Impulsivity

Mechanical stretch tests were made with the speed of (0,3-3,0) 10" m/s and with the simultaneous registration of the AE signals. Number of the AE impulses (Nl ) and AE amplitude (A) were selected as the measurable parameters of the AE. 

If the impulse response function g(x) of a system is known, the output signal y(x) of the system is given for any input signal u(x). The integral equation, which is called superposition integral. 

The function g(x) is named impulse response of the system, because it is the response to an unit pulse 5(x) applied at =0 [2]. This unit impulse 5(x), also called Dirac impulse or delta-function, is defined as... 

Eq.(2) describes an impulse with the area of 1 [1-3]. Fig. 1 (left) shows such an unit impulse S(x) and an example for an impulse response g(x) at the output of the system. 

Often an unit impulse is not available as a signal to get the impulse response function g(x). Therefore an other characteristic signal, the unit step, is be used. 

The step response function h(x) is also determined by the integral equation (1). The relationship between step response h(x) and the impulse response g(x) is represented by... 

The superposition integral (1) corresponds to a division of the input signal u(x) into a lot of Dirac impulses 5 x). which are scaled to the belonging value of the input. The output of each impulse 5fx) is known as the impulse response g(x). That means, the output y(x) is got by addition of a lot of local shifted and scaled impulse responses. 

Fig. 1 (right) shows upside an example of an input. The marked points are some of the scaled Dirac impulses. The belonging scaled impulse responses are shown downside. 

Unit impulse fucnction Unit step function Example for an input signal 5(x) f s(x)f u( ),... 

Unit impulse response Unit step response responses for input example... 

The equation system of eq.(6) can be used to find the input signal (for example a crack) corresponding to a measured output and a known impulse response of a system as well. This way gives a possibility to solve different inverse problems of the non-destructive eddy-current testing. Further developments will be shown the solving of eq.(6) by special numerical operations, like Gauss-Seidel-Method [4]. 

Chapter 4.3. discusses the explained theory for choosed examples. For several cracks the output is pre-calculated by using the impulse response and compared with measurement data. 

All described sensor probes scan an edge of the same material to get the characteristic step response of each system. The derivation of this curve (see eq.(4) ) causes the impulse responses. The measurement frequency is 100 kHz, the distance between sensor and structure 0. Chapter 4.2.1. and 4.2.2. compare several sensors and measurement methods and show the importance of the impulse response for the comparison. 

The first example presents the importance of the impulse response function for the comparison of several sensors with the same arrangement from chapter 3.1.. 

Figures Impulse responses of different coils on a material edge...

It should be a symmetrical form in the impulse response of a linear system. 

The following examples represent the importance of the impulse response for the comparison of different magnetic field sensors. For presentation in this paper only one data curve per method is selected and compared. The determined signals and the path x are related in the same way like in the previous chapter. 

Figure 7 Impulse responses of different sensor systems...

This is visible in the behaviour of the impulse responses as well (fig, 7), There the amplitude of curve (1) (gWng, )) is the highest, of curve (2) ig(L,)) the lowest, but the maxima are not located at the same place. 

The difference in widths of the impulse responses are small. Especially visible the pulse response of the inductive sensors, curves (1) and... 

For calculation the known data are the. .input signal", cracks of different widths, and the impulse response. The material of the crack model is assigned to the value 0, the air to 1. 

The determined eddy-eurrent parameter is the inductance of the eomplex impedance measured by impedance analyzer at j=100 kHz. Therefore the impulse response function from chapter 4.2.1. is used for calculation. The depth of the cracks is big in comparison to coil size. For presentation the measured and pre-calculated data are related to their maxima (in air). The path X is related to the winding diameter dy of the coil. 

Methods from the theory of LTI-systems are practicable for eddy-current material testing problems. The special role of the impulse response as a characteristic function of the system sensor-material is presented in the theory and for several examples. 

So, a comparison of different types of magnetic field sensors is possible by using the impulse response function. High amplitude and small width of this bell-formed function represent a high local resolution and a high signal-to-noise-characteristic of a sensor system. On the other hand the impulse response can be used for calculation of an unknown output. In a next step it will be shown a solution of an inverse eddy-current testing problem. 

Due to its importance the impulse-pulse response function could be named. .contrast function". A similar function called Green s function is well known from the linear boundary value problems. The signal theory, applied for LLI-systems, gives a strong possibility for the comparison of different magnet field sensor systems and for solutions of inverse 2D- and 3D-eddy-current problems. 

For the examination of the applied metallic or ceramic layer, the test object is heated up from the outside The heat applying takes place impulse-like (4ms) by xenon-flash lamps, which are mounted on a rack The surface temperature arises to approx 150 °C Due to the high temperature gradient the warmth diffuses quickly into the material An incorrect layer, e g. due to a delamiation (layer removal) obstructs the heat transfer, so that a higher temperature can be detected with an infrared camera. A complete test of a blade lasts approximatly 5 minutes. This is also done automatically by the system. In illustration 9, a typical delamination is to be recognized. 

With this testing method an evaluation is possible within shortest time, i.e. directly after the heat impulse. The high temperature difference between a delamination and sound material is affected - among other parameters - by the thickness of the layer. Other parameters are size and stage of the delamination Generally, a high surface temperature refers to a small wall thickness and/or layer separation [4],... 

Illustration 10 Wallthickness Measurement with Impulse-Video-Thermography... 

The large temperature difference of the remarkable borehole, opposite other boreholes and their environment is significant. This high temperature difference is a typical feature for a small wall thickness between borehole and blade surface. For technical reasons, precise eroding of the boreholes is difficult. Due to this, the remaining wallthickness between the boreholes and the blade surface has to be determined, in order to prevent an early failure, Siemens/Kwu developed a new method to determine the wallthickness with Impulse-Video-Thermography [5],... 

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