On choice and effect of weight matrix for response sensitivity-based damage identification with measurement and model errors

Generally, structures are susceptible to numerous types of failures that in one way or the other affects their performance. This includes structural stiffness degradation as a result of excess loading and material creep. As such, efficient systems capable of solving these problems are highly desirable. Presently, researchers have developed a preventive approach in monitoring, detection, and maintenance of structural related problems through a structural health monitoring system.

In a recently published literature, it was discovered that determination of damage locations and intensities is a significant step in identifying structural damage. This involves the use of various measured variables such as displacement, acceleration, eigenfrequencies and/or mode shapes. These measured variables are incorporated together into damage identification through the weight matrix. Different choices of the weight matrix would lead to different damage identification results and this calls for an optimal weight matrix to minimize the identification error.

To this end, Sun Yat-sen University researcher: Professor Zhong-Rong Lu, Mr. Junxian Zhou, and Dr. Li Wang from the Department of Applied of Mechanics and Engineering performed a detailed investigation of the sensitivity-based damage identification. Their main objective was to provide a guideline outlining the issues to be taken into consideration when selecting the weight matrix to be sued in structural damage identification as well as their effects. Their research work is currently published in the research journal, Mechanical Systems and Signals Processing.

In brief, the research team started by cross-examining the relationship between the optimal weight matrix and the squares expectation of the identification error. Then, they performed a theoretic derivation of the optimal weight matrix. The authors observed that when the squares identification error was minimized, the optimal weight matrix was inversely proportional to the measurement error covariance. In addition, when the model errors were taken into consideration, the optimal weight matrix was seen to depend on both model errors, measurement errors and model parameter sensitivity.

In summary, the research team successfully presented the factors to be taken into account when selecting the weight matrix for the sensitivity-based damage identification. To actualize their study, numerical tests were conducted on simply supported plates and plane beams using eigenfrequencies, acceleration and displacement. Results showed that the optimal weight matrix can indeed improve the identification accuracy under both measurement errors and non-negligible model errors. As was noteworthy, under the conventional identity weight matrix, use of more data including both eigenfrequencies and acceleration has even led to worse damage identification than use of less data containing only acceleration; the common conclusion that more data can result in better identification holds only under the optimal weight matrix. In general, the study provides vital information that will pave way for damage identification with fusion of various measured variables and non-negligible model errors.