Identification of modal parameters based on moving force excitation

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


This thesis proposed a two-stage input-output system identification methodology to investigate the possibility of estimating the bridge modal parameters, i.e., natural frequencies, damping ratios, and modal masses, under excitation of a moving vehicle with the simultaneous use of the moving input acceleration signal and the measured bridge acceleration responses. In the first stage, which is an output-only identification problem, the bridge mode shapes are estimated from the measured bridge forced and free vibration acceleration responses only. The obtained estimated bridge mode shapes are then served as a modal basis to re-express the coupled bridge and vehicle geometric coordinates as decoupled modal coordinates. This procedure then leads us to the second stage identification. With both the input and output information for each mode, a series of (Frequency Response Functions) FRFs can be constructed by using the Discrete Fourier Transform (DFT) technique, along with the parametric model of the Accelerance for a linear system, an optimization procedure is performed to extract the natural frequencies, damping ratios, as well as the modal masses simultaneously.
In order to verify the proposed method, a simply supported Euler-Bernoulli beam of known parameters is used as an example. Its responses to a moving load and a quarter car with the influence of the road roughness are calculated numerically, yielding simulated measured accelerations at a series of fixed locations on the structure. With these numerically generated data, the feasibility and efficacy of the proposed two-stage strategy are validated. A comparison work to examine the estimation accuracy and efficiency is conducted by using the free decay response of the bridge.
To make the proposed method more general, both models, i.e., moving load and quarter car traversing the bridge, are nondimensionalised, and they are simulated with and without noise. Upon verifying the proposed method, we discussed the impact factors, which can influence the estimation results. We discovered that the nondimensionalised spatial frequency is the most important one, which, if known beforehand, can give guidance to the identification results.
Apart from the nondimensionalised spatial frequency, we recognised that the mode shapes estimated from the first stage are also an important factor that can influence the identification accuracy. Therefore, we proposed a new concept real-valued one-sided spectral density matrix, which not only gives the same level of accuracy for the estimated natural frequencies and the damping ratios but also generates better mode shape estimation compared to the classical complex-valued two-sided spectral density matrix. This new approach is used throughout this study to give a better estimation of the mode shapes.
Notwithstanding that the proposed two-stage method is the main topic of this study, our research is far beyond the Vehicle-Bridge Interaction (VBI) analysis. One of the major contributions is made to the Frequency Domain Decomposition (FDD) technique, which serves as the output-only technique for the mode shape estimation in the first stage identification of the proposed method. We reinterpreted the FDD using the Principal Component Analysis (PCA) with a Periodogram-defined Power Spectral Density (PSD) estimator. With our new theory, the role of the singular values and singular vectors are better defined. And we conclude that the FDD is a good technique to be used to detect the presence of close modes. In order to apply the FDD to extract the bridge mode shapes from the vehicle-induced bridge vibration responses (i.e., nonstationary process) only, a simple case study is designed to assess its ability to deal with a similar kind of nonstationary random process.
While analysing a PSD estimator, which is a positive semidefinite self-adjoint compact operator on a Hilbert space, we introduced the concepts of pure state and mixed states from the quantum mechanics and defined a density operator based on a PSD estimator. With a density operator, we can calculate the corresponding Von Neumann entropy or the purity condition. By plotting the entropy or purity of a density operator against the frequency line, we can obtain a different picture of the behaviour of a system that the FDD fails to provide when two modes are very closely spaced. Particularly, we found that this new picture is mainly affected by three influence factors, i.e., correlation relation between the mode shapes of the two modes, damping ratios of the system, and the measurement noise level, which in turn can affect our mode shape estimation results.
Date of Award21 Jan 2021
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorJohn H G Macdonald (Supervisor) & Dario Di Maio (Supervisor)

Cite this