A Multi-Objective DIRECT Algorithm Towards Structural Damage Identification with Limited Dynamic Response Information

A major challenge in Structural Health Monitoring (SHM) is to accurately identify both the location and severity of damage using the dynamic response information acquired. While in theory the vibration-based and impedance-based methods may facilitate damage identification with the assistance of a credible baseline finite element model since the changes of stationary wave responses are used in these methods, the response information is generally limited and the measurements may be heterogeneous, making an inverse analysis using sensitivity matrix difficult. Aiming at fundamental advancement, in this research we cast the damage identification problem into an optimization problem where possible changes of finite element properties due to damage occurrence are treated as unknowns. We employ the multiple damage location assurance criterion (MDLAC), which characterizes the relation between measurements and predictions (under sampled elemental property changes), as the vector-form objective function. We then develop an enhanced, multi-objective version of the DIRECT approach to solve the optimization problem. The underlying idea of the multi-objective DIRECT approach is to branch and bound the unknown parametric space to converge to a set of optimal solutions. A new sampling scheme is established, which significantly increases the efficiency in minimizing the error between measurements and predictions. The enhanced DIRECT algorithm is particularly suitable to solving for unknowns that are sparse, as in practical situations structural damage affect only a small number of finite elements. A number of test cases using vibration response information are executed to demonstrate the effectiveness of the new approach

Structural Damage Identification Using Piezoelectric Impedance Measurement with Sparse Inverse Analysis

The impedance/admittance measurements of a piezoelectric transducer bonded to or embedded in a host structure can be used as damage indicator. When a credible model of the healthy structure, such as the finite element model, is available, using the impedance/admittance change information as input, it is possible to identify both the location and severity of damage. The inverse analysis, however, may be under-determined as the number of unknowns in high-frequency analysis is usually large while available input information is limited. The fundamental challenge thus is how to find a small set of solutions that cover the true damage scenario. In this research we cast the damage identification problem into a multi-objective optimization framework to tackle this challenge. With damage locations and severities as unknown variables, one of the objective functions is the difference between impedance-based model prediction in the parametric space and the actual measurements. Considering that damage occurrence generally affects only a small number of elements, we choose the sparsity of the unknown variables as another objective function, deliberately, the l0 norm. Subsequently, a multi-objective Dividing RECTangles (DIRECT) algorithm is developed to facilitate the inverse analysis where the sparsity is further emphasized by sigmoid transformation. As a deterministic technique, this approach yields results that are repeatable and conclusive. In addition, only one algorithmic parameter, the number of function evaluations, is needed. Numerical and experimental case studies demonstrate that the proposed framework is capable of obtaining high-quality damage identification solutions with limited measurement information

Data Sampling and Reasoning: Harnessing Optimization and Machine Learning for Design and System Identification

The recently rapid advancements in sensing devices and computational power have caused paradigm shift in engineering analyses: data driven and sampling-based approaches play more and more important roles. For example, with sampling-based global optimization techniques, mechanical components can be refined and redesigned; system parameters can be accurately identified. With advancements in data mining and machine learning, underlying input and output relations of complex systems can be developed to make predictions with unseen data or to expedite analytical process. In this dissertation, advanced optimization and machine learning techniques are developed and employed to multi-facet engineering tasks from system design to identification. First research task concerns a type of configuration designs, where the volume occupied components is to be minimized along with other objectives such as the length of connectivity lines. The formulation of computationally tractable optimization is difficult in practice as the objectives and constraints are usually complex. Moreover, the design optimization problems usually come with demanding constraints that are hard to satisfy, which results in the critical challenge of balancing feasibility with optimality. We develop an enhanced multi-objective simulated annealing approach, MOSA/R, to solve this problem. A versatile and efficient re-seed scheme that allows biased search while avoiding pre-mature convergence is designed in MOSA/R. Some generalization studies of the algorithm have also been carried out. In this second task, we exploit the impedance/admittance change of a piezoelectric transducer bonded to a host structure, aiming at the identification of system damage. To find a small set of solutions for such an under-determined system that indicates the true damage scenario, we cast the damage identification problem into a multi-objective optimization framework. With damage locations and severities as unknown variables, one objective function is the discrepancy between first-principal model predictions and actual measurements. The sparsity of the unknown variables is chosen as another objective function, deliberately, the l0 norm, because damage occurrence generally affects a small number of elements. A multi-objective algorithm (DIRECT) is devised to facilitate the inverse analysis where the sparsity is further emphasized by sigmoid transformation. As a deterministic technique, this approach yields repeatable and conclusive results. The third task concerns early diagnosis of gear transmission, which is challenging because gear faults occur primarily at microstructure but their effects can only be observed at a system level. The performance of a fault diagnosis system depends on the features extracted and the classifier subsequently applied. Fault-related features are conventionally identified based on domain expertise, which are system-specific. On the other hand, although deep neural networks enjoy adaptive feature extractions and inherent classifications, they require a substantial set of training data. We present a deep convolutional neural network-based transfer learning approach, which not only entertains preprocessing free adaptive feature extractions, but also requires only a small set of training data