Structural health monitoring, compressive sensing, l1 minimization, vibration based shm, operational deflection shape, modeshape, damage detection


One of the key areas that have attracted attention in the construction industry today is Structural Health Monitoring, more commonly known as SHM. It is a concept developed to monitor the quality and longevity of various engineering structures. The incorporation of such a system would help to continuously track health of the structure, indicate the occurrence/presence of any damage in real time and give us an idea of the number of useful years for the same. Being a recently conceived idea, the state of the art technique in the field is straight forward - populating a given structure with sensors and extracting information from them. In this regard, instrumenting with too many sensors may be inefficient as this could lead to superfluous data that is expensive to capture and process. This research aims to explore an alternate SHM technique that optimizes the data acquisition process by eliminating the amount of redundant data that is sensed and uses this sufficient data to detect and locate the fault present in the structure. Efficient data acquisition requires a mechanism that senses just the necessary amount of data for detection and location of fault. For this reason Compressive Sensing (CS) is explored as a plausible idea. CS claims that signals can be reconstructed from what was previously believed to be incomplete information by Shannon's theorem, taking only a small amount of random and linear non - adaptive measurements. As responses of many physical systems contain a finite basis, CS exploits this feature and determines the sparse solution instead of the traditional least - squares type solution.As a first step, CS is demonstrated by successfully recovering the frequency components of a simple sinusoid. Next, the question of how CS compares with the conventional Fourier transform is analyzed. For this, recovery of temporal frequencies and signal reconstruction is performed using the same number of samples for both the approaches and the errors are compared. On the other hand, the FT error is gradually minimized to match that of CS by increasing the number of regularly placed samples. Once the advantages are established, feasibility of using CS to detect damage in a single degree of freedom system is tested under unforced and forced conditions. In the former scenario, damage is indicated when there is a change in natural frequency of vibration of the system after an impact. In the latter, the system is excited harmonically and damage is detected by a change in amplitude of the system's vibration. As systems in real world applications are predominantly multi-DOF, CS is tested on a 2-DOF system excited with a harmonic forcing. Here again, damage detection is achieved by observing the change in the amplitude of vibration of the system. In order to employ CS for detecting either a change in frequency or amplitude of vibration of a structure subjected to realistic forcing conditions, it would be prudent to explore the reconstruction of a signal which contains multiple frequencies. This is accomplished using CS on a chirp signal. Damage detection is clearly a spatio-temporal problem. Hence it is important to additionally explore the extension of CS to spatial reconstruction. For this reason, mode shape reconstruction of a beam with standard boundary conditions is performed and validated with standard/analytical results from literature. As the final step, the operation deflection shapes (ODS) are reconstructed for a simply supported beam using CS to establish that it is indeed a plausible approach for a less expensive SHM. While experimenting with the idea of spatio-temporal domain, the mode shape as well as the ODS of the given beam are examined under two conditions - undamaged and damaged. Damage in the beam is simulated as a decrease in the stiffness coefficient over a certain number of elements. Although the range of modes to be examined heavily depends on the structure in question, literature suggests that for most practical applications, lower modes are more dominant in indicating damage. For ODS on the other hand, damage is indicated by observing the shift in the recovered spatial frequencies and it is confirmed by the reconstructed response.


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Graduation Date





Das, Tuhin


Master of Science in Mechanical Engineering (M.S.M.E.)


College of Engineering and Computer Science


Mechanical and Aerospace Engineering

Degree Program

Mechanical Engineering; Mechanical Systems








Release Date

August 2014

Length of Campus-only Access


Access Status

Masters Thesis (Open Access)


Dissertations, Academic -- Engineering and Computer Science; Engineering and Computer Science -- Dissertations, Academic