Dionisio Bernal is a Professor in the Civil and Environmental Engineering Department and a member of the Center for Digital Signal Processing at Northeastern University in Boston, MA. His research has focused in problems from earthquake engineering and structural dynamics as well as on vibration based techniques for system characterization and fault diagnosis. He is the recipient of the Moisseiff Award from the American Society of Civil Engineers for his work on Dynamic Instability of buildings subjected to earthquakes and of the Essigmann and Hayes awards for excellence in teaching and research, respectively, from Northeastern University. His research has had a significant impact in various areas, with the aggregate of papers on damage localization and dynamic instability receiving more than 650 and 220 citations, respectively. He is past chair of the American Society of Civil Engineers Task Group on Structural Health Monitoring and holds international faculty positions at the Harbin Institute of Technology in China and the University of Trento in Italy. He is the co-author of a McGraw-Hill textbook on the design of reinforced concrete structures, and has contributed chapters in several books on structural analysis and structural health monitoring. He has over 150 publications and has graduated 10 Ph.D students.
Civil and Environmental Engineering Department, Center for Digital Signal Processing, Northeastern University, Boston MA 02115
Restricting attention to the situation where loads are fixed in space the input identification problem factors into the following questions: 1) how many loads with independent histories are there, 2) what are the spatial distributions of these loads and 3) what are the time histories? The simplest and most common problem instance is that where the number of point loads is the same as the number of independent histories and we restrict most of the discussion to this condition. After quantifying the matter of dependency the paper shows that the number of independent histories can be determined without resorting to any structural model provided the number of inputs is smaller than the number of measurements. The paper goes on to examine localization and shows that when each history corresponds to a single point load the locations and lines of action can be ascertained without the need to solve a combinatorial problem. Examination of the posed-ness and conditioning of the inverse problem connected with the computation of the time histories illustrates the fundamental role played by wave propagation delay as well as the importance of the appropriate selection of the time discretization, given a system bandwidth.
Specifically, the paper shows that the rank deficiency that arises in the de-convolution of non-collocated input arrangements is connected with a kernel that is non-zero only over the part of the time axis that is affected by the physical delay. It is shown that when the kernel is appropriately treated time domain de-convolution follows identically in collocated and non-collocated scenarios. It is contended that with the exception of inputs of short duration de-convolution must be carried out on a sliding window and that this process is conditionally stable. The constraints that must be met to ensure stability are derived and are shown to require prediction delays that can be much larger than the lower bound imposed by wave propagation. Examination of the Cramer-Rao Lower Bound of the inputs in frequency shows that the inference model should be formulated such that the spectra of the inputs to be reconstructed, and of the realized measurement noise, are within the model bandwidth. An expression for the error in the reconstructed input as a function of the noise sequence is developed and is used to control the regularization, when regularization is needed. The paper brings attention to the fact that finite dimensional models cannot display true dead time and that failure to recognize this matter has led to algorithms that, in general, propose to violate the physical constraints. |

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