Pipe network blockage detection by frequency response and genetic algorithm technique

Blockage is an important fault in pipelines. It occurs in the pipe due to the deposition of debris and minerals. Blockage interrupts the expected fluid flow and sometimes may cause damage to the pipeline. So a blockage should be detected as early as possible. Different methodologies, viz. acoustic reflectometry, vibration analysis, frequency response method (FRM), stochastic successive linear estimator, radioisotope technology, etc., are used to find faults in long-length pipelines (length >1 km), which may be simply straight or branched (Liggett & Chen 1994; Jiang et al. 1996; Scott & Yi 1999; Massari et al. 2014; Datta & Sarkar 2016). Some of these methods are very costly, whereas some of the techniques are too lengthy. Among the above methods, FRM is versatile as it can be used to locate leakage along with blockages in a pipeline. It gives accurate fault locations by investigating the peak patterns of different parameters (Lee et al. 2005). Out of several FRMs, scattered waves are used for the rough blockage detection in the pipeline with some experimental validation (Duan et al. 2014a). In water pipelines, wave perturbation analysis provides a relationship between the positions of multiple discrete blockages in the pipeline (Duan et al. 2014b). In a high-pressure water pipeline, non-uniform blockages can be detected by analysing the behaviour of transient waves (Duan et al. 2017). Another method for detecting pipeline blockages is the impedance method. This is a type of FRM that contains a long algebraic equation and works within the time domain (Wang et al. 2005; Kim 2014, 2016). In addition, the resonance method, which uses the Bragg resonance condition, is used to locate the blockage position in a pipeline (Louati & Ghidaoui 2017; Louati et al. 2017). Out of these methods, FRM using the transfer matrix method (TMM) is found to be effortless and well organized (Mpesha et al. 2001, 2002). Initially, this method is used to detect leaks in a straight pipeline. Later, for both single and branched long pipelines, the frequency response technique using TMM was used for blockage detection (Mohapatra et al. 2006; Chaudhry 2014). Therefore, in accordance with the literature, the following objectives are considered for this research:

• To apply an analytical method (TMM method) on a case study proposed by Mohapatra et al. (2006) for a long pipeline (length >1 km), and further extend it for a complex long branched pipe network to show the applicability of the model.

• To modify the above-mentioned blockage detection process for the short length branched pipeline (length <1 km) using experimentation.

• To explore the applicability of the above-mentioned process for different percentages of the blockage, viz. 10%, 20%, 30% and 40% of mean pipeline diameter.

The methodology adopted in this study to fulfil the objective of the present work is described in a flowchart (Figure 1). In this research, such a blockage detection model is considered where the blockage position is near the reservoir or source of water. The whole process is divided mainly into two parts. Initially, TMM is used to show the relationship between locations of blockages with different parameters, which is generally considered as an analytical method to locate blockages for long branched pipelines. The applicability of this method is checked for short branched pipelines in this study. Later, an experiment is carried out on two models consisting of a short branched pipeline to determine responses of different parameters like velocity and pressure with respect to time. Finally, the frequency response technique is applied on these data to find out blockage location and simultaneously the relationship between different parameters is established.

Four branched pipeline models are considered for the analysis where two models are considered for analytical analysis and another two models are considered for experimental analysis. These pipeline models are named Model 1, Model 2, Model 3 and Model 4. Model 1 and Model 2 are considered as long length branched pipelines for analytical analysis shown in Figure 2(a) and 2(b) whereas Model 3 and Model 4 are considered as short branched pipelines for experimental analysis shown in Figure 2(c) and 2(d). For Model 1, L₁₁ is the distance of the blockage shown by ‘B’ from the water tank and is taken as 400 m. Similarly, lengths of other sections are L₂₁ = 400 m, L₃₁ = 800 m, and L₄₁ = 800 m. An oscillating valve is attached at the end of the pipeline shown by ‘OV’. J₁ is the junction of the pipeline and a closed valve is shown by ‘V’. Compared to Model 1, one extra branch pipe having a dead end is taken into consideration for Model 2 to create the complex pipe network, shown in Figure 2(b). L₁₂ is the distance of the blockage from the water tank and is taken as 600 m. Similarly, lengths of other sections are L₂₂ = 200 m, L₃₂ = 400 m, L₄₂ = 400 m, L₅₂ = 400 m, and L₆₂ = 400 m. J₁ and J₂ are junctions of the pipeline and V₁ and V₂ are closed valves. For Model 1 and Model 2, mean discharge is 0.1 m³/s, mean pressure head is 50 m, length of the main pipeline is 1,600 m, and diameter of the pipeline is 0.304 m. The friction coefficient for the pipe is considered as f= 0.01 and pressure wave velocity a = 1,200 m/s.

The experiment was performed in the Fluid Mechanics and Fluid Machine Laboratory of the Department of Mechanical Engineering, IIT(ISM) Dhanbad. The description of the experimental set-up is given as follows.

The experimental set-up for investigation of steady and unsteady analysis of flows is composed of (1) water tank, (2) pump, (3) mild steel (MS) pipe, (4) pressure reducing valve (PRV), (5) pressure sensor, (6) flow sensor, (7) globe valve, (8) ball valve, (9) non-return valve (NRV), (10) by-pass valve, (11) strainer, and (12) control panel. A schematic isometric view of the set-up with detailed description and position of nodes, sensors and pipe segments is shown in Figure 3. Using the above set-up, experiments are performed on Model 3 and Model 4. Length of the main pipeline for Model 3 is 8 m and for Model 4 it is 9.29 m.

In Model 3, V9, V11, V14, V17 and V18 (of Figure 3) are closed fully in order to disconnect the network from the other part of the set-up and to resemble a branch pipe network as shown in Figure 2(c) where L₁₃ is the distance of the blockage from the water tank, and is taken as 0.93 m. J_1, J₂ and J₃ are the junctions. The oscillating valve is shown by OV. Lengths of other sections are L₂₃ = 1.17 m, L₃₃ = 1.90 m, L₄₃ = 2.00 m, L₅₃ = 2.00 m, L₆₃ = 0.86 m, L₇₃ = 0.40 m, and L₈₃ = 1.67 m. Mean discharge is measured as 0.0018 m³/s.

In Model 4, V3, V5, V12 and V13 (of Figure 3) are closed in order to disconnect the network from the other part of the set-up and to resemble a branch pipe network as shown in Figure 2(d) where L₁₄ is the distance of the blockage from the water tank. The magnitude of L₁₄ is considered as 1.16 m. J_1, J₂, J₃ and J₄ are the junctions. The oscillating valve is shown by OV. Lengths of other sections are L₂₄ = 6.14 m, L₃₄ = 1.63 m, L₄₄ = 0.36 m, L₅₄ = 0.304 m, L₆₄ = 0.86 m, L₇₄ = 0.304 m, L₈₄ = 0.279 m, L₉₄ = 1.143 m, and L₁₀₄ = 0.56 m. Mean discharge through the pipeline is measured as 0.0016 m³/s.

V14 and V7 are the end valves used in Model 3 and Model 4 for creating oscillatory flow in the pipeline. The diameter of the pipeline is 0.08 m, and the length of the main pipeline for Model 3 is 8 m and for Model 4 it is 9.29 m. During the experiment, artificial blockages of approximately 10%, 20%, 30% and 40% of mean diameter are created. Manual oscillation having a frequency of 1 Hz (valve closing time is 1 second) is performed by end valves. The time domain data are collected and are converted to frequency domain by discrete Fourier transformation (DFT). Number of peaks from the frequency diagram by DFT are further used for the calculation of the blockage location in the pipeline (Jenkins & Desai 1986).

A genetic algorithm (GA) is a type of optimization algorithm that can find the optimal solution for a computational problem and minimizes or maximizes a particular function. This algorithm works similarly to the biological process of reproduction and natural selection to solve for the ‘fittest’ solutions (Azamathulla et al. 2008; Park et al. 2012; Fallah et al. 2013). In this paper, a GA is applied to estimate the value of ‘C’ (Equation (8)) based on experimental data, which was primarily processed by the frequency response technique in order to find ⁠.

Sensitivity analysis (SA) identifies the most influential variable in a model; that is, the change of which input variable will affect the output most for a model. Generally, two types of SA are performed: (i) deterministic approach and (ii) probabilistic approach. In deterministic SA (Loucks & Van Beek 2017), one input parameter is varied at a time while the others remain unchanged. This analysis uses different charts (tornado chart and spider chart) to show the sensitivity of the input variables. During this analysis, a range of input values and base values needs to be defined, upon which the analysis is to be carried out.

During the analysis of the pipeline, pressure frequency response and peak pressure frequency response diagrams are obtained. The number of peaks are shown in the PPFRD. The maximum frequency for both models is set as 50. For Model 1, the number of peaks obtained from the frequency response diagram (FRD) is 6 (Figure 4(a)). The blockage location for the corresponding peak is 400 m.

For Model 2, the number of peaks obtained from the FRD is 9 (Figure 4(b)). Blockage location for the corresponding peak is 600 m. For Model 2, the frequency range is the same as for Model 1.

Experiments were conducted on the two models. Manual oscillations having a frequency of 1 Hz were developed periodically by using end valves. Figure 4(c) shows a sample of the PFRD for Model 3 and Figure 4(d) shows a sample of the PFRD for Model 4 in 10% blockage condition. Here the number of peaks that cross the threshold line shown in Figure 4(c) and 4(d) are considered for the calculation. The number of peaks above the threshold value obtained from experiment under different operating conditions for Model 3 and Model 4 is shown in Table 1. It is observed that the number of peaks changes when the experiment is conducted under different line pressures and for greater head loss in the pipeline. Henceforth, GA is applied towards exploring the relationship between different parameters.

The GA optimizes different parameters such as ⁠, ⁠, ⁠, ⁠, and mentioned in Equation (9). Table 2 shows optimum values of blockage parameters for different blockage percentages in the pipeline. The optimum values of parameters are found after several trial runs in the GA. is the objective function (Equation (10)) of the parameters ⁠, ⁠, ⁠, ⁠, and ⁠. The objective function is basically the MSE error calculated between the actual blockage location and computed blockage location ⁠.

It is found that the minimum percentage error for a blockage location obtained for a pipeline having 10% blockage using Equation (12) is 1.9% whereas for a pipeline having 20%, 30% and 40% blockage it is 8.1%, 10.3%, and 4.4%. The value of varies a little, viz. 2.178, 2.185, 2.181, 2.162, corresponding to 10%, 20%, 30% and 40% blockage respectively. Other parameter values (⁠⁠, ⁠, ⁠, and ) obtained through the GA for different percentages of blockage vary very little. It is observed that the number of oscillations created manually has no effect on the calculation of blockage detection where it is used to carry out more accurate analysis of signals to obtain precise results. Also, velocity and pressure in the pipeline have negligible effect on blockage detection. Most importantly, the square root of the number of peaks above the threshold value is to be considered while the frequency value is obtained by DFT for short branched pipelines for minimum MSE value.

In this research, deterministic and variance based approaches are used to show the sensitivity of input variables on the output of blockage detection results shown in Equations (12)–(15) for Model 3 and Model 4 under different percentages of blockage conditions. Here, it is observed that input variables, viz. velocity of water through pipeline (v), pressure (P), length of main pipeline (L) and number of peaks ⁠, influence the detection of the location of the blockage in the pipeline. However, this exercise is carried out for different percentages of blockage. Here, ranges of data (i.e. minimum and maximum) and base value (average) are considered for analysis. Percentage of changes for different input values for 10% blockage condition and corresponding output values are shown by a tornado chart (Figure 5(a)) and spider chart (Figure 5(b)). The tornado chart indicates the comparison between the relative importance of input variables and the spider chart shows the dependency of the model's output on input variables by implementing the same percentage changes for each input variable. In this research, it is observed that the spider curve representing the number of peaks ⁠, is steeper than that for other variables. This means is an important variable for the detection of blockage in the pipeline.

In the variance based approach for the different samples of data, standard deviations and mean values are calculated. Finally, sensitivity indices (S_i) of input variables for different percentages of blockage conditions are shown in Table 2 and sensitivity indices of input variables for 10% blockage condition is shown in Figure 5(c). It is found (Table 2) that total sensitivity indices (S_i) capture approximately 98% of total variance for all blockage conditions. This means only 2% of the variation is due to non-linear effects. It is also observed that the number of peaks is most influential.

In this study, an objective is set to determine the position of a blockage in the pipeline network system. For this purpose, an FRD is used. The FRD is generated through both analytical and experimental analysis. Analytical analysis is carried out for a long pipeline (length >1 km) through two models, viz. Model 1 and Model 2, using the TMM, where the blockage location is estimated using a function of the straight length of the pipeline, and frequency and number of peaks above a threshold value (i.e. 85% of the peak pressure). During this analysis, the following observations were made:

• (i)

  With the increase in distance of blockage from the reservoir, the number of peaks generated corresponding to the oscillations made at the end node of the network also increases in the peak pressure frequency diagram.

• (ii)

  For a blockage having a fixed location, if inlet pressure head is increased, the number of peaks above the threshold value also increases in the PPFRD.

• (iii)

  The same method, when applied for the short pipeline (length <1 km), especially in a branched pipeline, with the same proposed relationship, is found to give inconsistent results.

Therefore the relationship is proposed to be modified in this study, where frequency data is obtained from measurement. In this process, a number of experiments have been carried out on an experimental set-up of a pipe network. Almost 150 sets of such data are considered for the analysis. A GA is used to obtain optimized values of different parameters towards modifying the blockage detection equation for the short branched pipeline by minimizing the summation of errors between the actual blockage location (in the set-up, which is known) and calculated blockage location by varying the above parameter values. In this analysis, the percentage of blockage is not considered as a parameter in the GA analysis, as in practical cases, since the location is unknown, measuring blockage percentage in the blockage area is difficult. However, an equation is developed for different blockage percentages. The following observations are made from this analysis:

• (i)

  Results show four distinct equations, viz. Equations (12)–(15) are obtained for blockage location corresponding to 10%, 20%, 30% and 40% blockage in pipeline with the help of the GA for the short length branched pipeline (length <1 km) within selected pressure limits (1.5–2.1 bar).

• (ii)

  In general, in the above-mentioned equations, the common aspects are: unlike the long length pipeline, for the short length branched pipe network, location of blockage is proportional to the square root of the number of peaks obtained from the FRD. Therefore, the influence of the number of peaks on detecting the blockage location is decreased.

• (iii)

  The possible reasons for this relationship may be that in a short branched pipeline, responses of other parameters are influencing the relationship, and lots of noise is present in the signal of the short length and short diameter pipeline, having highly turbulent flow, where the presence of bubbles is also greater compared to long pipelines.

• (iv)

  Furthermore, as manual operation is carried out for the creation of oscillations within a very close proximity to the placement of the pressure transducer and end node, pressure signals are noisy.

• (v)

  It is found that the location is independent of the number of oscillations created by the end valve. However, it is also observed during the experiment and FRD analysis that if pressure data is picked from the dataset having multiple numbers of oscillations (>6) and considered for analysis of FRD, it gives a very accurate result. The possible reason for this may be that after such oscillations, responses of the system became stable.

• (vi)

  Further, the above-mentioned results show that fluid velocity and line pressure have an effect on location of blockage; however, it is negligible. The possible reason for this may be the presence of lots of bends and valves within a very close proximity.

• (vii)

  From the results (Table 2), it is also observed for a pipeline having 10% blockage that the value of the coefficient in the empirical Equation (12) is 2.178, which differs from the value of the coefficient in Equation (8) for long length branched pipelines, i.e. 2.08.

• (viii)

  For 20% blockage, the value of the coefficient in Equation (13) is 2.185. Similarly, for 30% blockage and 40% blockage in Equations (14) and (15) the values are 2.181 and 2.162. Other parameter values (⁠⁠, ⁠, ⁠, and ) vary very little for different blockage conditions.

• (ix)

  Therefore it can be concluded that variation of percentage of blockage doesn't create a big impact on the detection process of blockage location in short branched pipelines and any one equation can be chosen for the detection of blockage in the pipe.

• (x)

  However, the percentage of error for blockage location using Equation (12) considering 10% blockage in the pipe is 1.9%, which is the minimum among other blockage conditions and the error percentage corresponding to the 30% blockage percentage gives the maximum error value of 10.3%. Therefore, Equation (12) can be used satisfactorily for finding the blockage location in the pipeline.

The authors gratefully acknowledge the Authority of Indian Institute of Technology (ISM), Dhanbad for providing the experimental facility through the project [FRS (71)/2013-14/MECH]. The authors would like to thank Dr Sachin Kumar Singh for his valuable suggestions towards processing of the pressure fluctuation data.