Flow pattern identification (FPI) is crucial for evaluating air entrapment in water pipelines and ensuring the safety of pipeline operations. The presence of two-phase flow in water pipelines not only leads to pressure fluctuations but also induces pipeline vibration. However, current research has primarily focused on using pressure-related signals for FPI, and the analysis of vibration signals in FPI is rare. In this study, FPI in water pipelines is investigated based on convolutional neural networks (CNNs) using high-frequency vibration signals. The information fusion of vibration signals in FPI is newly proposed via the stacked generalization technique. The proposed method is compared with pressure signal-based FPI methods and the effect of signal sampling parameters on FPI accuracy is discussed. The results show that the performance of vibration signals (including axial or radial acceleration signals) outperforms pressure signals in both time and frequency domains. Moreover, the fusion of vibration signals shows the superior results compared to any univariate signals. The duration of sampling has a more significant impact on the results of FPI than the sampling frequency. This study provides a new way that FPI theory is applied to solve air entrapment evaluation in water pipelines.

  • The high-frequency vibration signal was proposed for flow pattern identification.

  • Vibration signals outperform pressure signals for flow pattern recognition.

  • The vibration signals fused by stacked generalization have better performance than single signals.

  • For vibration signals, sampling duration has a greater impact on the flow pattern identification performance than sampling frequency.

Multi-phase flow identification has been widely studied and applied in many fields (Roshani et al. 2017; Wiedemann et al. 2019; Wang et al. 2022). The flow patterns of two-phase flow influence heat transfer, liquid transmission, system safety, etc. (Alsaydalani 2017; Bamidele et al. 2019). Owing to air existence, the fluid flows in water pipelines are usually in the form of air–water two-phase flow. Air existence is commonly caused by the small volume of air released from supersaturated water, atmospheric entrainment through pump inlets, downstream of drop shafts, or air intake at leaky valves (Ramezani et al. 2016). The air bubbles may aggregate into air pockets at up-elbow points along an undulating profile (Ramezani et al. 2016). On account of the possible negative effects of air pocket accumulation on the safe operation of water pipelines (Pozos-Estrada et al. 2015), the air entrapment evaluation at the critical location of the pipeline system is essential. The two-phase flow pattern evolution is related to air entrapment variation. Hence, the FPI can provide a reference for air entrapment evaluation and further contribute to the safe operation of water pipelines.

Many current studies focus on the mechanistic analysis of flow pattern generation by means of experiments and numerical simulations, etc. (He et al. 2022; Wang et al. 2022; Li et al. 2023). Nevertheless, the air–water two-phase FPI methods are relatively rare and remain less developed. The air–water two-phase FPI methods can be divided into two main categories. The first category pertains to visual observation methods (Angeli & Hewitt 2000; Cheng et al. 2008), which rely on subjective judgment from the observer. The limitations of this approach are the observer's bias and the impracticality of obtaining flow pattern images in the real-world projects due to buried pipes. The other category of FPI methods is based on the analysis of fluctuating signals derived from the two-phase flow, including void fraction (Tambouratzis & Pàzsit 2010), differential pressure signals (Shaban & Tavoularis 2014), pressure signals (De Giorgi et al. 2014; Tchowa Medjiade et al. 2017), etc. However, void fraction measurement using γ-ray techniques poses safety risks due to radioactivity, and the detection instruments are expensive. In addition, the installation technology of void fraction measurement needs to intrude into the pipe and potentially disrupts the air–water two-phase flow pattern. The measurements of pressure and differential pressure signals have advantages over void fraction measurement (Liu et al. 2019). It does not necessitate intrusion into the pipe and is relatively cost-effective. However, the pressure signal is easily disturbed by the local flow in the vicinity, which can lead to an inaccurate representation of the actual flow pattern. The differential pressure signal overcomes this drawback, but differential pressure measurement requires the selection of the appropriate distance of pressure monitoring sites, which is critical and challenging to achieve accurate flow pattern identification. Therefore, there is an urgent need for a low-cost, high-precision, and user-friendly FPI method.

In recent years, with the rapid development of sensors in water supply systems, various monitoring data (e.g., video, noise, vibration signals, etc.) can be obtained. Among them, the vibration signal is obtained through the acceleration sensor, which is a non-destructive testing (NDT) technology, and it can be conveniently moved to the monitoring locations with low-cost and simple operation (Shinozuka et al. 2010). Consequently, vibration signals are widely used for anomaly diagnosis in water distribution systems, such as leak detection, and pump and valve fault diagnosis (Xu et al. 2014; Xue et al. 2020; Gonçalves et al. 2021). Nevertheless, few studies have focused on using vibration signals for air–water two-phase flow pattern identification. The experimental findings indicate that the appearance of two-phase flow in water pipelines can be characterized not only by pressure fluctuations but also by pipeline vibrations (Miwa et al. 2015; Jung et al. 2019; Vieira et al. 2021). In addition, the greater the gas content in the pipeline, the greater the difference in the vibration intensity at different locations of the pipeline. Therefore, the effectiveness of pressure and vibration signals for FPI requires further discussion.

The signal features are extracted from the collected data to characterize the air–water two-phase flow pattern, and then FPI can be regarded as a classification task. With the development of artificial intelligence in urban water management, machine learning models can effectively learn knowledge from a mass of data, and trained machine learning models can produce the classification results effectively and efficiently (Fu et al. 2022). The machine learning algorithms (e.g., support vector machine, artificial neural networks) have been applied in FPI. Haifeng et al. (2011) identified flow patterns based on empirical mode decomposition of capacitance signals and least squares support vector machine. Hu et al. (2011) employed artificial neural networks for FPI based on the Hilbert–Huang transformation of electrostatic fluctuation signals. Hence, the extraction of feature vectors would directly influence the performance of the classification models (Aneesh et al. 2015; Pestana-Viana et al. 2016). Moreover, deep learning algorithms, e.g., convolutional neural networks (CNNs), show significant advantages in automatically learning discriminative features which are addressed by the connection weights and thresholds of neurons. The automatic feature extraction of CNNs avoids the intermediate process of hand-crafted feature vector extraction and analysis (Tokozume & Harada 2017). In this paper, CNNs are adopted to realize the end-to-end FPI model, by using the vibration signal data.

The vibration signals detected by an accelerometer are typically triaxial, i.e., measuring acceleration parameters along the X, Y, and Z spatial coordinate axes. Using unidirectional acceleration sensors to identify flow patterns may result in incorrect identifying results, and therefore the fusion of information from triple-direction acceleration sensors can improve the accuracy and reliability of FPI (Cao et al. 2020; Zhou & Song 2020; Shi et al. 2021; Zhong et al. 2023). Multi-source data fusion has been investigated for classification accuracy improvement in many aspects, for example, sea ice image classification, fruit recognition in smart refrigerators, and human activity classification and fall detection (Li et al. 2017; Zhang et al. 2018; Han et al. 2021). One of the information fusion methods in machine learning is Stacked Generalization (SG), which is an ensemble method integrating several different prediction algorithms for deeper information mining and higher prediction performance (Naimi & Balzer 2018; Li et al. 2022). Using the same datasets, different information can be extracted by different classifiers. The final classes are predicted comprehensively by integrating the predictions from several base-classifiers. Hence, SG outperforms individual models in many fields (Ness et al. 2009; Javadi et al. 2011). Here, SG is combined with CNN to solve the FPI issues.

In this paper, the air–water two-phase flow pattern identification in water pipelines is investigated based on vibration signals and CNNs. Vibration signals are collected from the laboratory experiments, in which the axial acceleration signals and radial acceleration signals are recorded simultaneously by the accelerometer sensors. The signal data as inputs are mapped to the final flow patterns by the adopted CNN-based classification models. This study mainly contributes to three aspects of investigating vibration signals on air–water two-phase flow pattern characterization:

  • (1)

    The FPI accuracies of pressure signals and vibration signals are compared in both time and frequency domains.

  • (2)

    The predictions derived from axial and radial acceleration signals are fused for the FPI, by means of the SG method, to further improve the classification performance.

  • (3)

    The influence of the sampling parameters of accelerometer sensors on FPI accuracy is analyzed.

The research provides a potential guidance for FPI and air entrapment evaluation in water pipelines.

Laboratory facility and data collection

The vibration data used in this study were collected from the laboratory experiments, and the experimental facility was shown in Figure 1. There were two tanks connected by the gravity flow pipeline. The two water tanks had the same size of 1.5 × 1 × 1.6 m3. The circular supply system was powered by the pumps. The pipe was made of plexiglass material, with an inner diameter of 90 mm and a wall thickness of 10 mm. The downward inclined section of the gravity flow pipeline (i.e., targeted pipe) was monitored by the pressure and accelerometer sensors, as this section was most likely to entrap and accumulate air pockets.
Figure 1

The schematic diagram of the laboratory experimental facility. (1) water tank; (2) pump; (3) ultrasonic flowmeter; (4) electric ball valve (EBV); (5) pneumatic butterfly valve; (6) manual ball valve; (7) water tank at high position; (8) gas rotameter; (9) air compressor; (10) accelerometer sensor; (11) data acquisition instrument; (12) computer.

Figure 1

The schematic diagram of the laboratory experimental facility. (1) water tank; (2) pump; (3) ultrasonic flowmeter; (4) electric ball valve (EBV); (5) pneumatic butterfly valve; (6) manual ball valve; (7) water tank at high position; (8) gas rotameter; (9) air compressor; (10) accelerometer sensor; (11) data acquisition instrument; (12) computer.

Close modal

In the laboratory experiments, water velocity and air flow rate of the two-phase flow were controlled by the opening degree of the electric ball valves (ODEBVs) and the outlet pressure of the air compressor, respectively. To ensure stable flow conditions in the air–water two-phase flow scenarios, the ODEBVs were adjusted to regulate the water velocity, and the water level in the tanks was maintained at 1 m. The orthogonal design of the combined air flow rates and water velocities provided 49 scenarios. Seven water velocities (as shown in Table 1) and seven air flow rates ranging from 0 to 3.0 m3/h were tested in parallel for each scenario, and each experiment was conducted three times. The accelerometer sensor was used to collect axial and radial acceleration signals simultaneously, with a sampling frequency of 1 kHz and a sampling duration of 20 s. Note that the axial acceleration signals were collected along the direction of water flow in the gravity flow pipeline, while the radial acceleration signals were measured along the horizontal line perpendicular to the water flow direction.

Table 1

The water velocity adjustments and the corresponding opening degree of the electric ball valves (ODEBVs)

ODEBV in the gravity flow pipeline (%)ODEVB in the pressurized flow pipeline (%)Water velocity (m/s)
55.4 33.5 1.9 
45.1 29 1.7 
39.9 28.3 1.5 
34.3 24.4 1.3 
30.4 21.5 1.1 
26 18.7 0.9 
21.5 16 0.7 
ODEBV in the gravity flow pipeline (%)ODEVB in the pressurized flow pipeline (%)Water velocity (m/s)
55.4 33.5 1.9 
45.1 29 1.7 
39.9 28.3 1.5 
34.3 24.4 1.3 
30.4 21.5 1.1 
26 18.7 0.9 
21.5 16 0.7 

Signal data preprocessing

In the 49 scenarios of air–water two-phase flow, 7 scenarios are the air flow rate of 0 m3/h which was identified as single-phase flow (i.e., water flow), while the remaining 42 scenarios were identified according to the criteria in Liu et al. (2019). The flow patterns observed in the downward-sloping pipelines were classified into four categories: bubbly flow, plug flow, blow-back flow, and stratified flow (Pothof & Clemens 2010, 2011). Considering that the number of stratified flow scenarios was the least, both blow-back and stratified flows (short for B&S flow) represented the severe air entrapment states. Similarly, single-phase flow and bubbly flow were regarded as normal and safe flow patterns.

The experimental results of 49 scenarios were extended by the sample amplification technique for CNNs training and testing. The individual sample was produced by slicing 5-s signal data. The start points between two consecutive samples had 1-s intervals. As a result, a scenario containing 20-s signal data can produce 16 samples. Hence, a total of 2,352 samples were generated for the 147 scenarios, which were derived from 49 scenarios conducted three times repeatedly. The detailed description of the sample amplification technique was introduced by Liu et al. (2019).

CNNs used for flow pattern identification

CNNs are used to establish an end-to-end air–water two-phase FPI model. The FPI model based on the univariate signal is shown in Figure 2(a), in which the input end is the signal data series and the output end comprises the respective predicted probabilities of three flow patterns (i.e., B&S flow, plug flow, and bubbly flow). The flow pattern with the largest probability value is selected as the final flow pattern prediction. The signal data with the high sampling frequency can be analyzed by using time and frequency domain methods (Too et al. 2017), thus resulting in two forms of signal data series used as FPI model inputs. In the experiments, the raw signals are collected in the form of time series, while time-domain data are transformed into frequency series by the fast Fourier transform (FFT) algorithm.
Figure 2

The schematic diagram of the FPI model in water pipelines based on CNNs. (a) Model establishment based on univariate signals. (b) Model establishment based on multivariate signals fusion.

Figure 2

The schematic diagram of the FPI model in water pipelines based on CNNs. (a) Model establishment based on univariate signals. (b) Model establishment based on multivariate signals fusion.

Close modal
In Figure 2(a), CNNs consist of convolutional layers, pooling layers, and fully connected (FC) layers. The three-stage convolution process is adopted. The details of the structure and hyperparameters are provided in Figure 3 and Table 2, respectively. The dropout layer with a ratio of 0.4 is used to prevent neural networks from overfitting (Srivastava et al. 2014; Liang & Liu 2015; Ha et al. 2019). The FC and Softmax layers contain five and three neurons, respectively. The activation function for the CNN layers is ReLU, while the Softmax layer uses the Softmax function.
Table 2

The setting of the multi-stage layer hyperparameters in the proposed CNNs

StagesConvolutional layer
Pooling layer pooling sizeDropout
KernelsKernel sizeStrides
Stage 1 20 20 10 0.4 
Stage 2 20 20 10 0.4 
Stage 3 25 10 0.4 
StagesConvolutional layer
Pooling layer pooling sizeDropout
KernelsKernel sizeStrides
Stage 1 20 20 10 0.4 
Stage 2 20 20 10 0.4 
Stage 3 25 10 0.4 
Figure 3

Structure of the proposed CNNs.

Figure 3

Structure of the proposed CNNs.

Close modal

In addition, the SG is introduced to assess the efficacy of multivariate signal information fusion on FPI performance. The SG model is a hierarchical model that improves classification performance through a combination of base-classifiers and a meta-classifier (Healey et al. 2018). The base-classifiers receive external data (i.e., signal data series), while the meta-classifier outputs the final predictions. As shown in Figure 2(b), the model comprises two CNNs that serve as the base-classifiers and another FC layer is used as the meta-classifier. The two CNNs input two kinds of signals (i.e., axial and radial acceleration signals), respectively, and their results (i.e., the predicted probabilities of flow patterns) are input to the FC layer. The FC layer outputs the three probabilities corresponding to the predictions of three flow patterns, in which the largest one is considered to be the final flow pattern category. The SG model is trained to adjust CNN hyperparameters, i.e., weights and thresholds of neurons.

Confusion matrix analysis

The identification of air–water two-phase flow pattern is a multi-classification problem, involving the prediction of three distinct flow patterns. In order to analyze the performance of the classifier for each flow pattern, the confusion matrix analysis is employed in this paper. The classical confusion matrix of binary classification is introduced for example. In Figure 4, when a sample is to be predicted, there are four possible behaviors for the classifier: true positive (TP), false negative (FN), false positive (FP), true negative (TN) (Perelman et al. 2012; Farah & Shahrour 2017; Luque et al. 2019). Therefore, in the binary classification problem, the overall accuracy is defined in the following equation (1) (Farah & Shahrour 2017; Jalal & Ezzedine 2019).
formula
(1)
Figure 4

The binary classification confusion matrix.

Figure 4

The binary classification confusion matrix.

Close modal
The larger the proportion of TP and TN, the higher the . For the ternary classification problem in this paper, nine possible behaviors are derived from the CNN-based FPI model. The elements in the confusion matrix are represented by: (1) direct representation in which the number of samples in different model prediction behaviors is counted directly; and (2) normalized representation in which the matrix elements are normalized on the basis of the former direct representation, and each value is therefore scaled between 0 and 100%, as shown in the following equation.
formula
(2)
where represents the element in which i and j denote the observed flow pattern and the predicted flow pattern, respectively. represents the number of samples with the observed flow pattern i, predicted to be flow pattern j. refers to the total number of samples with the real flow pattern i. n is equal to 3, as there are three kinds of flow patterns to be predicted (i.e., bubbly flow, plug flow, blow-back & stratified flow). Since the number of samples of each flow pattern is not equal, the normalized representation is employed in this study.

The comparative analysis of different signals for FPI performance

The study examines the prediction performance of CNNs based on different input data, including pressure signals and vibration signals (axial or radial acceleration), in both time and frequency domains. The pressure signal data utilized in this study are obtained from the experiments. As shown in Figure 5, 41 air–water two-phase flow scenarios are generated, with water velocity and air flow rate ranging from 0.7 to 1.9 m/s and 0.5 to 3.0 m3/s, respectively. However, a B&S flow scenario with water velocity and air flow rate of 0.7 m/s and 2.0 m3/h, respectively, is excluded due to missing pressure signals. In Table 3, 480 samples from 30 scenarios are divided into training and validation sets while 176 samples from the remaining 11 scenarios (circles in red in Figure 5) are used for testing. The CNNs model for the univariate signals shown in Figure 2(a) is used for the FPI. The CNNs are trained for 500 epochs and evaluated using the validation and testing sets.
Table 3

The datasets for air–water two-phase flow samples

Flow patternsscenariosTraining or validationSamples after preprocessingTestingSamples after preprocessing
Bubbly flow 80 32 
Plug flow 19 14 224 80 
B & S flow 15 11 176 64 
Total 41 30 480 11 176 
Flow patternsscenariosTraining or validationSamples after preprocessingTestingSamples after preprocessing
Bubbly flow 80 32 
Plug flow 19 14 224 80 
B & S flow 15 11 176 64 
Total 41 30 480 11 176 
Figure 5

The diagram of flow pattern distribution under different scenarios.

Figure 5

The diagram of flow pattern distribution under different scenarios.

Close modal
The prediction results of CNNs based on different types of signals are shown in Figure 6. The results in time series are depicted in Figures 6(a), 6(c) and 6(e), while the results in frequency series are shown in Figures 6(b), 6(d) and 6(f). During the training process, both axial and radial acceleration signals demonstrate accuracy rates exceeding 95% after sufficient training epochs, whereas the model trained with pressure signals achieves an accuracy below 75%. During the validation and testing process, the best validation and testing accuracies of pressure signals are about 89 and 84%, respectively, while the accuracies of the model with the axial and radial acceleration signals exceed 90% within the given training epochs. Generally, both the axial and radial acceleration signals outperform pressure signals in both the time and frequency domains. This is because acceleration signals exhibit greater sensitivity in characterizing pipeline flow patterns, primarily due to their ability to detect minute amplitude fluctuations. In contrast, pressure signals can be influenced by the state of the flowing fluid within the pipeline, which may lead to pressure signal variations not solely attributed to two-phase flow dynamics. Especially, the only results of the CNNs trained by time-domain pressure signals fail to characterize the air–water two-phase flow patterns. This limitation could potentially be attributed to the necessity for a more extensive dataset when a CNN is trained by using time-domain pressure signals. Moreover, the training, validation, and testing accuracies derived from three types of signals in frequency series are greater than those in time series. In other words, the performance of FPI models with frequency series inputs is superior to that of time series. This observation suggests that the frequency domain representations allow the model to effectively capture distinct frequency components within the signals, facilitating the extraction of critical features related to the FPI.
Figure 6

The accuracy results of different signals for flow pattern identification. (a) Pressure signals time series; (b) pressure signals frequency series; (c) axial acceleration time series; (d) axial acceleration frequency series; (e) radial acceleration time series; (f) radial acceleration frequency series.

Figure 6

The accuracy results of different signals for flow pattern identification. (a) Pressure signals time series; (b) pressure signals frequency series; (c) axial acceleration time series; (d) axial acceleration frequency series; (e) radial acceleration time series; (f) radial acceleration frequency series.

Close modal

Vibration signals fusion for FPI

Considering that each type of vibration signal may have an individual merit in extracting information of two-phase flows, the fusion of the two signals using the SG approach is investigated to further improve the FPI performance. The scenarios of 49 are simulated by the laboratory experiments, in which 1,728 samples from 36 scenarios are divided into the training and validation sets, as shown in Table 4, and 624 samples from the remaining 13 scenarios are used for testing the FPI model (see Figure 2(b)).

Table 4

The training set, validation set, and testing set of air–water two-phase flow samples in vibration signal fusion

Flow patternsScenariosTraining or validationSamples after preprocessingTestingSamples after preprocessing
Single-phase 7 × 3 5 × 3 240 2 × 3 96 
Bubbly flow 7 × 3 5 × 3 240 2 × 3 96 
Plug flow 19 × 3 14 × 3 672 5 × 3 240 
B & S flow 16 × 3 12 × 3 576 4 × 3 192 
Total 49 × 3 36 × 3 1,728 13 × 3 624 
Flow patternsScenariosTraining or validationSamples after preprocessingTestingSamples after preprocessing
Single-phase 7 × 3 5 × 3 240 2 × 3 96 
Bubbly flow 7 × 3 5 × 3 240 2 × 3 96 
Plug flow 19 × 3 14 × 3 672 5 × 3 240 
B & S flow 16 × 3 12 × 3 576 4 × 3 192 
Total 49 × 3 36 × 3 1,728 13 × 3 624 

The classification results based on vibration signal fusion are shown in Figure 7. The yellow, blue, and gray lines represent the results of the FPI model based on axial acceleration signals, radial acceleration signals, and the information fusion, respectively. Figure 7 shows that the results of vibration signal fusion are better than any univariate signals and in particular the accuracy in the validation and testing. The performance improvement of the time-domain series (see Figures 7(a) and 7(c)) is more significant than that of the frequency domain series (see Figures 7(b) and 7(d)). The possible reason is that the univariate signals depicted in the frequency domain have already performed well in FPI based on the trained CNNs, which restrains the further improvement compared to the signals depicted in the time domain. Therefore, the proposed information fusion approach is effective to improve the FPI performance.
Figure 7

The results of vibration signals information fusion for flow pattern identification. (a) Time series of the validation set; (b) frequency series of the validation set; (c) time series of the testing set; (d) frequency series of the testing set.

Figure 7

The results of vibration signals information fusion for flow pattern identification. (a) Time series of the validation set; (b) frequency series of the validation set; (c) time series of the testing set; (d) frequency series of the testing set.

Close modal

The influence of sampling parameters of the accelerometer sensor

The influences of sampling parameters, e.g., sampling duration and frequency, are analyzed based on the CNN models with vibration signal information fusion in the form of frequency series. After the sample building up mentioned in Section 3.2, the sampling duration and frequency of the samples are 5 s and 1,024 Hz, respectively.

Sampling duration

In order to analyze the influence of the sampling duration on the FPI of air–water two-phase flow in water pipelines, the two new datasets (the sampling duration of 1 and 3 s, respectively) are used to compare with the original datasets (sampling duration of 5 s). The two new datasets are created by intercepting the first 1 and 3 s data points of each sample time series from the original datasets. Hence, for the datasets with different sampling durations, the number of training, validation and testing samples, and the labels of the samples (i.e., air–water two-phase flow patterns) remain consistent with the original datasets.

The performance of the CNN model using three datasets with different sampling durations is shown in Figure 8. It shows that the longer sampling duration results in the higher accuracy of FPI in water pipelines. The main reason may be that the signals recorded by the accelerometer sensor with shorter sampling duration tend to contain the significant noise interference, which may have a negative effect on the flow pattern characterization. The performance of the FPI model becomes stable after 100 training epochs. Therefore, the results with 200 epochs are selected for analysis. The confusion matrices in Figure 9 illustrate the improvement of the FPI model for each flow pattern with an increase in sampling duration. The elements in each confusion matrix represent the corresponding behavior probabilities of the FPI model predictions. The darker blue colors indicate higher probabilities. It can be seen that the identification accuracy of the B&S flow is improved most significantly when the sampling duration is increased from 1 to 3 s, while the greatest increase in the accuracy of plug flow is shown when the sampling duration is increased from 3 to 5 s. In addition, the bubbly flow has the best identification performance compared to the other two flow patterns, regardless of variations in sampling duration. It shows that a reasonable increase in the sampling time to improve the model performance should be considered in practice. These findings are beneficial for effectively detecting two-phase flow in pipeline systems.
Figure 8

The overall accuracy analysis of vibration signals information fusion under the variation of sensor sampling duration. (a) Validation set; (b) testing set.

Figure 8

The overall accuracy analysis of vibration signals information fusion under the variation of sensor sampling duration. (a) Validation set; (b) testing set.

Close modal
Figure 9

The confusion matrix analysis of vibration signal information fusion under the variation of accelerometer sensor sampling duration. (a) Sampling duration: 1 s; (b) sampling duration: 3 s; (c) sampling duration: 5 s.

Figure 9

The confusion matrix analysis of vibration signal information fusion under the variation of accelerometer sensor sampling duration. (a) Sampling duration: 1 s; (b) sampling duration: 3 s; (c) sampling duration: 5 s.

Close modal

Sampling frequency

In order to analyze the influence of the sampling frequency on the FPI of air–water two-phase flow in water pipelines, the two new datasets (sampling frequency of 256 and 512 Hz, respectively) are used to compare with the original datasets (sampling frequency of 1,024 Hz). The two new datasets are created by intercepting the first 25 and 50% data points of each sample frequency series from the original datasets. Hence, for the datasets with different sampling frequency, the number of training, validation, and testing samples, and the labels of the samples remain consistent with the original datasets.

The performance of the FPI model using three datasets with different sampling frequencies is shown in Figure 10. It shows that the validation accuracies derived from the three sampling frequencies are almost consistent. And the accuracy in the testing dataset with the sampling frequency of 1,024 Hz shows only a small advantage over that with the other two sampling frequencies, as shown in Figure 10(b). Therefore, the sampling frequency may not be a sensitive parameter for air–water two-phase flow pattern identification in water pipelines. Furthermore, the confusion matrices under three sampling frequencies are analyzed based on the FPI model within the 200 training epochs, as shown in Figure 11. The identification accuracy of bubbly flow is superior to plug flow and B&S flow. It shows that we can reduce the cost due to data communication by not using an excessive sampling frequency during data acquisition.
Figure 10

The overall accuracy analysis of vibration signals information fusion under the variation of sensor sampling frequency. (a) Validation set; (b) testing set.

Figure 10

The overall accuracy analysis of vibration signals information fusion under the variation of sensor sampling frequency. (a) Validation set; (b) testing set.

Close modal
Figure 11

The confusion matrix analysis of vibration signals information fusion under the variation of accelerometer sensor sampling frequency. (a) Sampling frequency: 256 Hz; (b) sampling frequency: 512 Hz; (c) sampling frequency: 1,024 Hz.

Figure 11

The confusion matrix analysis of vibration signals information fusion under the variation of accelerometer sensor sampling frequency. (a) Sampling frequency: 256 Hz; (b) sampling frequency: 512 Hz; (c) sampling frequency: 1,024 Hz.

Close modal

The new method of air–water two-phase flow pattern identification (FPI) is investigated based on vibration signals and CNNs. Vibration signals (including axial and radial acceleration signals) are collected by the accelerometer sensor in the laboratory experiments. The discriminative features are implicitly extracted by the CNNs from the given raw data, which avoids the process of hand-crafted feature design. The main conclusions are drawn as follows.

  • (1)

    The vibration signal is the first attempt at FPI in this study, which is compared to the traditional input (i.e., pressure signals) based on the CNNs. The new finding is that the performance of vibration signals is better than pressure signals in terms of the input data series in both time domain and frequency domain. The signal data in the form of frequency domain achieve the better accuracy of air–water two-phase FPI.

  • (2)

    The axial- and radial-vibration signals are fused for the FPI prediction by means of the SG technique. With respect to the FPI accuracy, the fusion of vibration signals shows a certain superiority to any univariate signals. Hence, the information fusion approach proposed in this paper is effective for the FPI performance improvement. Moreover, the performance improvement of the signal time series is more significant than that of the signal frequency series.

  • (3)

    The influences of the accelerometer sensor sampling parameters on the FPI performance are analyzed. The accuracies of FPI in water pipelines improve with the increase in sampling duration. However, the influence of the variation of sampling frequency is not significant. Bubbly flow has the best identification accuracy based on the confusion matrix analysis under various parameterization conditions.

The limitation of this study is that the signals collected in the laboratory experiments show the effectiveness of the FPI model; however, the conclusions need to be further verified by the data collected from the real water supply systems. Meanwhile, more scenarios of the practical engineering such as different pipeline materials and structural parameters should be considered for a more comprehensive understanding of the effects of different factors on vibration signals and flow patterns. To enhance the comprehensiveness of the study, increasing the number of sensors along the pipeline can help identify changes in flow patterns more effectively. Additionally, this paper exclusively focuses on the application of pressure and acceleration signals in CNNs, and these findings should be validated when the models are extended to other classification problems. In future studies, the effectiveness of acceleration signals in FPI should be investigated by a variety of signal processing techniques and machine learning methods.

This work was financially supported by the National Natural Science Foundation of China through grant no. 52122901, 52079016, and 52009015 which are greatly appreciated.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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