Recursive Form Research Articles

An automatic real-time cable modal frequency identification and tracking algorithm by combining recursive band-pass filter and recursive Hilbert transform

Cables are essential elements in bridge engineering. The cable force is usually determined by the vibration method using the cable modal frequency. This paper proposes a real-time online identification method of cable modal frequency based on band-pass filter and Hilbert transform. A recursive form of band-pass filtering (RBF) is employed so that the original signal can be filtered for the target frequency band to obtain a single modal signal of the target order of the cable. The recursive Hilbert transform (RHT) is then used to obtain a real-time resolved signal for real-time frequency identification, allowing for real-time identification and tracking of the time-varying modal frequencies at the cable's target order. This method is more efficient than traditional time–frequency analysis methods. According to numerical simulations and actual measurement data. The method is noise-resistant and does not necessitate priori information of the order. The method allows online identification and tracking of time-varying frequency of interest at a specific order. The procedure can be applied to the real-time identification of cable incident frequencies in an online monitoring system, and can also provide a basis for further real-time identification of time-varying cable forces.

KOALA: A Kalman Optimization Algorithm with Loss Adaptivity

Optimization is often cast as a deterministic problem, where the solution is found through some iterative procedure such as gradient descent. However, when training neural networks the loss function changes over (iteration) time due to the randomized selection of a subset of the samples. This randomization turns the optimization problem into a stochastic one. We propose to consider the loss as a noisy observation with respect to some reference optimum. This interpretation of the loss allows us to adopt Kalman filtering as an optimizer, as its recursive formulation is designed to estimate unknown parameters from noisy measurements. Moreover, we show that the Kalman Filter dynamical model for the evolution of the unknown parameters can be used to capture the gradient dynamics of advanced methods such as Momentum and Adam. We call this stochastic optimization method KOALA, which is short for Kalman Optimization Algorithm with Loss Adaptivity. KOALA is an easy to implement, scalable, and efficient method to train neural networks. We provide convergence analysis and show experimentally that it yields parameter estimates that are on par with or better than existing state of the art optimization algorithms across several neural network architectures and machine learning tasks, such as computer vision and language modeling. The project page with the code and the supplementary materials is available at https://araachie.github.io/koala/.

A novel isogeometric boundary element approach for solving phase change problems with the level set method

In this study a new algorithm is proposed for numerically solving phase change problems. The algorithm (PTE-IGBEM) integrates the precise time domain expanding method (PTE) and the isogeometric boundary element method (IGBEM). The governing equations are transformed into recursive form by expanding the variables within the time period. The domain integral is transformed into boundary integral by the dual reciprocity method (DRM). An adaptive checking scheme is used to determine the number of expanding items required for a time period. In addition, the level set method (LSM) is used to capture the trajectory of the front separating the solid and liquid phases. Several classical examples are given to demonstrate the accuracy and robustness of the algorithm.

Echo State Networks for Practical Nonlinear Model Predictive Control of Unknown Dynamic Systems.

Nonlinear model predictive control (NMPC) of industrial processes is changeling in part because the model of the plant may not be completely known but also for being computationally demanding. This work proposes an extremely efficient reservoir computing (RC)-based control framework that speeds up the NMPC of processes. In this framework, while an echo state network (ESN) serves as the dynamic RC-based system model of a process, the practical nonlinear model predictive controller (PNMPC) simplifies NMPC by splitting the forced and the free responses of the trained ESN, yielding the so-called ESN-PNMPC architecture. While the free response is generated by the forward simulation of the ESN model, the forced response is obtained by a fast and recursive calculation of the input-output sensitivities from the ESN. The efficiency not only results from the fast training inherited by RC but also from a computationally cheap control action given by the aforementioned novel recursive formulation and the computation in the reduced dimension space of input and output signals. The resulting architecture, equipped with a correction filter, is robust to unforeseen disturbances. The potential of the ESN-PNMPC is shown by application to the control of the four-tank system and an oil production platform, outperforming the predictive approach with a long-short term memory (LSTM) model, two standard linear control algorithms, and approximate predictive control.

A recursive formulation for open-loop gyroelastic multibody dynamics

A recursive formulation for open-loop gyroelastic multibody dynamics

Rigid-flexible coupling dynamic modeling and analysis of dumbbell-shaped spacecraft

In this paper, the dynamic modeling of a new configuration spacecraft is investigated. The significance of dumbbell-shaped spacecraft to deep space exploration and the configuration of dumbbell-shaped spacecraft are introduced firstly. Then the dynamic equations of the single flexible body and the kinematic recursive relation between adjacent bodies are deduced. The rigid-flexible coupling dynamic model of the system is established by Jourdain's velocity variation principle and the forward recursive construction formulation for flexible multibody dynamics. The validity of the dynamic model is verified by comparing results with ADAMS. Moreover, the simplification of the dynamic model is investigated to meet the requirements of controller design and the feasibility of conventional simplification method is analyzed. The simulation results show that the conventional simplified model of spacecraft cannot accurately describe the dynamic behaviors of dumbbell-shaped spacecraft. Lastly, a modified attitude dynamic model is proposed and an attitude controller is designed based on this model. The numerical simulations show that the modified model can precisely reflect the dynamic characteristics of dumbbell-shaped spacecraft.

Dynamic Event-triggered State Estimation for Nonlinear Coupled Output Complex Networks Subject to Innovation Constraints

This letter investigates the recursive state estimation (RSE) problem for a class of coupled output complex networks via the dynamic event-triggered communication mechanism (DETCM) and innovation constraints (ICs). Firstly, a DETCM is employed to regulate the transmission sequences. Then, in order to improve the reliability of network communication, a saturation function is introduced to constrain the measurement outliers. A new RSE method is provided such that, for all output coupling, DETCM and ICs, an upper bound of state estimation error covariance (SEEC) is presented in a recursive form, whose trace can be minimized via parameterizing the state estimator gain matrix (SEGM). Moreover, the theoretical analysis is given to guarantee that the error dynamic is uniformly bounded. Finally, a simulation example is illustrated to show the effectiveness of the proposed RSE method.

Blockwise Recursive Moore–Penrose Inverse for Network Learning

Training neural networks with the Moore–Penrose (MP) inverse has recently gained attention in view of its noniterative training nature. However, a significant drawback of learning based on the MP inverse is that the computational memory consumption grows along with the size of a dataset. In this article, based on the partitioning of the MP inverse, we propose a blockwise recursive MP inverse formulation (BRMP) for network learning with low-memory property while preserving its training effectiveness. The BRMP is an equivalent formulation to its batchwise counterpart since neither approximation nor assumption is made in the derivation process. Our further exploration of this recursive method leads to a switching structure among three different scenarios. This structure also reveals that the well-known recursive least squares method is a special case of our proposed technique. Subsequently, we apply BRMP to the training of radial basis function networks as well as multilayer perceptrons. The experimental validation covers both regression and classification tasks.

A Method For Generating Plane Wave And Zero-Offet Vsp Synthetic Seismograms

Synthetic Vertical Seismic Profiles (VSP) seianograms are a useful aid to the interpretation of VSP re- conds, Plane wave VSP syntherics multiples and mode conversions can be computed rapldly n the frequency domain using a new recursive formulation. The method urilises the concept of "renultanz" phase related reflection and tranamission coefficients for a layer atack. High frequerncy signals can be handled with relative euse. The ability to control the order of the multiple avolds wraparound problems with the discrete Fourier transform. Several examples are used to lhustrate the method with relewance to seismic exploration.

Derivative-Free Power Flow Solution for Bipolar DC Networks with Multiple Constant Power Terminals.

This paper analyzes the power flow solution in bipolar direct current networks with radial structures considering multiple monopolar and bipolar constant power loads. The electrical configuration of the bipolar DC grid considers that the reference pole is non-grounded along the feeder, which produces important neutral currents and voltage imbalances along the DC grid. The power flow problem is formulated through the triangular-based representation of the grid topology, which generates a recursive formulation that allows determining the voltage values in the demand nodes through an iterative procedure. The linear convergence of the triangular-based power flow method is tested through multiple load variations with respect to the nominal grid operative condition. Numerical results in the 21- and the 85-bus grids reveal the relevant variations in the voltage profiles and total grid power losses when the neutral cable is solidly grounded or not.

Nonbinary I-Polar Coded Modulation

Polar codes were shown to be weak at finite block lengths even under maximum-likelihood (ML) decoding. To enhance polar codes, CRC-aided polar codes were proposed. It has been shown that CRC-aided polar codes under the successive cancellation list (SCL) decoder outperform LDPC codes and turbo codes. Recently, interleaved polar (i-polar) codes were proposed. By using a new bit channel selection algorithm, i-polar codes without CRC were shown to outperform the 5G LDPC codes. However, most research on polar codes focuses on the binary case. In this paper, a new family of nonbinary i-polar codes with random constellation mapping is proposed. A recursive form for calculating the average weight enumerating function (WEF) of the nonbinary i-polar code is derived. With the random constellation mapping, the upper bound on the BLER under ML decoding depends on the WEF of the nonbinary i-polar code. Then a new channel selection algorithm is proposed based on the polarization effect and the BLER upper bound. The algorithm generates a sequence, termed the i-polar sequence (IPS). Simulation results show that the nonbinary i-polar codes with the IPS outperform the 5G LDPC codes.

Galerkin finite element method for damped nonlinear Schrödinger equation

In this paper, we study Leap-frog finite element methods for a class of nonlinear Schrödinger equation with damped term. We mainly focus on the optimal convergence estimate without any time-step restrictions. The key of our analysis is the time-space error splitting technique, with which the error is split into two parts: the temporal error and the spatial error. Since the spatial error is τ-independent, the numerical solution in L∞-norm is proved to be unconditionally bounded by using an inverse inequality. Then, the optimal L2-norm error estimate can be obtained unconditionally by a routine method. In addition, we show that both the continuous and discrete systems can keep mass and energy conservation in recursive forms. Furthermore, we also apply the proposed Leap-frog finite element methods to solve the logarithmic damped Schrödinger model by introducing a regularized system with a small regularization parameter 0<ε≪1. The detailed theoretical analysis, including the mass, momentum and energy conservation laws of the continuous regularized system and corresponding numerical schemes, and the convergence result, are presented as prolongation of the previous work. Finally, numerical results are given to confirm our theoretical analysis.

(ℓ,p)-Jones-Wenzl idempotents

The Jones-Wenzl idempotents of the Temperley-Lieb algebra are celebrated elements defined over characteristic zero and for generic loop parameter. Given a pointed field (R,δ), we extend the existing results of Burrull, Libedinsky and Sentinelli to determine a recursive form for the idempotents describing the projective cover of the trivial TLnR(δ)-module.

Recursive Optimal Finite Impulse Response Filter and Its Application to Adaptive Estimation

In this paper, the recursive form of an optimal finite impulse response filter is proposed for discrete time-varying state-space models. The recursive form of the finite impulse response filter is derived by employing finite horizon Kalman filtering with optimally estimated initial conditions. The horizon initial state and its error covariance on the horizon are optimally estimated by using recent finite measurements, in the sense of maximum likelihood estimation, then initiating the finite horizon Kalman filter. The optimality and unbiasedness of the proposed filter are proved by comparison with the conventional optimal finite impulse response filter in batch form. Moreover, an adaptive FIR filter is also proposed by applying the adaptive estimation scheme to the proposed recursive optimal FIR filter as its application. To evaluate the performance of the proposed algorithms, a computer simulation is performed to compare the conventional Kalman filter and adaptive Kalman filters for the gas turbine aircraft engine model.

Large deflection of composite beams by finite elements with node-dependent kinematics

In this paper, the use of the node-dependent kinematics concept for the geometrical nonlinear analysis of composite one-dimensional structures is proposed With the present approach, the kinematics can be independent in each element node. Therefore the theory of structures changes continuously over the structural domain, describing remarkable cross-section deformation with higher-order kinematics and giving a lower-order kinematic to those portion of the structure which does not require a refinement. In this way, the reliability of the simulation is ensured, keeping a reasonable computational cost. This is possible by Carrera unified formulation, which allows writing finite element nonlinear equilibrium and incremental equations in compact and recursive form. Compact and thin-walled composite structures are analyzed, with symmetric and unsymmetric loading conditions, to test the present approach when dealing with warping and torsion phenomena. Results show how finite element models with node-dependent behave as well as ones with uniform highly refined kinematic. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by node-dependent kinematics analysis.

Consensus‐based robust least‐squares filter for multi‐sensor systems

SummaryIn this article, a consensus‐based robust regularized least‐squares filter is designed for multi‐sensor systems with norm‐bounded uncertainties. In this approach, a min‐max optimization problem is presented based on a consensus protocol on estimates. The advantage of a consensus filter is that each node estimates its local states, in addition to reaching an agreement on estimates made by all sensors on the network. By introducing appropriate conversions the proposed optimization problem is converted to a robust regularized least‐squares problem. Solving this problem results in the structure of the proposed filter. Then, the recursive formulation of the filter is obtained in measurement form and information form. Finally, in order to investigate the efficacy, good proficiency, and robustness of the proposed consensus‐based robust least‐squares filter, it has been applied to an uncertain multi‐sensor system with 100 nodes and its results have been compared with existing consensus filters.

Hierarchical Control for DC Microgrids Using an Exact Feedback Controller with Integral Action

This paper addresses the problem of the optimal stabilization of DC microgrids using a hierarchical control design. A recursive optimal power flow formulation is proposed in the tertiary stage that ensures the global optimum finding due to the convexity of the proposed quadratic optimization model in determining the equilibrium operative point of the DC microgrid as a function of the demand and generation inputs. An exact feedback controller with integral action is applied in the primary and secondary controller layers, which ensures asymptotic stability in the sense of Lyapunov for the voltage variables. The dynamical model of the network is obtained in a set of reduced nodes that only includes constant power terminals interfaced through power electronic converters. This reduced model is obtained by applying Kron’s reduction to the linear loads and step nodes in the DC grid. Numerical simulations in a DC microgrid with radial structure demonstrate the effectiveness and robustness of the proposed hierarchical controller in maintaining the stability of all the voltage profiles in the DC microgrid, independent of the load and generation variations.

Bequest motives in consumption-portfolio decisions with recursive utility

This paper studies finite-horizon consumption-portfolio decisions with recursive utility. We show that the parameter seemingly representing the individual’s bequest preference in traditional recursive utility formulations is quantitatively and qualitatively misleading. The parameter value is uninformative about the optimal bequest which, in some cases, is even inversely related to the magnitude of the apparent bequest weight. We argue that the ratio between optimal bequest and the optimal consumption rate just before the terminal date is a much better representation of the strength of the bequest motive. Numerical examples illustrate the pitfalls using the traditional specification and clarifies how the bequest preference affects optimal decisions and the life-cycle patterns of consumption and wealth assuming constant investment opportunities or stochastic interest rates. We show that the typical utility representation for a unit elasticity of intertemporal substitution actually assumes a strong bequest preference.

Solving the Distance-Based Critical Node Problem

In critical node problems, the task is to identify a small subset of so-called critical nodes whose deletion maximally degrades a network’s “connectivity” (however that is measured). Problems of this type have been widely studied, for example, for limiting the spread of infectious diseases. However, existing approaches for solving them have typically been limited to networks having fewer than 1,000 nodes. In this paper, we consider a variant of this problem in which the task is to delete b nodes so as to minimize the number of node pairs that remain connected by a path of length at most k. With the techniques developed in this paper, instances with up to 17,000 nodes can be solved exactly. We introduce two integer programming formulations for this problem (thin and path-like) and compare them with an existing recursive formulation. Although the thin formulation generally has an exponential number of constraints, it admits an efficient separation routine. Also helpful is a new, more general preprocessing procedure that, on average, fixes three times as many variables than before. Summary of Contribution: In this paper, we consider a distance-based variant of the critical node problem in which the task is to delete b nodes so as to minimize the number of node pairs that remain connected by a path of length at most k. This problem is motivated by applications in social networks, telecommunications, and transportation networks. In our paper, we aim to solve large-scale instances of this problem. Standard out-of-the-box approaches are unable to solve such instances, requiring new integer programming models, methodological contributions, and other computational insights. For example, we propose an algorithm for finding a maximum independent set of simplicial nodes that runs in time O(nm) that we use in a preprocessing procedure; we also prove that the separation problem associated with one of our integer programming models is NP-hard. We apply our branch-and-cut implementation to real-life networks from a variety of domains and observe speedups over previous approaches.

The God-given Naturals: Induction and Recursion

We discuss some basic issues underlying the natural numbers: induction and recursion. We examine recursive formulations and their use in establishing universal and particular properties.