<abstract xml:lang="en"><title style='display:none'>Control flow graphs and code coverage</title>The control flow of programs can be represented by directed graphs. In this paper we provide a uniform and detailed formal basis for control flow graphs combining known definitions and results with new aspects. Two graph reductions are defined using only syntactical information about the graphs, but no semantical information about the represented programs. We prove some properties of reduced graphs and also about the paths in reduced graphs. Based on graphs, we define statement coverage and branch coverage such that coverage notions correspond to node coverage, and edge coverage, respectively.</abstract>

Control flow graphs and code coverage

<abstract><title style='display:none'>Abstract</title>In this work a new algorithm for quaternion-based spatial rotation is presented which reduces the number of underlying real multiplications. The performing of a quaternion-based rotation using a rotation matrix takes 15 ordinary multiplications, 6 trivial multiplications by 2 (left-shifts), 21 additions, and 4 squarings of real numbers, while the proposed algorithm can compute the same result in only 14 real multiplications (or multipliers—in a hardware implementation case), 43 additions, 4 right-shifts (multiplications by 1/4), and 3 left-shifts (multiplications by 2).</abstract>

An Algorithm for Quaternion–Based 3D Rotation

<abstract><title style='display:none'>Abstract</title> Naive Bayes is among the simplest probabilistic classifiers. It often performs surprisingly well in many real world applications, despite the strong assumption that all features are conditionally independent given the class. In the learning process of this classifier with the known structure, class probabilities and conditional probabilities are calculated using training data, and then values of these probabilities are used to classify new observations. In this paper, we introduce three novel optimization models for the naive Bayes classifier where both class probabilities and conditional probabilities are considered as variables. The values of these variables are found by solving the corresponding optimization problems. Numerical experiments are conducted on several real world binary classification data sets, where continuous features are discretized by applying three different methods. The performances of these models are compared with the naive Bayes classifier, tree augmented naive Bayes, the SVM, C4.5 and the nearest neighbor classifier. The obtained results demonstrate that the proposed models can significantly improve the performance of the naive Bayes classifier, yet at the same time maintain its simple structure.</abstract>

Centre for Informatics and Applied Optimization School of Science, Information Technology and Engineering, University of Ballarat, Victoria 3353, Australia

Victoria Research Laboratory National ICT Australia, Victoria 3010, Australia

Learning the naive Bayes classifier with optimization models

<abstract xml:lang="en"><title style='display:none'>Circular Object Detection Using a Modified Hough Transform</title>A practical modification of the Hough transform is proposed that improves the detection of low-contrast circular objects. The original circular Hough transform and its numerous modifications are discussed and compared in order to improve both the efficiency and computational complexity of the algorithm. Medical images are selected to verify the algorithm. In particular, the algorithm is applied to localize cell nuclei of cytological smears visualized using a phase contrast microscope.</abstract>

Circular Object Detection Using a Modified Hough Transform

<abstract xml:lang="en"><title style='display:none'>K3M: A universal algorithm for image skeletonization and a review of thinning techniques</title>This paper aims at three aspects closely related to each other: first, it presents the state of the art in the area of thinning methodologies, by giving descriptions of general ideas of the most significant algorithms with a comparison between them. Secondly, it proposes a new thinning algorithm that presents interesting properties in terms of processing quality and algorithm clarity, enriched with examples. Thirdly, the work considers parallelization issues for intrinsically sequential algorithms of thinning. The main advantage of the suggested algorithm is its universality, which makes it useful and versatile for a variety of applications.</abstract>

Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland

Faculty of Computer Science, Bialystok Technical University, ul. Wiejska 45 A, 15-351 Białystok, Poland

Faculty of Mathematics and Informatics, University of Białystok, ul. M. Skłodowskiej-Curie 14, 15-097 Białystok, Poland

K3M: A universal algorithm for image skeletonization and a review of thinning techniques

<abstract><title style='display:none'>Abstract</title> The focus of this paper is to develop reliable observer and filtering techniques for finite-dimensional battery models that adequately describe the charging and discharging behaviors. For this purpose, an experimentally validated battery model taken from the literature is extended by a mathematical description that represents parameter variations caused by aging. The corresponding disturbance models account for the fact that neither the state of charge, nor the above-mentioned parameter variations are directly accessible by measurements. Moreover, this work provides a comparison of the performance of different observer and filtering techniques as well as a development of estimation procedures that guarantee a reliable detection of large parameter variations. For that reason, different charging and discharging current profiles of batteries are investigated by numerical simulations. The estimation procedures considered in this paper are, firstly, a nonlinear Luenberger-type state observer with an offline calculated gain scheduling approach, secondly, a continuous-time extended Kalman filter and, thirdly, a hybrid extended Kalman filter, where the corresponding filter gains are computed online.</abstract>

Nonlinear state observers and extended Kalman filters for battery systems

<abstract><title style='display:none'>Abstract</title>
The aim of this paper is to develop a new recursive identification algorithm for autoregressive (AR) models corrupted by additive white noise. The proposed approach relies on a set of both low-order and high-order Yule–Walker equations and on a modified version of the overdetermined recursive instrumental variable method, leading to the estimation of both the AR coefficients and the additive noise variance. The main motivation behind our proposition is introducing model identification procedures suitable for implementation on edge-computing platforms and programmable logic controllers (PLCs), which are known to have limited capabilities and resources when dealing with complex mathematical computations (i.e., matrix inversion). Indeed, our development is focused on condition monitoring systems, with particular attention paid to their integration onboard industrial machinery. The performance of the recursive approach is tested using both numerical simulations and a laboratory case study. The obtained results are very promising.
</abstract>

Recursive Identification of Noisy Autoregressive Models Via a Noise–Compensated Overdetermined Instrumental Variable Method

<abstract><title style='display:none'>Abstract</title>
This paper concerns the synthesis of a nonlinear robust output controller based on a full-order observer for a class of uncertain disturbed systems. The proposed method guarantees that, in finite time, the system trajectories go inside a minimal neighborhood ultimately bounded. To this end, the attractive ellipsoid method is enhanced by applying the dynamic sliding mode control performance properties. Furthermore, in order to guarantee the stability of the trajectory around the trivial solution in the uniform-ultimately bounded sense, the feasibility of a specific matrix inequality problem is provided. With this feasible set of matrix inequalities, the separation principle of the controller/observer scheme considered also holds. To achieve a system performance improvement, a numerical algorithm based on the small size ultimate bound is presented. Finally, to illustrate the theoretical performance of the designed controller/observer, a numerical example dealing with the stabilization of a disturbed electromechanical system with uncertain and unmodeled dynamics is presented.
</abstract>

Dynamic Sliding Mode Control Based on a Full–Order Observer: Underactuated Electro–Mechanical System Regulation

<abstract><title style='display:none'>Abstract</title>
Safety-critical and mission-critical systems are often sensitive to functional degradation at the system or component level. Such degradation dynamics are often dependent on system usage (or control input), and may lead to significant losses and a potential system failure. Therefore, it becomes imperative to develop control designs that are able to ensure system stability and performance whilst mitigating the effects of incipient degradation by modulating the control input appropriately. In this context, this paper proposes a novel approach based on an optimal control theory framework wherein the degradation state of the system is considered in the augmented system model and estimated using sensor measurements. Further, it is incorporated within the optimal control paradigm leading to a control law that results in deceleration of the degradation rate at the cost of system performance whilst ensuring system stability. To that end, the speed of degradation and the state of the system in discrete time are considered to develop a linear quadratic tracker (LQT) and regulator (LQR) over a finite horizon in a mathematically rigorous manner. Simulation studies are performed to assess the proposed approach.
</abstract>

Degradation Tolerant Optimal Control Design for Stochastic Linear Systems

<abstract><title style='display:none'>Abstract</title>
The problem of estimation of unmeasured state variables and unknown reaction kinetic functions for selected biochemical processes modelled as a continuous stirred tank reactor is addressed in this paper. In particular, a new hierarchical (sequential) state observer is derived to generate stable and robust estimates of the state variables and kinetic functions. The developed hierarchical observer uses an adjusted asymptotic observer and an adopted super-twisting sliding mode observer. The stability of the proposed hierarchical observer is investigated under uncertainty in the system dynamics. The stability analysis of the estimation error dynamics is carried out based on the methodology associated with linear parameter-varying systems and sliding mode regimes. The developed hierarchical observer is implemented in the Matlab/Simulink environment and its performance is validated via simulation. The obtained satisfactory estimation results demonstrate high effectiveness of the devised hierarchical observer.
</abstract>

A Hierarchical Observer for a Non–Linear Uncertain CSTR Model of Biochemical Processes

<abstract><title style='display:none'>Abstract</title>
When constructing a new data classification algorithm, relevant quality indices such as classification accuracy (ACC) or the area under the receiver operating characteristic curve (AUC) should be investigated. End-users of these algorithms are interested in high values of the metrics as well as the proposed algorithm’s understandability and transparency. In this paper, a simple evolving vector quantization (SEVQ) algorithm is proposed, which is a novel supervised incremental learning classifier. Algorithms from the family of adaptive resonance theory and learning vector quantization inspired this method. Classifier performance was tested on 36 data sets and compared with 10 traditional and 15 incremental algorithms. SEVQ scored very well, especially among incremental algorithms, and it was found to be the best incremental classifier if the quality criterion is the AUC. The Scott–Knott analysis showed that SEVQ is comparable in performance to traditional algorithms and the leading group of incremental algorithms. The Wilcoxon rank test confirmed the reliability of the obtained results. This article shows that it is possible to obtain outstanding classification quality metrics while keeping the conceptual and computational simplicity of the classification algorithm.
</abstract>

An Empirical Study of a Simple Incremental Classifier Based on Vector Quantization and Adaptive Resonance Theory

<abstract><title style='display:none'>Abstract</title>
The existence of mild solutions and approximate controllability for Riemann–Liouville fractional neutral evolution systems with nonlocal conditions of a fractional order is investigated. The Laplace transform and semigroup theory are the tools used to prove the existence. In turn, approximate controllability is proved on the basis of a Nemytskii operator, a Mittag-Leffler function and certain hypotheses using fixed point theorems, as well as the construction of a Cauchy sequence. An example is provided to highlight the main results.
</abstract>

The Existence of Mild Solutions and Approximate Controllability for Nonlinear Fractional Neutral Evolution Systems

<abstract>In the paper we present some guidelines for the application of nonparametric statistical tests and post-hoc procedures devised to perform multiple comparisons of machine learning algorithms. We emphasize that it is necessary to distinguish between pairwise and multiple comparison tests. We show that the pairwise Wilcoxon test, when employed to multiple comparisons, will lead to overoptimistic conclusions. We carry out intensive normality examination employing ten different tests showing that the output of machine learning algorithms for regression problems does not satisfy normality requirements. We conduct experiments on nonparametric statistical tests and post-hoc procedures designed for multiple 1<italic>×N </italic>and <italic>N ×N </italic>comparisons with six different neural regression algorithms over 29 benchmark regression data sets. Our investigation proves the usefulness and strength of multiple comparison statistical procedures to analyse and select machine learning algorithms.</abstract>

Institute of Informatics Wrocław University of Technology, Wybrzeźe Wyspiańskiego 27, 50-370 Wrocław, Poland

Department of Spatial Management
Wrocław University of Environmental and Life Sciences, ul. Norwida 25/27, 50-375 Wrocław, Poland

Nonparametric statistical analysis for multiple comparison of machine learning regression algorithms

<abstract>This paper presents an identification method of dynamic systems based on a group method of data handling approach. In particular, a new structure of the dynamic multi-input multi-output neuron in a state-space representation is proposed. Moreover, a new training algorithm of the neural network based on the unscented Kalman filter is presented. The final part of the work contains an illustrative example regarding the application of the proposed approach to robust fault detection of a tunnel furnace.</abstract>

An unscented Kalman filter in designing dynamic GMDH neural networks for robust fault detection

<abstract><title style='display:none'>Abstract</title> In recent years, FCA has received significant attention from research communities of various fields. Further, the theory of FCA is being extended into different frontiers and augmented with other knowledge representation frameworks. In this backdrop, this paper aims to provide an understanding of the necessary mathematical background for each extension of FCA like FCA with granular computing, a fuzzy setting, interval-valued, possibility theory, triadic, factor concepts and handling incomplete data. Subsequently, the paper illustrates emerging trends for each extension with applications. To this end, we summarize more than 350 recent (published after 2011) research papers indexed in Google Scholar, IEEE Xplore, ScienceDirect, Scopus, SpringerLink, and a few authoritative fundamental papers.</abstract>

Centre for Mobile Cloud Computing Research, Faculty of Computer Science and Information Technology University of Malaya, Kuala Lumpur 50603, Malaysia

School of Information Technology and Engineering VIT University, Vellore 632014, India

A comprehensive survey on formal concept analysis, its research trends and applications

<abstract>In the present article, an attempt is made to derive optimal data-driven machine learning methods for forecasting an average daily and monthly rainfall of the Fukuoka city in Japan. This comparative study is conducted concentrating on three aspects: modelling inputs, modelling methods and pre-processing techniques. A comparison between linear correlation analysis and average mutual information is made to find an optimal input technique. For the modelling of the rainfall, a novel hybrid multi-model method is proposed and compared with its constituent models. The models include the artificial neural network, multivariate adaptive regression splines, the <italic>k</italic>-nearest neighbour, and radial basis support vector regression. Each of these methods is applied to model the daily and monthly rainfall, coupled with a pre-processing technique including moving average and principal component analysis. In the first stage of the hybrid method, sub-models from each of the above methods are constructed with different parameter settings. In the second stage, the sub-models are ranked with a variable selection technique and the higher ranked models are selected based on the leave-one-out cross-validation error. The forecasting of the hybrid model is performed by the weighted combination of the finally selected models.</abstract>

Department of Systems Design and Informatics Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka, Japan

Department of Systems Design and Informatics Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka, Japan, School of Electronic Engineering Dublin City University, Glasnevin, Dublin, Ireland

A rainfall forecasting method using machine learning models and its application to the Fukuoka city case

<abstract><title style='display:none'>Abstract</title> A solution for fault tolerant control (FTC) of a quadrotor unmanned aerial vehicle (UAV) is proposed. It relies on model reference-based control, where a reference model generates the desired trajectory. Depending on the type of reference model used for generating the reference trajectory, and on the assumptions about the availability and uncertainty of fault estimation, different error models are obtained. These error models are suitable for passive FTC, active FTC and hybrid FTC, the latter being able to merge the benefits of active and passive FTC while reducing their respective drawbacks. The controller is generated using results from the robust linear parameter varying (LPV) polytopic framework, where the vector of varying parameters is used to schedule between uncertain linear time invariant (LTI) systems. The design procedure relies on solving a set of linear matrix inequalities (LMIs) in order to achieve regional pole placement and H∞ norm bounding constraints. Simulation results are used to compare the different FTC strategies.</abstract>

Automatic Control Department Polytechnic University of Catalonia (UPC), Rambla de Sant Nebridi, 11, 08222 Terrassa, Spain

Institute of Robotics and Industrial Informatics UPC-CSIC, Carrer de Llorens i Artigas, 4-6, 08028 Barcelona, Spain

Robust Quasi–LPV Model Reference FTC of a Quadrotor Uav Subject to Actuator Faults

<abstract><title style='display:none'>Abstract</title>The paper deals with the modeling and fault-tolerant control of a real battery assembly system which is under implementation at the RAFI GmbH company (one of the leading electronic manufacturing service providers in Germany). To model and control the battery assembly system, a unified max-plus algebra and model predictive control framework is introduced. Subsequently, the control strategy is enhanced with fault-tolerance features that increase the overall performance of the production system being considered. In particular, it enables tolerating (up to some degree) mobile robot, processing and transportation faults. The paper discusses also robustness issues, which are inevitable in real production systems. As a result, a novel robust predictive fault-tolerant strategy is developed that is applied to the battery assembly system. The last part of the paper shows illustrative examples, which clearly exhibit the performance of the proposed approach.</abstract>

Department of Research & Development, RAFI GmbH Co. KG, Ravensburger Straße, 128–134, D-88276 Berg/Ravensburg, Germany

Institute of Control and Computation Engineering, University of Zielona Góra, ul. prof. Z. Szafrana 2, 65-516 Zielona Góra, Poland

Faculty of Mechanical Engineering, University of Applied Sciences Ravensburg–Weingarten, Building D., Doggenriedstraße, Weingarten, Germany

Towards Robust Predictive Fault–Tolerant Control for a Battery Assembly System

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International Journal of Applied Mathematics and Computer Science

Journal of the University of Zielona Góra

 The International Journal of Applied Mathematics and Computer Science is a quarterly published in Poland since 1991 by the University of Zielona Góra in partnership with...

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