In Section 3, the dynamic effects of the pipe and the sensors on the measured leak noise are described. Section 4 is devoted to the experimental work and the processing of the data, while Section 5 discusses the results. Conclusions from this work are summarised in Section 6.2.?Overview Lapatinib buy of Leak Detection using Acoustic/Vibration SignalsFigure 1 depicts a situation typically encountered in leak detection, in which a leak occurs at an unknown position in a buried water pipe.Figure 1.Schematic of buried water pipe in which sensors are positioned at access points either side of a leak.The leak generates broadband noise, which propagates along the pipe, both in the fluid and along the pipe-wall Inhibitors,Modulators,Libraries either side of the leak, to sensors that are located at convenient access points. These are often fire hydrants.

In plastic water pipes the pipe-wall and water are strongly Inhibitors,Modulators,Libraries coupled in an acoustical sense [6,7]. This means that measurements of leak noise can, in principle, be made on the pipe Inhibitors,Modulators,Libraries or associated fittings (velocity and acceleration using geophones or accelerometers), or in the water directly (acoustic pressure using hydrophones). The difference in the arrival times of the noise at the sensors (time delay) is used to determine the position of the leak and the distance of the leak from the right-hand sensor can then be determined from [9]:d2=d?cT02(1)where c is the speed of propagation of the leak noise, d is the total distance between the sensors, and T0=(d1 ? d2)/c Inhibitors,Modulators,Libraries is the time delay estimate. In many cases the wavespeed is estimated from tables, but it can be directly measured in-situ [12].

Note that it is often extremely difficult Carfilzomib to obtain an accurate estimate of the propagation of leak noise from measurements, as the estimate is highly dependent upon the signal to noise ratio. This has a profound influence on the bandwidth over which there is useful data and this has a consequent effect on the estimate of c [12].Setting the means of the two measured signals x1(t) and x2(t) to zero, the cross-correlation function is given by [15]:Rx1x2(��)=E[x1(t)x2(t+��)](2)where �� is time delay and E[ ] is the expectation operator. The value of �� that corresponds to the peak in in the cross-correlation function provides an estimate of the time delay T0. It is preferable to express the cross-correlation function in a normalized form, which has a scale of ?1 to +1.

This is called the cross-correlation coefficient and is given by:��(��)=Rx1x2(��)Rx1x1(0)Rx2x2(0)(3)where Rx1x1(0) and Rx2x2(0) are the autocorrelation functions at Positions 1 and 2 respectively useful handbook when �� = 0. The cross-correlation function Rx1x2(��), is related to the Fourier Transform of the cross-spectral density (CSD) function Sx1x2(��) by [16]:Rx1x2(��)=12�С�?��+��Sx1x2(��)ei�ئ�d��(4)where i=?1. Note that Sx1x2(��) can be written as |Sx1x2(��)|ei(��) in which |Sx1x2(��)| is the modulus and (��) is the phase between the two signals at frequency ��.