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A large number of fully normalized associated Legendre function (fnALF) calculations are required to compute Earth's gravity field elements using ultra high-order gravity field coefficient models. In the surveying and mapping industry, researchers typically rely on CPU-based systems for these calculations, which leads to limitations in execution speed and power efficiency. Although modern CPUs improve instruction execution efficiency through instruction-level parallelism, the constraints of a shared memory architecture impose further limitations on the execution speed and power efficiency. This results in exponential increases in computation time as demand rises alongside high power consumption. In this article, we present a new computational implementation of an fnALF based on the ZYNQ platform. We design a task-parallel "pipeline" architecture which converts the original serial logic into a more efficient hardware implementation, and we utilize a redundant calculation layer to handle repetitive coefficient computations separately. The experimental results demonstrate that our system achieved accurate and rapid calculations. Under the only one geocentric residual latitude condition, we measured the computation times for spherical harmonic coefficient degrees of 360, 720, and 1080 to be 0.155922 s, 0.520950 s, and 1.401609 s, respectively. In the case of the multiple geocentric residual latitudes condition, our design generally yielded efficiency gains of over three times those of MATLAB R2020b implementation. Additionally, our calculated results were used to determine the geoid height in the field with an error of less than ± 0.1 m , confirming the reliability of our computations. [ABSTRACT FROM AUTHOR]

It is essential for meeting the stringent real-time demands encountered in actual production scenarios. Employing the low computational complexity of recursive algorithms, some new schemes are developed for the parameter estimation of a class of time-varying systems. The temporal evolution of parameters is characterized through the autoregressive process, facilitating the construction of the identification model with regard to the autoregressive coefficients. Based on the computational efficiency of the gradient search, a parametric autoregression-based stochastic gradient algorithm is derived with an appropriate step size, achieving a compromise between the steepest descent and convergence rate. In order to address the limitation of the low estimation accuracy in gradient algorithms, a parametric autoregression-based multi-innovation stochastic gradient algorithm is explored by making use of the favorable information for corrections. The simulation results are given to demonstrate the effectiveness of the proposed algorithms. Therefore, for a class of time-varying systems whose parameters become the further insight through the autoregressive process, the proposed gradient methods can obtain the parameter estimates faster and more accurately while ensuring the real-time performance of time-varying systems. [ABSTRACT FROM AUTHOR]

Copyright of Coal Science & Technology (0253-2336) is the property of Coal Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Buffer allocation is a critical issue in the design stage of manufacturing systems, as buffer capacities may have a great impact on system performance. In this paper, we consider the problem of minimizing the total buffer capacity of a flow line to achieve a desired production rate. A recursive optimization approach is proposed to solve the problem in large production lines. Instead of optimizing a long line directly, the proposed approach decomposes it into two sub-lines, optimizes them recursively, and combines their solutions to find the optimal buffer distribution of the original line. Two different recursive algorithms are developed and their performance is demonstrated by comparing them with a gradient search algorithm. The numerical results show that the recursive algorithms are almost as accurate as the gradient algorithm, but much more efficient, especially for large production lines. [ABSTRACT FROM AUTHOR]

Color shift keying is a modulation scheme for visible light communication that uses fixtures with three or more narrow-spectral light-emitting diodes to transmit data while fulfilling the primary function of illumination. When this modulation is used indoors, the reflectivity of the walls strongly affects the inter-channel interference and illumination quality. In this paper we present an indoor channel model that takes into account multi-wavelength propagation. This model is available as an open-source Python package. The model calculates the inter-channel interference, illuminance, correlated color temperature, and color rendering index at the receiver position. The Python package includes a module for estimating the symbol error rate. To validate the model, we computed the received power at each color photodetector for four different indoor scenarios. The model demonstrated a color rendering index of less than 15 when using IEEE-based color shift keying and non-uniform illumination on a horizontal plane. The simulation determined the required luminous flux to achieve a symbol error rate of less than 10 − 5 when the photodetector is at the center of the indoor space and vertically below the light source. To maintain a symbol error rate less than 10 − 5 , the luminous flux increases when the photodetector is displaced in a diagonal direction from the center of the plane. [ABSTRACT FROM AUTHOR]

The complex underground environment of coal coalmines, influenced by lighting, coal dust, and water mist, often results in collected images with blurred details and missing textures, leading to decreased image resolution and posing significant limitations to the intelligent development of coal coalmine safety monitoring. Image super-resolution reconstruction, an essential image processing technology, aims to recover clear high-resolution images from low-resolution coalmine images, thereby significantly enhancing the reliability of intelligent monitoring and safety management in coal coalmines. To address issues such as the loss of edge texture information and blurring of details in coalmine images, a coalmine image super-resolution reconstruction method integrating multi-dimensional features and residual attention networks is proposed. First, a multi-branch network is employed to parallelly integrate dynamic convolution and channel attention mechanisms, capturing different spatial statistical characteristics through “horizontal-channel” and “vertical-channel” interactions. Secondly, a recursive sparse self-attention mechanism is designed to aggregate representative feature maps under linear complexity, adaptively selecting weight distribution and reducing information redundancy during computation. Finally, the basic unit of deep feature extraction is constructed based on the standard multi-head self-attention mechanism and residual connection, with the obtained feature information and shallow features jointly input into the reconstruction module via skip connections to complete super-resolution reconstruction of coalmine images. Experimental results indicate that the proposed method significantly outperforms existing mainstream algorithms in both objective evaluation metrics and subjective visual analysis. In tests on the coalmine dataset, LPIPS (Learned Perceptual Image Patch Similarity) decreases by an average of 10.97% and 9.91%, while PSNR (Peak Signal-to-Noise Ratio) increases by an average of 4.10% and 2.30% for 2x and 4x scaling factors, respectively, demonstrating the method's effectiveness in restoring the structure and texture details of coalmine images.

In this study, discrete event time-variant parameter of a lumped SISO dynamical system is obtained for a novel energy harvester. The harvester utilizes the resonance vibration of a coupled fluid-mechanic system, which is comprised of a reciprocating-piston, a tunable oscillator and twin electric turbine generators. The system model is simplified by an underdamped spring-mass-damper with tunable parameters subjected to periodic or arbitrary impulse forces. We developed a method that solves general problems underlining non-homogenous ordinary second order differential equation with discrete event time-variant parameters. The method uses the superposition to compile the general solution by segmenting the problem into ODE equations with constant coefficient. Each segment corresponds to a change in system, and it is solved analytically with recursively updated initial conditions. We utilized this method to tune the system's natural frequency such that the accumulated energy is maximum within desired time range. We obtained the general solution of the displacement response due to varying parameters and input impulse force. We obtained the displacement peaks and their time of occurrence that could help understand the structural design limitation. We showed system displacement responses (constructive and destructive) corresponding to various impulse repetition patterns. We derived the relationship between energy, volume displacement, and volumetric flow rate (or piston velocity) and provided illustrative case studies. One finding shows that for a given impulse condition the accumulative energy exhibits local maximum and minimum within a narrow band of natural frequency range. The simulations showed the feasibility of generating considerable power from electric turbine when the air flow is driven by a resonating piston. [ABSTRACT FROM AUTHOR]

In this paper, a novel recursive and efficient algorithm for real-time implementation of the adaptive and passivity-based controllers in model-based control of robot manipulators is proposed. Many of the previous methods on these topics involve the computation of the regressor matrix explicitly or non-recursive computations, which remains as the main challenge in practical applications. The proposed method achieves a compact and fully recursive reformulation without computing the regressor matrix or its elements. This paper is based on a comprehensive literature review of the previously proposed methods, presented in a unified mathematical framework suitable for understanding the fundamentals and making comparisons. The considered methods are implemented on several processors and their performances are compared in terms of real-time computational efficiency. Computational results show that the proposed Adaptive Newton-Euler Algorithm significantly reduces the computation time of the control law per cycle time in the implementation of adaptive control laws. In addition, using the dynamic simulation of an industrial robot with 6-DoF, trajectory tracking performances of the adaptive controllers are compared with those of non-adaptive control methods where dynamic parameters are assumed to be known. [ABSTRACT FROM AUTHOR]

A large number of fully normalized associated Legendre function (fnALF) calculations are required to compute Earth’s gravity field elements using ultra high-order gravity field coefficient models. In the surveying and mapping industry, researchers typically rely on CPU-based systems for these calculations, which leads to limitations in execution speed and power efficiency. Although modern CPUs improve instruction execution efficiency through instruction-level parallelism, the constraints of a shared memory architecture impose further limitations on the execution speed and power efficiency. This results in exponential increases in computation time as demand rises alongside high power consumption. In this article, we present a new computational implementation of an fnALF based on the ZYNQ platform. We design a task-parallel “pipeline” architecture which converts the original serial logic into a more efficient hardware implementation, and we utilize a redundant calculation layer to handle repetitive coefficient computations separately. The experimental results demonstrate that our system achieved accurate and rapid calculations. Under the only one geocentric residual latitude condition, we measured the computation times for spherical harmonic coefficient degrees of 360, 720, and 1080 to be 0.155922 s, 0.520950 s, and 1.401609 s, respectively. In the case of the multiple geocentric residual latitudes condition, our design generally yielded efficiency gains of over three times those of MATLAB R2020b implementation. Additionally, our calculated results were used to determine the geoid height in the field with an error of less than ±0.1m, confirming the reliability of our computations.

Buffer allocation is a critical issue in the design stage of manufacturing systems, as buffer capacities may have a great impact on system performance. In this paper, we consider the problem of minimizing the total buffer capacity of a flow line to achieve a desired production rate. A recursive optimization approach is proposed to solve the problem in large production lines. Instead of optimizing a long line directly, the proposed approach decomposes it into two sub-lines, optimizes them recursively, and combines their solutions to find the optimal buffer distribution of the original line. Two different recursive algorithms are developed and their performance is demonstrated by comparing them with a gradient search algorithm. The numerical results show that the recursive algorithms are almost as accurate as the gradient algorithm, but much more efficient, especially for large production lines.

Color shift keying is a modulation scheme for visible light communication that uses fixtures with three or more narrow-spectral light-emitting diodes to transmit data while fulfilling the primary function of illumination. When this modulation is used indoors, the reflectivity of the walls strongly affects the inter-channel interference and illumination quality. In this paper we present an indoor channel model that takes into account multi-wavelength propagation. This model is available as an open-source Python package. The model calculates the inter-channel interference, illuminance, correlated color temperature, and color rendering index at the receiver position. The Python package includes a module for estimating the symbol error rate. To validate the model, we computed the received power at each color photodetector for four different indoor scenarios. The model demonstrated a color rendering index of less than 15 when using IEEE-based color shift keying and non-uniform illumination on a horizontal plane. The simulation determined the required luminous flux to achieve a symbol error rate of less than 10−5 when the photodetector is at the center of the indoor space and vertically below the light source. To maintain a symbol error rate less than 10−5, the luminous flux increases when the photodetector is displaced in a diagonal direction from the center of the plane.

As an important aspect of reliability theory, availability has now been considered a very meaningful design criterion of repairable system. This paper investigates the availability evaluation and design optimization of the multi-state k-out-of-n: G systems considering random weight threshold. The system availability is evaluated by extending the recursive algorithm (RA) and universal generating function (UGF) technique. Based on the traditional recursive algorithm, the total probability theorem is used to solve the discrete random weight threshold. Another better UGF method combines a new stochastic joint operator, which is suitable for both continuous and discrete random weight thresholds. Furthermore, we constructed two system design optimization models under availability or cost constraint respectively, and genetic algorithm (GA) programming can be applied to obtain the optimal state probability distribution and weight distribution of multi-state components of the suggested system. Finally, through numerical examples, the flexibility and effectiveness of the proposed methods for design optimization are demonstrated. In addition, two evaluation methods are compared to show that the customized UGF method features higher generality than RA in the case of continuous stochastic weight threshold, and higher operational efficiency in the case of increasing component quantity and state. The results can be helpful for engineers to optimize the design of complex systems.

Vulnerability refers to the ability of a network to continue functioning when part of the network is either naturally damaged or targeted for attack. In this paper, the rupture degree of graphs is employed to measure the vulnerability of uniform linear hypergraphs. First, we discuss the bounds of the rupture degrees of k-uniform linear hypergraphs. Then, we give a recursive algorithm for computing the rupture degree of k-uniform hypertrees. [ABSTRACT FROM AUTHOR]

Aiming at the problem of quantitative inertia evaluation of a new energy electric power system, the system inertia constant tracking method based on system identification is studied. The method is divided into two categories: non-recursive algorithm and recursive algorithm. The non-recursive algorithm uses a batch of data for batch processing to obtain the estimated value of the identification model parameters. The recursive algorithm is based on the estimated value of the model parameter at the previous moment and corrects the estimated value based on the new data currently obtained. From the perspective of the identification principle, the difference and internal relationship between the two in terms of calculation storage and identification speed are analyzed. The IEEE typical system is used to compare and verify the experimental examples. Theoretical analysis and experimental results show that the recursive algorithm has high identification accuracy, stable identification results and fast identification speed. It is suitable for the identification of objects with large numbers of nodes and complex structures, which is conducive to real-time monitoring and fast perception of the inertia constant of the new energy power system.

In recent years, research and development of robots that exist in the same space as humans and can collaborate with humans have been actively carried out. If the body of a robot is made of a hard material, it may cause injury. Therefore, attempts have been made to make a robot with a soft body using rubber or resin. In order to accelerate such research on soft robotics, it is necessary to establish fast and stable simulation algorithm for robots containing viscoelastic bodies such as rubber and resin. Therefore, in this study, we consider to approximate viscoelastic bodies with finite rigid body segments and connect them with joints and linear viscoelastic elements such as Voigt model, Maxwell model and generalized Maxwell model to approximate viscoelastic properties. The recursive dynamics algorithm is used to speed up the calculation, and the generalized-α method is used to stabilize the numerical integration. In particular, we propose a new method on how to incorporate the Maxwell model and generalized Maxwell model into recursive dynamics algorithm and generalized-α method. The effectiveness of the proposed method is confirmed by some numerical examples. In addition, the effectiveness of the proposed method is verified on a real system by applying Particle Swarm Optimization (PSO) to identify the dynamic parameters in linear viscoelastic elements.

The main research object of this paper is to present a systematic computational procedure for computing the inverse of a generalized Vandermonde matrix. Short and rigorous proofs for the formulas of the determinant and the inverse of a generalized Vandermonde matrix are proposed. The computational cost of this method is O (n 2) . The proposed method can be used efficiently for hand calculation as well as for computer programming. Some examples are given for the sake of illustration. Furthermore, we present a simulation study to compare the time spent to calculate the inverse using the proposed algorithm and the inverse function in Maple. [ABSTRACT FROM AUTHOR]

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, we consider the problem of estimating diffraction attenuation from the approximation of terrain using a multiple bridged knife-edge model. This model can be considered as a generalization of the well-known multiple knife-edge (MKE) one where spaces between knife-edges are bridged by reflecting surfaces. A series-based-standard solution is presented in the literature but suffers from its very high computational complexity. We, thus, propose to generalize the recursive Vogler algorithm developed for the MKE model to tackle this problem. To reduce complexity, the proposed algorithm exploits the recursive form to avoid repeated calculations of the existing solution. Moreover, we provide a complexity analysis of both the standard algorithm and the proposed algorithm based on the number of computed integrals. Both theoretical and numerical results show that our proposed algorithm is faster than the original one while having identical accuracy, hence proving the effectiveness of our solution. [ABSTRACT FROM AUTHOR]

The identification of reliability-critical primary input leads (RCPIs) plays an important role in the testing and prediction of reliability boundaries of logic circuits. This article presents a gate-sensitive-attributes-based approach to estimate the criticality of the primary input leads in combinational circuits to their reliability. Oriented to the input vector, a subcircuit-based traversal method marks the critical input leads of each gate in a circuit. Gate-sensitive attributes and a reverse recursive algorithm quantify the effect of each RCPI on circuit reliability under the input vector. A parallel calculation method based on subcircuits with only one primary output reduces the computational complexity to accelerate the calculation process. Similarity-based clustering avoids unnecessary calculations, and a self-adaptive strategy is used to check convergence. Experimental results on benchmark circuits show that the average accuracy of this approach is 0.9634 with Monte Carlo (MC) as the reference and it is 3445 times faster than the MC on average while its average memory cost is 1.67 greater than the MC model. Although the fitness of the worst input vector obtained by other reference methods is 1.09 times better than that of this approach on average, this approach is approximately 21 times faster than that reference method on average. [ABSTRACT FROM AUTHOR]

The discretization of fractional-order differential operators is the key to the digital realization of fractional-order controllers. This paper proposes an improved second-order fractional differential equation operation method based on power series expansion. The algorithm's operation speed and accuracy performance are analyzed. The research found that the algorithm proposed in this paper is suitable for the fractional operation of arbitrary signals, including discrete data sequences whose mathematical model is unknown and the solution of linear systems.

The suitable aircraft performance monitoring(APM)parameters selection method can realize the efficient selection of domestic civil cruising APM parameters,which can provide the reliable data basis of aircraft performance analysis and calculation.The Sage-Husa noise estimator is introduced into unscented Kalman filter(UKF),and the adaptive unscented Kalman filter(AUKF)is constructed.AUKF is used to denoise the quick access recorder(QAR)data.The stable cruise parameter screening criteria are given,and the improved sliding time window algorithm is used to realize the stable cruise parameter selecting.The algorithm is verified by the sample data of the domestic ARJ21 aircraft.The results show that the adaptive unscented Kalman filter algorithm can improve the reliability of data,and the improved sliding time window algorithm can improve the selecting efficiency by about 50%.

The electrodynamic tether (EDT) system is used as one of the end-of-life disposal technologies to deorbit defunct satellites with the benefit of Earth's magnetic field and plasma environment. However, due to the flexibility of the conductive tether, the orbit-attitude coupling effects as well as the influence of Multiphysics fields, this system suffers from time-consuming computations using complicated mathematical model in long-term simulations. Therefore, this paper proposes a high-fidelity high-efficiency dynamics model for the EDT system, in which the tether libration and transverse motions are described by the articulated model, and the system equations are formulated using recursive dynamics algorithm. Computational cost of the recursive method is compared with a nonrecursive method, and the result shows that with the number of tether elements larger than 15, the recursive method would show better computational efficiency. Since the conductive tether tends to be kilometers long in application, this new model would definitely contribute to the numerical efficiency. In addition, simulations are conducted with 2 and 16 tether elements solutions. By comparing the obtained results, it is found that the two cases show large differences over time. For a long tether, it is reasonable to use a larger number of elements in the dynamics analysis. Besides, in order to suppress the libration motion and avoid unstable states in the EDT system, a current control strategy is proposed and verified by a deorbit simulation in low Earth orbit. • A high-fidelity high-efficiency model is proposed for the electrodynamic tether system. • The recursive method shows better efficiency with the number of elements larger than 15. • Different tether elements would result in large differences in simulation. • A current control strategy is proposed to stabilize the libration motion. [ABSTRACT FROM AUTHOR]

The health status of the running gear in high-speed trains changes dynamically with time in a complete life cycle. Running gear systems composed of many coupled components are complex, and health statuses of which are difficult to predict in real time through a traditional health status prediction scheme. Lately, belief rule base (BRB), which is able to combine quantitative information and expert knowledge, has shown excellent expression in modeling complex systems. In the procedure of health status prediction, expert expertise can sufficiently enhance the accuracy and efficiency of this model. Therefore, this paper puts forwards a real-time health status prediction framework based on a multi-layer BRB with priority scheduling strategies for running gears. In the first-layer BRB, a time-series prediction model of multiple module BRB considering complete features is established. In the second-layer model, grey relation analysis (GRA) is employed in priority scheduling strategies of features. The third-layer BRB is used for assessing the health status of running gears by combining the features. In addition, the initial parameters of all module BRB given by experts may not be precise. Accordingly, the initial parameters in the BRB are updated by the recursive algorithm online. Finally, the proposed method is tested on the testing platform in running gears. The results make it clear the proposed method can predict the health status of running gears with much accuracy in real time. [ABSTRACT FROM AUTHOR]

A coiled coil is a structural motif in proteins that consists of at least two α-helices wound around each other. For structural stabilization, these α-helices form interhelical contacts via their amino acid side chains. However, there are restrictions as to the distances along the amino acid sequence at which those contacts occur. As the spatial period of the α-helix is 3.6, the most frequent distances between hydrophobic contacts are 3, 4, and 7. Up to now, the multitude of possible decompositions of α-helices participating in coiled coils at these distances has not been explored systematically. Here, we present an algorithm that computes all non-redundant decompositions of sequence periods of hydrophobic amino acids into distances of 3, 4, and 7. Further, we examine which decompositions can be found in nature by analyzing the available data and taking a closer look at correlations between the properties of the coiled coil and its decomposition. We find that the availability of decompositions allowing for coiled-coil formation without putting too much strain on the α-helix geometry follows an oscillatory pattern in respect of period length. Our algorithm supplies the basis for exploring the possible decompositions of coiled coils of any period length. [ABSTRACT FROM AUTHOR]

• Contact forces of frictional unilateral constraints are added to recurrence relations. • Modeling non-smooth systems by defining a frictional unilateral constraint pair. • The linear complementarity problem is constructed using the recurrence relations. • The proposed algorithm incorporates Moreau time-stepping method and recursive method. The contact impact problem in planar multibody systems can be efficiently solved by formulating it as the linear complementarity problem, which requires a complex modeling process. To simplify the process, a recursive algorithm for the dynamics of planar multibody systems with frictional unilateral constraints is proposed based on the reduced multibody system transfer matrix method. Firstly, the contact forces of frictional unilateral constraints are integrated into the recurrence relations of system components using Lagrange multipliers. Subsequently, the relative motion equations of the contact positions are discretized in time, which are then utilized to describe the linear complementarity problem for systems. The dynamics of the system is solved by the Moreau time-stepping method with the recursive method. Finally, the proposed algorithm was validated using the woodpecker toy and used to model a slider-crank mechanism with clearance, which shows its characteristics of facilitating modeling, universal, and highly programmable. This recursive algorithm provides an effective tool for solving non-smooth planar multibody systems while extending the application of the multibody system transfer matrix method. [ABSTRACT FROM AUTHOR]

Vulnerability refers to the ability of a network to continue functioning when part of the network is either naturally damaged or targeted for attack. In this paper, the rupture degree of graphs is employed to measure the vulnerability of uniform linear hypergraphs. First, we discuss the bounds of the rupture degrees of k-uniform linear hypergraphs. Then, we give a recursive algorithm for computing the rupture degree of k-uniform hypertrees.

Based on the image method and addition theorem of spherical vector wave functions, an analytical solution of the multiple scattering by a buried medium-coated conducting sphere is proposed in this paper. An iterative process to obtain the scattered electromagnetic field is discussed on the basis of the continuous boundary condition in the plane boundary, the medium inner and the outer surface of a coated conducting sphere, respectively. Applying an image method and the addition theorem of spherical vector wave functions, the scattering electromagnetic fields by the plane in a local coordinate system can be transformed into the globe coordinate, and they can be regarded as the next incident electromagnetic fields to the buried medium-coated conducting sphere. This process does not end until the scattering electrical field on the plane boundary is accurate enough. Numerical results are given and compared with commercial software FEKO, they coincide enough; the calculation times of the present method are very short compared to those of the software FEKO, and some discussion is given at the end of this paper. [ABSTRACT FROM AUTHOR]

A method for recursive subspace identification of continuous-time systems based on generalized Poisson moment functionals is proposed. Most of the existing subspace identification methods have concentrated mainly on the time-invariant discrete-time systems. The results of subspace identification methods are confined to the discrete-time cases, due to the difference on the construction of Hankel matrices. In addition, the time-invariant identification algorithms are not suitable for online identification cases. In order to solve the problems above, the time derivatives of Hankel matrices can be evaluated by generalized Poisson moment functionals, which provides a simple linear mapping for identification algorithm without the amplification of stochastic noises. The size of the data matrices is fixed a priori to fade the influence of old data to the updated data, which is a key to reduce computational burden and storage cost of recursive algorithms. The efficiency of the presented method is provided by comparing simulation results. [ABSTRACT FROM AUTHOR]

Recently, a multiple-resonator structure was proposed as a robust and computationally efficient tool for harmonic analysis. Two trivial cases have been previously observed. The first case exhibits good out-of-band suppression and elimination of unwanted harmonics, but with a high latency. In the second case, a phase frequency response around the passband centre is zero-flat, that provides fast estimates. However, in this case, resonant peaks at the ends of the passband and high interharmonic gains cause large overshoots. In general, the basic algorithm performance requirements: selectivity and speed, are contradictory which makes it impossible to completely fulfil both of them. In this paper, the Constrained Linear Least-Squares (CLLS) optimization method is used to obtain a compromise solution. As a result, the resonant peaks in the passband are avoided and side lobes are mitigated, simultaneously minimizing the group delay in the middle of the passband. Performed simulations confirmed the effectiveness of the proposed algorithm.

This paper proposes an accurate and computationally efficient implementation of the IEEE Std. 1459-2010 for power measurements. An implementation is based on digital resonators embedded in a feedback loop. In the first algorithm stage, the unknown signal harmonic parameters are estimated. By this, the voltage and current signals are processed independently of each other. In the second algorithm stage, the unknown power components are estimated (calculated) based on estimated spectra. To demonstrate the performance of the developed algorithm, computer-simulated data and laboratory testing records are processed. Simple LabView implementation, based on the point-by-point processing feature, demonstrates techniques modest computation requirements and confirms that the proposed algorithm is suitable for real-time applications.

In recent years, many industrialfacilities have been required to install sensing system to monitor the health status of the equipment. Although the PC-based diagnosis system is a good alternative, it undoubtedly increases the hardware cost greatly, and also causes restrictions on system assembly. In some critical environments, installation of the PC-based system is not suitable because of high temperature, dust, and humidity. On the contrary, a high mobility portable smart sensor will be relatively adequate for onsite inspections. To solve this problem, we developed a low-cost embedded handheld smart sensor. Instead of using sophisticated algorithms, certain frequently used statistic indicators are considered. Nevertheless, due to the resource limitations of the embedded systems, it causes difficulty for real-time realization and therefore, the recursive architecture of the statistic indicators is derived. These statistical factors are then fed into a Gaussian classifier for online defect detection, which gives a great contribution to field operators for onsite inspections. The highly integrated hardware/software co-design of the developed device provides user-friendly and high mobility for field inspections. Finally, a practical industrial application regarding the online diagnosis of a solenoid valve actuator defect is presented to demonstrate the effectiveness of the developed embedded smart sensor.

The recursive and hierarchical structure of full rooted trees is applicable to statistical models in various fields, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting is problematic. One method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc. [ABSTRACT FROM AUTHOR]

The study of vehicular networks has attracted considerable interest in academia and the industry. In the broad area, connected vehicles and autonomous driving are technologies based on wireless data communication between vehicles or between vehicles and infrastructures. A Vehicle-to-Infrastructure (V2I) system consists of communications and computing over vehicles and related infrastructures. In such a system, wireless sensors are installed in some selected points along roads or driving areas. In autonomous driving, it is crucial for a vehicle to figure out the ideal routes by the communications between its equipped sensors and infrastructures then the vehicle is automatically moving along the routes. In this paper, we propose a Bezier curve based recursive algorithm, which effectively creates routes for vehicles through the communication between the On-Board Unit (OBU) and the Road-Side Units (RSUs). In addition, this approach generates a very low overhead. We conduct simulations to test the proposed algorithm in various situations. The experiment results demonstrate that our algorithm creates almost ideal routes.

A scattering (S-) parameter method has been proposed for electromagnetic property extraction of a target layer within metal-backed inhomogeneous metamaterial (MM) structures. It relies on recursive S-parameters for two different polarizations (parallel and perpendicular). Two different algorithms depending on the value of the incidence angles were proposed to add flexibility to our method. The algorithms were first validated by a metal-backed quasi-one-port method applicable only for one-layer (homogeneous) samples. Then, they were applied to extract electromagnetic properties of the split-ring-resonator-wire MM slab of a metal-backed two-layer inhomogeneous structure and the Omega MM slab of a metal-backed four-layer inhomogeneous structure, and extracted properties by our algorithms were compared with those retrieved by different methods applicable for homogeneous samples only. The accuracy of our method was also examined when there was some noise in S-parameters, when there was a misalignment in incidence angles, and a when large value of iteration number was used.

In a graph $G$ , two spanning trees $T_{1}$ and $T_{2}$ are rooted at the same vertex $r$ . If, for every $v \in V(G)$ , the paths from $v$ to the root $r$ in $T_{1}$ and $T_{2}$ are internally vertex-disjoint, they are called independent spanning trees (ISTs). ISTs can be applied in numerous fields, such as fault-tolerant broadcasting and secure message distribution. The ( $n$ , $k$ )-star graphs $S_{n,k}$ constitute a generalized version of the star network. The method of constructing ISTs in ( $n$ , $k$ )-star graphs remains unknown. In this paper, we propose one recursive algorithm and one parallel algorithm for constructing ISTs on ( $n$ , $k$ )-star graphs. The main ideas of the recursive algorithm are to use induction to change small trees into large trees, to use a modified breadth-first search (MBFS) traversal to create a frame for an IST, and to use a breadth-first search (BFS) traversal to connect the rest of nodes. The main ideas of the parallel algorithm are to create frames through MBFS traversals in parallel, and to use some specific rules to connect the rest of nodes in parallel. We also present validation proofs for both algorithms, and analyze the time complexities of both algorithms. The time complexity of the recursive algorithm in $S_{n,k}$ is $O\left({n\times \frac {n!}{(n-k)!}}\right)$ , where $\frac {n!}{(n-k)!}$ is the number of nodes of $S_{n,k}$ . The time complexity of the parallel algorithm can be reduced to $O\left({\frac {n!}{(n-k)!}}\right)$ if the system has $n-1$ processors computing in parallel. Both algorithms are correct with the stated time complexity values; the parallel algorithm is more efficient than the recursive algorithm.

Information data protection is necessary to ward off and overcome various fraud attacks that may be encountered. A secret sharing scheme that implements cryptographic methods intends to maintain the security of confidential data by a group of trusted parties is the answer. In this paper, we choose the application of recursive algorithm on Shamir-based linear scheme as the primary method. In the secret reconstruction stage and since the beginning of the share distribution stage, these algorithms have been integrated by relying on a detection parameter to ensure that the secret value sought is valid. Although the obtained scheme will be much simpler because it utilizes the Vandermonde matrix structure, the security aspect of this scheme is not reduced. Indeed, it is supported by two detection parameters formulated from a recursive algorithm to detect cheating and identify the cheater(s). Therefore, this scheme is guaranteed to be unconditionally secure and has a high time efficiency (polynomial running time).

The main research object of this paper is to present a systematic computational procedure for computing the inverse of a generalized Vandermonde matrix. Short and rigorous proofs for the formulas of the determinant and the inverse of a generalized Vandermonde matrix are proposed. The computational cost of this method is O(n2). The proposed method can be used efficiently for hand calculation as well as for computer programming. Some examples are given for the sake of illustration. Furthermore, we present a simulation study to compare the time spent to calculate the inverse using the proposed algorithm and the inverse function in Maple.

In connection with the development of next-generation wireless networks based on LTE technology, demands for high-speed services are increasing leading to an exponential increase in the volume of traffic generated in mobile networks. According to the latest data from Cisco Systems, this volume will increase by 46 percent by 2021. At the same time, requirements for the level of quality of service (QoS) are increasing. The rapid growth of traffic in the conditions of providing users with a wide range of high-quality multimedia services leads to a lack of available frequency resources. This problem be-comes the main one in the development of modern wireless technologies. In this regard, cellular net-work operators offer various methods for its solution, for example, using the LAA (Licensed Assist-ed-Access) or LSA (Licensed Shared Access) systems allowing more efficient use of available frequency resources. In addition, in the framework of the implementation of various technologies to ensure the required QoS, radio resource management mechanisms (RRM) such as reducing data transmission power and interrupting users’ service can be applied. Models implementing such mechanisms can be described as queuing systems (QS) with unreliable servers. In the paper, a model of a wireless network cell is constructed, presented in the form of a QS, servers of which are in a random environment (RE). RE state can change, which is technically equivalent to a decrease or increase in the transmission pow-er. Reducing power may interrupt users’ service. Exact and approximate methods are proposed for calculating the stationary probability distribution of the model.

Modifications are proposed to the recursive algorithm of combinations generation by reducing the number of non-performing recursive calls and recovering this gap through iterative processes.

We consider the problem of multiple knife-edge diffraction estimation that is a fundamental task in many wireless communication applications. So far, one of the most accurate methods for this problem is the Vogler one whose recursive implementation is efficient to reduce the high computational complexity of the direct one. However, in the original report, Vogler only presented the final result of the recursive algorithm without a rigorous mathematical proof, thus making the method difficult to understand and implement in practice. To tackle this shortcoming, we first analyze the mathematical structure of the problem and then present a formal proof of the result. To gain intuition of the proof and the key steps, we provide a simplified study case of four knife edges. The insight from our proposed analysis and proof can be used to obtain a comprehensive interpretation, initiate a practical implementation, and develop new efficient algorithms with similar structure. [ABSTRACT FROM AUTHOR]

Collaborative filtering (CF) is a recommendation technique that analyzes the behavior of various users and recommends the items preferred by users with similar preferences. However, CF methods suffer from poor recommendation accuracy when the user preference data used in the recommendation process is sparse. Data imputation can alleviate the data sparsity problem by substituting a virtual part of the missing user preferences. In this paper, we propose a k-recursive reliability-based imputation (k-RRI) that first selects data with high reliability and then recursively imputes data with additional selection while gradually lowering the reliability criterion. We also propose a new similarity measure that weights common interests and indifferences between users and items. The proposed method can overcome disregarding the importance of missing data and resolve the problem of poor data imputation of existing methods. The experimental results demonstrate that the proposed approach significantly improves recommendation accuracy compared to those resulting from the state-of-the-art methods while demanding less computational complexity. [ABSTRACT FROM AUTHOR]

The reliability evaluation of multistate networks is primarily using minimal path (cut) vectors, namely d-MPs (d-MCs), which are the lower (upper) boundary vectors that satisfy the system demand d. The generation of all d-MPs (d-MCs) is an NP-hard problem. Thus, it is important to develop an efficient algorithm to search for d-MPs (d-MCs). Existing algorithms searching for d-MPs based on MPs all generate duplicate d-MP candidates, and extra steps are required to detect and remove those duplicates. In this article, we propose an improved algorithm to search for d-MPs for all d levels without generating duplicate d-MP candidates for two-terminal multistate networks. First, we discover and prove the mechanism of generating duplicate d-MP candidates based on MPs. Second, a novel method is proposed to prevent generating duplicate d-MP candidates. Third, an improved algorithm is developed by combining the proposed method to search for d-MPs without generating duplicate d-MP candidates for all d levels. Through computational experiments, it is found that the proposed algorithm is more efficient than existing algorithms for finding all d-MPs for all possible d values. [ABSTRACT FROM AUTHOR]

The recursive and hierarchical structure of full rooted trees is applicable to statistical models in various fields, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting is problematic. One method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc.

The existing method for blind identification of a punctured convolutional code involves searching for dual words and the puncturing pattern exhaustively. As the length of the dual words and the code rate increase, the computational complexity of this method expands exponentially. To address this problem, a fast scheme for blind identification of punctured convolutional codes is proposed. First, a recursive algorithm for solving the parity check equation set is proposed. The dual word and generator polynomial bases of the punctured convolutional code are estimated by using the recursive algorithm. After this, by using the structural properties of the generator matrix of the blocked code, possible generator matrices of the punctured convolutional code are obtained. Finally, since a generator polynomial of the parent convolutional code can be recovered from any column of its polycyclic pseudocirculant matrix, the corresponding generator matrix of the parent code and the puncturing pattern are reconstructed simultaneously from an estimation of the generator matrix of the punctured code. The reconstructed generator matrix of the parent code with a minimal constraint length is determined to be the identification result. Simulation experiments show the effectiveness of the proposed method. As there is no need to search for the dual word and puncturing pattern exhaustively, the method can achieve fast identification of punctured convolutional codes. Additionally, the method is robust to bit errors in the received sequence.

The identification for process control systems is considered in this paper based on the impulse response signals from the discrete measurements. By taking advantage of impulse signals and through the model parameter decomposition, two dependent identification models are constructed and two identification sub-algorithms are presented based on the nonlinear gradient optimization. In terms of the associated items of the parameters to be estimated between two derived sub-algorithms, a separable recursive gradient parameter estimation method is proposed by designing an interactive and recursive estimation. The performance tests and the comparison experiments are carried out by the simulation examples. [ABSTRACT FROM AUTHOR]

The power grid is developing towards intelligence. Therefore, as important electrical equipment of the power grid, miniature circuit breaker (MCB) should need to meet the requirements of the smart grid for terminal apparatuses. However, because the bending process of bimetal widely used in MCB overload protection is dispersive, which is difficult to realise electronisation, it is urgent to study the intelligent algorithm of MCB to protect the power grid well. For this purpose, a current calculation method based on temperature rise caused by load current of traditional non‐communicable MCB is proposed in this study. Compared with the present current calculation method, there is no iron core saturation problem even in the case of a huge load current. Also, in order to solve the problem of long time delay for stable temperature rise, a recursive algorithm that can rapidly calculate stable temperature rise is proposed. Furthermore, the current can be calculated rapidly. The influence of the initial temperature rise on the current calculation is also taken into account in the proposed algorithm. The simulation and experiment results show that the speed of stable temperature rise obtained by the recursive algorithm can meet the requirement of overload protection, and the error of calculating current is less than 5%. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the modeling problem of the multi-frequency signals which contain many different frequency components. Based on the Newton search and the measured data, a Newton recursive parameter estimation algorithm is developed to estimate the amplitude, the angular frequency and the phase of a multi-frequency signal. In order to improve the performance of the identification algorithm, a convergence factor is introduced in the Hessian matrix of the developed Newton recursive method. The numerical examples verify that the proposed algorithm is effective for modeling the multi-frequency sine signals. [ABSTRACT FROM AUTHOR]