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Conventional mesh-based methods for solid mechanics problems suffer from issues resulting from the use of a mesh, therefore, various meshless methods that can be grouped into those based on weak or strong forms of the underlying problem have been proposed to address these problems by using only points for discretisation. Compared to weak form meshless methods, strong form meshless methods have some attractive features because of the absence of any background mesh and avoidance of the need for numerical integration, making the implementation straightforward. The objective of this thesis is to develop a novel numerical method based on strong form point collocation methods for solving problems with geometric non-linearity including membrane problems. To address some issues in existing strong form meshless methods, the local maximum entropy point collocation method is developed, where the basis functions possess some advantages such as the weak Kronecker-Delta property on boundaries. r- and h-adaptive strategies are investigated in the proposed method and are further combined into a novel rh-adaptive approach, achieving the prescribed accuracy with the optimised locations and limited number of points. The proposed meshless method with h-adaptivity is then extended to solve geometrically non-linear problems described in a Total Lagrangian formulation, where h-adaptivity is again employed after the initial calculation to improve the accuracy of the solution effciently. This geometrically non-linear method is finally developed to analyse membrane problems, in which the out-of-plane deformation for membranes complicates the governing PDEs and the use of hyperelastic materials makes the computational modelling of membrane problems challenging. The Newton-Raphson arc-length method is adopted here to capture the snap-through behaviour in hyperelastic membrane problems. Several numerical examples are presented for each proposed algorithm to validate the proposed methodology and suggestions are made for future work leading on from the findings of this thesis.

Terrestrial laser scanning (TLS) is a remote sensing tool that can record a large amount of accurate topographical information with a fine spatial resolution over a short period of time. It has been used increasingly for measuring ground surfaces (i.e. topographical survey) and monitoring surface movements, such as those caused by landslides. However, the capability of this technique in these applications has not been fully explored in the literature, and thus forms the focus of this thesis. A quantitative study has been carried out to investigate the major error sources that affect the accuracy of digital elevation models (DEMs) derived from TLS survey data, and the magnitude of deformation that can be detected by repeated TLS surveys, at a local scale. In this research, vegetation-induced elevation errors in TLS measurements and the ways in which they can be minimised have been investigated experimentally. The presence of short vegetation was found to be a significant limiting factor for TLS surveys of terrain surfaces, with the average grass-induced elevation error being roughly 65% of the grass height. A finer resolution scan with a lower incidence angle (greater visibility) can effectively reduce vegetation error, as will scanning the same area from multiple scanner locations. The influence of measurement errors in source data points (or a point cloud) on a triangulated irregular network (TIN) with linear interpolation has been analysed. Based on the law of error propagation, an analytical solution was derived to calculate the error variance at any location within a TIN model, due to vertical and horizontal errors in source data points. For the special case of equal and independent error variances in source data points, the maximum, average and minimum values of propagated error variance within a TIN were found to be equal to unity, a half and a third respectively of the error variance in source data points. Errors in DEMs created from the TLS data points representing four terrain surfaces of different characteristics have been quantified using a statistical resampling method. The results show that terrain surface complexity can considerably affect the accuracy of DEMs. The effects of data point density (equivalent point spacing) on the DEM errors have also been analysed. For the data point spacings (35-100 mm) considered in the analyses, the DEM errors increased almost linearly with increasing data point spacing. The results also show that the DEM errors can be decomposed into two parts: a noise-related part and a data-density dependent part. Repeat TLS surveys of some fixed objects have been carried out, to seek to empirically quantify the georeferencing-induced positional errors involved in repeated TLS surveys. The results indicate that repeated TLS surveys can measure millimetric deformations of smooth surfaces if a high georeferencing accuracy is achieved. The DEM errors, along with the georeferencing-induced positional errors, were used to infer the minimum magnitude of movements that can be measured by multi-temporal TLS surveys of rough terrain surfaces. In the case of the Newbury cutting considered in this study, the minimum level of detection was approximately 20 mm (at a 95% confidence level) for the data point spacing of 35 mm. The findings in this research can aid in assessing the fitness of TLS surveys of terrain surfaces for a particular project, and thus are of use in the survey planning. The methods presented in this thesis can be applied to analyse errors in DEMs for making more meaningful interpretations of DEMs or surface variations derived from repeated TLS surveys.

Abstract: Data-driven modeling approaches have been widely studied and applied to the process industries for inferential sensor development, process monitoring and fault detection and early warnings, etc. Essential information of process, like dynamic and relationships between process variables are buried in the massive archived historical data. They are often with high dimensionality and corrupted by diffident kinds of data irregularities, e.g. outliers, missing and multi-rate samples, uncertain time delays, etc. To address all these data irregularities and build a computational efficient modeling approach, the latent variable modeling has become a preferred and successful method. In most chemical processes, the process condition does not vary too fast and often contains large inertia. It is naturally considered that the features with small varying velocity are informative and carry most of the information of the process. With a probabilistic formulation, dynamic latent variable models, based on extracting slowly varying features, are developed in this thesis to address the aforementioned data irregularities, thus give reliable prediction results of quality variables that are otherwise difficult to measure. Outliers are observations that are distant from other observations and they are common in process variable measurements. A robust dynamic latent feature extraction model is first proposed in this thesis to handle the outlier issue. By assuming the observations following the Student's t-distribution that has heavier tails, more weights can be assigned to the outliers thus they can be properly accounted for during modeling process. In feature extraction phase, a weighted Kalman gain is proposed since it violates the Gaussian assumption of the traditional Kalman filter. Smoother and slower features can be extracted and the impact of outliers is alleviated by the latent variance scale. The next contribution of this thesis is to develop a semi-supervised model based on probability slow feature analysis to include the information from quality variables in the extracted latent features while accounting for the missing data issues in quality variables. An approach by augmenting both input and output variables is proposed. It can deal with the different missing data issues, i.e. either missing at random or multi-rate sampling. In latent feature extracting process, the quality variable samples can be utilized whenever they are available. The compensation by the past quality variable samples leads to better predictability of its future samples. Another irregular property of the lab samples of quality variable is its uncertain time delays. In many cases, the quality variables are sampled and analyzed manually by operators if the real-time on-line analysis is not possible. Various factors during manual sampling, i.e. human errors, manual sample, lab analysis and data recording procedures, etc can result in time-varying time delays on the quality variable samples. Another latent variable, delay indicator which evolves following a hidden Markov model, is introduced in the variational Bayesian framework to address this issue. The preference of model parameters is given as their prior distributions. More accurate and meaningful dynamic latent features can be extracted using the shifted samples of quality variables. Time-varying time delays not only exist in the quality variables, but also in the fast-sampled process variables since their distributed locations in the plant. The changes of process conditions, varying velocity of flows, changing viscosity of transmission materials, etc., will cause the changes of delay to the target quality variable. The generalization formulation of the earlier work is proposed to address this issue. Multiple Markov chains are introduced to represent the different time-varying time delay sequences for different process variables. Dynamic latent features are extracted using both the shift process variables and scattered quality variable samples. With the consideration of the shifted observations, better prediction results of quality variable are provided. The validity and practicality of these proposed probabilistic latent variable modeling approaches are verified through numerical examples, benchmark simulations, experimental studies and industrial applications. Specifically, the application to the SAGD well pair water content prediction performance is improved by applying proposed methods when data irregularities are considered.

Hyperspectral imaging provides the capability of increased sensitivity and discrimination over traditional imaging methods by combining standard digital imaging with spectroscopic methods. For each individual pixel in a hyperspectral image (HSI), a continuous spectrum is sampled as the spectral reflectance/radiance signature to facilitate identification of ground cover and surface material. The abundant spectrum knowledge allows all available information from the data to be mined. The superior qualities within hyperspectral imaging allow wide applications such as mineral exploration, agriculture monitoring, and ecological surveillance, etc. The processing of massive high-dimensional HSI datasets is a challenge since many data processing techniques have a computational complexity that grows exponentially with the dimension. Besides, a HSI dataset may contain a limited number of degrees of freedom due to the high correlations between data points and among the spectra. On the other hand, merely taking advantage of the sampled spectrum of individual HSI data point may produce inaccurate results due to the mixed nature of raw HSI data, such as mixed pixels, optical interferences and etc. Fusion strategies are widely adopted in data processing to achieve better performance, especially in the field of classification and clustering. There are mainly three types of fusion strategies, namely low-level data fusion, intermediate-level feature fusion, and high-level decision fusion. Low-level data fusion combines multi-source data that is expected to be complementary or cooperative. Intermediate-level feature fusion aims at selection and combination of features to remove redundant information. Decision level fusion exploits a set of classifiers to provide more accurate results. The fusion strategies have wide applications including HSI data processing. With the fast development of multiple remote sensing modalities, e.g. Very High Resolution (VHR) optical sensors, LiDAR, etc., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems.