3.3.2. Error and Uncertainty

Uncertainties associated with the model have various sources which may be grouped as follows:


1. Measurement error: This is the error caused by imperfect measuring equipment and/or human observation errors. There are some inherent variations resulting from the method of observation. The image processing method used for measuring the specimen's crack length based on the high-resolution photography with the close-up lens carried some measurement errors due to difficulties in finding the crack tip in images.

Some methods were applied to reduce the crack length measurement error. If the measurement value is known to be constant from one measurement to another and if the measurement can be made several times, information about the uncertainty of the measuring method can be obtained. In this case, this type of uncertainty can be reduced through averaging. It was attempted in this research to reduce the measurement uncertainty using the measurement data produced by two different individual testers on each data point. Since these measurements are mutually independent the mean value of the measured crack length was used for each data point.

2. Modeling error: Besides the error of crack length measurement, filtration method and insufficient data, there is an important model uncertainty that must be captured. This model uncertainty is related to the formulation of the proposed probabilistic model. There might be some other sources of uncertainty that can be considered such as the uncertainty resulting from the de-noising technique. For example, the noise reduction method may filter out some crack growth related signals and contribute to the model uncertainty. Improvement can be made by exploring alternate methods of classification of AE-related data and filtration techniques.

In Section 3.3.2.1, the AE model error is estimated, which expresses the sum of aleatory and epistemic uncertainties described above. Later in Section 3.4, the model is validated and the uncertainties are estimated.
