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Guided wave technique is an efficient method for monitoring structural integrity by detecting and forecasting possible damages in distributed pipe networks. Efficient detection depends on appropriate selection of guided wave modes as well as signal processing techniques. Fourier analysis and wavelet analysis are two popular signal processing techniques that provide a flexible set of tools for solving various fundamental problems in science and engineering. In this paper, effective ways of using Fourier and Wavelet analyses on guided wave signals for detecting defects in steel pipes are discussed for different boundary conditions. This research investigates the effectiveness of Fourier transforms and Wavelet analysis in detecting defects in steel pipes. Cylindrical Guided waves are generated by piezo-electric transducers and propagated through the pipe wall boundaries in a pitch-catch system. Fourier transforms of received signals give information regarding the propagating guided wave modes which helps in detecting defects by selecting appropriate modes that are affected by the presence of defects. Continuous wavelet coefficients are found to be sensitive to defects. Several types of mother wavelet functions such as Daubechies, Symlet, and Meyer have been used for the continuous wavelet transform to investigate the most suitable wavelet function for defect detection. This research also investigates the effect of different boundary conditions on wavelet transforms for different mother wavelet functions.

Early forecasting of the degradation process caused by adverse environmental effects or mechanical damages in pipe network systems can avoid many catastrophic accidents. Now a days, the detection of the existing defects in pipes is one of the major challenges for the structural health monitoring of pipes. Propagation of cylindrical guided waves through pipes for damage detection is becoming an increasingly popular technique for pipe inspection.

Gazis [

Successful damage detection requires not only the appropriate guided wave modes but also proper use of signal processing techniques or tools. In recent years, wavelet analysis has become a popular technique for processing received signals with time-varying spectra. Many investigators have used the wavelet analysis to characterize damages in materials. Cho et al. [

Gabor transform can be used as another form of wavelet analysis. Gabor [

Murase and Kawashima [

A wavelet is described by the function

The continuous wavelet transform or CWT is given by:

In simple words, the continuous wavelet transform is defined as the sum over all time of the signal multiplied by scaled, shifted version of the wavelet function,

The primary objective of this research is to investigate how cylindrical guided waves can be used effectively to detect defects in steel pipes under different boundary conditions. In the process, it will be explored how different signal processing techniques like Fourier transform and continuous wavelet analysis (CWA) influence the detection process. Fourier transforms will endow with possible propagating modes, and CWA provides scaled coefficients affected by the presence of defects. CWA was performed using Daubechies, Symlet, and Meyer mother wavelet functions on the signals received for both defect free and defective pipes. The pipes were kept under three different boundary conditions:

(a) experimental setup (i) pipe in traction-free boundary condition, (ii) when water flows through the pipes, and (iii) pipes embedded in soil. (b) schematic diagram of the instrumental arrangement.

A specimen set, consisting of three steel pipes, were fabricated. All three pipes were 1200 mm (~4 ft) long and had 21.4 mm (13.5/16 inch) outer and 15.6 mm (10/16 inch) inner diameters. One pipe was defect-free, and the other two had mechanical defects: a gouge and a dent, that were artificially fabricated on the pipe. The gouge anomaly was fabricated by pressing the outer wall of the pipe while keeping the inner diameter unchanged by placing a rigid rod inside. The dent type anomaly was formed by pressing the outer wall, keeping the inner wall free to deform. In both types of defect, the outer walls were cold-pressed. The defect covered a complete (360°) revolution. Table

Different types of pipe defects and their dimensions.

Type | Pipe length (mm) | Diameter | Thickness (mm) | Damage dimension | ||
---|---|---|---|---|---|---|

Outer (mm) | Inner (mm) | Depth (mm) (percentage of thickness) | Width/diameter (mm) | |||

Defect-free (pipe A) | 1200 | 21.4 | 15.6 | 2.9 | — | — |

Gouge (pipe B) | 1200 | 21.4 | 15.6 | 2.9 | 1.26 (43.4%) | 5.92 |

Dent (pipe C) | 1200 | 21.4 | 15.6 | 2.9 | 1.41 (48.6%) | 5.21 |

Acoustic properties of steel.

P-wave speed (km/s) | S-wave speed (km/s) | Density (gm/cc) |
---|---|---|

5.96 | 3.26 | 7.932 |

Soil properties.

(1) coefficient of uniformity, |

(2) coefficient of concavity, |

(3) moisture content = 0.58% |

(4) compressional wave velocity, |

(5) shear wave velocity, |

Experiments were carried out in three phases for pipes with three boundary conditions. During the experiment, cylindrical guided waves were generated by piezoelectric transducers. Guided waves were generated at one end of the pipe and received at the other end by another receiving transducer in a pitch-catch configuration. The received signals were in the form of

The effect of different signal processing techniques for detecting defects in pipes was then investigated. Two separate signal processing techniques were used:

the first segment used experimental

the next segment applied continuous wavelet analysis (CWA) on experimental time series signals, using different types of mother wavelet functions to investigate which mother functions are more effective in identifying defects in pipes for all three boundary conditions.

Effects of these signal processing techniques are discussed in the following sections.

In this section, the sensitivity of pipe defects on the propagating guided wave modes is investigated under different boundary conditions. Generation of guided waves in pipes is very sensitive to the incident angle of the transducers. The first challenge is to find the appropriate incident angles for which strong guided waves can be generated. The incident angles of the transmitter were adjusted experimentally to obtain strong signals. The incident angles

Figure

(a) experimental

Figure

Figure

(a) experimental

Figure

(a) experimental

For the defect-free pipe, peaks are observed at 660, 860, 980, and 1140 kHz. Peaks at 660 and 860 kHz represent

This section investigates the effectiveness of continuous wavelet transforms (CWTs) as a signal processing tool in assessing the integrity of pipes for the three stated boundary conditions. CWT has a broad spectrum and is associated with proper choice of mother wave function and appropriate scaling. Wavelet analysis produces a time-scale view of a signal that has a scale aspect and a time aspect. Scaling a wavelet means stretching it. The smaller the scale factor, the more compressed the wavelet; while higher scales correspond to the more stretched wavelets. In this section, CWTs are performed on experimental time-series signals obtained for the 3 sets of boundary conditions. To efficiently use CWT as a signal processing tool for health monitoring, it is important to select appropriate mother function with proper scaling which will facilitate the integrity assessment. In Section

Fixing the proper scale for a mother wave function is particularly important for processing a signal. The effectiveness of a CWT depends on the right scaling, which stretches or contracts a wave function. For this investigation, signals received for the defect-free pipe in traction free boundary conditions were used. The wave functions that were used for this investigation are Daubechies (db4), Symlet (sym4), Coiflet (coif2), Gaussian (gauss1), Meyer, and Mexican Hat with scaling of 16, 64 and 256.

Figures

Comparison of experimental signals for defective and defect-free pipes using different wavelet functions with a scale of 16 for (a) db4, (b) sym4, (c) coif2, (d) gauss1, (e) Meyer, and (f) Mexican hat wavelet functions.

Comparison of experimental signals for defective and defect-free pipes using different wavelet functions with a scale of 64 for (a) db4, (b) sym4, (c) coif2, (d) gauss1, (e) Meyer, and (f) Mexican hat wavelet functions.

Comparison of experimental signals for defective and defect-free pipes using different wavelet functions with a scale of 256 for (a) db4, (b) sym4, (c) coif2, (d) gauss1, (e) Meyer, and (f) Mexican hat wavelet functions.

The effectiveness of continuous wavelet analysis (CWA) in detecting defects in pipes under different boundary conditions mentioned in the previous section (Section

Figures

(a) denoised signals for defect-free, gouged, and dent pipes. Continuous wavelet transforms for defect-free, gouged and dented pipes under traction-free boundary conditions, (b) for Daubechies (db4) function, (c) for Symlet (sym4) function, and (d) for Meyer function.

Figure

(a) denoised signals for defect-free, gouged, and dent pipes. Continuous wavelet transforms for defect-free, gouged and dented pipes when water flows through the pipes, (b) for Daubechies (db4) function, (c) for Symlet (sym4) function, and (d) for Meyer function.

The continuous wavelet transforms for the defect-free and defective pipes embedded in soil are shown in Figures

(a) denoised signals for defect-free, gouged, and dent pipes. Continuous wavelet transforms for defect-free, gouged, and dented pipes when pipes are embedded in soil, (b) for Daubechies (db4) function, (c) for Symlet (sym4) function, (d) for Meyer function.

This paper investigates the importance of signal processing techniques in guided wave application for detecting defects in pipes. Two different approaches were investigated and compared. Fourier transforms of experimental signals provide information regarding the propagating modes and help in identifying modes that are sensitive to defects. Continuous wavelet analysis is helpful in identifying defective pipes by comparing wavelet coefficients for pipes under different boundary conditions. This research also investigates which mother wave functions are more effective in distinguishing defective pipes from a defect-free pipe. Depending on the application, any or both approaches could be utilized for successful monitoring of structural integrity of pipes.

This paper was financially supported from the National Science Foundation, Grant no. CMS-9901221 and CMMI-0530991, Dr. S. C. Liu (program manager).