29
Crude oil	1.21	1.08	1.28	1.19	1.42	1.30
Gasoil	1.49	1.07	1.73	1.54	1.60	1.41

shows the calculated errors for each of the predictor networks. The general process of determining the volume ratios of each oil product is shown in Figure 9.

6. Conclusions

In this study, the monitoring system included an X-ray tube and one NaI detector, simulated using the MCNPX transport code. After simulating the mixture of four petroleum products in different volume ratios and collecting data recorded by the detector, the DWT technique was used to extract the data features. Then, the extracted features were used to implement three MLP neural networks. It should be noted that after obtaining the volume ratio of three products, the volume ratio of the fourth product could easily be calculated. The three implemented neural networks predicted the volume ratio of ethylene glycol, crude oil, and gasoil with RMSEs of less than 1.77, 1.43, and 1.74, respectively. Although the X-ray tube, as well as radioisotopes, have been used in previous studies, applying the DWT method for feature extraction to improve the precision of this system is the most significant novelty of the current study.