Mathematical model based methods for characterising defects within ultrasonic non destructive evaluation

  • Laura Cunningham

Student thesis: Doctoral Thesis


This thesis considers the inverse problem of detecting and characterising flaws within heterogeneous materials using ultrasonic phased array transducers. Many imaging techniques include subjective measurements and the aim of this thesis is to develop objective mathematical model based methods which alleviate such subjectivity. Within the first method, the Kirchhoff model is used to derive an explicit expression which relates the maximum eigenvalue from a scattering matrix to the length of a crack in a homogeneous medium. It is shown that there exists a one to one relationship between this maximum eigenvalue and the crack length. The advantage of deriving this analytical approximation is that it can then be analysed to assess the crack sizing capabilities of the method given some scattering matrices from experimental data (the inverse problem). The procedure for using this method is then demonstrated by applying it to finite element simulated data from a homogeneous medium with a 5 mm long crack inclusion, the crack length recovered using this method is 4.4 mm. A second method is then presented which exploits another feature of the scattering matrix. An analytical expression which is an approximation to the first minimum in the pulse echo response of a scattering matrix is derived from the Kirchhoff model. This approach is also illustrated by sizing a 5 mm long crack within a homogeneous medium from finite element simulated data, the crack length recovered using this method is 5.8 mm. The method is then extended to form a multi-frequency technique which enables it to be applied to finite element simulated data from a 5mm long crack inclusion in a heterogeneous medium. The method is enhanced by using a convolution method to reduce the noise prior to the multi-frequency method being used. The recovered crack length using this method once the noise has been reduced is 4 mm. Finally, a detection technique based on the first stage of a time reversal is presented, within which a detection threshold specific to steel welds is proposed. This method is applied to both finite element simulated data and experimental data. Having detected a flaw the time reversal algorithm (DORT) is then used to create images which are then compared to those obtained using the Total Focusing Method.
Date of Award6 May 2015
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsEPSRC (Engineering and Physical Sciences Research Council)
SupervisorAnthony Mulholland (Supervisor) & Matthias Langer (Supervisor)

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