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This thesis suggests a formulation for updating physically meaningful parameters in analytical finite element(FE) models using scanning laser Doppler vibrometer(SLDV) dynamic response data. The update formulation is demonstrated in several computer simulations. The formulation is the result of incorporating an analytical FE model into an experimental model. The experimental model efficiently utilizes SLDV data to fully exploit the instrument's capability to automatically make measurements at many locations. The data in the experimental model is posed in a manner consistent with an analytical FE model's representation for harmonic response, simplifying comparison between the two. The experimental model, which uses finite element shape functions as a basis for a least squares fit to the data, can be solved to give a velocity field based only on that data. The function resulting from inserting the analytical model into the experimental model is an expression of the prediction error of the FE model as compared to the test data. This function is minimized using a quasi-Newton optimization routine, reducing the error and resulting in an updated model. Computer simulations of the update algorithm indicate that: 1. Analytically supplied derivatives and variable scaling are required by the optimization routine to consistently converge, 2. The percentage error of updated parameters falls within two standard deviations of the data's percentage error, 3. Error in the position of the laser results in the update algorithm's failure, and, 4. Error in the parameters not included in the update will appear as error in the updated parameters' solution. / Master of Science

Structural system identification is traditionally related to the estimation of modal parameters (natural frequencies, modal damping ratios, and mode shapes). Various well known modal methods often fail to extract these parameters for heavily damped structures with high modal densities due to the high coupling between densely packed adjacent modes. The recent development of the scanning laser Doppler vibrometer (SLDV) technology that provides efficient and massive dynamic data acquisition with high spatial density makes the new non-modal system identification techniques feasible. The proposed non-modal system identification method is based on the singular value decomposition (SVD) of the spatial mobility matrices that are acquired by the SLDV technique. Data reduction, filtering, periodization, and remapping techniques are applied to the measured data in the spatial domain. Linear and polynomial singular vector interpolation and subspace rotation techniques are applied in the frequency domain for the prediction of the spatial mobility over the frequency range of interest. This non-modal method uses measured frequency response data directly and involves neither curve fitting nor modal parameter extraction. The proposed non-modal technique was applied to a commercial business jet airplane fuselage. The measured mobility data of the fuselage were reduced to a much smaller and very efficient data set that could be easily managed, stored, and retrieved for the reconstruction and/or prediction the dynamic responses of the fuselage in both frequency and spatial domains / Ph. D.

Relatively new transducers permit the measurement of dynamic response at many structure locations. Included among such transducers is the scanning laser Doppler vibrometer (LDV). A scanning LDV can measure velocity at many structure locations. An important new technique, Experimental Spatial Dynamics Modeling (ESDM), utilizes such spatially dense velocity data. ESDM models continuous, three-dimensional velocity fields using LDV velocity data. Thus, ESDM is a powerful structural dynamics analysis tool that significantly enhances the usefulness of a scanning LDV. However, heretofore, ESDM has not been experimentally evaluated. The results contained herein partially satisfy this need. Specifically, this research evaluated the ability of ESDM to reconstruct velocity response fields with large in-plane components parallel to a surface in the presence of small out-of-plane components transverse to the surface. To fulfill this objective, a test structure was developed and fabricated; the structure had certain dynamic properties which aided ESDM evaluation. Subsequently, the test structure was harmonically excited at a single frequency such that large in-plane and small out-of-plane velocity components were present on a particular surface. LDV and accelerometer data were then collected. Ultimately, velocity results were obtained from the LDV data via ESDM and the accelerometer data. Velocity results derived from the accelerometer data served as an experimental standard against which ESDM results were compared. Result comparisons clearly indicate that ESDM accurately reconstructs surface velocity fields with large in-plane and small out-of-plane components. / Master of Science

The objective of this research is to determine the longitudinal stress in rails by using the polarization of Rayleigh waves. Analytical models are developed to describe the effect of applied stress on wave speed and on the polarization of Rayleigh waves. A numerical simulation is performed to find the effect of applied stress on wave velocity and Rayleigh wave polarization. The effect of uncertainties in material properties on wave velocity and polarization of Rayleigh wave is also examined in the simulation. The experiment uses a laser Doppler vibrometer (LDV) to measure the particle velocities. The in-plane and out-of-plane velocity components are obtained from the measured particle velocities. The polarization of Rayleigh wave, which is defined as the ratio between the in-plane and out-of-plane displacements, is calculated. Furthermore, the polarization of the Rayleigh wave is considered as a measure to identify applied stress. The experiment is performed on unstressed and stressed rail specimen. Thus, Rayleigh wave polarization is obtained as a function of applied stress. The experimental results are compared with the analytical model. The result shows a good agreement with the theoretical values for unstressed rail.

This research presents improvements to the velocity field reconstruction process achieved through computer vision. The first improvement of the velocity reconstruction process is the automation of the scanning laser Doppler vibrometer (SLDV) pose procedure. This automated process results in superior estimates of the position and orientation of the SLDV. The second improvement is the refinement of the formulation for reconstruction of the velocity field. The refined formulation permits faster computation, evaluation, and interpretation of the reconstructed structural velocity field. Taken together, these new procedures significantly improve the overall velocity reconstruction process which results in better, unbiased out-of-plane velocity estimates in the presence of noise. The automation of the SLDV pose procedure is achieved through a computer vision model of the SLDV. The SLDV is modeled as a projective camera, i.e. an imager which preserves projectivities. This projective camera model permits the precise association of object features with image features. Specifically, circular features in the object space are seen by the SLDV as ellipses in the image space. In order to extract object points, the bitangents among the circular features are constructed and the bitangent points selected. The accuracy and precision of the object points are improved through the use of a calibrated object whose circular features are measured with a coordinate measuring machine. The corresponding image points are determined by constructing the bitangents among the ellipses and selecting the tangent points. Taken together, these object/image bitangent point sets are a significantly improved data set for previously developed SLDV pose algorithms. Experimental verification of this automated pose procedure includes demonstrated repeatability, independent validation of the estimated pose parameters, and comparison of the estimated poses with previous methods. The refinement of the velocity reconstruction formulation is a direct result of the computer vision viewpoint adapted for this research. By viewing the velocity data as images of the harmonically excited structure's velocity field, analytical techniques developed for holographic interferometry are extended and applied to SLDV velocity images. Specifically, the "absolute" and "relative" fringe-order methods are used to reconstruct the velocity field with the "best" set of bases. Full and partial least squares solutions with experimental velocity data are calculated. Statistical confidence bounds of the regressed velocity coefficients are analyzed and interpreted to reveal accurate out-of-plane, but poor in-plane velocity estimates. Additionally, the reconstruction process is extended to recover the velocity field of a family of surfaces in the neighborhood of the "real" surface. This refinement relaxes the need for the exact experimental geometry. Finally, the velocity reconstruction procedure is reformulated so that independent least squares solutions are obtained for the two in-plane directions and the out-of plane direction. This formulation divides the original least squares problem into three smaller problems which can be analyzed and interpreted separately. These refinements to the velocity reconstruction process significantly improve the out-of-plane velocity solution and interpretation of the regressed velocity parameters. / Ph. D.

To simplify the measurement of energy-based structural metrics, a general registration process for the scanning laser doppler vibrometer (SLDV) has been developed. Existing registration techniques, also known as pose estimation or position registration, suffer from mathematical complexity, instrument specificity, and the need for correct optimization initialization. These difficulties have been addressed through development of a general linear laser model and hybrid registration algorithm. These are applicable to any SLDV and allow the registration problem to be solved using straightforward mathematics. Additionally, the hybrid registration algorithm eliminates the need for correct optimization initialization by separating the optimization process from solution selection. The effectiveness of this approach is demonstrated through simulated application and by validation measurements performed on a specially prepared pipe. To increase understanding of the relationships between structural energy metrics and the acoustic response, the use of structural energy density (SED) in active structural acoustic control (ASAC) has also been studied. A genetic algorithm and other simulations were used to determine achievable reduction in acoustic radiation, characterize control system design, and compare SED-based control with the simpler velocity-based control. Using optimized sensor and actuator placements at optimally excited modal frequencies, attenuation of net acoustic intensity was proportional to attenuation of SED. At modal and non-modal frequencies, optimal SED-based ASAC system design is guided by establishing general symmetry between the structural disturbing force and the SED sensor and control actuator. Using fixed sensor and actuator placement, SED-based control has been found to provide superior performance to single point velocity control and very comparable performance to two-point velocity control. Its greatest strength is that it rarely causes unwanted amplifications of large amplitude when properly designed. Genetic algorithm simulations of SED-based ASAC indicated that optimal control effectiveness is obtained when sensors and actuators function in more than one role. For example, an actuator can be placed to simultaneously reduce structural vibration amplitude and reshape the response such that it radiates less efficiently. These principles can be applied to the design of any type of ASAC system.

The International Organization for Standardization (ISO) provides no vibration-based sound power measurement standard that provides Precision (Grade 1) results. Current standards that provide Precision (Grade 1) results require known acoustic environments or complex setups. This thesis details the Vibration Based Radiation Mode (VBRM) method as one approach that could potentially be used to develop a Precision (Grade 1) standard. The VBRM method uses measured surface velocities of a structure and combines them with the radiation resistance matrix to calculate sound power. In this thesis the VBRM method is used to measure the sound power of a single-plate and multiple plate system. The results are compared to sound power measurements using ISO 3741 and good alignment between the 200 Hz and 4 kHz one-third octave band is shown. It also shows that in the case of two plates separated by a distance and driven with uncorrelated sources, the contribution to sound power of each individual plate can be calculated while they are simultaneously excited. The VBRM method is then extended to account for acoustically radiating cylindrical geometries. The mathematical formulations of the radiation resistance matrix and the accompanying acoustic radiation modes of a baffled cylinder are developed. Numberical sound power calculations using the VBRM method and a boundary element method (BEM) are compared and show good alignment. Experimental surface velocity measurements of a cylinder are taken using a scanning laser Doppler vibrometer (SLDV) and the VBRM method is used to calculate the sound power of a cylinder experimentally. The results are compared to sound power measurements taken using ISO 3741.

Thesis (MScEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: This thesis investigates the feasibility of the laser Doppler vibrometer (LDV) for use in the autonomous auscultation of the human heart. As a non-contact measurement device, the LDV could become a very versatile biomedical sensor. LDV, stethoscope, piezoelectric accelerometer (PA) and electrocardiogram (ECG) signals were simultaneously recorded from 20 volunteers at Tygerberg Hospital. Of the 20 volunteers, 17 were confirmed to have cardiovascular disease. 3 patients with normal heart sounds were recorded for control data. The recorded data was successfully denoised using soft threshold wavelet denoising and ensemble empirical mode decomposition. The LDV was compared to the PA in common biomedical applications and found to be equally accurate. The heart sound cycles for each participant were segmented using a combination of ECG data and a simplicity curve. Frequency domain features were extracted from each heart cycle and input into a k-nearest neighbours classifier. It was concluded that the LDV can form part of an autonomous, non-contact auscultation system. / AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek die haalbaarheid daarvan om die laser Doppler vibrasiemeter (LDV) vir die outonome beluistering van die menslike hart te gebruik. As 'n kontaklose meettoestel kan die LDV werklik 'n veelsydige biomediese sensor word. Twintig vrywilligers by die Tygerberg Hospitaal se LDV-, stetoskoop-, piësoelektriese versnellingsmeter (PV)- en elektrokardiogram (EKG) seine is gelyktydig opgeneem. Uit die 20 vrywilligers was daar 17 bevestigde gevalle van kardiovaskulêre siektes. Die data van drie pasiënte met normale hartklanke is as kontroledata opgeneem. Geraas is suksesvol uit die opgeneemde data verwyder deur 'n kombinasie van sagtedrempelgolf en saamgestelde empiriese modus ontladingstegnieke. Die LDV was vergelyk met die PV vir algemene biomediese gebruike en daar was gevind dat dit vergelykbare akkuraatheid het. Die hartklanksiklusse van elke deelnemer is gesegmenteer deur EKG data en 'n eenvoudskromme te kombineer. Frekwensiegebiedskenmerke is uit elke hartsiklus onttrek en in 'n k-naastebuurpunt klassifiseerder ingevoer. Daar is tot die gevolgtrekking gekom dat die LDV deel van 'n outonome, kontaklose beluisteringstelsel kan uitmaak.

Laser Doppler Vibrometry (LDV) is a non-contact technique for sensing surface vibrations. Traditionally, LDV uses one or more fixed beams to measure the vibrational velocity of specific points and orientations. In order to measure an angular velocity at least two laser beams are required. Instead, this research proposes to develop a Continuous Scanning Laser Doppler Vibrometer (CSLDV) technique, based on a single laser beam continuously sweeping the area of interest using a scanning mirror. Linear scans allow the measurement of normal and angular velocity while circular scans allow the measurement of normal velocity and two angular velocities. The first part of the study analyzes the performance of rigid body models of both the short line and circular scans (< 1 cm) for measuring low broadband frequency vibrations of gel samples. This thesis focused on low frequency broadband vibration since natural human body vibrations (such as tremor or breathing) are typically below a few hundred hertz. Results for normal and angular velocity measurements are validated against conventional method of using two fixed LDVs. The second part of this research investigates the CSLDV technique for longer scans (< 5 cm). These long scans will be used to act as an array of virtual transducers at multiple points along the scanning path of the single laser beam; thus yielding similar information obtained using an array of several real fixed LDVs. A practical challenge encountered when using CSLDV is speckle noise, that is generated when a coherent light source is reflected back from an optically rough surface. The effect of speckle noise will be quantified by varying different parameters such as scan lengths, scanning frequency, target to sensor distance and the amplitude of excitation. These parameters will be optimized in order to reduce the error of vibration measurements obtained from the CSLDV. Such systems will be used to monitor multiple degrees of freedom of human skeletal muscle vibrations for elastography purposes. The forced vibration of human muscles will be analyzed using these CSLDV techniques. Overall contributions of this work include: (1) Validation of rigid body models of both short line and circular scans CSLDV for broadband low frequency linear and angular velocity measurements; (2) application to sensing natural human body vibrations (e.g., hand tremors); (3) replacement of an array of vibration sensors by a single long line scan CSLDV. (4) development of a dynamic elastography technique for skeletal muscles using CSLDV.