Modal parameter estimation in the presence of non-linearities

This paper investigates the use of time-frequency techniques to assist in the estimation of power system modes which are resolvable by a Digital Fourier Transform (DFT). The limitations of linear estimation techniques in the presence of large disturbances which excite system non-linearities, particularly the swing equation non-linearity are shown. Where a nonlinearity manifests itself as time varying modal frequencies the Wigner-Ville Distribution (WVD) is used to describe the variation in modal frequencies and construct a window over which standard linear estimation techniques can be used. The error obtained even in the presence of multiple resolvable modes is better than 2%.

Quantifying axial deformations of core shear walls using modal parameters

Differential axial deformation between column elements and shear wall elements of cores increase with building height and geometric complexity. Adverse effects due to the differential axial deformation reduce building performance and life time serviceability. Quantifying axial deformations using ambient measurements from vibrating wire, external mechanical and electronic strain gauges in order to acquire adequate provisions to mitigate the adverse effects is well established method. However, these gauges require installing in or on elements to acquire continuous measurements and hence use of these gauges is uneconomical and inconvenient. This motivates to develop a method to quantify the axial deformations. This paper proposes an innovative method based on modal parameters to quantify axial deformations of shear wall elements in cores of buildings. Capabilities of the method are presented though an illustrative example.

Fourier active appearance models

Gaining invariance to camera and illumination variations has been a well investigated topic in Active Appearance Model (AAM) fitting literature. The major problem lies in the inability of the appearance parameters of the AAM to generalize to unseen conditions. An attractive approach for gaining invariance is to fit an AAM to a multiple filter response (e.g. Gabor) representation of the input image. Naively applying this concept with a traditional AAM is computationally prohibitive, especially as the number of filter responses increase. In this paper, we present a computationally efficient AAM fitting algorithm based on the Lucas-Kanade (LK) algorithm posed in the Fourier domain that affords invariance to both expression and illumination. We refer to this as a Fourier AAM (FAAM), and show that this method gives substantial improvement in person specific AAM fitting performance over traditional AAM fitting methods.

Evaluation of modal analysis techniques using physical models to detect osseointegration of implants in transfemoral amputees

Non-invasive vibration analysis has been used extensively to monitor the progression of dental implant healing and stabilization. It is now being considered as a method to monitor femoral implants in transfemoral amputees. This paper evaluates two modal analysis excitation methods and investigates their capabilities in detecting changes at the interface between the implant and the bone that occur during osseointegration. Excitation of bone-implant physical models with the electromagnetic shaker provided higher coherence values and a greater number of modes over the same frequency range when compared to the impact hammer. Differences were detected in the natural frequencies and fundamental mode shape of the model when the fit of the implant was altered in the bone. The ability to detect changes in the model dynamic properties demonstrates the potential of modal analysis in this application and warrants further investigation.

Assessment of “change in flexibility method” in structural health monitoring systems

The modern structural diagnosis process is rely on vibration characteristics to assess safer serviceability level of the structure. This paper examines the potential of change in flexibility method to use in damage detection process and two main practical constraints associated with it. The first constraint addressed in this paper is reduction in number of data acquisition points due to limited number of sensors. Results conclude that accuracy of the change in flexibility method is influenced by the number of data acquisition points/sensor locations in real structures. Secondly, the effect of higher modes on damage detection process has been studied. This addresses the difficulty of extracting higher order modal data with available sensors. Four damage indices have been presented to identify their potential of damage detection with respect to different locations and severity of damage. A simply supported beam with two degrees of freedom at each node is considered only for a single damage cases throughout the paper.

Innovative damage assessment of steel truss bridges using modal strain energy correlation

As a part of vital infrastructure and transportation network, bridge structures must function safely at all times. Bridges are designed to have a long life span. At any point in time, however, some bridges are aged. The ageing of bridge structures, given the rapidly growing demand of heavy and fast inter-city passages and continuous increase of freight transportation, would require diligence on bridge owners to ensure that the infrastructure is healthy at reasonable cost. In recent decades, a new technique, structural health monitoring (SHM), has emerged to meet this challenge. In this new engineering discipline, structural modal identification and damage detection have formed a vital component. Witnessed by an increasing number of publications is that the change in vibration characteristics is widely and deeply investigated to assess structural damage. Although a number of publications have addressed the feasibility of various methods through experimental verifications, few of them have focused on steel truss bridges. Finding a feasible vibration-based damage indicator for steel truss bridges and solving the difficulties in practical modal identification to support damage detection motivated this research project. This research was to derive an innovative method to assess structural damage in steel truss bridges. First, it proposed a new damage indicator that relies on optimising the correlation between theoretical and measured modal strain energy. The optimisation is powered by a newly proposed multilayer genetic algorithm. In addition, a selection criterion for damage-sensitive modes has been studied to achieve more efficient and accurate damage detection results. Second, in order to support the proposed damage indicator, the research studied the applications of two state-of-the-art modal identification techniques by considering some practical difficulties: the limited instrumentation, the influence of environmental noise, the difficulties in finite element model updating, and the data selection problem in the output-only modal identification methods. The numerical (by a planer truss model) and experimental (by a laboratory through truss bridge) verifications have proved the effectiveness and feasibility of the proposed damage detection scheme. The modal strain energy-based indicator was found to be sensitive to the damage in steel truss bridges with incomplete measurement. It has shown the damage indicator's potential in practical applications of steel truss bridges. Lastly, the achievement and limitation of this study, and lessons learnt from the modal analysis have been summarised.

Ability of modal analysis to detect osseointegration of implants in transfemoral amputees : a physical model study

Owing to the successful use of non-invasive vibration analysis to monitor the progression of dental implant healing and stabilization, it is now being considered as a method to monitor femoral implants in transfemoral amputees. This study uses composite femur-implant physical models to investigate the ability of modal analysis to detect changes at the interface between the implant and bone simulating those that occur during osseointegration. Using electromagnetic shaker excitation, differences were detected in the resonant frequencies and mode shapes of the model when the implant fit in the bone was altered to simulate the two interface cases considered: firm and loose fixation. The study showed that it is beneficial to examine higher resonant frequencies and their mode shapes (rather than the fundamental frequency only) when assessing fixation. The influence of the model boundary conditions on the modal parameters was also demonstrated. Further work is required to more accurately model the mechanical changes occurring at the bone-implant interface in vivo, as well as further refinement of the model boundary conditions to appropriately represent the in vivo conditions. Nevertheless, the ability to detect changes in the model dynamic properties demonstrates the potential of modal analysis in this application and warrants further investigation.

Fourier Lucas-Kanade Algorithm

In this paper we propose a framework for both gradient descent image and object alignment in the Fourier domain. Our method centers upon the classical Lucas & Kanade (LK) algorithm where we represent the source and template/model in the complex 2D Fourier domain rather than in the spatial 2D domain. We refer to our approach as the Fourier LK (FLK) algorithm. The FLK formulation is advantageous when one pre-processes the source image and template/model with a bank of filters (e.g. oriented edges, Gabor, etc.) as: (i) it can handle substantial illumination variations, (ii) the inefficient pre-processing filter bank step can be subsumed within the FLK algorithm as a sparse diagonal weighting matrix, (iii) unlike traditional LK the computational cost is invariant to the number of filters and as a result far more efficient, and (iv) this approach can be extended to the inverse compositional form of the LK algorithm where nearly all steps (including Fourier transform and filter bank pre-processing) can be pre-computed leading to an extremely efficient and robust approach to gradient descent image matching. Further, these computational savings translate to non-rigid object alignment tasks that are considered extensions of the LK algorithm such as those found in Active Appearance Models (AAMs).

Investigation of the airborne submicrometer particles emitted by dredging vessels using a plume capture method

This paper presents a method for investigating ship emissions, the plume capture and analysis system (PCAS), and its application in measuring airborne pollutant emission factors (EFs) and particle size distributions. The current investigation was conducted in situ, aboard two dredgers (Amity: a cutter suction dredger and Brisbane: a hopper suction dredger) but the PCAS is also capable of performing such measurements remotely at a distant point within the plume. EFs were measured relative to the fuel consumption using the fuel combustion derived plume CO2. All plume measurements were corrected by subtracting background concentrations sampled regularly from upwind of the stacks. Each measurement typically took 6 minutes to complete and during one day, 40 to 50 measurements were possible. The relationship between the EFs and plume sample dilution was examined to determine the plume dilution range over which the technique could deliver consistent results when measuring EFs for particle number (PN), NOx, SO2, and PM2.5 within a targeted dilution factor range of 50-1000 suitable for remote sampling. The EFs for NOx, SO2, and PM2.5 were found to be independent of dilution, for dilution factors within that range. The EF measurement for PN was corrected for coagulation losses by applying a time dependant particle loss correction to the particle number concentration data. For the Amity, the EF ranges were PN: 2.2 - 9.6 × 1015 (kg-fuel)-1; NOx: 35-72 g(NO2).(kg-fuel)-1, SO2 0.6 - 1.1 g(SO2).(kg-fuel)-1and PM2.5: 0.7 – 6.1 g(PM2.5).(kg-fuel)-1. For the Brisbane they were PN: 1.0 – 1.5 x 1016 (kg-fuel)-1, NOx: 3.4 – 8.0 g(NO2).(kg-fuel)-1, SO2: 1.3 – 1.7 g(SO2).(kg-fuel)-1 and PM2.5: 1.2 – 5.6 g(PM2.5).(kg-fuel)-1. The results are discussed in terms of the operating conditions of the vessels’ engines. Particle number emission factors as a function of size as well as the count median diameter (CMD), and geometric standard deviation of the size distributions are provided. The size distributions were found to be consistently uni-modal in the range below 500 nm, and this mode was within the accumulation mode range for both vessels. The representative CMDs for the various activities performed by the dredgers ranged from 94-131 nm in the case of the Amity, and 58-80 nm for the Brisbane. A strong inverse relationship between CMD and EF(PN) was observed.

A statistical strategy to select optimal structural health monitoring data in operational modal analysis

Operational modal analysis (OMA) is prevalent in modal identifi cation of civil structures. It asks for response measurements of the underlying structure under ambient loads. A valid OMA method requires the excitation be white noise in time and space. Although there are numerous applications of OMA in the literature, few have investigated the statistical distribution of a measurement and the infl uence of such randomness to modal identifi cation. This research has attempted modifi ed kurtosis to evaluate the statistical distribution of raw measurement data. In addition, a windowing strategy employing this index has been proposed to select quality datasets. In order to demonstrate how the data selection strategy works, the ambient vibration measurements of a laboratory bridge model and a real cable-stayed bridge have been respectively considered. The analysis incorporated with frequency domain decomposition (FDD) as the target OMA approach for modal identifi cation. The modal identifi cation results using the data segments with different randomness have been compared. The discrepancy in FDD spectra of the results indicates that, in order to fulfi l the assumption of an OMA method, special care shall be taken in processing a long vibration measurement data. The proposed data selection strategy is easy-to-apply and verifi ed effective in modal analysis.

Damage assessment in beams and plates using variations in modal properties

Damage detection using modal properties is a widely accepted method. However, quantifying such damage using modal properties is still not well established. With this in mind, a research project is presently underway towards the development of a procedure to detect, locate and quantify damage in structural components using the variations in modal properties. A novel vibration based parameter called Vibration based Damage Index is introduced into the damage assessment procedure. This paper presents the early part of the research project which treats flexural members. The proposed procedure is validated using experimental data and/or theoretical techniques and illustrated through application. Outcomes of this research highlight the ability of the proposed procedure to successfully detect, locate and quantify damage in flexural structural components using the modal properties of the first few modes.

Estimation of vibration amplitude in Fourier domain optical coherence tomography interferometric signals from Doppler spectrum

In presented method combination of Fourier and Time domain detection enables to broaden the effective bandwidth for time dependent Doppler Signal that allows for using higher-order Bessel functions to calculate unambiguously the vibration amplitudes.

Fourier active appearance models

Gaining invariance to camera and illumination variations has been a well investigated topic in Active Appearance Model (AAM) fitting literature. The major problem lies in the inability of the appearance parameters of the AAM to generalize to unseen conditions. An attractive approach for gaining invariance is to fit an AAM to a multiple filter response (e.g. Gabor) representation of the input image. Naively applying this concept with a traditional AAM is computationally prohibitive, especially as the number of filter responses increase. In this paper, we present a computationally efficient AAM fitting algorithm based on the Lucas-Kanade (LK) algorithm posed in the Fourier domain that affords invariance to both expression and illumination. We refer to this as a Fourier AAM (FAAM), and show that this method gives substantial improvement in person specific AAM fitting performance over traditional AAM fitting methods.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.