Using ultrasonic pulse-echo B-scan signals for estimation of time of flight

• Published in: Measurement : journal of the International Measurement Confederation 2013-11, Vol.46 (9), p.3593-3599
• Main Authors: Hoseini, Mohammad R., Zuo, Ming J., Wang, Xiaodong
• Format: Article
• Language: English
• Subjects: B-scan; Complement; Computer simulation; Cramer Rao bound; Estimators; Lower bounds; Mathematical analysis; Maximum likelihood estimators; Nondestructive testing; Time of flight estimation; Ultrasonic testing; Variance
• ISSN: 0263-2241; 1873-412X
• DOI: 10.1016/j.measurement.2013.06.014

•Investigated the accuracy of the ultrasonic time of flight (TOF) estimation.•Evaluated and showed that B-scan provides more accurate TOF estimation than A-scan.•Evaluated the accuracy using Cramer–Rao bounds on the variance of TOF estimator.•Compared parametric CRB values obtained for B-scan signals and A-scan signals.•There exist unbiased estimators which can achieve the Cramer–Rao lower bounds. Time of flight based methods are extensively used for detecting, locating and sizing faults in ultrasonic non-destructive testing and evaluation. In this paper, we investigate model-based estimation of the ultrasonic time of flight using B-scan signals. The Cramer–Rao bounds on the time of flight estimator for B-scan signals are derived and then compared to the Cramer–Rao bounds on the time of flight estimator for A-scan signals. Through this theoretical analysis, we show that the estimation based on B-scan signals significantly reduces the Cramer–Rao bound on the time of flight estimator. In addition, the resulting theoretical equation allows evaluating the improvement in the accuracy of estimating the time of flight. The theoretical lower bound is then compared to the variance of a maximum likelihood estimator which is obtained using a Monte Carlo simulation. The results show that the maximum likelihood estimator can achieve the lower bound on the variance of the time of flight estimator and hence it is an efficient estimator. This numerical result will complement the theoretical analysis by showing that the Cramer–Rao bound can be reached if a proper estimator is selected.