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 Feed the Number of Luts for Mealy FSMS with State Transformation<abstract><title style='display:none'>Abstract</title> <p>In many digital systems, various sequential blocks are used. This paper is devoted to the case where the model of a Mealy finite state machine (FSM) represents the behaviour of a sequential block. The chip area occupied by an FSM circuit is one of the most important characteristics used in logic synthesis. In this paper, a method is proposed which aims at reducing LUT counts for FPGA-based Mealy FSMs with transformation of state codes into FSM outputs. This is done using the combined state codes. Such an approach allows excluding a block of transformation of binary state codes into extended state codes. The proposed method leads to LUT-based Mealy FSM circuits having exactly three levels of logic blocks. Under certain conditions, each function for any logic level is represented by a circuit including a single LUT. The proposed approach is illustrated with an example of synthesis. The results of experiments conducted using standard benchmarks show that the proposed method produces LUT-based FSM circuits with significantly smaller LUT counts than is the case for circuits produced by other investigated methods (Auto and One-hot of Vivado, JEDI, and transformation of binary codes into extended state codes). The LUT count is decreased by an average of 17.96 to 91.8%. Moreover, if some conditions are met, the decrease in the LUT count is accompanied with a slight improvement in the operating frequency compared with circuits based on extended state codes. The advantages of the proposed method multiply with increasing the numbers of FSM inputs and states.</p> </abstract>ARTICLEtrue Gaps and Kleinberg’s Clustering Axioms for –Means<abstract><title style='display:none'>Abstract</title> <p>The widely applied <italic>k</italic>-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density within/between clusters and is in conflict with Kleinberg’s axiomatic system for distance based clustering algorithms that formalizes those expectations. In particular, <italic>k</italic>-means violates the consistency axiom. We hypothesise that this clash is due to the unexplained expectation that the data themselves should have the property of being clusterable in order to expect the algorithm clustering them to fit a clustering axiomatic system. To demonstrate this, we introduce two new clusterability properties, i.e., variational <italic>k</italic>-separability and residual <italic>k</italic>-separability, and show that then Kleinberg’s consistency axiom holds for <italic>k</italic>-means operating in the Euclidean or non-Euclidean space. Furthermore, we propose extensions of the <italic>k</italic>-means algorithm that fit approximately Kleinberg’s richness axiom, which does not hold for <italic>k</italic>-means. In this way, we reconcile <italic>k</italic>-means with Kleinberg’s axiomatic framework in Euclidean and non-Euclidean settings. Besides contribution to the theory of axiomatic frameworks of clustering and to clusterability theory, the practical benefit is the possibility to construct datasets for testing purposes of algorithms optimizing the <italic>k</italic>-means cost function. This includes a method of construction of clusterable data with a global optimum known in advance.</p> </abstract>ARTICLEtrue Useful Life Prediction of a Lithium–Ion Battery Based on a Temporal Convolutional Network with Data Extension<abstract><title style='display:none'>Abstract</title> <p>Unmanned underwater vehicles are typically deployed in deep sea environments, which present unique working conditions. Lithium-ion power batteries are crucial for powering underwater vehicles, and it is vital to accurately predict their remaining useful life (RUL) to maintain system reliability and safety. We propose a residual life prediction model framework based on complete ensemble empirical mode decomposition with an adaptive noise-temporal convolutional net (CEEMDAN-TCN), which utilizes dilated causal convolutions to improve the model’s ability to capture local capacity regeneration and enhance the overall prediction accuracy. CEEMDAN is employed to denoise the data and prevent RUL prediction errors caused by local regeneration, and feature expansion is utilized to extend the temporal dimension of the original data. The NASA and CALCE battery capacity datasets are used as input to train the network framework. The output is the current predicted residual capacity, which is compared with the real residual battery capacity. The MAE, RMSE and RE are used as the evaluation indexes of the RUL prediction performance. The proposed network model is verified on the NASA and CACLE datasets. The evaluation results show that our method has better life prediction performance. At the same time, it is proved that both feature expansion and modal decomposition can improve the generalization ability of the model, which is very useful in industrial scenarios.</p> </abstract>ARTICLEtrue Discrete Approximations and an Error Analysis of a Two–Temperature Thermo–Elastic Model with Microtemperatures<abstract><title style='display:none'>Abstract</title> <p>In this paper, we consider, from a numerical point of view, a two-temperature poro-thermoelastic problem. The model is written as a coupled linear system of hyperbolic and elliptic partial differential equations. An existence result is proved and energy decay properties are recalled. Then we introduce a fully discrete approximation by using the finite element method and the implicit Euler scheme. Some <italic>a priori </italic>error estimates are obtained, from which the linear convergence of the approximation is deduced under an appropriate additional regularity. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximation, the decay of the discrete energy and the behaviour of the solution depending on a constitutive parameter.</p> </abstract>ARTICLEtrue Integral and MRAC–Based Approach to the Adaptive Stabilisation of a Class of Linear Time–Delay Systems with Unknown Parameters<abstract><title style='display:none'>Abstract</title> <p>The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the sign of the control gain is known. First, the integral operator is applied to obtain a new representation of the original system, where the whole state is known. The use of the integral operator decomposes the control problem into two subproblems that are solved by using the model reference adaptive control method and the backstepping procedure. The effectiveness of the proposed approach is illustrated through an academic example and a practical application case regarding a chemical reactor recycle system.</p> </abstract>ARTICLEtrue Multi–Criteria Approach for Selecting an Explanation from the Set of Counterfactuals Produced by an Ensemble of Explainers<abstract><title style='display:none'>Abstract</title> <p>Counterfactuals are widely used to explain ML model predictions by providing alternative scenarios for obtaining more desired predictions. They can be generated by a variety of methods that optimize various, sometimes conflicting, quality measures and produce quite different solutions. However, choosing the most appropriate explanation method and one of the generated counterfactuals is not an easy task. Instead of forcing the user to test many different explanation methods and analysing conflicting solutions, in this paper we propose to use a multi-stage ensemble approach that will select a single counterfactual based on the multiple-criteria analysis. It offers a compromise solution that scores well on several popular quality measures. This approach exploits the dominance relation and the ideal point decision aid method, which selects one counterfactual from the Pareto front. The conducted experiments demonstrate that the proposed approach generates fully actionable counterfactuals with attractive compromise values of the quality measures considered.</p> </abstract>ARTICLEtrue Existence of Mild Solutions and Approximate Controllability for Nonlinear Fractional Neutral Evolution Systems<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue Empirical Study of a Simple Incremental Classifier Based on Vector Quantization and Adaptive Resonance Theory<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue Hierarchical Observer for a Non–Linear Uncertain CSTR Model of Biochemical Processes<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue Tolerant Optimal Control Design for Stochastic Linear Systems<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue Sliding Mode Control Based on a Full–Order Observer: Underactuated Electro–Mechanical System Regulation<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue Identification of Noisy Autoregressive Models Via a Noise–Compensated Overdetermined Instrumental Variable Method<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue Modeling and Insurance Premium Pricing Under A Bonus–Malus System in Motor Insurance<abstract> <title style='display:none'>Abstract</title> <p>Accurately modeling claims data and determining appropriate insurance premiums are vital responsibilities for non-life insurance firms. This article presents novel models for claims that offer improved precision in fitting claim data, both in terms of claim frequency and severity. Specifically, we suggest the Poisson-GaL distribution for claim frequency and the exponential-GaL distribution for claim severity. The traditional method of assigning automobile premiums based on a bonus-malus system relies solely on the number of claims made. However, this may lead to unfair outcomes when an insured individual with a minor severity claim is charged the same premium as someone with a severe claim. The second aim of this article is to propose a new model for calculating bonus-malus premiums. Our proposed model takes into account both the number and size of claims, which follow the Poisson-GaL distribution and the exponential-GaL distribution, respectively. To calculate the premiums, we employ the Bayesian approach. Real-world data are used in practical examples to illustrate how the proposed model can be implemented. The results of our analysis indicate that the proposed premium model effectively resolves the issue of overcharging. Moreover, the proposed model produces premiums that are more tailored to policyholders’ claim histories, benefiting both the policyholders and the insurance companies. This advantage can contribute to the growth of the insurance industry and provide a competitive edge in the insurance market.</p> </abstract>ARTICLEtrue Flat Filtering Control of a Two Degrees of Freedom Helicopter Subject to Tail Rotor Disturbances<abstract> <title style='display:none'>Abstract</title> <p>This article deals with modelling and a flatness-based robust trajectory tracking scheme for a two degrees of freedom helicopter, which is subject to four types of tail rotor disturbances to validate the control scheme robustness. A mathematical model of the system, its differential flatness and a differential parametrization are obtained. The flat filtering control is designed for the system control with a partially known model, assuming the non-modelled dynamics and the external disturbances (specially the tail rotor ones) to be rejected by means of an extended state model (ultra-local model). Numerical and experimental assessments are carried out on a characterized prototype whose yaw angle (<italic>ψ</italic>), given by the <italic>z</italic> axis, is in free form, while the pitch angle (<italic>θ</italic>), which results from rotation about the <italic>y</italic> axis, is mechanically restricted. The proposed controller performance is tested through a set of experiments in trajectory tracking tasks with different disturbances in the tail rotor, showing robust behaviour for the different disturbances. Besides, a comparison study against a widely used controller of LQR type is carried out, in which the proposed controller achieves better results, as illustrated by a performance index.</p> </abstract>ARTICLEtrue Autonomous Switching of Task–Level Strategies<abstract> <title style='display:none'>Abstract</title> <p>Autonomous coordination of multi-agent systems can improve the reaction and dispatching ability of multiple agents to emergency events. The existing research has mainly focused on the reactions or dispatching in specific scenarios. However, task-level coordination has not received significant attention. This study proposes a framework for autonomous switching of task-level strategies (ASTS), which can automatically switch strategies according to different scenarios in the task execution process. The framework is based on the blackboard system, which takes the form of an instance as an agent and the form of norm(s) as a strategy; it uses events to drive autonomous cooperation among multiple agents. A norm may be triggered when an event occurs. After the triggered norm is executed, it can change the data, state, and event in ASTS. To demonstrate the autonomy and switchability of the proposed framework, we develop a fire emergency reaction dispatch system. This system is applied to emergency scenarios involving fires. Five types of strategies and two control modes are designed for this system. Experiments show that this system can autonomously switch between different strategies and control modes in different scenarios with promising results. Our framework improves the adaptability and flexibility of multiple agents in an open environment and represents a solid step toward switching strategies at the task level.</p> </abstract>ARTICLEtrue–D Lossless FIR Filter Design Using Synthesis of the Paraunitary Transfer Function Matrix<abstract> <title style='display:none'>Abstract</title> <p>A synthesis method for designing two-dimensional lossless finite impulse response (FIR) filters for various digital signal processing tasks is proposed. The synthesis method is based on using a 2-D embedding approach to obtain the paraunitary transfer function matrix of the lossless FIR filter. The elements of the paraunitary transfer function matrix are the transfer function of a given lossy FIR structure and the transfer functions for its complementary structures. The embedding method is used to design complementary FIR filter structures for several known lossy FIR filters. The lossless FIR filter matrix obtained in this article has a size of 3 × 1 and satisfies the paraunitary conditions. The conditions are described by a set of nonlinear equations. A modified Newton method is used to solve this set of equations. The proposed design method is used to determine the lossless structures of two-dimensional FIR filters for various digital processing tasks.</p> </abstract>ARTICLEtrue of the -norm for High Level Classification Features Pruning in Modern Convolutional Neural Networks With Local Sensitivity Analysis<abstract> <title style='display:none'>Abstract</title> <p>Transfer learning has surfaced as a compelling technique in machine learning, enabling the transfer of knowledge across networks. This study evaluates the efficacy of ImageNet pretrained state-of-the-art networks, including DenseNet, ResNet, and VGG, in implementing transfer learning for prepruned models on compact datasets, such as Fashion MNIST, CIFAR10, and CIFAR100. The primary objective is to reduce the number of neurons while preserving high-level features. To this end, local sensitivity analysis is employed alongside p-norms and various reduction levels. This investigation discovers that VGG16, a network rich in parameters, displays resilience to high-level feature pruning. Conversely, the ResNet architectures reveal an interesting pattern of increased volatility. These observations assist in identifying an optimal combination of the norm and the reduction level for each network architecture, thus offering valuable directions for model-specific optimization. This study marks a significant advance in understanding and implementing effective pruning strategies across diverse network architectures, paving the way for future research and applications.</p> </abstract>ARTICLEtrue Waves for Low–Grade Glioma Growth and Response to A Chemotherapy Model<abstract> <title style='display:none'>Abstract</title> <p>Low-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the existence of travelling wave solutions in the framework of Fenichel’s invariant manifold theory. The estimates of the minimum speeds of the travelling wave solutions are provided. The obtained analytical results are illustrated by numerical simulations.</p> </abstract>ARTICLEtrue for Single Image Deraining<abstract> <title style='display:none'>Abstract</title> <p>Image is one of the most important forms of information expression in multimedia. It is the key factor to determine the visual effect of multimedia software. As an image restoration task, image deraining can effectively restore the original information of the image, which is conducive to the downstream task. In recent years, with the development of deep learning technology, CNN and Transformer structures have shone brightly in computer vision. In this paper, we summarize the key to success of these structures in the past, and on this basis, we introduce the concept of a layer aggregation mechanism to describe how to reuse the information of the previous layer to better extract the features of the current layer. Based on this layer aggregation mechanism, we build the rain removal network called DenseformerNet. Our network strengthens feature promotion and encourages feature reuse, allowing better information and gradient flow. Through a large number of experiments, we prove that our model is efficient and effective, and expect to bring some illumination to the future rain removal network.</p> </abstract>ARTICLEtrue Model Reference Control for Synchronization of a Vehicle Platoon with Limited Output Information and Subject to Periodical Intermittent Information<abstract> <title style='display:none'>Abstract</title> <p>Vehicles involved in platoon formation may experience difficulties in obtaining full-state information that can be exchanged and used for controller synthesis. Therefore, a distributed controller based on a model reference and designed utilizing a cooperative observer is proposed for vehicle platoon synchronization. The proposed controller is composed of three main blocks, namely, the reference model, the cooperative observer and the main controller. The reference model is developed by using a homogeneous vehicle platoon that utilizes cooperative full-state information. The cooperative observer is a state estimator which is constructed based on the cooperative output estimation error. It provides state estimates to be used by the main controller. The main controller is constructed from a nominal control and a synchronization input. The nominal control has the main task of tracking the lead vehicle, while in order to reduce the synchronization error, the synchronization input is added by utilizing the cooperative disagreement error. Stability analysis is focused on the vehicle platoon when it is subjected to completely periodical intermittent information. The condition on the information rate is derived for guaranteeing the synchronization of the platoon. Numerical simulation of a vehicle platoon consisting of one leader and five followers is used to examine the performance of the controller.</p> </abstract>ARTICLEtrue