Analysis of Faceted Gratings Using C-Method and Polynomial Expansion

The radiative transfer equation (RTE) is fundamental in modelling photon transport across various scientific and engineering domains, including biomedical optics, atmospheric physics, and nuclear engineering. This study investigates photon propagation in a homogeneous medium using the Henyey-Greenstein (HG) scattering function, which is widely applied in biophysics to describe light scattering in biological tissues. The anisotropy parameter g characterizes scattering properties, playing a crucial role in photon movement. To solve the RTE for a steady-state homogeneous system, we employed two polynomial approximation methods: Legendre polynomial expansion (PN method) and second-kind Chebyshev polynomial expansion (UN method). The eigenvalues play a central role in classical problems such as the albedo problem, the Milne problem, and criticality analysis in slab geometry. We iteratively solve the RTE up to the fifth order and compare the convergence and accuracy of both methods. The results indicated that increasing the number of iterations improves accuracy, with both methods exhibiting stable convergence behaviour. A detailed comparison was conducted and the numerical results were validated against existing literature. Additionally, the tabulated results highlighted the forward and backward scattering components of the HG function, illustrating the influence of the anisotropy parameter on photon transport. The consistency between the proposed methods and the literature was confirmed by comparing discrete eigenvalues in tables. The maximum deviation between the P₉ and U₉ methods remained below 0.08, while both approaches closely matched the benchmark results in literature, supporting the reliability and numerical robustness of the polynomial expansions used. This study offers a valuable reference for future research, enabling comparisons and validation of computational approaches in radiative transfer modelling, particularly in biophysics and optical applications.

An efficient nonlinear interval uncertain optimization method using Legendre polynomial chaos expansion

In this paper, we present a new algorithm to estimate a signal from its short-time Fourier transform modulus (STFTM). This algorithm is computationally simple and is obtained by an acceleration of the well-known Griffin-Lim algorithm (GLA). Before deriving the algorithm, we will give a new interpretation of the GLA and formulate the phase recovery problem in an optimization form. We then present some experimental results where the new algorithm is tested on various signals. It shows not only significant improvement in speed of convergence but it does as well recover the signals with a smaller error than the traditional GLA.

Spectrum scarcity is a major challenge in wireless communications systems requiring efficient usage and utilization. Cognitive radio network (CRN) is found as a promising technique to solve this problem of spectrum scarcity. It allows licensed and unlicensed users to share the same licensed spectrum band. Interference resulting from cognitive radios (CRs) has undesirable effects on quality of service (QoS) of both licensed and unlicensed systems where it causes degradation in received signal-to-noise ratio (SIR) of users. Power control is one of the most important techniques that can be used to mitigate interference and guarantee QoS in both systems. In this paper, we develop a new approach of a distributed power control for CRN based on utility and pricing. QoS of CR user is presented as a utility function via pricing and a distributed power control as a non-cooperative game in which users maximize their net utility (utility-price). We define the price as a real function of transmit power to increase pricing charge of the farthest CR users. We prove that the power control game proposed in this study has Nash Equilibrium as well as it is unique. The obtained results show that the proposed power control algorithm based on a new utility function has a significant reduction in transmit power consumption and high improvement in speed of convergence.

The advances in kernel-based learning necessitate the study on solving a large-scale non-sparse positive definite linear system. To provide a deterministic approach, recent researches focus on designing fast matrix-vector multiplication techniques coupled with a conjugate gradient method. Instead of using the conjugate gradient method, our paper proposes to use a domain decomposition approach in solving such a linear system. Its convergence property and speed can be understood within von Neumann's alternating projection framework. We will report signi ficant and consistent improvements in convergence speed over the conjugate gradient method when the approach is applied to recent machine learning problems.

Strategically injected noise can speed up convergence during Neural Network training using backpropagation algorithm. Noise injection during Neural Network training have been proven empirically to improve convergence and generalizability. In this work, a new methodology proven to be efficient for speeding up learning convergence using weight noise in Single Layer Feed-forward Network (SLFN) architecture is presented. We present efficient and effective methods in which local minimum entrapment can be avoided. Our proposed controlled introduction of noise is based on 4 proven analytical and experimental methods. We show that criteria-based mini-batch noise injection to the weights during training often outperforms the noiseless weights as well as fixed noise introduction as seen in literature both in network generalization and convergence speed. The effectiveness of this methodology has been empirically shown as well as it achieving on an average 15%–25% improvement in convergence speed when compared to fixed and noiseless networks. The proposed method is evaluated on the MNIST dataset and other datasets from UCI repository. The comparative analysis confirms that the proposed method achieves superior performance regarding convergence speed.

This paper studies the convergence behavior of the vectorial modal method (VMM) recently applied to model diffraction from gratings. Results of the VMM are compared with the well established Fourier modal method (FMM) commonly used to analyze interaction of the electromagnetic waves from periodic structures. Numerical simulations carried out for the VMM and FMM demonstrate practically identical convergence of the diffraction efficiencies for the case of incident illumination being TE polarized. However for TM polarization the convergence of VMM is poor as compared to the FMM for metallic gratings. The reason for this is the formulation of the eigenvalue method used to find the fields in the grating region. An alternate formulation of the eigenvalue equation for the VMM for TM polarization is devised which provides the same level of convergence as the FMM. Numerical simulations are carried out to confirm the validity of this formulation.

This study addresses the challenges encountered by traditional multi-agent pathfinding methods in the applications of fixed-wing UAVs, including inadequate adaptation to dynamic constraints, lack of energy optimization, low exploration efficiency, and inefficient data utilization. To tackle these issues, we propose an improved independent Q-learning algorithm that incorporates the dynamics of fixed-wing UAVs. Initially, we expand the traditional multi-agent pathfinding action space and incorporate constraints to develop a model that is compatible with the motion characteristics of fixed-wing UAVs. Next, we develop a multi-dimensional reward function system based on independent Q-learning. Additionally, we introduce a heuristic policy that utilizes directional weights, effectively balancing exploration efficiency and algorithm convergence speed. Finally, we implement a shared experience replay buffer and a reward reconstruction mechanism to enable multi-agent experience sharing and collaborative optimization. Experimental results indicate that our proposed algorithm surpasses the A* algorithm in total path energy consumption. Furthermore, the heuristic policy demonstrates a twofold improvement in convergence speed and the success rate of path planning compared to the $ \varepsilon $-greedy policy. The shared experience replay buffer also shows enhanced performance in convergence speed.

This paper presents a global fixed-time control framework to address the target circumnavigation tracking problem of underactuated unmanned surface vehicles (USV) under unknown velocity states, lumped uncertainties, and actuator saturation. At the core of this approach is a novel fixed-time target-enclosing line-of-sight (FTTELOS) guidance law, designed to generate the desired heading angle and surge velocity. To estimate unknown velocities, external disturbances, and unmeasured system states, a set of fixed-time observers is constructed, consisting of a velocity observer, a disturbance observer, and a high-dimensional extended state observer (HFTESO). Moreover, to enhance robustness and effectively tackle actuator saturation, the control scheme incorporates a fixed-time sliding mode controller, a dynamic auxiliary system, and a fixed-threshold event-triggered mechanism. Simulation results using SimuNPS demonstrate that the proposed method enables rapid and smooth target circumnavigation, with all system errors converging to an arbitrarily small neighborhood of the origin within a fixed time. Theoretical analysis and simulation studies confirm the effectiveness and robustness of both the FTTELOS guidance law and the integrated control strategy. Quantitatively, compared with the traditional target-enclosing line-of-sight (TELOS) method, the proposed FTTELOS reduces the convergence time of the distance error δe from 13.64 s to 10.22 s and the angular error ϕe from 10.46 s to 7.52 s, demonstrating a significant improvement in convergence speed and overall control performance.

The multi‐filament carbon fiber winding technique is an advanced and novel process, where tension control and regulation during winding play a crucial role in determining product performance. Based on this, this paper introduces fractional‐order modeling to derive the physical model of the fiber winding process and optimizes the design of the traditional fractional‐order proportional‐integral‐derivative (FOPID) controller, to obtain the self‐coupling time delay fractional‐order proportional‐integral‐derivative control strategy (ST‐FOPID). The stability region of the tension control system is numerically computed and visually analyzed. Furthermore, this study improves the metaheuristic Ivy algorithm (IVYA) and proposes an improved version, the improved Ivy algorithm (IIVYA). Large‐scale benchmark function experiments and performance comparisons with various algorithms, including the original Ivy algorithm, demonstrate significant improvements in convergence speed, global search capability, and avoidance of local optima. As a result, we propose a self‐coupling time delay fractional‐order proportional‐integral‐derivative control strategy (IIVYA‐ST‐FOPID) based on the improved Ivy algorithm, which is successfully applied to industrial systems such as simple mathematical model, DC motor speed control system, servo tension control system, and hybrid multi‐area power system. Comparative analyses with various existing control strategies confirm the superior performance and broad applicability of the proposed method. Finally, both numerical simulations and experimental results show that the tension control system has excellent dynamic performance and stability under the proposed control strategy, with a significant performance improvement. Tension fluctuations can be controlled within 5% in slow winding conditions, while in fast winding scenarios, they remain around 6%. Moreover, the proposed control strategy reduces the settling time by more than 0.1 s, demonstrating the excellent performance of the proposed control strategy in complex industrial control systems.

A technique for accelerated multiple-plane phase retrieval is demonstrated by creating adaptive support through the statistical analysis of phase estimates. Its technical advantage arises from, what we believe to be, the first time use of both phase estimates and a statistical metric, enabling the fast generation of noise-robust support masks. This results in a fourfold improvement in convergence speed when compared to the conventional multiple-plane method. Evaluating data fitting performance with fewer intensity recordings showed that using four or more recordings resulted in accurate fitting, three recordings caused overfitting, and two recordings led to underfitting for the test object waves used. In principle, the adaptive support strategy based on the statistical analysis of phase estimates may be applied to other iterative phase retrieval methods.

This paper proposes a novel intelligent optimization algorithm, ICPMSHOA, that effectively balances population diversity and convergence performance by integrating an iterative chaotic map with infinite collapses (ICMIC), centroid opposition-based learning, and periodic mutation strategy. To verify its performance, we adopted benchmark functions from the IEEE CEC 2017 and 2022 standard test suites and compared it with six algorithms, including OOA and BWO. The results show that ICPMSHOA has significant improvements in convergence speed, global search capability, and stability, with statistically significant advantages. Furthermore, the algorithm performs outstandingly in three practical engineering constrained optimization problems: Haverly’s pooling problem, hybrid pooling–preparation problem, and optimization design of industrial refrigeration systems. This study confirms that ICPMSHOA provides efficient and reliable solutions for complex optimization tasks and has strong practical value in engineering scenarios.

Federated learning is a distributed learning framework designed to protect user privacy, widely applied across various domains. However, existing federated learning algorithms face challenges, including slow convergence, significant loss fluctuations during aggregation, and imbalanced client sampling. To address these issues, this paper introduces a high-performance federated learning aggregation algorithm. This algorithm combines a cyclic adaptive learning rate adjustment strategy with client-weighted random sampling, addressing the aforementioned problems. Weighted random sampling assigns client weights based on their sampling frequency, balancing client sampling rates and contributions to enhance model aggregation. Additionally, it adapts the learning rate based on client loss variations and communication rounds, accelerating model convergence and reducing communication costs. To evaluate this high-performance algorithm, experiments are conducted using well-known datasets MNIST and CIFAR-10. The results demonstrate significant improvements in convergence speed and loss stability. Compared to traditional federated learning algorithms, our approach achieves faster and more stable convergence while effectively reducing training costs.

Distributed model predictive control (DMPC) is a widely used approach especially for large-scale systems like transportation, traffic control or power distribution systems where solving the MPC problem in a centralized manner is not desirable or even not possible due to the size of the problem, maintenance issues, cabling burden, etc. Distributed optimization methods, which are being employed to solve the DMPC problems, normally suffer from having an enormous number of communications to reach a consensus between the local controllers. Therefore trying to find distributed optimization schemes that can realize an agreement among the local controllers with a lower communication load deserves attention. The alternating direction method of multipliers (ADMM) is a well known method to solve consensus problems. Since the local problems in ADMM can be handled with second-order methods, the convergence will be reached with a lower number of iterations in comparison to first-order methods, e.g. the fast gradient method. In this paper, ADMM is formulated and applied to a DMPC problem first in the primal domain. The main contribution of this paper is, however, the application of ADMM to the dual of the DMPC problem, introducing an augmented connection graph, which shows considerable improvement in convergence speed and therefore requires a lower number of communications in comparison with primal ADMM.

Alignment is a critical pre-processing step before initiating inertial navigation operations. The extended Kalman filter (EKF), commonly employed for aligning strap-down inertial navigation systems (SINS), faces challenges due to linearization limitations. In response to some of these challenges, the invariant extended Kalman filter (IEKF) was developed. A key requirement for utilizing IEKF is that the system dynamics must exhibit a group affine property. However, considering inertial measurement unit (IMU) errors as state variables violates this condition. This paper introduces an improved version of IEKF, named the proportional-integral invariant Extended Kalman Filter (PI-IEKF). This approach initially ignores IMU bias and drift to preserve the group affine property. To compensate for these uncertainties, the Kalman filter's innovation term is reformulated into a proportional-integral (PI) structure. The PI gains are tuned based on Lyapunov stability criteria by solving a Linear Matrix Inequality (LMI). The PI-IEKF not only addresses the uncertainties but also enhances alignment accuracy. The proposed approach was evaluated through simulations and field tests. Simulations addressed the nonlinear alignment problem in marine environment with typical wave disturbances, while field tests used an open-source dataset from vehicle-mounted sensors. Comparative results with conventional IEKF demonstrated significant improvements in convergence speed and robustness.