Rahul Rathnakumar

Rahul Rathnakumar, Yutian Pang, Yongming Liu

Accurately detecting crack boundaries is crucial for reliability assessment and risk management of structures and materials, such as structural health monitoring, diagnostics, prognostics, and maintenance scheduling. Uncertainty quantification of crack detection is challenging due to various stochastic factors, such as measurement noises, signal processing, and model simplifications. A machine learning-based approach is proposed to quantify both epistemic and aleatoric uncertainties concurrently. We introduce a Bayesian Boundary-Aware Convolutional Network (B-BACN) that emphasizes uncertainty-aware boundary refinement to generate precise and reliable crack boundary detections. The proposed method employs a multi-task learning approach, where we use Monte Carlo Dropout to learn the epistemic uncertainty and a Gaussian sampling function to predict each sample's aleatoric uncertainty. Moreover, we include a boundary refinement loss to B-BACN to enhance the determination of defect boundaries. The proposed method is demonstrated with benchmark experimental results and compared with several existing methods. The experimental results illustrate the effectiveness of our proposed approach in uncertainty-aware crack boundary detection, minimizing misclassification rate, and improving model calibration capabilities.

Rahul Rathnakumar, Jiayu Huang, Hao Yan et al.

This paper addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring flexible model behavior to incorporate non-data sample information. We introduce Bayesian Entropy Neural Networks (BENN), a framework grounded in Maximum Entropy (MaxEnt) principles, designed to impose constraints on Bayesian Neural Network (BNN) predictions. BENN is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. To achieve simultaneous uncertainty quantification and constraint satisfaction, we employ the method of multipliers approach. This allows for the concurrent estimation of neural network parameters and the Lagrangian multipliers associated with the constraints. Our experiments, spanning diverse applications such as beam deflection modeling and microstructure generation, demonstrate the effectiveness of BENN. The results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.