Abstract
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.
HIGHLIGHTS
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.
INTRODUCTION
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.
METHODOLOGY
Laboratory facility and data collection
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.
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.
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.
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
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.
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.
The setting of the multi-stage layer hyperparameters in the proposed CNNs
| Stages | Convolutional layer | Pooling layer pooling size | Dropout | ||
|---|---|---|---|---|---|
| Kernels | Kernel size | Strides | |||
| Stage 1 | 20 | 20 | 10 | 2 | 0.4 |
| Stage 2 | 20 | 20 | 10 | 2 | 0.4 |
| Stage 3 | 25 | 10 | 5 | 2 | 0.4 |
| Stages | Convolutional layer | Pooling layer pooling size | Dropout | ||
|---|---|---|---|---|---|
| Kernels | Kernel size | Strides | |||
| Stage 1 | 20 | 20 | 10 | 2 | 0.4 |
| Stage 2 | 20 | 20 | 10 | 2 | 0.4 |
| Stage 3 | 25 | 10 | 5 | 2 | 0.4 |
Structure of the proposed CNNs.
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
is defined in the following equation (1) (Farah & Shahrour 2017; Jalal & Ezzedine 2019).
The binary classification confusion matrix.
. 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.
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.RESULTS AND DISCUSSION
The comparative analysis of different signals for FPI performance
The datasets for air–water two-phase flow samples
| Flow patterns | scenarios | Training or validation | Samples after preprocessing | Testing | Samples after preprocessing |
|---|---|---|---|---|---|
| Bubbly flow | 7 | 5 | 80 | 2 | 32 |
| Plug flow | 19 | 14 | 224 | 5 | 80 |
| B & S flow | 15 | 11 | 176 | 4 | 64 |
| Total | 41 | 30 | 480 | 11 | 176 |
| Flow patterns | scenarios | Training or validation | Samples after preprocessing | Testing | Samples after preprocessing |
|---|---|---|---|---|---|
| Bubbly flow | 7 | 5 | 80 | 2 | 32 |
| Plug flow | 19 | 14 | 224 | 5 | 80 |
| B & S flow | 15 | 11 | 176 | 4 | 64 |
| Total | 41 | 30 | 480 | 11 | 176 |
The diagram of flow pattern distribution under different scenarios.
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.
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.
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)).
The training set, validation set, and testing set of air–water two-phase flow samples in vibration signal fusion
| Flow patterns | Scenarios | Training or validation | Samples after preprocessing | Testing | Samples 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 patterns | Scenarios | Training or validation | Samples after preprocessing | Testing | Samples 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 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.
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.
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 overall accuracy analysis of vibration signals information fusion under the variation of sensor sampling duration. (a) Validation set; (b) testing set.
The overall accuracy analysis of vibration signals information fusion under the variation of sensor sampling duration. (a) Validation set; (b) testing set.
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.
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.
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 overall accuracy analysis of vibration signals information fusion under the variation of sensor sampling frequency. (a) Validation set; (b) testing set.
The overall accuracy analysis of vibration signals information fusion under the variation of sensor sampling frequency. (a) Validation set; (b) testing set.
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.
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.
CONCLUSIONS
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.
ACKNOWLEDGEMENTS
This work was financially supported by the National Natural Science Foundation of China through grant no. 52122901, 52079016, and 52009015 which are greatly appreciated.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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