Reliability and System Safety:
Reliability and system safety are crucial aspects in the design, development, and operation of various systems, especially in the field of engineering. Reliability refers to the ability of a system or component to perform its intended function without failure for a specified period under given conditions. It is essential for minimizing downtime, ensuring user satisfaction, and maintaining operational efficiency. On the other hand, system safety involves identifying, assessing, and mitigating risks and hazards associated with a system to prevent accidents, injuries, and damage to property. Therefore, reliability and system safety are important because reliability focuses on the consistent performance of a system, while system safety emphasizes the identification and mitigation of risks and hazards to prevent accidents and ensure the well-being of users and the environment. A reliable system is less likely to experience unexpected failures that could lead to safety hazards.
There are different traditional methods available to estimate the reliability of the system, such as FORM, SORM, Subset simulation, Importance sampling etc. These methods are either approximate method (FORM, SORM: approximated by Taylor series) or take large computational time as it needs to multiple model evaluation to estimate small probability of failure which leads to infeasible for high-fidelity model. To alleviate the computational time, the data-driven machine learning algorithms such as PCE, Kriging, PCE-Kriging, SVM, ANN etc., used where surrogate models are trained with few observations and predicted for large samples set, leads to reduction in computational time. With these concepts, our group aims to form an efficient reliability-based optimization of structures. In traditional optimization, the goal is to find the best design that satisfies certain constraints. Reliability-based optimization, on the other hand, takes into account the uncertainties and variations in the system by incorporating reliability constraints. Different types of uncertainties are considered in the structure design such as uncertainties in the design variables, material properties, loading conditions, and other factors that can influence the system's performance and reliability. Various optimization algorithms are used in reliability-based optimization, such as Genetic Algorithms, Sequential Quadratic Programming, or Gradient-Based Methods.
[1] Das, S., Tesfamariam, S., Chen, Y., Qian, Z., Tan, P. and Zhou, F., 2020. Reliability-based optimization of nonlinear energy sink with negative stiffness and sliding friction. Journal of Sound and Vibration, 485, p.115560.
[2] Chakraborty, S., Das, S. and Tesfamariam, S., 2021. Robust design optimization of nonlinear energy sink under random system parameters. Probabilistic Engineering Mechanics, 65, p.103139.
[3] Das, S. and Tesfamariam, S., 2020. Optimization of SMA based damped outrigger structure under uncertainty. Engineering Structures, 222, p.111074.
[4] Das, S. and Tesfamariam, S., 2022. Multiobjective design optimization of multi-outrigger tall-timber building: Using SMA-based damper and Lagrangian model. Journal of Building Engineering, 51, p.104358.
The data-driven machine learning algorithms often do not capture the physics of the system and require many training samples to generate the predicted response surface, which may need comparatively more computational time. Therefore, our research group focuses on physics-informed deep learning for estimation of reliability of structures. It combines principles from physics-based modeling and deep learning techniques. It aims to merge physics-based models which encode domain knowledge and governing equations that describe the underlying physical processes with data-driven machine learning models. This approach is particularly useful in scenarios where data is limited, expensive, or noisy, and where leveraging existing knowledge about the underlying physical processes can enhance the learning process. With this in view, our group focuses on Physics informed deep learning-based solution of probability density evolution method (PDEM) which consists of stochastic differential equations.
[1] Das, S. and Tesfamariam, S., 2023. Reliability assessment of stochastic dynamical systems using physics informed neural network based PDEM. Reliability Engineering & System Safety, p.109849.
High-dimensional reliability analysis of structures is one of the concerns in our research group especially when considering random fields, involves assessing the reliability or probability of failure in systems characterized by a large number of uncertain parameters or random variables. Random fields introduce spatial variability into the system, making the analysis more complex. In this scenario, physics informed neural networks suffers the curse of dimensionality. With this in view, we are working on dimensional reduction using principal component analysis (PCA), sparse grid methods, generative modeling, multi-fidelity simulation (establishing a trade-off model between low and high-fidelity models) and use the physics informed deep learning on low-dimensional space. Adaptive sampling strategies, guided by Bayesian optimization or other probabilistic methods, can be employed to selectively sample the most informative points in the high-dimensional space, reducing the number of evaluations needed. High-dimensional reliability analysis often requires significant computational resources. Parallel computing can be utilized to distribute the workload and accelerate the analysis.
[1] Skandalos, K., Chakraborty, S. and Tesfamariam, S., 2022. Seismic reliability analysis using a multi-fidelity surrogate model: Example of base-isolated buildings. Structural Safety, 97, p.102222.
[2] Dey, S., Chakraborty, S. and Tesfamariam, S., 2021. Multi-fidelity approach for uncertainty quantification of buried pipeline response undergoing fault rupture displacements in sand. Computers and Geotechnics, 136, p.104197.
Derivative-free optimization (DFO) is a class of optimization algorithms that does not rely on the gradients of the objective function. Traditional optimization methods, such as gradient descent, use information about the first or higher-order derivatives of the objective function to guide the search for the optimal solution. However, in some cases, obtaining these derivatives may be difficult, expensive, or even impossible. Derivative-free optimization methods are particularly useful in situations where the objective function is non-smooth, discontinuous, noisy, or computationally expensive. Different methods are used in this group such as genetic algorithm, Nelder-Mead algorithm, pattern search, random search etc.
[1] Laguardia, R., Franchin, P. and Tesfamariam, S., 2023. Risk‐based optimization of concentrically braced tall timber buildings: Derivative free optimization algorithm. Earthquake Engineering & Structural Dynamics.
[2] Skandalos, K., Afshari, H., Hare, W. and Tesfamariam, S., 2020. Multi-objective optimization of inter-story isolated buildings using metaheuristic and derivative-free algorithms. Soil Dynamics and Earthquake Engineering, 132, p.106058.