Mandal, Sukomal; (1992) On the identification and parametric modelling of offshore dynamic systems. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis describes an investigation into the analysis methods arising from identification aspects of the theory of dynamic systems with application to full-scale offshore monitoring and marine environmental data including target spectra. Based on the input and output of the dynamic system, the System Identification (SI) techniques are used first to identify the model type and then to estimate the model parameters. This work also gives an understanding of how to obtain a meaningful matching between the target (power spectra or time series data sets) and SI models with minimal loss of information. The SI techniques, namely. Autoregressive (AR), Moving Average (MA) and Autoregressive Moving Average (ARMA) algorithms are formulated in the frequency domain and also in the time domain. The above models can only be economically applicable provided the model order is low in the sense that it is computationally efficient and the lower order model can most appropriately represent the offshore time series records or the target spectra. For this purpose, the orders of the above SI models are optimally selected by Least Squares Error, Akaike Information Criterion and Minimum Description Length methods. A novel model order reduction technique is established to obtain the reduced order ARMA model. At first estimations of higher order AR coefficients are determined using modified Yule-Walker equations and then the first and second order real modes and their energies are determined. Considering only the higher energy modes, the AR part of the reduced order ARMA model is obtained. The MA part of the reduced order ARMA model is determined based on partial fraction and recursive methods. This model order reduction technique can remove the spurious noise modes which are present in the time series data. Therefore, firstly using an initial optimal AR model and then a model order reduction technique, the time series data or target spectrum can be reduced to a few parameters which are the coefficients of the reduced order ARMA model. The above univariate SI models and model order reduction techniques are successfully applied for marine environmental and structural monitoring data, including ocean waves, semi-submersible heave motions, monohull crane vessel motions and theoretical (Pierson- Moskowitz and JONSWAP) spectra. Univariate SI models are developed based on the assumption that the offshore dynamic systems are stationary random processes. For nonstationary processes, such as, measurements of combined sea waves and swells, or coupled responses of offshore structures with short period and long period motions, the time series are modelled by the Autoregressive Integrated Moving Average algorithms. The multivariate autoregressive (MAR) algorithm is developed to reduce the time series wave data sets into MAR model parameters. The MAR algorithms are described by feedback weighting coefficients matrices and the driving noise vector. These are obtained based on the estimation of the partial correlation of the time series data sets. Here the appropriate model order is selected based on auto and cross correlations and multivariate Akaike information criterion methods. These algorithms are applied to estimate MAR power spectral density spectra and then phase and coherence spectra of two time series wave data sets collected at a North Sea location. The estimation of MAR power spectral densities are compared with spectral estimates computed from a two variable fast Fourier transform, which show good agreement.

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