Arman Melkumyan

Influence of imperfect bonding on interface waves guided by piezoelectric/piezomagnetic composites

Interface waves, which can be guided by imperfectly bonded piezoelectric and piezomagnetic half-spaces, are studied. The cases of absorbent and permeable interfaces are discussed in detail. It is shown that imperfection of the interface bonding has significant impact on the existence of interface waves and on their velocities of propagation. Some interface waves present in the case of imperfect bonding vanish when the bonding becomes perfect. The waves that are guided by an imperfect interface are shown to be dispersive, although there is no explicit characteristic length in the structure model. The results obtained show that possible imperfections of interface bonding must be considered in the design and fabrication of piezoelectric/piezomagnetic composites.

On the linear and nonlinear observability analysis of the SLAM problem

Research in Simultaneous Localization and Mapping (SLAM) has been progressing for almost two decades. Although several researchers attempted recently to investigate its observability (mostly without proofs for the general cases) the established facts have often been left unnoticed or ignored by the research community. In this paper rigorous proofs have been provided as an enlightenment for the observability properties of the general two dimensional SLAM problem incorporating a car like kinematic model in the context of piece-wise constant systems theory and non-linear Lie derivative theory. Observable and Unobservable states of the general n landmark SLAM problem have been established with proofs. A comparison of linear and non-linear techniques to evaluate the observability of SLAM is provided using simulations.

Multi-kernel Gaussian processes

Multi-task learning remains a difficult yet important problem in machine learning. In Gaussian processes the main challenge is the definition of valid kernels (covariance functions) able to capture the relationships between different tasks. This paper presents a novel methodology to construct valid multi-task covariance functions (Mercer kernels) for Gaussian processes allowing for a combination of kernels with different forms. The method is based on Fourier analysis and is general for arbitrary stationary covariance functions. Analytical solutions for cross covariance terms between popular forms are provided including Matern, squared exponential and sparse covariance functions. Experiments are conducted with both artificial and real datasets demonstrating the benefits of the approach.

A Novel Spectral Unmixing Method Incorporating Spectral Variability Within Endmember Classes

Some spectral unmixing methods incorporate endmember variability within endmember classes. It is, however, uncertain whether these methods work well when endmember spectra do not completely describe the variability that exists within endmember classes. This paper proposes a novel spectral unmixing method, Spectral Unmixing within a multi-task Gaussian Process framework (SUGP), which is more resistant to problems caused by the use of a small number of endmember spectra. SUGP models the latent function between spectra and abundances in a training set and predicts abundances from a given pixel spectrum. SUGP is different from existing methods in that it incorporates all spectra within each endmember class to estimate abundances within a probabilistic framework. Using simulated data, SUGP was compared with existing linear unmixing methods and was found to be superior in determining the number of endmember classes within each pixel and in estimating abundances. It was also more effective in cases where a small number of spectra within endmember classes were specified and was more resistant to the effects of spectral noise. Methods were applied to the hyperspectral imagery of a mine wall and to imagery acquired over Cuprite, Nevada. Abundance maps generated by SUGP were consistent with the validated reference maps. SUGP opens up possibilities for estimating accurate abundances under conditions where endmember variability is present and where endmember spectra incompletely describe the true variability of each endmember class.

An Observation Angle Dependent Nonstationary Covariance Function for Gaussian Process Regression

Despite the success of Gaussian Processes (GPs) in machine learning, the range of applications and expressiveness of GP models are confined by the limited set of available covariance functions. This paper presents a new non-stationary covariance function which allows simple geometric interpretation and depends on the angle at which points can be seen from an observation centre. The construction of the new covariance function and the proof of its positive semi-definiteness are based on geometric reasoning combined with analytic computations. Experiments conducted with both artificial and real datasets demonstrate the advantages of the developed covariance function.

Automated recognition of stratigraphic marker shales from geophysical logs in iron ore deposits

The mining of stratiform ore deposits requires a means of determining the location of stratigraphic boundaries. A variety of geophysical logs may provide the required data but, in the case of banded iron formation hosted iron ore deposits in the Hamersley Ranges of Western Australia, only one geophysical log type (natural gamma) is collected for this purpose. The information from these logs is currently processed by slow manual interpretation. In this paper we present an alternative method of automatically identifying recurring stratigraphic markers in natural gamma logs from multiple drill holes.Our approach is demonstrated using natural gamma geophysical logs that contain features corresponding to the presence of stratigraphically important marker shales. The host stratigraphic sequence is highly consistent throughout the Hamersley and the marker shales can therefore be used to identify the stratigraphic location of the banded iron formation (BIF) or BIF hosted ore.The marker shales are identified using Gaussian Processes (GP) trained by either manual or active learning methods and the results are compared to the existing geological interpretation. The manual method involves the user selecting the signatures for improving the library, whereas the active learning method uses the measure of uncertainty provided by the GP to select specific examples for the user to consider for addition.The results demonstrate that both GP methods can identify a feature, but the active learning approach has several benefits over the manual method. These benefits include greater accuracy in the identified signatures, faster library building, and an objective approach for selecting signatures that includes the full range of signatures across a deposit in the library. When using the active learning method, it was found that the current manual interpretation could be replaced in 78.4% of the holes with an accuracy of 95.7%. We apply Gaussian Processes to identify marker shales in iron ore mines.We examine manual and active learning methods of training Gaussian Processes.The active learnings use of uncertainty increases the accuracy of results.The active learning method can replace more than 3/4 of the manual interpretations.

Gaussian Processes with OAD Covariance Function for Hyperspectral Data Classification

A new method is presented which combines a deterministic analytical method and a probabilistic measure to classify rock types on the basis of their hyperspectral curve shape. This method is a supervised learning algorithm using Gaussian Processes (GPs) and the Observation Angle Dependent (OAD) covariance function. The OAD covariance function makes use of the properties of the Spectral Angle Mapper (SAM) which is used frequently for classifying hyperspectral data. Results show that it is possible to identify and classify rocks in an ‘One vs. One’ and an ‘One vs. All’ approach using the entire spectral curve (0.35-2.5 microm). The results show an average classification accuracy of 98% and an F-score of 92% for the new method in an ‘One vs. All’ approach. Slightly higher classification accuracy and F-measure for the new method can be achieved for the ‘One vs. One’ binary approach. This paper extends the ideas of the deterministic SAM method to a probabilistic framework and enables data fusion with similar and disparate kinds of sensors. This paper demonstrates a superior classification performance of the new probabilistic method over the classical SAM.

Detection of geological structure using gamma logs for autonomous mining

This work is motivated by the need to develop new perception and modeling capabilities to support a fully autonomous, remotely operated mine. The application differs from most existing robotics research in that it requires a detailed world model of the sub-surface geological structure. This in-ground geological information is then used to drive many of the planning and control decisions made on a mine site. This paper formulates a method for automatically detecting in-ground geological boundaries using geophysical logging sensors and a supervised learning algorithm. The algorithm uses Gaussian Processes (GPs) and a single length scale squared exponential covariance function. The approach is demonstrated on data from a producing iron-ore mine in Australia. Our results show that two separate distinctive geological boundaries can be automatically identified with an accuracy of over 99 percent. The alternative approach to automatic detection involves manual examination of these data.

Incorporating Spatial Information and Endmember Variability Into Unmixing Analyses to Improve Abundance Estimates

Incorporating endmember variability and spatial information into spectral unmixing analyses is important for producing accurate abundance estimates. However, most methods do not incorporate endmember variability with spatial regularization. This paper proposes a novel 2-step unmixing approach, which incorporates endmember variability and spatial information. In step 1, a probability distribution representing abundances is estimated by spectral unmixing within a multi-task Gaussian process framework (SUGP). In step 2, spatial information is incorporated into the probability distribution derived by SUGP through an a priori distribution derived from a Markov random field (MRF). The proposed method (SUGP-MRF) is different to the existing unmixing methods because it incorporates endmember variability and spatial information at separate steps in the analysis and automatically estimates parameters controlling the balance between the data fit and spatial smoothness. The performance of SUGP-MRF is compared with the existing unmixing methods using synthetic imagery with precisely known abundances and real hyperspectral imagery of rock samples. Results show that SUGP-MRF outperforms the existing methods and improves the accuracy of abundance estimates by incorporating spatial information.

A Dynamic Time Warping based covariance function for Gaussian Processes signature identification

Modelling stratiform deposits requires a detailed knowledge of the stratigraphic boundaries. In Banded Iron Formation (BIF) hosted ores of the Hamersley Group in Western Australia these boundaries are often identified using marker shales. Both Gaussian Processes (GP) and Dynamic Time Warping (DTW) have been previously proposed as methods to automatically identify marker shales in natural gamma logs. However, each method has different advantages and disadvantages. We propose a DTW based covariance function for the GP that combines the flexibility of the DTW with the probabilistic framework of the GP. The three methods are tested and compared on their ability to identify two natural gamma signatures from a Marra Mamba type iron ore deposit. These tests show that while all three methods can identify boundaries, the GP with the DTW covariance function combines and balances the strengths and weaknesses of the individual methods. This method identifies more positive signatures than the GP with the standard covariance function, and has a higher accuracy for identified signatures than the DTW. The combined method can handle larger variations in the signature without requiring multiple libraries, has a probabilistic output and does not require manual cut-off selections. A DTW based covariance function is developed for Gaussian Processes.We apply this method to identify marker shales in iron ore mines.The results are compared to those using only Gaussian Processes or Dynamic Time Warping.The new function combines the flexibility of the DTW with the probabilistic framework of the GP.