Factor Mapping and Metamodelling

In this work we present some techniques, within the realm of Global Sensitivity Analysis, which permit to address fundamental questions in term of model's understanding. In particular we are interested in developing tools which allow to determine which factor (or group of factors) are most responsible for producing model outputs Y within or outside specified bounds ranking the importance of the various input factors in terms of their influence on the variation of Y. On the other hand, we look for representing in a direct way (graphically, analytically, etc.) the relationship between input factors X_1,..., X_k and output Y in order to get a better understanding of the model itself.JRC.G.9-Econometrics and statistical support to antifrau

Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

Improved model identification for nonlinear systems using a random subsampling and multifold modelling (RSMM) approach

In nonlinear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of ‘hold-out’ or ‘split-sample’ data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. Firstly, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

Nonlinear system identification using wavelet based SDP models

System identification has played an increasingly dominant role in a wide range of engineering applications. While linear system's theory is mature, nonlinear system identification remains an open research area in recent years. This thesis develops a new, efficient and systematic approach to the identification of nonlinear dynamic systems using wavelet based State Dependent Parameter (SDP) models, from structure determination to parameter estimation. In this approach, the system's nonlinearities are analysed and effectively represented by a SDP model structure in the form of wavelets. This provides a computationally efficient tool to open up the `black-box', offering valuable insights into the system's dynamics. In this thesis, 1-dimensional (1-D) approach is first developed based on a conventional SDP model structure which relies on a single state variable dependency. It is then extended into a multi-dimensional approach in order to solve the identification problem of systems with significant multi-variable dependence nonlinear dynamics. Here, parametrically efficient nonlinear model is obtained by the application of an effective model structure selection algorithm based on the Predicted Residual Sums of Squares (PRESS) criterion in conjunction with Orthogonal Decomposition (OD) to avoid any ill-conditioning problems associated with the parameter estimation. This thesis also investigates the aspects of noise, stability and other engineering application of the proposed approaches. More specifically, this includes: (1) nonlinear identification in the presence of noise, (2) development of bounded characteristics of the estimated models and (3) application studies where the developed approaches have been used in various engineering applications. Particularly, the modelling and forecast of daily peak power demand in the state of Victoria, Australia have been effectively studied using the proposed approaches. This strongly motivates a great deal of potential future research to be carried out in the area of power system modelling

Nonlinear system identification for model-based condition monitoring of wind turbines

This paper proposes a data driven model-based condition monitoring scheme that is applied to wind turbines. The scheme is based upon a non-linear data-based modelling approach in which the model parameters vary as functions of the system variables. The model structure and parameters are identified directly from the input and output data of the process. The proposed method is demonstrated with data obtained from a simulation of a grid-connected wind turbine where it is used to detect grid and power electronic faults. The method is evaluated further with SCADA data obtained from an operational wind farm where it is employed to identify gearbox and generator faults. In contrast to artificial intelligence methods, such as artificial neural network-based models, the method employed in this paper provides a parametrically efficient representation of non-linear processes. Consequently, it is relatively straightforward to implement the proposed model-based method on-line using a field-programmable gate array

Developing models for the data-based mechanistic approach to systems analysis:Increasing objectivity and reducing assumptions

Stochastic State-Space Time-Varying Random Walk models have been developed, allowing the existing Stochastic State Space models to operate directly on irregularly sampled time-series. These TVRW models have been successfully applied to two different classes of models benefiting each class in different ways. The first class of models - State Dependent Parameter (SDP) models and used to investigate the dominant dynamic modes of nonlinear dynamic systems and the non-linearities in these models affected by arbitrary State Variables. In SDP locally linearised models it is assumed that the parameters that describe system’s behaviour changes are dependent upon some aspect of the system (it’s ‘state’). Each parameter can be dependent on one or more states. To estimate the parameters that are changing at a rate related to that of it’s states, the estimation procedure is conducted in the state-space along the potentially multivariate trajectory of the states which drive the parameters. The introduction of the newly developed TVRW models significantly improves parameter estimation, particularly in data rich neighbourhoods of the state-space when the parameter is dependent on more than one state, and the ends of the data-series when the parameter is dependent on one state with few data points. The second class of models are known as Dynamic Harmonic Regression (DHR) models and are used to identify the dominant cycles and trends of time-series. DHR models the assumption is that a signal (such as a time-series) can be broken down into four (unobserved) components occupying different parts of the spectrum: trend, seasonal cycle, other cycles, and a high frequency irregular component. DHR is confined to uniformly sampled time-series. The introduction of the TVRW models allows DHR to operate on irregularly sampled time-series, with the added benefit of forecasting origin no longer being confined to starting at the end of the time-series but can now begin at any point in the future. Additionally, the forecasting sampling rate is no longer limited to the sampling rate of the time-series. Importantly, both classes of model were designed to follow the Data-Based Mechanistic (DBM) approach to modelling environmental systems, where the model structure and parameters are to be determined by the data (Data-Based) and then the subsequent models are to be validated based on their physical interpretation (Mechanistic). The aim is to remove the researcher’s preconceptions from model development in order to eliminate any bias, and then use the researcher’s knowledge to validate the models presented to them. Both classes of model lacked model structure identification procedures and so model structure was determined by the researcher, against the DBM approach. Two different model structure identification procedures, one for SDP and the other for DHR, were developed to bring both classes of models back within the DBM framework. These developments have been presented and tested here on both simulated data and real environmental data, demonstrating their importance, benefits and role in environmental modelling and exploratory data analysis

Damage identification in FRP-retrofitted concrete structures using linear and nonlinear guided waves

Structural health monitoring (SHM) involves the implementation of damage identification methods in engineering structures to ensure structural safety and integrity. The paramount importance of SHM has been recognised in the literature. Among different damage identification methods, guided wave approach has emerged as a revolutionary technique. Guided wave-based damage identification has been the subject of intensive research in the past two decades. Meanwhile, applications of fibre reinforced polymer (FRP) composites for strengthening and retrofitting concrete structures have been growing dramatically. FRP composites offer high specific stiffness and high specific strength, good resistance to corrosion and tailorable mechanical properties. On the other hand, there are grave concerns about longterm performance and durability of FRP applications in concrete structures. Therefore, reliable damage identification techniques need to be implemented to inspect and monitor FRPretrofitted concrete structures. This thesis aims to explore applications of Rayleigh wave for SHM in FRP-retrofitted concrete structures. A three-dimensional (3D) finite element (FE) model has been developed to simulate Rayleigh wave propagation and scattering. Numerical simulation results of Rayleigh wave propagation in the intact model (without debonding at FRP/concrete interface) are verified with analytical solutions. Propagation of Rayleigh wave in the FRP-retrofitted concrete structures and scattering of Rayleigh waves at debonding between FRP and concrete are validated with experimental measurements. Very good agreement is observed between the FE results and experimental measurements. The experimentally and analytically validated FE model is then used in numerical case studies to investigate the scattering characteristic. The scattering directivity pattern (SDP) of Rayleigh wave is studied for different debonding size to wavelength ratios and in both backward and forward scattering directions. The suitability of using bonded mass to simulate debonding in the FRP-retrofitted concrete structures is also investigated. Besides, a damage localisation method is introduced based on the time-of-flight (ToF) of the scattered Rayleigh wave. Numerical case studies, involving different locations and sizes of debonding, are presented to validate the proposed debonding localisation method. Nonlinear ultrasonics is a novel and attractive concept with the potential of baseline-free damage detection. In this thesis, nonlinear Rayleigh wave induced at debondings in FRPretrofitted concrete structures, is studied in detail. Numerical results of nonlinear Rayleigh wave are validated with experimental measurements. The study considers both second and third harmonics of Rayleigh wave. A very good agreement is observed between numerical and experimental results of nonlinear Rayleigh wave. Directivity patterns of second and third harmonics for different debonding size to the wavelength ratios, and in both backward and forward scattering directions, are presented. Moreover, a damage image reconstruction algorithm is developed based on the second harmonic of Rayleigh wave. This method provides a graphical representation for debonding detection and localisation in FRP-retrofitted concrete structures. Experimental case studies are used to demonstrate the performance of the proposed technique. It is shown that the proposed imaging method is capable of detecting the debonding in the FRP-retrofitted concrete structures. Overall, this PhD study proves that Rayleigh wave is a powerful and reliable means of damage detection and localisation in FRP-retrofitted concrete structures.Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 201

Convex Identifcation of Stable Dynamical Systems

This thesis concerns the scalable application of convex optimization to data-driven modeling of dynamical systems, termed system identi cation in the control community. Two problems commonly arising in system identi cation are model instability (e.g. unreliability of long-term, open-loop predictions), and nonconvexity of quality-of- t criteria, such as simulation error (a.k.a. output error). To address these problems, this thesis presents convex parametrizations of stable dynamical systems, convex quality-of- t criteria, and e cient algorithms to optimize the latter over the former. In particular, this thesis makes extensive use of Lagrangian relaxation, a technique for generating convex approximations to nonconvex optimization problems. Recently, Lagrangian relaxation has been used to approximate simulation error and guarantee nonlinear model stability via semide nite programming (SDP), however, the resulting SDPs have large dimension, limiting their practical utility. The rst contribution of this thesis is a custom interior point algorithm that exploits structure in the problem to signi cantly reduce computational complexity. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, in which superior generalization to new data is demonstrated. Equipped with this algorithmic machinery, the second contribution of this thesis is the incorporation of model stability constraints into the maximum likelihood framework. Speci - cally, Lagrangian relaxation is combined with the expectation maximization (EM) algorithm to derive tight bounds on the likelihood function, that can be optimized over a convex parametrization of all stable linear dynamical systems. Two di erent formulations are presented, one of which gives higher delity bounds when disturbances (a.k.a. process noise) dominate measurement noise, and vice versa. Finally, identi cation of positive systems is considered. Such systems enjoy substantially simpler stability and performance analysis compared to the general linear time-invariant iv Abstract (LTI) case, and appear frequently in applications where physical constraints imply nonnegativity of the quantities of interest. Lagrangian relaxation is used to derive new convex parametrizations of stable positive systems and quality-of- t criteria, and substantial improvements in accuracy of the identi ed models, compared to existing approaches based on weighted equation error, are demonstrated. Furthermore, the convex parametrizations of stable systems based on linear Lyapunov functions are shown to be amenable to distributed optimization, which is useful for identi cation of large-scale networked dynamical systems