# A Method of Defect Depth Estimation for Simulated Infrared Thermography Data with Deep Learning
## 1 Introduction  
Non-destructive evaluation (NDE) has emerged as an important method for the evaluation of the properties of components or systems without damaging their structure. Several state of the arts methodologies such as Pulsed Phase Thermography (PPT) [1], Principal Component Thermography (FCT) [2], Differential of Absolute Contrast (DAC) [3], Thermographic Signal Reconstruction (TSR) [4], as well as Candid Covariance Free Incremental Principal Component Thermography [5], have been implemented to process thermographic sequences and improve the defect visibility. These techniques can be beneficial for qualitative analysis of composite materials. However, to introduce a method for conducting quantitative study (defect depth estimation) with deep learning is a novel topic to be explored.  
Quantitative analysis is playing an important role in the modern industrial field of non-destructive testing (NDT). Defect characterization is one of the current topics of interest in quantitative data analysis of active thermography. In this topic, thermographic information involves extracting quantitative subsurface properties from defects such as defect depth, lateral size, thermal resistivity, from an experimental Thermal Non-destructive Testing (TNDT) dataset utilized to characterize defects. Several approaches have already been proposed to analyze the depth in the region of defects in pulsed thermography. In general, these approaches evaluate the defects depth by using the maximum thermal contrast C_max, the instant of maximum thermal contrast _Tc_max_ or artificial neural networks to analyze the depth of defects based on mathematical equations. The Peak Temperature Contrast Method [6] estimated the depth based on the characteristic time from peak contrast. The peak contrast corresponding to the maximum contrast has a proportional correlation with the square of the defect depth. [PERSON] et al. [7] proposed neural networks for defect characterization of defect depth. The resultsdemonstrated that the networks should be trained by representative and non-redundant data in order to obtain a high degree of classification accuracy.  
In this work, there is an attempt to detect the depth of defects in Carbon Fiber Reinforced Polymer (CFRP) via Gated Recurrent Units (GRUs) [8]. GRU is an updated recurrent neural network (RNN) particularly designed for time series prediction. GRU can be considered as a variation of Long Short-Term Memory (LSTM) [9]. Compared with the LSTM and RNN temporal model, the GRU has adapted a few learning parameters which could save computational expenses for training and obtained an excellent performance. According to our knowledge, this is the first time that the thermal temporal characteristic model (GRU; RNN; LSTM etc.) is used to qualify the depth of defects.  
We modeled a 3D version of CFRP specimen stimulation from COMSOL. Then, it was further tested on the systemic data by the GRU model to validate its accuracy. The remainder of this paper is structured as follows: Section 2 provides the pulsed thermography theory and conception indication, as well as the detailed characteristics of FEM simulations. Section 3 proposed a GRU model-based defects depth estimation strategy and introduces the GRU deep learning model architectures. Section 4 provides the experimental results analysis. Section 5 concludes this paper.