The new AESMART 2000 from DECI has a feature that will allow valid signals from a source to be located. The LF-HF feature of the instrument measures the time between when the high frequency channel triggers (usually on an extensional wave), and the low frequency channel triggers (on a low frequency flexure wave. Since these two waves have different velocities, the further away the source is from the transducer the larger the time interval measured between the two types of waves. The location measured is the radius of a circle with the transducer at the center. This feature can provide a unique means of doing a global survey of a structure such as a bridge. The procedure would be to set the ratio filter for only accepting crack like signals, and when such a signal is detected, read the time in microseconds from the LF-HF window to determine the distance to the source. The location can be determined by moving the transducer to two other known locations and recording signals from the same source. A string and crayon can be used to draw the circles and the intersection of the three circles near a single point determines the location. By laying out an XY coordinate system showing the transducer location in XY coordinates, the source can also be calculated. The theory for this calculation is developed next.
AE event location may be accomplished using one sensor and the LF-HF feature of the AESMART 2000 to measure the difference in arrival times of two waves from the same event that travel at different velocities. If the waves travel with velocities c1 and c2, and the signals arrive at times t1 and t2, then the distance, r, from the event to the sensor is given by the equation below.
(1) r=(LF-HF) X constant
where (LF-HF) = time difference in microseconds between the extensional and flexure wave, measured from the AESMART 2000
If an event is picked up by three sensors, the distances from the event to each of the three known sensor locations may be computed using the formula above. Equivalently, a series of events from the same location could be picked up by a single sensor moved about to three known locations. In either event, the situation is as shown in the following diagram.
The diagram and analysis which follows is based on a Cartesian coordinate system with the x,y plane the plane determined by the three sensors. If the event is in the x,y plane, and there are no errors, then the three vectors, ri, will define a point in the x,y plane. On the other hand, if there are errors due to quantization, mode conversion, etc., the location may end up outofplane. This turns out to be an advantage, because the quality of an event can be determined, at least approximately, by the distance from the point to the plane. Theoretically errors could cancel and locate the event back on the plane, but generally errors will move the location away from the plane.
Though the diagram is twodimensional, assume a third, z, dimension normal to the x,y plane of the diagram. Then, from the Pythagorean theorem,
These equations may be expanded and re-arraigned to give
where r2 = x2 + y2 + z2 is the distance from the event to the origin.
These three equations can be solved simultaneously to find x, y, and r2. In matrix notation,
Since the left side coefficient matrix is a function of sensor locations only, it can be calculated as soon as sensor locations have been determined. Furthermore, its inverse can be calculated once and for all, and the solution found by matrix multiplication:
The distance out-of-plane, z, is given by
Note that z can be real or imaginary. In either event, if z is large, the event is bogus as a result of either measurement error or calculation error.
An aluminum plate 700mm X 600mm was laid out
with a 100mm square grid with the 700mm distance forming the Y
axis and the 600mm distance forming the X axis. A SE9125-M transducer
was coupled with petroleum jelly at (300,100), and 0.3mm pencil
lead breaks were made at (300,200), (300,300), (300,400), and
(300,500) up the center of the plate. The instrument was set at
a gain of 60dB. A 100mv threshold was used for the high frequency
(HF) channel and a 200mv threshold was used for the low frequency
(LF) channel. The time in microseconds for each pencil lead break
was recorded from the LF-HF window of the AESMART 2000. An average
of three pencil lead breaks was used for each point. There was
very little scatter in the three data points, in fact several
times the same value was recorded for all three lead breaks. Figure
1 shows a graph of the results . The straight line passing through
the data yields an equation: r=((LF-HF)-8)/0.141 as shown in figure
1. Both the high frequency and low frequency channel thresholds
could be raised by a factor of 2 without effecting the data. This
threshold insensitivity is due in part to full wave rectification
of the signals and peak detection prior to threshold detection.
This eliminates phase sensitivity errors present when threshold
detecting the raw signals.
Matrix inversion and multiplication are two functions that can be accomplished by Excel. A spread sheet in Excel was set up to solve the distance equation in figure 1 and once this ® value is available and the three transducer locations are specified, xy coordinates of a source of AE signals such as breaking 0.3mm pencil leads at specific locations can be calculated by the location algorythm. Two such experiments were performed on the aluminum plate. Pencil lead breaks were made at (400,400) and (300,400) to act as AE sources. The SE9125-M transducer was placed in three positions (200,200), (200, 500), and (400,200). Note that only the center portion of the plate is being utilized for these measurements. This was done in order to prevent contamination of the first arrival signals by edge reflections. The following table gives the results of the above experiment.
POSITION CALCULATED LEAD BREAKS POSITION (400,400) (403,409) (300,400) (300,404)
The accuracy of this method is phenomenal on this well prepared aluminum plate over short distances. It is anticipated that the accuracy will be as good or better for longer distances than traditional time of flight and cross correlation methods presently being used for locating AE events.
Recent experiments with long wave guides with different end configurations led to the design of a waveguide adapter that would allow DECI Mseries and Hseries transducers to be easily exchanged for different waveguide configurations. The main body of the WGadapter is constructed from teflon and is designed to provide electrical isolation from the waveguide used, provided the transducer itself has an electrical isolation faceplate. The main body can be machined to accept any diameter waveguide up to 0.500 inch, and any transducer body diameter up to 0.850 inch. A set screw in the main body allows for securing the waveguide in the main body and a Teflon coated screw is used to adjust contact force between the transducer faceplate and the end of the waveguide. A small amount of petroleum jelly is used for couplant between transducer and waveguide. When ordering specify: transducer diameter, height, and waveguide diameter and length along with end configuration for the waveguide.