Optimization: A Journal of Mathematical Programming and Operations Research

In this article we study support vector machine (SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior knowledge is in the form of uncertain linear constraints, results in an uncertain convex optimization problem with a set containment constraint. Using a new extension of Farkas' lemma, we reformulate the robust counterpart of the uncertain convex optimization problem in the case of interval uncertainty as a convex quadratic optimization problem. We then reformulate the resulting convex optimization problems as a simple quadratic optimization problem with non-negativity constraints using the Lagrange duality. We obtain the solution of the converted problem by a fixed point iterative algorithm and establish the convergence of the algorithm. We finally present some preliminary results of our computational experiments of the metho

Simultaneous classification and feature selection via convex quadratic programming with application to HIV-associated neurocognitive disorder assessment

Support vector machines (SVMs), that utilize a mixture of the L1-norm and the L2-norm penalties, are capable of performing simultaneous classification and selection of highly correlated features. These SVMs, typically set up as convex programming problems, are re-formulated here as simple convex quadratic minimization problems over non-negativity constraints, giving rise to a new formulation - the pq SVM method. Solutions to our re-formulation are obtained efficiently by an extremely simple algorithm. Computational results on a range of publicly available datasets indicate that these methods allow greater classification accuracy in addition to selecting groups of highly correlated features. These methods were also compared on a new dataset assessing HIV-associated neurocognitive disorder in a group of 97 HIVinfected individuals

Simultaneous classification and feature selection via convex quadratic programming with application to HIV-associated neurocognitive disorder assessment

Support vector machines (SVMs), that utilize a mixture of the L1-norm and the L2-norm penalties, are capable of performing simultaneous classification and selection of highly correlated features. These SVMs, typically set up as convex programming problems, are re-formulated here as simple convex quadratic minimization problems over non-negativity constraints, giving rise to a new formulation - the pq-SVM method. Solutions to our re-formulation are obtained efficiently by an extremely simple algorithm. Computational results on a range of publicly available datasets indicate that these methods allow greater classification accuracy in addition to selecting groups of highly correlated features. These methods were also compared on a new dataset assessing HIV-associated neurocognitive disorder in a group of 97 HIV-infected individuals.Quadratic optimization Support vector machines Classification Feature selection Nonnegativity constraints HIV Neurocognitive disorder

Machine Learning Aided Stochastic Elastoplastic and Damage Analysis of Functionally Graded Structures

The elastoplastic and damage analyses, which serve as key indicators for the nonlinear performances of engineering structures, have been extensively investigated during the past decades. However, with the development of advanced composite material, such as the functionally graded material (FGM), the nonlinear behaviour evaluations of such advantageous materials still remain tough challenges. Moreover, despite of the assumption that structural system parameters are widely adopted as deterministic, it is already illustrated that the inevitable and mercurial uncertainties of these system properties inherently associate with the concerned structural models and nonlinear analysis process. The existence of such fluctuations potentially affects the actual elastoplastic and damage behaviours of the FGM structures, which leads to the inadequacy between the approximation results with the actual structural safety conditions. Consequently, it is requisite to establish a robust stochastic nonlinear analysis framework complied with the requirements of modern composite engineering practices. In this dissertation, a novel uncertain nonlinear analysis framework, namely the machine leaning aided stochastic elastoplastic and damage analysis framework, is presented herein for FGM structures. The proposed approach is a favorable alternative to determine structural reliability when full-scale testing is not achievable, thus leading to significant eliminations of manpower and computational efforts spent in practical engineering applications. Within the developed framework, a novel extended support vector regression (X-SVR) with Dirichlet feature mapping approach is introduced and then incorporated for the subsequent uncertainty quantification. By successfully establishing the governing relationship between the uncertain system parameters and any concerned structural output, a comprehensive probabilistic profile including means, standard deviations, probability density functions (PDFs), and cumulative distribution functions (CDFs) of the structural output can be effectively established through a sampling scheme. Consequently, by adopting the machine learning aided stochastic elastoplastic and damage analysis framework into real-life engineering application, the advantages of the next generation uncertainty quantification analysis can be highlighted, and appreciable contributions can be delivered to both structural safety evaluation and structural design fields

Lattice Based Elastic Metamaterials with Ultra-wide Stopbands at Low Frequency

Lattice-based elastic metamaterials (EMMs) with periodically engineered cells exhibit unprecedented properties. One exotic attribute of EMMs is the bandgap, in which elastic waves， within specific frequency ranges are prohibited from transmitting. While putting EMMs into use in real-life applications, nonetheless, their applicability remains limited due to the deficiency in the well-established design methods for EMMs, especially three-dimensional (3D) EMMs (including both infinite and finite EMMs) to achieve low frequency and ultra-wide stopbands. Moreover, the inevitable system uncertainties stemming from heterogeneous sources in practical EMMs can lead to significant fluctuations in structural performance, and worse still, catastrophic structural failure may occur. Consequently, to facilitate the wide and safe application of these advanced materials, it is requisite to develop a comprehensive framework to analyze and design 3D EMMs with ultra-wide wave attenuation bands at low frequencies and implement reliability analysis for them. In this research, a systematic framework is developed for 3D latticed EMMs in order to improve their applicability across multiple engineering disciplines. Within the framework, the key components are the novel modal-based approaches, proposed for elaborating wave attenuation mechanisms, guiding the structural modifications, and manipulating geometrical parameters of 3D EMMs aiming at achieving low-frequency and ultra-wide stopbands. Besides, another core in the framework is the new virtual model-aided approach, which is introduced for estimating statistical information, including means, standard deviations, probability density functions (PDFs), and cumulative distribution functions (CDFs), and failure probabilities of the random bandgap characteristics for 3D EMMs involving material and geometrical uncertainties. Based on the numerical investigations, the wave attenuation mechanisms in latticed 3D EMMs are elaborated. Moreover, the effectiveness of the developed modal-based approaches to design 3D EMMs and the computational performance, such as robustness, efficiency, and accuracy of the virtual model-aided framework are demonstrated. Convincedly, the developed framework facilitates the wide and safe applications of EMMs, significantly benefiting their applicability in real-life scenarios across diverse fields

Fracture characterisation and performance evaluation of corroded RC members by AE-based data analysis

Steel reinforcement corrosion has been regarded as one of the major causes of reinforced concrete (RC) structures failing prematurely, posing a serious structural durability problem worldwide. Detailed assessment of corrosion-induced damage and its effects on RC structures is critical for sustaining structural reliability and safety. This study develops and examines the feasibility of acoustic emission (AE) monitoring and data analysis methodologies to characterise corrosion-induced damage in RC members, followed by an evaluation of the effect of corrosion on load behaviour. Experimental investigations were conducted on a series of specimens of different configurations, namely concrete cubes with steel bars for pull-out tests and RC beams of different dimensions to be subjected to static and cyclic loading regimes. Focusing on developing evaluation methods based on AE monitoring and data analysis, a summary of work completed, and the associated findings are given as follows. Characterisation of the concrete cracking using parametric and waveform analysis was conducted to investigate the effect of corrosion on steel-concrete bond behaviour in the pull-out tests of concrete cubes. It was found that a small amount of corrosion (approximately 6%) could slightly increase the bond strength as a result of the rust expansion and reactionary confinement of concrete. Corrosion was also found to be able to mitigate the damage caused by cyclic loading. AE signal analysis indicates that the concrete cracking mode during the steel-concrete de-bonding process has changed as a result of steel corrosion. Characterisation of load behaviour and failure mode of corroded RC beams was conducted by flexural load tests aided by AE monitoring and digital image correlation (DIC). The DIC strain mapping results and AE signal features revealed that corrosion has an influence on the concrete cracking mechanism of the beam specimens. Corrosion has also altered the failure mode of a shear-critical beam specimen series to flexure owing to the change of steel-concrete bond behaviour. Numerical simulation of AE wave front propagation in RC media and tomographic evaluation of internal damage was implemented on one group of RC beam specimens tested in this study. The numerical model of the specimens was discretised using finite-difference grid meshing, and the different acoustic properties of steel and concrete were defined. On this basis, simulation of AE wave front propagation considering concrete cover cracking and steel rust layer formation was carried out using the fast-marching method. The effect of corrosion-induced damage on the AE rays was studied by examining non-linear ray tracing in the simulation. A tomographic reconstruction approach that solved by the quasi-Newton method provided a potential way to quantitatively evaluate the internal damage of RC beams using AE monitoring data. A novel method was developed for assessing the corrosion level in RC beams using a data-driven approach. Normalization of AE data was applied using principal component analysis to minimise variations in AE signal features caused by differences in the geometrical and material properties of RC beams as well as in the AE monitoring instrumentation setup. The machine learning models, including k-nearest neighbours (KNN) and support vector machines (SVM), were trained using the normalised AE features. The trained KNN models were found effective at predicting the corrosion level in RC beams using the secondary AE signals as input, which could be acquired from the cyclic loading of beams. Key words: Steel Corrosion, Concrete cracking, Steel-Concrete Bond, Reinforced Concrete Beam, Load Behaviour, Acoustic Emission, Digital Image Correlation, Tomographic Reconstruction, Data-driven