rss_2.0International Journal of Applied Mathematics and Computer Science FeedSciendo RSS Feed for International Journal of Applied Mathematics and Computer Science Journal of Applied Mathematics and Computer Science 's Cover–Tolerant Tracking Control for a Non–Linear Twin–Rotor System Under Ellipsoidal Bounding<abstract> <title style='display:none'>Abstract</title> <p>A novel fault-tolerant tracking control scheme based on an adaptive robust observer for non-linear systems is proposed. Additionally, it is presumed that the non-linear system may be faulty, i.e., affected by actuator and sensor faults along with the disturbances, simultaneously. Accordingly, the stability of the robust observer as well as the fault-tolerant tracking controller is achieved by using the ℋ<sub>∞</sub> approach. Furthermore, unknown actuator and sensor faults and states are bounded by the uncertainty intervals for estimation quality assessment as well as reliable fault diagnosis. This means that narrow intervals accompany better estimation quality. Thus, to cope with the above difficulty, it is assumed that the disturbances are over-bounded by an ellipsoid. Consequently, the performance and correctness of the proposed fault-tolerant tracking control scheme are verified by using a non-linear twin-rotor aerodynamical laboratory system.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00Joint Feature Selection and Classification for Positive Unlabelled Multi–Label Data Using Weighted Penalized Empirical Risk Minimization<abstract> <title style='display:none'>Abstract</title> <p>We consider the positive-unlabelled multi-label scenario in which multiple target variables are not observed directly. Instead, we observe surrogate variables indicating whether or not the target variables are labelled. The presence of a label means that the corresponding variable is positive. The absence of the label means that the variable can be either positive or negative. We analyze embedded feature selection methods based on two weighted penalized empirical risk minimization frameworks. In the first approach, we introduce weights of observations. The idea is to assign larger weights to observations for which there is a consistency between the values of the true target variable and the corresponding surrogate variable. In the second approach, we consider a weighted empirical risk function which corresponds to the risk function for the true unobserved target variables. The weights in both the methods depend on the unknown propensity score functions, whose estimation is a challenging problem. We propose to use very simple bounds for the propensity score, which leads to relatively simple forms of weights. In the experiments we analyze the predictive power of the methods considered for different labelling schemes.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00Hybrid Deep Learning Model–Based Prediction of Images Related to Cyberbullying<abstract> <title style='display:none'>Abstract</title> <p>Cyberbullying has become more widespread as a result of the common use of social media, particularly among teenagers and young people. A lack of studies on the types of advice and support available to victims of bullying has a negative impact on individuals and society. This work proposes a hybrid model based on transformer models in conjunction with a support vector machine (SVM) to classify our own data set images. First, seven different convolutional neural network architectures are employed to decide which is best in terms of results. Second, feature extraction is performed using four top models, namely, ResNet50, EfficientNetB0, MobileNet and Xception architectures. In addition, each architecture extracts the same number of features as the number of images in the data set, and these features are concatenated. Finally, the features are optimized and then provided as input to the SVM classifier. The accuracy rate of the proposed merged models with the SVM classifier achieved 96.05%. Furthermore, the classification precision of the proposed merged model is 99% in the bullying class and 93% in the non-bullying class. According to these results, bullying has a negative impact on students’ academic performance. The results help stakeholders to take necessary measures against bullies and increase the community’s awareness of this phenomenon.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00A Graph Theory–Based Approach to the Description of the Process and the Diagnostic System<abstract> <title style='display:none'>Abstract</title> <p>The paper proposes an original, comprehensive, and methodically consistent graph theory-based approach to the description of the diagnosed process and the diagnosing system. The main baseline of the presented approach is in the dichotomous approach to diagnosing. It involves a separate description of both the process and the diagnostic system. This approach reflects the practice of designing implementable diagnostic systems. Thus, it can be seen as a proposal of a new, alternative, and, at the same time, flexible design procedure with great potential for applications. The primary motivation behind it was an attempt to circumvent the numerous limitations of well-known and well-established diagnosis approaches proposed by the communities working on fault detection and isolation (FDI) and artificial intelligence theories for diagnosis (DX). Accordingly, the paper identifies and provides an extensive discussion and a critical analysis of the existing limitations. Numerous examples and references to practical applications of the approach are indicated.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00Reliability–Aware Zonotopic Tube–Based Model Predictive Control of a Drinking Water Network<abstract> <title style='display:none'>Abstract</title> <p>A robust economic model predictive control approach that takes into account the reliability of actuators in a network is presented for the control of a drinking water network in the presence of uncertainties in the forecasted demands required for the predictive control design. The uncertain forecasted demand on the nominal MPC may make the optimization process intractable or, to a lesser extent, degrade the controller performance. Thus, the uncertainty on demand is taken into account and considered unknown but bounded in a zonotopic set. Based on this uncertainty description, a robust MPC is formulated to ensure robust constraint satisfaction, performance, stability as well as recursive feasibility through the formulation of an online tube-based MPC and an accompanying appropriate terminal set. Reliability is then modelled based on Bayesian networks, such that the resulting nonlinear function accommodated in the optimization setup is presented in a pseudo-linear form by means of a linear parameter varying representation, mitigating any additional computational expense thanks to the formulation as a quadratic optimization problem. With the inclusion of a reliability index to the economic dominant cost of the MPC, the network users’ requirements are met whilst ensuring improved reliability, therefore decreasing short and long term operational costs for water utility operators. Capabilities of the designed controller are demonstrated with simulated scenarios on the Barcelona drinking water network.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00On Some Ways to Implement State–Multiplicative Fault Detection in Discrete–Time Linear Systems<abstract> <title style='display:none'>Abstract</title> <p>New design conditions on the observer based residual filter design for the linear discrete-time linear systems with zoned system parameter faults are presented. With respect to time evolution of residual signals and with a guarantee of their robustness, the design task is stated in terms of linear matrix inequalities, while the recursive implementation of algorithms is motivated by the platform existence for real-time processing. A major objective is to analyze the configuration required and, in particular, a new characterization of the norm boundaries of the multiplicative zonal parametric faults to be projected onto the structure of the set of linear matrix inequalities.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00A Multi–Model Based Adaptive Reconfiguration Control Scheme for an Electro–Hydraulic Position Servo System<abstract> <title style='display:none'>Abstract</title> <p>Reliability and safety of an electro-hydraulic position servo system (EHPSS) can be greatly reduced for potential sensor and actuator faults. This paper proposes a novel reconfiguration control (RC) scheme that combines multi-model and adaptive control to compensate for the adverse effects. Such a design includes several fixed models, one adaptive model, and one reinitialized adaptive model. Each of the models has its own independent controller that is based on a complete parametrization of the corresponding fault. A proper switching mechanism is set up to select the most appropriate controller to control the current plant. The system output can track the reference model asymptotically using the proposed method. Simulation results validate robustness and effectiveness of the proposed scheme. The main contribution is a reconfiguration control method that can handle component faults and maintain the acceptable performance of the EHPSS.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00A Kalman Filter with Intermittent Observations and Reconstruction of Data Losses<abstract> <title style='display:none'>Abstract</title> <p>This paper deals with the problem of joint state and unknown input estimation for stochastic discrete-time linear systems subject to intermittent unknown inputs on measurements. A Kalman filter approach is proposed for state prediction and intermittent unknown input reconstruction. The filter design is based on the minimization of the trace of the state estimation error covariance matrix under the constraint that the state prediction error is decoupled from active unknown inputs corrupting measurements at the current time. When the system is not strongly detectable, a sufficient stochastic stability condition on the mathematical expectation of the random state prediction errors covariance matrix is established in the case where the arrival binary sequences of unknown inputs follow independent random Bernoulli processes. When the intermittent unknown inputs on measurements represent intermittent observations, an illustrative example shows that the proposed filter corresponds to a Kalman filter with intermittent observations having the ability to generate a minimum variance unbiased prediction of measurement losses.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00Global Behavior of a Multi–Group Seir Epidemic Model with Spatial Diffusion in a Heterogeneous Environment<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we propose a multi-group SEIR epidemic model with spatial diffusion, where the model parameters are spatially heterogeneous. The positivity and ultimate boundedness of the solution, as well as the existence of a global attractor of the associated solution semiflow, are established. The definition of the basic reproduction number is given by utilizing the next generation operator approach, whereby threshold-type results on the global dynamics in terms of this number are established. That is, when the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, while if it is greater than one, uniform persistence of this model is proved. Finally, the feasibility of the main theoretical results is shown with the aid of numerical examples for a model with two groups.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00Bootstrap Methods for Epistemic Fuzzy Data<abstract> <title style='display:none'>Abstract</title> <p>Fuzzy numbers are often used for modeling imprecise perceptions of the real-valued observations. Such epistemic fuzzy data may cause problems in statistical reasoning and data analysis. We propose a universal nonparametric technique, called the epistemic bootstrap, which could be helpful when the existing methods do not work or do not give satisfactory results. Besides the simple epistemic bootstrap, we develop its several refinements that aim to reduce the variance in statistical inference. We also perform an extended simulation study to examine statistical properties of the approaches considered. The discussion of the results is supplemented by some hints for practical use.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00Revisiting Strategies for Fitting Logistic Regression for Positive and Unlabeled Data<abstract> <title style='display:none'>Abstract</title> <p>Positive unlabeled (PU) learning is an important problem motivated by the occurrence of this type of partial observability in many applications. The present paper reconsiders recent advances in parametric modeling of PU data based on empirical likelihood maximization and argues that they can be significantly improved. The proposed approach is based on the fact that the likelihood for the logistic fit and an unknown labeling frequency can be expressed as the sum of a convex and a concave function, which is explicitly given. This allows methods such as the concave-convex procedure (CCCP) or its variant, the disciplined convex-concave procedure (DCCP), to be applied. We show by analyzing real data sets that, by using the DCCP to solve the optimization problem, we obtain significant improvements in the posterior probability and the label frequency estimation over the best available competitors.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00Parameter Identifiability for Nonlinear LPV Models<abstract> <title style='display:none'>Abstract</title> <p>Linear parameter varying (LPV) models are being increasingly used as a bridge between linear and nonlinear models. From a mathematical point of view, a large class of nonlinear models can be rewritten in LPV or quasi-LPV forms easing their analysis. From a practical point of view, that kind of model can be used for introducing varying model parameters representing, for example, nonconstant characteristics of a component or an equipment degradation. This approach is frequently employed in several model-based system maintenance methods. The identifiability of these parameters is then a key issue for estimating their values based on which a decision can be made. However, the problem of identifiability of these models is still at a nascent stage. In this paper, we propose an approach to verify the identifiability of unknown parameters for LPV or quasi-LPV state-space models. It makes use of a parity-space like formulation to eliminate the states of the model. The resulting input-output-parameter equation is analyzed to verify the identifiability of the original model or a subset of unknown parameters. This approach provides a framework for both continuous-time and discrete-time models and is illustrated through various examples.</p> </abstract>ARTICLE2022-07-04T00:00:00.000+00:00Template Chart Detection for Stoma Telediagnosis<abstract> <title style='display:none'>Abstract</title> <p>The paper presents the concept of using color template charts for the needs of telemedicine, particularly telediagnosis of the stoma. Although the concept is not new, the current popularity and level of development of digital cameras, especially those embedded in smartphones, allow common and reliable remote advice on various medical problems, which can be very important in the case of limitations in a physical contact with a doctor. The article focuses on the initial stages of photo processing for the needs of telemedicine, i.e., on the assumptions and the process of designing the appropriate template and detecting it in photos for stoma telediagnosis. Research on the developed algorithms for the location of fiducial markers and reference color fields, carried out on the basis of over 2,000 photos, showed a very high tolerance to scene exposure, lighting conditions and the camera used. The obtained results allowed the initial image intensity normalization of the stoma area as well as correct localization and measurement of changes detected on the skin and the mucosa, which, in the opinion of doctors, significantly increased the diagnostic value of the photographs.</p> </abstract>ARTICLE2022-03-31T00:00:00.000+00:00Hybrid Cryptography with a One–Time Stamp to Secure Contact Tracing for COVID–19 Infection<abstract> <title style='display:none'>Abstract</title> <p>The COVID-19 pandemic changed the lives of millions of citizens worldwide in the manner they live and work to the so-called new norm in social standards. In addition to the extraordinary effects on society, the pandemic created a range of unique circumstances associated with cybercrime that also affected society and business. The anxiety due to the pandemic increased the probability of successful cyberattacks and as well as their number and range. For public health officials and communities, location tracking is an essential component in the efforts to combat the disease. The governments provide a lot of mobile apps to help health officials to trace the infected persons and contact them to aid and follow up on the health status, which requires an exchange of data in different forms. This paper presents the one-time stamp model as a new cryptography technique to secure different contact forms and protect the privacy of the infected person. The one-time stamp hybrid model consists of a combination of symmetric, asymmetric, and hashing cryptography in an entirely new way that is different from conventional and similar existing algorithms. Several experiments have been carried out to analyze and examine the proposed technique. Also, a comparison study has been made between our proposed technique and other state-of-the-art alternatives. Results show that the proposed one-time stamp model provides a high level of security for the encryption of sensitive data relative to other similar techniques with no extra computational cost besides faster processing time.</p> </abstract>ARTICLE2022-03-31T00:00:00.000+00:00A Feasible Schedule for Parallel Assembly Tasks in Flexible Manufacturing Systems<abstract> <title style='display:none'>Abstract</title> <p>The paper concerns the design of a framework for implementing fault-tolerant control of hybrid assembly systems that connect human operators and fully automated technical systems. The main difficulty in such systems is related to delays that result from objective factors influencing human operators’ work, e.g., fatigue, experience, etc. As the battery assembly system can be considered a firm real-time one, these delays are treated as faults. The presented approach guarantees real-time compensation of delays, and the fully automated part of the system is responsible for this compensation. The paper begins with a detailed description of a battery assembly system in which two cooperating parts can be distinguished: fully automatic and semi-automatic. The latter, nonderministic in nature, is the main focus of this paper. To describe and analyze the states of the battery assembly system, instead of the most commonly used simulation, the classic max-plus algebra with an extension allowing one to express non-deterministic human operators’ work is used. In order to synchronize tasks and schedule (according to the reference schedule) automated and human operators’ tasks, it is proposed to use a wireless IoT platform called KIS.ME. As a result, it allows a reference model of human performance to be defined using fuzzy logic. Having such a model, predictive delays tolerant planning is proposed. The final part of the paper presents the achieved results, which clearly indicate the potential benefits that can be obtained by combining the wireless KIS.ME architecture (allocated in the semi-automatic part of the system) with wired standard production networks.</p> </abstract>ARTICLE2022-03-31T00:00:00.000+00:00A Data Association Model for Analysis of Crowd Structure<abstract> <title style='display:none'>Abstract</title> <p>The paper discusses a non-deterministic model for data association tasks in visual surveillance of crowds. Using detection and tracking of crowd components (i.e., individuals and groups) as baseline tools, we propose a simple algebraic framework for maintaining data association (continuity of labels assigned to crowd components) between subsequent video-frames in spite of possible disruptions and inaccuracies in tracking/detection algorithms. Formally, two alternative schemes (which, in practice, can be jointly used) are introduced, depending on whether individuals or groups can be prospectively better tracked in the current scenario. In the first scheme, only individuals are tracked, and the continuity of group labels is inferred without explicitly tracking the groups. In the second scheme, only group tracking is performed, and associations between individuals are inferred from group tracking. The associations are built upon non-deterministic estimates of memberships (individuals in groups) and estimates obtained directly from the baseline detection and tracking algorithms. The framework can incorporate any detectors and trackers (both classical or DL-based) as long as they can provide some geometric outlines (e.g., bounding boxes) of the crowd components. The formal analysis is supported by experiments in exemplary scenarios, where the framework provides meaningful performance improvements in various crowd analysis tasks.</p> </abstract>ARTICLE2022-03-31T00:00:00.000+00:00Sensor Location for Travel Time Estimation Based on the User Equilibrium Principle: Application of Linear Equations<abstract> <title style='display:none'>Abstract</title> <p>Travel time is a fundamental measure in any transportation system. With the development of technology, travel time can be automatically collected by a variety of advanced sensors. However, limited by objective conditions, it is difficult for any sensor system to cover the whole transportation network in real time. In order to estimate the travel time of the whole transportation network, this paper gives a system of linear equations which is constructed by the user equilibrium (UE) principle and observed data. The travel time of a link which is not covered by a sensor can be calculated by using the observed data collected by sensors. In a typical transportation network, the minimum number and location of sensors to estimate the travel time of the whole network are given based on the properties of the solution of a systems of linear equations. The results show that, in a typical network, the number and location of sensors follow a certain law. The results of this study can provide reference for the development of transportation and provide a scientific basis for transportation planning.</p> </abstract>ARTICLE2022-03-31T00:00:00.000+00:00Non–Standard Analysis Revisited: An Easy Axiomatic Presentation Oriented Towards Numerical Applications<abstract> <title style='display:none'>Abstract</title> <p>Alpha-Theory was introduced in 1995 to provide a simplified version of Robinson’s non-standard analysis which overcomes the technicalities of symbolic logic. The theory has been improved over the years, and recently it has been used also to solve practical problems in a pure numerical way, thanks to the introduction of algorithmic numbers. In this paper, we introduce Alpha-Theory using a novel axiomatic approach oriented towards real-world applications, to avoid the need to master mathematical logic and model theory. To corroborate the strong link of this Alpha-Theory axiomatization and scientific computations, we report numerical illustrative applications never carried out by means of non-standard numbers within a computer, i.e., the computation of the eigenvalues of a non-Archimedean matrix, some computations related to non-Archimedean Markov chains, and the Cholesky factorization of a non-Archimedean matrix. We also highlight the differences between our numerical routines and pure symbolic approaches: as expected, the former scales better when the dimension of the problem increases.</p> </abstract>ARTICLE2022-03-31T00:00:00.000+00:00A Comprehensive Study of Clustering a Class of 2D Shapes<abstract> <title style='display:none'>Abstract</title> <p>The paper is concerned with clustering with respect to the shape and size of 2D contours that are boundaries of cross-sections of 3D objects of revolution. We propose a number of similarity measures based on combined disparate Procrustes analysis (PA) and dynamic time warping (DTW) distances. A motivation and the main application for this study comes from archaeology. The computational experiments performed refer to the clustering of archaeological pottery.</p> </abstract>ARTICLE2022-03-31T00:00:00.000+00:00A Multi–Source Fluid Queue Based Stochastic Model of the Probabilistic Offloading Strategy in a MEC System With Multiple Mobile Devices and a Single MEC Server<abstract> <title style='display:none'>Abstract</title> <p>Mobile edge computing (MEC) is one of the key technologies to achieve high bandwidth, low latency and reliable service in fifth generation (5G) networks. In order to better evaluate the performance of the probabilistic offloading strategy in a MEC system, we give a modeling method to capture the stochastic behavior of tasks based on a multi-source fluid queue. Considering multiple mobile devices (MDs) in a MEC system, we build a multi-source fluid queue to model the tasks offloaded to the MEC server. We give an approach to analyze the fluid queue driven by multiple independent heterogeneous finite-state birth-and-death processes (BDPs) and present the cumulative distribution function (CDF) of the edge buffer content. Then, we evaluate the performance measures in terms of the utilization of the MEC server, the expected edge buffer content and the average response time of a task. Finally, we provide numerical results with some analysis to illustrate the feasibility of the stochastic model built in this paper.</p> </abstract>ARTICLE2022-03-31T00:00:00.000+00:00en-us-1