Double Accelerated Convergence ZNN with Noise-Suppression for Handling Dynamic Matrix Inversion

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.

Extension of the Wittrick-Williams Algorithm for Free Vibration Analysis of Hybrid Dynamic Stiffness Models Connecting Line and Point Nodes

This paper extends the Wittrick-Williams (W-W) algorithm for hybrid dynamic stiffness (DS) models connecting any combinations of line and point nodes. The principal novelties lie in the development of both the DS formulation and the solution technique in a sufficiently systematic and general manner. The parent structure is considered to be in the form of two dimensional DS elements with line nodes, which can be connected to rigid/spring point supports/connections, rod/beam point supports/connections, and point connections to substructures. This is achieved by proposing a direct constrain method in a strong form which makes the modeling process straightforward. For the solution technique, the W-W algorithm is extended for all of the above hybrid DS models. No matrix inversion is needed in the proposed extension, making the algorithm numerically stable, especially for complex built-up structures. A mathematical proof is provided for the extended W-W algorithm. The proposed DS formulation and the extended W-W algorithm are validated by the FE results computed by ANSYS. This work significantly extends the application scope of the DS formulation and the W-W algorithm in a methodical and reliable manner, providing a powerful eigenvalue analysis tool for beam-plate built-up structures.

Антенная решетка и эквалайзер с обратной связью как единое адаптивное устройство

В статье рассмотрена адаптивная антенная решетка (ААР), весовые коэффициенты которой совмещены с весовыми коэффициентами части эквалайзера без обратной связи, а выходной сигнал комбинируется с выходным сигналом части эквалайзера с обратной связью. Такие решетка и распределенный эквалайзер функционируют как единый многоканальный адаптивный фильтр, обеспечивающий прием полезного сигнала в условиях его многолучевости и наличия сигналов источников внешних помех. Представлены архитектура антенной решетки/эквалайзера, математическое описание многоканальных адаптивных алгоритмов его работы: рекурсивного алгоритма по критерию наименьших квадратов RLS (Recursive Least Mean Squares) на основе леммы об обращении матрицы MIL (Matrix Inversion Lemma), QR-разложения и преобразования Хаусхолдера с квадратичной вычислительной сложностью, а также простых алгоритмов по критерию наименьшего квадрата LMS (Least Mean Square), нормализованного LMS-алгоритма NLMS (Normalized LMS) и алгоритма аффинных проекций AP (Affine Projection) с линейной вычислительной сложностью. Результаты моделирования линейной антенной решетки с числом антенн/каналов, равным восьми, принимающей полезный сигнал 16-PSK, прошедший через двухлучевой канал связи, при наличии от одного до четырех источников помех с отношением сигнал–помеха (ОСП) –30 дБ по каждой помехе, при отношении сигнал–шум (ОСШ) в каналах решетки 10–30 дБ, демонстрируют эффективность предлагаемого решения.

Efficient Implementations of Rainbow and UOV using AVX2

A signature scheme based on multivariate quadratic equations, Rainbow, was selected as one of digital signature finalists for NIST Post-Quantum Cryptography Standardization Round 3. In this paper, we provide efficient implementations of Rainbow and UOV using the AVX2 instruction set. These efficient implementations include several optimizations for signing to accelerate solving linear systems and the Vinegar value substitution. We propose a new block matrix inversion (BMI) method using the Lower-Diagonal-Upper decomposition of blocks matrices based on the Schur complement that accelerates solving linear systems. Compared to UOV implemented with Gaussian elimination, our implementations with the BMI result in speedups of 12.36%, 24.3%, and 34% for signing at security categories I, III, and V, respectively. Compared to Rainbow implemented with Gaussian elimination, our implementations with the BMI result in speedups of 16.13% and 20.73% at the security categories III and V, respectively. We show that precomputation for the Vinegar value substitution and solving linear systems dramatically improve their signing. UOV with precomputation is 16.9 times, 35.5 times, and 62.8 times faster than UOV without precomputation at the three security categories, respectively. Rainbow with precomputation is 2.1 times, 2.2 times, and 2.8 times faster than Rainbow without precomputation at the three security categories, respectively. We then investigate resilience against leakage or reuse of the precomputed values in UOV and Rainbow to use the precomputation securely: leakage or reuse of the precomputed values leads to their full secret key recoveries in polynomial-time.

An Efficient Approach For the Nodal Water Demand Estimation in Large-Scale Water Distribution Systems

Real-time modeling of the water distribution system (WDS) is a critical step for the control and operation of such systems. The nodal water demand as the most important time-varying parameter must be estimated in real-time. The computational burden of nodal water demand estimation is intensive, leading to inefficiency for the modeling of the large-scale network. The Jacobian matrix computation and Hessian matrix inversion are the processes that dominate the main computation time. To address this problem, an approach to shorten the computational time for the real-time demand estimation in the large-scale network is proposed. The approach can efficiently compute the Jacobian matrix based on solving a system of linear equations, and a Hessian matrix inversion method based on matrix partition and Iterative Woodbury-Matrix-Identity Formula is proposed. The developed approach is applied to a large-scale network, of which the number of nodal water demand is 12523, and the number of measurements ranging from 10 to 2000. Results show that the time consumptions of both Jacobian computation and Hessian matrix inversion are significantly shortened compared with the existing approach.