Recursive Method Research Articles

Analyzing performance: Error-efficient, low-power recursive inexact multipliers for CNN applications

In present scenario, significant data manipulations can be espied in image processing and Convolutional Neural Networks (CNNs) applications. The quality performance of these applications relies ponderously on arithmetic operations. In this context, Approximate Computing frequently finds its application, where a certain margin of error is deemed acceptable, on prioritizing circuit speed over absolute precision and the common focus lies on optimizing the binary multiplier which is a crucial yet power-intensive component, so as to streamline the complexity of above mentioned applications. Furthermore, Inexact Multipliers (IMs) are developed by using recursive method, thereby purveying enhanced design and error metrics. This paper introduces higher order Recursive-Based Inexact Multipliers (RBIMs), which integrates the suggested 4-bit IMs, and exact multipliers along with the recursive method, aiming to provide a delicate balance between design performance metrics and error tolerance. For evaluating the proposed approach, most of the existing and recently suggested IMs operating at 8-bit and 16-bit, are designed in Verilog, coded in Python, synthesized and simulated using Cadence Register Transfer Language (RTL) Compiler, Google Colabs. Eventually, the simulation results bespeak a notable improvement in power consumption, with the 8-bit and 16-bit RBIMs by outperforming the previous designs up to 36.9 %, and 35.5 % respectively. Further, the efficacies of the RBIMs are validated through its usage in image processing and CNN applications.

The implicit inversion method for calculating the forward dynamics input Jacobian

AbstractThis paper presents the implicit inversion method (IIM), a recursive method to evaluate the Jacobian of the forward dynamics w.r.t. the system inputs, using intermediate results obtained from an O(n) forward dynamics algorithm. The resulting coefficient matrix, called the inertia-weighted input matrix (IWIM), can be used to significantly improve the performance of solving optimal control problems that take into account system dynamics for only the current time step. As the relationship between inputs and accelerations appears fixed within a time step, this matrix can be evaluated in the initialization step of the optimization. This means that the forward dynamics only needs to be solved once at the initialization of the optimization, rather than having to solve the equations in every iteration of the optimization. The method presented in this paper especially targets a case where the forward dynamics are calculated using an O(n) method and takes advantage of variables that are already known through the evaluation of that method. These quantities allow us to obtain the inertia-weighted input matrix without having to convert the system to its generalized coordinate form. Exploiting the shape of the resulting equation, it is even possible to avoid an explicit inversion of any matrices in the process. Finally, runtime comparisons between three different methods to calculate the IWIM are made for several examples.

Robust topological bound states in the continuum in a quantum Hall bar with an anti-dot

Bound states in the continuum (BICs) are quantum states with normalizable wave functions and energies that lie within the continuous spectrum for which extended or dispersive states are also available. These special states, which have shown great applicability in photonic systems for devices such as lasers and sensors, are also predicted to exist in electronic low-dimensional solid-state systems. The non-trivial topology of materials is within the known mechanisms that prevent the bound states to couple with the extended states. In this work we search for topologically protected BICs in a quantum Hall bar with an anti-dot formed by a pore far from the borders of the bar. The bound state energies and wavefunctions are calculated by means of the Recursive S-Matrix method. The resulting bound state energies coexist with extended states and exhibit a pattern complimentary to the Hofstadter butterfly. A symmetry-breaking diagonal disorder was introduced, showing that the BICs with energies far from the Landau levels remain robust. Moreover, the energy difference between consecutive BICs multiplied by the anti-dot perimeter follows the same curve despite disorder. Finally, a BIC-mediated current switching effect was found in a multi-terminal setup for zero and finite temperature, which might permit their experimental detection.

Dynamic Programming-Based Track-before-Detect Algorithm for Weak Maneuvering Targets in Range–Doppler Plane

This paper focuses on detecting and tracking maneuvering weak targets in the range–Doppler (RD) plane with the track-before-detect (TBD) algorithm based on dynamic programming (DP). Traditional DP-TBD algorithms integrate target detection and tracking in their framework while searching the paths provided by a predefined model of the kinematic properties within the constraints allowed. However, both the approximate motion model used in the RD plane and the model mismatch caused when the target undergoes a maneuver can degrade the TBD performance sharply. To address these issues, this paper accurately describes the evolution of the RD equation based on Constant Acceleration (CA) and Coordinated Turn (CT) motion models with the process noise in the Cartesian coordinate system, and it also employs a recursive method to estimate the parameters in the equations for efficient energy accumulation and path searches. Facing the situation that targets energy accumulation during the DP iteration process will lead to an expansion of the target energy accumulation process. This paper designs a more efficient Optimization Function (OF) to inhibit the expansion effect, improve the resolution of the nearby targets, and increase the detection probability of the weak targets simultaneously. In addition, to search the trajectory more efficiently and accurately, we improved the process of DP multi-frame accumulation, thus reducing the computation amount of large-scale searches. Finally, the effectiveness of the proposed method for CA and CT motion target detection and tracking is verified by many of the simulation experiments that were conducted in this paper.

Characterizing the dispersion behavior of poly-atomic magnetic metamaterials

The propagation of magnetoinductive (MI) waves across magnetic metamaterials known as magnetoinductive waveguides (MIWs) has been an area of interest for many applications due to the flexible design and low-loss performance in challenging radio-frequency (RF) environments. Thus far, the dispersion behavior of MIWs has been limited to mono- and diatomic geometries. In this work, we present a recursive method to generate the dispersion equation for a general poly-atomic MIW. This recursive method greatly simplifies the ability to create closed-form dispersion equations for unique poly-atomic MIW geometries versus the previous method. To demonstrate, four MIW geometries that have been selected for their unique symmetries are analyzed using the recursive method. Using applicable simplifications brought on by the geometric symmetries, a closed-form dispersion equation is reported for each case. The equations are then validated numerically and show excellent agreement in all four cases. This work simultaneously aids in the further development of MIW theory and offers new avenues for MIW design in the presented dispersion equations.

DoS attacks resilience of heterogeneous complex networks via dynamic event-triggered impulsive scheme for secure quasi-synchronization

This paper addresses the secure quasi-synchronization issue of heterogeneous complex networks (HCNs) under aperiodic denial-of-service (DoS) attacks with dynamic event-triggered impulsive scheme (ETIS). The heterogeneity of networks and the aperiodic DoS attacks, which hinder communication channels and synchronization goals, present challenges to the analysis of secure quasi-synchronization. The ETIS leverages impulsive control and dynamic event-triggered scheme (ETS) to handle the network heterogeneity and the DoS attacks. We give specific bounds on the attack duration and frequency that the network can endure, and obtain synchronization criteria that relate to event parameters, attack duration, attack frequency, and impulsive gain by the variation of parameter formula and recursive methods. Moreover, we prove that the dynamic ETS significantly reduces the controller updates, saves energy without sacrificing the system decay rate, and prevents the Zeno phenomenon. Finally, we validate our control scheme with a numerical example.

Analytical quaternion-based bias estimation algorithm for fast and accurate stationary gyro-compassing

This work introduces a novel approach to Strapdown Inertial Navigation System (SINS) alignment, distinct from recursive methods like Kalman filtering. The proposed methodology expedites bias error calculations by utilizing quaternion-based analytical relationships, which bypasses the slow convergence behavior associated with recursive algorithms, particularly in azimuth angle error estimation. In addition, the proposed approach demonstrates comparable accuracy to traditional fine alignment methods. Simulations and experiments validate that in contrast to the 10-min time requirement of traditional fine alignment methods (for azimuth angle estimation in stationary conditions), the proposed approach achieves the same accuracy within 20 s. However, limitations exist as the algorithm is applicable only in stationary conditions, and necessitating a high-grade IMU capable of measuring the earth’s rotation rate.

Block Lanczos method for excited states on a quantum computer

The method of quantum Lanczos recursion is extended to solve for multiple excitations on the quantum computer. While quantum Lanczos recursion is, in principle, capable of obtaining excitations, the extension to a block Lanczos routine can resolve degeneracies with better precision and only costs O(d2) for d excitations on top of the previously introduced quantum Lanczos recursion method. Extension to non-Hermitian operators is also discussed. Published by the American Physical Society 2024

Errorless robust JPEG steganography using steganographic polar codes

Recently, a robust steganographic algorithm that achieves errorless robustness against JPEG recompression has been proposed. The method employs a lattice embedding scheme and utilizes the syndrome-trellis code (STC) for practical embedding. However, we have noticed that errorless robust embedding with STC may encounter failures due to modifications on wet coefficients, especially when a high quality factor is used by the compression channel. To solve this problem, we have discovered that using steganographic polar code (SPC) for embedding has better performance in avoiding modifications on wet coefficients. In this paper, we conduct theoretical analysis to prove the better performance of SPC in wet paper embedding. We establish the condition of avoiding modifications on wet coefficients, followed by presenting a recursive calculation method for determining the distribution of columns in the generator matrix of SPC. The findings reveal that SPC can avoid modifications on wet coefficients under a larger number of wet coefficients compared with STC, and therefore we propose a better errorless robust embedding method employing SPC. The experimental results demonstrate that under close security performance, the proposed method achieves a higher success rate compared with embedding with STC. Specifically, when the quality factor of the compressor is 95 and the payload size is 0.4 bpnzac, our method achieves a success rate of 99.85%, surpassing the 91.95% success rate of the embedding with STC.

Models for depression recognition and efficacy assessment based on clinical and sequencing data

Major depression is a complex psychiatric disorder that includes genetic, neurological, and cognitive factors. Early detection and intervention can prevent progression, and help select the best treatment. Traditional clinical diagnosis tends to be subjective and misdiagnosed. Based on this, this study leverages clinical scale assessments and sequencing data to construct disease prediction models. Firstly, data undergoes preprocessing involving normalization and other requisite procedures. Feature engineering is then applied to curate subsets of features, culminating in the construction of a model through the implementation of machine learning and deep learning algorithms. In this study, 18 features with significant differences between patients and healthy controls were selected. The depression recognition model was constructed by deep learning with an accuracy of 87.26 % and an AUC of 91.56 %, which can effectively distinguish patients with depression from healthy controls. In addition, 33 features selected by recursive feature elimination method were used to construct a prognostic effect model of patients after 2 weeks of treatment, with an accuracy of 75.94 % and an AUC of 83.33 %. The results show that the deep learning algorithm based on clinical and sequencing data has good accuracy and provides an objective and accurate method for the diagnosis and pharmacodynamic prediction of depression. Furthermore, the selected differential features can serve as candidate biomarkers to provide valuable clues for diagnosis and efficacy prediction.

Parsimonious Random-Forest-Based Land-Use Regression Model Using Particulate Matter Sensors in Berlin, Germany.

Machine learning (ML) methods are widely used in particulate matter prediction modelling, especially through use of air quality sensor data. Despite their advantages, these methods' black-box nature obscures the understanding of how a prediction has been made. Major issues with these types of models include the data quality and computational intensity. In this study, we employed feature selection methods using recursive feature elimination and global sensitivity analysis for a random-forest (RF)-based land-use regression model developed for the city of Berlin, Germany. Land-use-based predictors, including local climate zones, leaf area index, daily traffic volume, population density, building types, building heights, and street types were used to create a baseline RF model. Five additional models, three using recursive feature elimination method and two using a Sobol-based global sensitivity analysis (GSA), were implemented, and their performance was compared against that of the baseline RF model. The predictors that had a large effect on the prediction as determined using both the methods are discussed. Through feature elimination, the number of predictors were reduced from 220 in the baseline model to eight in the parsimonious models without sacrificing model performance. The model metrics were compared, which showed that the parsimonious_GSA-based model performs better than does the baseline model and reduces the mean absolute error (MAE) from 8.69 µg/m3 to 3.6 µg/m3 and the root mean squared error (RMSE) from 9.86 µg/m3 to 4.23 µg/m3 when applying the trained model to reference station data. The better performance of the GSA_parsimonious model is made possible by the curtailment of the uncertainties propagated through the model via the reduction of multicollinear and redundant predictors. The parsimonious model validated against reference stations was able to predict the PM2.5 concentrations with an MAE of less than 5 µg/m3 for 10 out of 12 locations. The GSA_parsimonious performed best in all model metrics and improved the R2 from 3% in the baseline model to 17%. However, the predictions exhibited a degree of uncertainty, making it unreliable for regional scale modelling. The GSA_parsimonious model can nevertheless be adapted to local scales to highlight the land-use parameters that are indicative of PM2.5 concentrations in Berlin. Overall, population density, leaf area index, and traffic volume are the major predictors of PM2.5, while building type and local climate zones are the less significant predictors. Feature selection based on sensitivity analysis has a large impact on the model performance. Optimising models through sensitivity analysis can enhance the interpretability of the model dynamics and potentially reduce computational costs and time when modelling is performed for larger areas.

RETRACTED ARTICLE: Constructions for t-designs and s-resolvable t-designs

The purpose of the present paper is to introduce recursive methods for constructing simple t-designs, s-resolvable t-designs, and large sets of t-designs. The results turn out to be very effective for finding these objects. In particular, they reveal a fundamental property of the considered designs. Consequently, many new infinite series of simple t-designs, t-designs with s-resolutions and large sets of t-designs can be derived from the new constructions. For example, by starting with an important result of Teirlinck stating that for every natural number t and for all N>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N > 1$$\\end{document} there is a large set LS[N](t,t+1,t+N·ℓ(t))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$LS[N](t, t+1, t+N\\cdot \\ell (t))$$\\end{document}, where ℓ(t)=∏i=1tλ(i)·λ∗(i)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell (t)=\\prod _{i=1}^t \\lambda (i)\\cdot \\lambda ^*(i)$$\\end{document}, λ(t)=lcm(tm|m=1,2,…,t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda (t)=\\mathop {\ extrm{lcm}}(\\left( {\\begin{array}{c}t\\\\ m\\end{array}}\\right) \\,\\vert \\, m=1,2,\\ldots , t)$$\\end{document} and λ∗(t)=lcm(1,2,…,t+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda ^*(t)=\\mathop {\ extrm{lcm}}(1,2, \\ldots , t+1)$$\\end{document}, we obtain the following statement. If (t+2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(t+2)$$\\end{document} is composite, then there is a large set LS[N](t,t+2,t+1+N·ℓ(t))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$LS[N](t, t+2, t+1+N\\cdot \\ell (t))$$\\end{document} for all N>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N > 1$$\\end{document}. If (t+2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(t+2)$$\\end{document} is prime, then there is an LS[N](t,t+2,t+1+N·ℓ(t))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$LS[N](t, t+2, t+1+N\\cdot \\ell (t))$$\\end{document} for any N with gcd(t+2,N)=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gcd (t+2,N)=1$$\\end{document}.

Parameter‐free predictive control with flexibility in power adjustment for grid‐connected converters under unbalanced grid conditions

AbstractThis paper introduces a novel finite control set predictive direct power control method for grid‐connected converters without cost function evaluations. Unlike conventional predictive direct power control, since the proposed method does not use the model parameters, their uncertainties do not cause prediction error and inappropriate voltage vector selection. The method employs a new form of voltage vector selection based on the slopes of active and reactive powers. The slopes are predicted in a manner with a low sensitivity to sampling noise, without updating a look‐up table, and recursive methods. Hence, there are no stagnation and convergence issues. Also, the proposed method avoids startup problems caused by data‐lacking due to directly regulating the active and reactive power by a switching logic. Flexible power oscillations control with balanced sinusoidal grid currents without any signal sequence extraction can also be achieved under this method in unbalanced grid conditions. The proposed method is assessed by both simulation and experimental studies, and its performance is compared with existing robust combined and model predictive control methods. The outcomes highlight the influence of the proposed approach and establish its superiority over the other considered methods.

A novel adaptive trajectory tracking control for complex environments based on accelerated back-propagation neural network

This work addresses the issue of trajectory tracking accuracy degradation for vehicle dynamics parameters and road conditions changing, an adaptive trajectory tracking controller is designed for the intelligent vehicle. Based on the yaw dynamics model, a model predictive controller (MPC) is developed for the trajectory tracking process. Meanwhile, the impacts of different control parameters on trajectory tracking at various speeds are compared. And the change rule between optimal control parameter values and reference speeds is determined by cubic polynomial fitting to ensure minimal error during the trajectory following process. Then, an estimator for vehicle tire cornering stiffness and road adhesion coefficient is designed and tested based on the accelerated back-propagation neural network (ABPNN) model, with its estimation values being compared to those obtained through recursive least square method. Last, a co-simulation platform combining MATLAB/Simulink and CarSim software is established to conduct the trajectory tracking experiment under variable working conditions. Experimental results show that the proposed adaptive controller not only exhibits high accuracy in trajectory tracking but also demonstrates excellent stability and adaptability under medium to low speed conditions, particularly when encountering changing road conditions.

Research on coupling dynamics modeling and composite control of the multi-flexible space robot

Space robots can assist astronauts in accomplishing a variety of space missions in high-risk environments. As spacecraft become increasingly lightweight, large-scale, and integrated, space robots are a type of large-scale robots with flexible links and flexible joints. However, the flexibility of the components complicates robot modeling and controller design. Therefore, to address the issue of stable trajectory tracking for multi-flexible space robots, a dynamics model of space robots with multiple flexibilities is established, and a composite controller is designed to enhance control stability. In modeling, comprehensively considering the rigid joints, joint flexibility and link flexibility, the kinematics is consistently described by using the component deformation matrix and recursive method. An accurate dynamics model is established by Lagrange’s equations. In control, using fuzzy neural network sliding mode control, a rigid subsystem controller is designed to suppress the system jitter caused by sudden parameter changes. And it implements the robust tracking of the robot trajectory. Meanwhile, the weighted average fuzzy controller is designed to control the link deformation. The regulation of the flexible joint by the fast feedback controller is implemented using the virtual torque feedback control. Finally, the validity of the dynamics and control models is verified using Matlab and Adams. Compared with previous studies, this study considers multiple flexibility factors more fully. The vibration of multiple flexible components is suppressed during the stable trajectory tracking of the robot.

Serum levels of soluble receptor activator for nuclear factor kB ligand play a crucial role in the association of osteoprotegerin with coronary artery disease.

Osteoprotegerin (OPG) is a soluble decoy receptor for receptor activator of nuclear factor kB ligand (RANKL), and is implicated in the pathogenesis of atherosclerosis. The aim of the present study was to examine the hypothesis that serum OPG concentrations are increased in patients with stable coronary artery disease (CAD) at different serum levels of soluble RANKL (sRANKL). The study used a case-control design in which consecutively hospitalized individuals were recruited. Fasting blood samples were taken upon admission for serum testing. Participants with previously diagnosed CAD that was asymptomatic or had controlled symptoms constituted the stable CAD group, whereas patients with negative coronary computed tomography angiography results constituted the control non-CAD group. Exclusion criteria included recent acute coronary syndrome, severe heart failure, CAD-complicating autoimmune, blood or thyroid diseases, cancer, elevated temperature with or without infection, severe liver or kidney dysfunction, abnormal calcium metabolism, recent surgery and trauma history. A total of 118 individuals were included in the study. Smoothed plots generated using the recursive method and multivariate models showed that the incidence of stable CAD increased with serum OPG level up to the turning point of 18 pg/ml. This trend was observed at both high [odds ratio (OR), 1.61; 95% confidence interval (CI), 1.04-2.50; P=0.032) and low sRANKL concentrations (OR, 1.52; 95% CI, 1.06-2.17; P=0.022) after adjustment for cardiovascular risk factors. In conclusion, serum OPG levels ≤18 pg/ml are positively associated with stable CAD, regardless of sRANKL levels. In addition, at the same serum OPG level, higher sRANKL levels are associated with a greater incidence of stable CAD compared with lower sRANKL levels. This study identified the relationship between OPG, sRANKL, and stable CAD, and established the reference range for future clinical use.

Bent functions satisfying the dual bent condition and permutations with the $$(\mathcal {A}_m)$$ property

AbstractThe concatenation of four Boolean bent functions $$f=f_1||f_2||f_3||f_4$$ f = f 1 | | f 2 | | f 3 | | f 4 is bent if and only if the dual bent condition $$f_1^* + f_2^* + f_3^* + f_4^* =1$$ f 1 ∗ + f 2 ∗ + f 3 ∗ + f 4 ∗ = 1 is satisfied. However, to specify four bent functions satisfying this duality condition is in general quite a difficult task. Commonly, to simplify this problem, certain relations between $$f_i$$ f i are assumed, as well as functions $$f_i$$ f i of a special shape are considered, e.g., $$f_i(x,y)=x\cdot \pi _i(y)+h_i(y)$$ f i ( x , y ) = x · π i ( y ) + h i ( y ) are Maiorana-McFarland bent functions. In the case when permutations $$\pi _i$$ π i of $$\mathbb {F}_2^m$$ F 2 m have the $$(\mathcal {A}_m)$$ ( A m ) property and Maiorana-McFarland bent functions $$f_i$$ f i satisfy the additional condition $$f_1+f_2+f_3+f_4=0$$ f 1 + f 2 + f 3 + f 4 = 0 , the dual bent condition is known to have a relatively simple shape allowing to specify the functions $$f_i$$ f i explicitly. In this paper, we generalize this result for the case when Maiorana-McFarland bent functions $$f_i$$ f i satisfy the condition $$f_1(x,y)+f_2(x,y)+f_3(x,y)+f_4(x,y)=s(y)$$ f 1 ( x , y ) + f 2 ( x , y ) + f 3 ( x , y ) + f 4 ( x , y ) = s ( y ) and provide a construction of new permutations with the $$(\mathcal {A}_m)$$ ( A m ) property from the old ones. Combining these two results, we obtain a recursive construction method of bent functions satisfying the dual bent condition. Moreover, we provide a generic condition on the Maiorana-McFarland bent functions $$f_1,f_2,f_3,f_4$$ f 1 , f 2 , f 3 , f 4 stemming from the permutations of $$\mathbb {F}_2^m$$ F 2 m with the $$(\mathcal {A}_m)$$ ( A m ) property, such that the concatenation $$f=f_1||f_2||f_3||f_4$$ f = f 1 | | f 2 | | f 3 | | f 4 does not belong, up to equivalence, to the Maiorana-McFarland class. Using monomial permutations $$\pi _i$$ π i of $$\mathbb {F}_{2^m}$$ F 2 m with the $$(\mathcal {A}_m)$$ ( A m ) property and monomial functions $$h_i$$ h i on $$\mathbb {F}_{2^m}$$ F 2 m , we provide explicit constructions of such bent functions; a particular case of our result shows how one can construct bent functions from APN permutations, when m is odd. Finally, with our construction method, we explain how one can construct homogeneous cubic bent functions, noticing that only very few design methods of these objects are known.

Multistatic Passive Radar for drone detection based Random Finite State

Considering the implication of radar sensors in our daily life and environment. Localizing and identifying drones are becoming a research with a greater focus in recent years. Consequently, when an unmanned aerial vehicle is used with bad intention, this can lead to a serious public safety and privacy probem. This study investigate pratical use of spectrum range for multistatic passive radar (MSPR) signal processing . Firstly, signal processing is performed after MSPR sensing detection range ,this include multipath energy detection, reference signal extraction, and receiving antenna configuration. Secondly, based on the MSPR nature, the reference signal is extracted and analyzed. In addition,taking into consideration the vulnerability of passive radar when comes to a moving target localization and real time tracking detection ,a novel method for spectrum sensing and detection which relies on Gaussian filter is proposed. The main goal is to optimize the use of the reference signal extracted with minimum interference as the shared reference signal in spectrum sensing. This will improve the system detection capability and spectrum access. Finally, a recursive method based on Bernoulli random filter is proposed, this takes consideration of drone’s present and unknown states based on time. Moreover, a system is developed meticulously to track and enhance detection of the target. A careful result of the experiment demonstrated that spectral detection can be achieved accurately even when the drone is moving while chasing its position. It shows that Cramer Rao lower error bounds remains significantly within 3% range.

Safe Autonomous Docking of Spacecraft: A RRT-combined Output-constrained Recursive Control Method

In addressing the challenges of short-range spacecraft docking in the presence of obstacles and disturbances, it is critical to integrate guidance and motion control to ensure autonomous and reliable operation. Traditional methods that separate these two layers often struggle with accurately tracking predefined paths, increasing the risk of collisions. In light of this, a proposed scheme integrating guidance and control in an organic manner has been put forth. This scheme employs the rapidly-exploring random trees (RRT) algorithm within the guidance layer to generate a collision-avoidance trajectory for the control layer, efficiently navigating the spacecraft towards its target. Then the control layer implements a second-order output-constrained controller by adding a power integrator and a novel barrier Lyapunov function (BLF) together, to guarantee that the tracking error of the predefined trajectory remains bounded and the system asymptotically converges to the target. To account for tracking errors, obstacle radii are expanded during path planning through a dilation constant. Based on theoretical derivation and simulation experiments, the effectiveness and advancement of the proposed method are validated.

A recursive calculation method of vibration displacements using blade tip timing in angular domain

Blade tip timing (BTT) is a non-contact measurement technique that can be used to monitor blade vibration in turbomachinery. The raw data measured by BTT is the arrival time of all blades at the same stage. However, most blade vibration monitoring methods based on BTT require the use of blade vibration displacements, which are derived from the raw arrival time data, the blade rotation radius and speed. Conventional BTT methods calculate blade tip displacements by comparing the measured arrival time with the ideal arrival time. The ideal arrival time is obtained by assuming that the rotational speed is constant in a revolution, which is inconsistent with the fact, especially when the rotational speed changes rapidly. In this paper, a recursive calculation method called recursive BTT is proposed to reduce the influence of rotational speed fluctuation on the accuracy of blade tip displacement calculation. Recursive BTT calculates the displacements in the angular domain instead of the time domain. A recursive formula is constructed in the angular domain to calculate the blade vibration displacement by using the angle between the vibrating blades. Compared with the conventional BTT method, which relies on the once-per-revolution (OPR) signal, recursive BTT makes full use of the arrival time of all blades at the same stage to calculate the displacements. The advantage of recursive BTT is illustrated through a simulation, a laboratory test and a full-scale aeroengine test. To evaluate the reliability of the calculated displacements, strain signals are resampled to compare with the calculated displacements in the laboratory test. In the full-scale aeroengine test, due to the lack of strain signals, BTT displacements are used to track the blade natural frequency to qualitatively indicate the influence of displacements on blade vibration monitoring. The results of finite element analysis and modal test are used for verification in the full-scale aeroengine test. Simulation and experimental results demonstrate that compared with existing methods, recursive BTT is robust for calculating blade vibration displacements.