Recursive Scheme Research Articles

An efficient recursive rotational-coordinate-based formulation of a planar Euler–Bernoulli beam

A recursive rotational-coordinate-based formulation of a planar Euler–Bernoulli beam is developed, where large displacements, deformations, and rotations are considered. Different from the traditional rotational-coordinate-based formulations, relative rotational angles rather than absolute ones are used as generalized coordinates. The number of generalized coordinates is minimized, which is inherited from traditional rotational-coordinate-based formulations. A recursive scheme is used for adjacent elements of the beam that is considered as a chain-like structure. Integrals in the mass matrix and generalized force vector of each element of the beam can be analytically derived, and a numerical trick based on Taylor polynomial approximations is adopted to avoid numerical singularity. The current formulation entirely avoids the evaluation of integrals in each time step, which greatly improves the computational efficiency. Three widely-used examples are studied to illustrate the performance of the proposed method. Results indicate that the present formulation can achieve the same accuracy, as well as much higher efficiency, compared to some traditional formulations. In addition, calculation time of the current formulation almost linearly increases with the increasing number of elements of the beam, indicating that the computational complexity of the current formulation is $O\left ( N \right )$ .

Unlocking the power of big data analytics in new product development: An intelligent product design framework in the furniture industry

New product development to enhance companies’ competitiveness and reputation is one of the leading activities in manufacturing. At present, achieving successful product design has become more difficult, even for companies with extensive capabilities in the market, because of disorganisation in the fuzzy front end (FFE) of the innovation process. Tremendous amounts of information, such as data on customers, manufacturing capability, and market trend, are considered in the FFE phase to avoid common flaws in product design. Because of the high degree of uncertainties in the FFE, multidimensional and high-volume data are added from time to time at the beginning of the formal product development process. To address the above concerns, deploying big data analytics to establish industrial intelligence is an active but still under-researched area. In this paper, an intelligent product design framework is proposed to incorporate fuzzy association rule mining (FARM) and a genetic algorithm (GA) into a recursive association-rule-based fuzzy inference system to bridge the gap between customer attributes and design parameters. Considering the current incidence of epidemics, such as the COVID-19 pandemic, communication of information in the FFE stage may be hindered. Through this study, a recursive learning scheme is established, therefore, to strengthen market performance, design performance, and sustainability on product design. It is found that the industrial big data analytics in the FFE process achieve greater flexibility and self-improvement mechanism on the evolution of product design.

Method and Algorithm for Implementation of Decoding Operation in the Threshold Cryptomodule of Secret Separation Using a Minimally Redundant Modular Number System

The article presents a new development of method and algorithm for performing secret separation in a threshold cryptomodule with masking transformation of the decoding operation. To solve this problem a recursive binary exponent division scheme and computational technology on the ranges of large numbers of the table-adder type, based on minimally redundant modular arithmetic (MRMA) are applied. A distinctive feature of the developed approach is usage the secret-original domain of finite residue rings for modules that have the form of powers of the number 2. This significantly reduces the complexity of the resulting decoding MRMA-procedure. Decomposition of scalable residues into large modules allows you to efficiently map the computational process being implemented to sets of easily implemented data extraction operations from table memory and their summation, providing a high level of performance, uniformity, and unification of basic structures. In terms of speed, the created MIMA decoding algorithm surpasses non-redundant analogues by at least l(19l-3)/(22l-6) times (l is the number of subscribers restoring the secret original). When l = 7...40 a (6.15...34.65)-fold increase in productivity is achieved.

Decentralized event-triggered adaptive control of a class of uncertain interconnected nonlinear systems using local state feedback corrupted by unknown injection data

This paper investigates a decentralized event-triggered adaptive control problem of uncertain interconnected lower-triangular nonlinear systems using corrupted local state feedback. The unknown injection data such as sensor faults or cyber attacks are assumed to be added to full state feedback measurements of each subsystem with unknown nonlinearities. Under this assumption, exactly measured local state variables are unknown during Lyapunov-stability-based recursive control design steps. The primary contributions of this study are (i) to develop a recursive adaptive control design strategy for achieving decentralization of unmatched interconnected nonlinearities using corrupted local state feedback information and (ii) to design a decentralized asynchronous event-triggering mechanism using the corrupted local state variables. To this end, local injection data compensators using neural networks and adaptive tuning laws are designed to compensate for unknown injection data and nonlinear interaction effects. It is shown that the proposed decentralized control system via the corrupted local state feedback ensures the practical stability of the total closed-loop system and the exclusion of Zeno behavior.

Passive Shallow Water Automated Target Recognition using Deep Convolutional Bi directional Long Short Term Memory

The extremely challenging nature of passive acoustic surveillance makes it a key area of research in NavalNon-Co-operative Target Recognition especially in Anti-Submarine Warfare systems. In shallow waters, thecomplex acoustics due to the highly varying ambient background noise as well as the multi-modal propagation in the surface-bottom bounded channel makes surveillance even difficult. In this work, an ensemble of Convolutional Neural Networks and Bidirectional Long Short Term Memory stages employing soft attention is used to effectively capture the spectro-temporal dynamics of the target signature. In order to alleviate the overall computational cost associated with the optimal model search in the extensive hyperparameter space, a recursive model elimination scheme, making frugal use of the available resources, is also proposed. Experimental analysis on acoustic target records, collected from the shallows of Arabian Sea, has yielded encouraging results in terms of model accuracy, precision and recall.

A recursive implementation of the ALIENOR optimization method

PurposeA recursive scheme for the ALIENOR method is proposed as a remedy for the difficulties induced by the method. A progressive focusing on the most promising region, in combination with a variation of the density of the alpha-dense curve, is proposed.Design/methodology/approachALIENOR method is aimed at reducing the space dimensions of an optimization problem by spanning it by using a single alpha-dense curve: the curvilinear abscissa along the curve becomes the only design parameter for any design space. As a counterpart, the transformation of the objective function in the projected space is much more difficult to tackle.FindingsA fine tuning of the procedure has been performed in order to identity the correct balance between the different elements of the procedure. The proposed approach has been tested by using a set of algebraic functions with up to 1,024 design variables, demonstrating the ability of the method in solving large scale optimization problem. Also an industrial application is presented.Originality/valueIn the knowledge of the author there is not a similar paper in the current literature.

A Real-Time 3D Reconstruction of Staircases for Rehabilitative Exoskeletons

In medical contexts, the use of assistive exoskeletons for the rehabilitation of people with impaired mobility represents a common practice. Recent advances suggest that, soon, such mechatronic systems will also be used to assist people in their everyday life. In order to reach such target, exoskeletons must become able to perceive the environment. To this purpose, a system for the parametric identification of a staircase is proposed in this article. More precisely, given a staircase of unknown geometry, the system identifies its 3D shape. Furthermore, it also estimates the reciprocal orientation and distance between the exoskeleton and the staircase. Differently from other approaches, this result is achieved by means of low cost devices: an inertial measurement unit, two ranging sensors, and an Arm-Cortex processor. Starting from the ranging sensors acquisitions, the staircase model is identified in real time, during the execution of a step. The proposed procedure is based on an extended recursive total least squares strategy, in order to fully exploit the computational capabilities of the Arm processor, and it is characterized by execution times smaller than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> s. The estimation algorithm has been tested on an actual exoskeleton and the resulting experimental outcomes are compared with the results obtained through alternative methods.

Distribution of the number of losses in busy-periods of oscillating [formula omitted] systems

We analyze customer losses in busy-periods of preemptive and non-preemptive oscillating MX/G/1/(n,a,b) systems. Specifically, we propose a recursive scheme to compute the probability function of the number of customer losses in busy-periods of such systems. The effectiveness and usefulness of the proposed method is illustrated through the presentation of numerical examples that consider different arrival rates and service time and group size distributions.

Two-Step Adaptive Chirp Mode Decomposition for Time-Varying Bearing Fault Diagnosis

Fault diagnosis of rolling bearing has always been the focus of research in the engineering field. Due to the nonstationary conditions, this work has suffered huge challenges. The adaptive chirp mode decomposition (ACMD) is a signal decomposition method developed recently. By using a recursive framework embedded with an iterative algorithm, it can decompose signals one by one. Although this scheme has strong adaptability, the accuracy of reconstructed signals is very rough. Moreover, the estimated components will even deviate from the true results as the iteration progresses when two components are very close. In order to solve the above problems, a novel two-step ACMD is proposed in this article. Specifically, the recursive scheme without an iterative algorithm is only used to decompose signals first, which can determine the number of components. Then, the joint-estimation framework using an iterative algorithm is used to achieve high-resolution component reconstruction. The main idea of this two-step method is to let different schemes do what they do best. Subsequently, we proposed a new fault diagnosis method for rolling bearing under variable speeds based on the proposed two-step ACMD. Finally, both simulation and actual bearing diagnosis cases verify the potential of the proposed method and successfully diagnosed different kinds of rolling bearing faults.

Short-Term Wind Power Forecasting Using R-LSTM

Renewable energies such as wind and solar begin receiving remarkable popularity in accordance with the energy demand, expeditious expansion of solar and wind energy generation involves acute forecasting of wind and solar power, so in past and recent years it has become an intensive research area. An accurate forecast of wind power to maintain an affordable, secure, and economical power supply is most significant. Numerous investigations and research have been performed in this area in recent years. This research article aims to develop a short-term wind power forecasting model to improve the accuracy of the prediction. Therefore, a novel approach based on LSTM (Long Short-Term Memory) is proposed to forecast from 1 to 6 hours ahead of wind power. A recursive strategy is used when predicting short-term wind power, unlike the conventional LSTM approach. The proposed model is implemented using historical generated wind power data for Gujarat state. A comparative analysis is performed between the proposed and existing approach presented in the literature, from the analysis, it is noted that the proposed R-LSTM (Rolling-LSTM) model outperformed with minimal error and better accuracy.

Motion-Robust Multimodal Heart Rate Estimation Using BCG Fused Remote-PPG With Deep Facial ROI Tracker and Pose Constrained Kalman Filter

The heart rate (HR) signal is so weak in remote photoplethysmography (rPPG) and ballistocardiogram (BCG) that HR estimation is very sensitive to face and body motion disturbance caused by spontaneous head and body movements as well as facial expressions of subjects in conversation. This article proposed a novel multimodal quasi-contactless HR sensor to ensure the robustness and accuracy of HR estimation under extreme facial poses, large-motion disturbances, and multiple faces in a video for computer-aided police interrogation. Specifically, we propose a novel landmark-based approach for a deep facial region of interest (ROI) tracker and face pose constrained Kalman filter to continuously and robustly track target facial ROIs for estimating HR from face and head motion disturbances in rPPG. This motion-disturbed rPPG signal is further fused with a minimally disturbed BCG signal by the face and head movements via a bank of notch filters with a recursive weighting scheme to obtain the dominant HR frequency for final accurate HR estimation. To facilitate reproducible HR estimation research, we synchronously acquire and publicly share a multimodal data set that contains 20 sets of ECG and BCG signals as well as uncompressed, rPPG-dedicated videos from ten subjects in a stable state and large-motion state (MS) without and with large face and body movements in a sitting position. We demonstrate through experimental comparisons that the proposed multimodal HR sensor is more robust and accurate than the state-of-the-art single-modal HR sensor solely with rPPG- or BCG-based methods. The mean absolute error (MAE) of HR estimation is 7.13 BPM lower than the BCG algorithm and 3.12 BPM lower than the model-based plane-orthogonal-to-skin (POS) algorithm in the MS.

Under the same (Chole)sky: DNK models, timing restrictions and recursive identification of monetary policy shocks

Recent structural VAR studies of the monetary transmission mechanism have voiced concerns about the use of recursive identification schemes based on short-run exclusion restrictions. We trace out the effects on impulse propagation of informational constraints embodying classical Cholesky-timing restrictions in otherwise standard Dynamic New Keynesian (DNK) models. By reinforcing internal propagation mechanisms and enlarging a model's equilibrium state space, timing restrictions may produce a non-trivial moving average component of the equilibrium representation, making finite order VARs a poor approximation of true adjustment paths to monetary impulses, albeit correctly identified. They can even serve as an independent source of model-based nonfundamentalness, thereby hampering shock identification via VAR methods. This notwithstanding, restricted DNK models are shown to feature (i) invertible equilibrium representations for the observables and (ii) fast-converging VAR coefficient matrices under empirically tenable parameterizations. This alleviates concerns about identification and lag truncation bias: low-order Cholesky-VARs do well at uncovering the transmission of monetary impulses in a truly Cholesky world.

Adaptive Practical Fast Finite-Time Consensus Protocols for High-Order Nonlinear Multi-Agent Systems With Full State Constraints

This paper mainly addresses the issue of fast finite-time consensus (FTC) algorithms for a group of high-order uncertain nonlinear non-strict-feedback Multi-agent Systems (MASs) with time-varying asymmetric full state constraints. In order to guarantee the state constraints are satisfied, an appropriate asymmetric nonlinear mapping (NM) is employed to transform the original full state constrained system into a corresponding unconstrained one. Combining neural networks technology, graph theory, fast finite-time control theory and backstepping recursive design scheme, the uncertainties and non-strict-feedback form are considered to propose a distributed adaptive FTC protocol which can guarantee tracking error reaching a region in finite time. Finally, an example is given to show that the designed control law can perform effective control.

Time-Varying Dynamics of the German Business Cycle: A Comprehensive Investigation

This paper provides insights into the time-varying dynamics of the German business cycle over the last five decades. To do so, I employ an open-economy time-varying parameter VAR with stochastic volatility, which I estimate by quasi-Bayesian techniques. The reduced-form analysis reveals substantial shifts in the variables’ long-run growth rates and shock volatilities over time. German trend inflation has strongly decreased and settled at a historically low level. GDP growth volatility exhibits marked fluctuations over time and has dropped to historically low levels only after the global financial crisis. The structural analysis employs externally identified oil supply shocks along with a recursive identification scheme to identify key macroeconomic shocks. The analysis reveals strong fluctuations in both the impact responses of macroeconomic aggregates to these shocks and the shock propagation processes. Thus, I conclude that business cycle stabilization in Germany is driven by both good policy and good luck.

On the Structure and Realization of Real-Time Coding and Estimation Over Noiseless Channel

This paper presents the optimal structural analysis and realization scheme of real-time coding and estimation for linear discrete-time system over rate-constrained noiseless channel. The mean-squared error (MSE) is adopted as the estimation performance criterion. Without any loss of performance, the optimal real-time coding and estimation functions can be represented in recursive forms, which may reduce the potential computational complexity and storage burden. Furthermore, we put forward a recursive realization scheme via standard Kalman filter and vector Lloyd-Max quantization, which is also shown to be structurally equivalent to the established structural results. Moreover, to synchronize the encoder-decoder pair instantaneously, there are two synchronizers respectively arranged at the encoder and decoder sides, which utilize the common information between the encoder and the decoder to synchronize the encoding and decoding operations. Our proposed realization scheme is demonstrated with simulation results, and the designed algorithm performs well even for very low rate region.

Ascent Guidance Based on Onboard Trajectory Regeneration for Vehicles With a Combined Cycle Engine

For a vehicle with a combined cycle engine, an ascent guidance method based on onboard trajectory regeneration is proposed to meet the requirements of adaptability and robustness. This method combines onboard trajectory planning with reference trajectory tracking and modifies the computational model. In the onboard trajectory planning, a hierarchical receding horizon optimization is developed to update the reference trajectory depending on the current state. Further, the optimization problem subject to multiple constraints is solved by an improved segmented pseudospectral method, in which a recursive initialization strategy is introduced to improve the computational efficiency for onboard application. In reference trajectory tracking, the active disturbance rejection control theory is used to improve the robustness of the tracking process. Based on the theory, an extended state observer for the multi-input and multi-output system is designed to estimate the state and the disturbance. Then, the trajectory tracking law is derived by linearizing the model with dynamic compensation. Besides, the scale factors of the dynamic system are defined to compensate for the uncertainty of the model, and an online estimation method is used to identify the parameters. Numerical simulation validates the efficiency of the proposed method.

Unsupervised Monocular Depth Estimation via Recursive Stereo Distillation.

Existing unsupervised monocular depth estimation methods resort to stereo image pairs instead of ground-truth depth maps as supervision to predict scene depth. Constrained by the type of monocular input in testing phase, they fail to fully exploit the stereo information through the network during training, leading to the unsatisfactory performance of depth estimation. Therefore, we propose a novel architecture which consists of a monocular network (Mono-Net) that infers depth maps from monocular inputs, and a stereo network (Stereo-Net) that further excavates the stereo information by taking stereo pairs as input. During training, the sophisticated Stereo-Net guides the learning of Mono-Net and devotes to enhance the performance of Mono-Net without changing its network structure and increasing its computational burden. Thus, monocular depth estimation with superior performance and fast runtime can be achieved in testing phase by only using the lightweight Mono-Net. For the proposed framework, our core idea lies in: 1) how to design the Stereo-Net so that it can accurately estimate depth maps by fully exploiting the stereo information; 2) how to use the sophisticated Stereo-Net to improve the performance of Mono-Net. To this end, we propose a recursive estimation and refinement strategy for Stereo-Net to boost its performance of depth estimation. Meanwhile, a multi-space knowledge distillation scheme is designed to help Mono-Net amalgamate the knowledge and master the expertise from Stereo-Net in a multi-scale fashion. Experiments demonstrate that our method achieves the superior performance of monocular depth estimation in comparison with other state-of-the-art methods.

Single-Index Model Tree

In this paper, a novel single-index model tree (SIMTree) is proposed. It adopts the recursive partitioning strategy and each data segment is modeled by a single-index model (SIM), which is a flexible extension of linear regression with non-parametric link functions. The proposed SIMTree has 2 major advantages: a) with only a few leaf nodes, it can achieve competitive predictive performance compared to complicated black-box models; b) SIMs fitted on each local data segment are intrinsically interpretable. However, using conventional techniques to build such a SIMTree can be extremely time-consuming. SIM estimation typically involves iterative optimization via Newton-type algorithms; such a resource-intensive estimation procedure is repeatedly used for fitting leaf node SIMs and the search of optimal splits. To make the computation burden affordable, an effective training algorithm is proposed as enabled by the efficient utilization of Stein's lemma and several accelerating strategies in the tree construction algorithm. Moreover, a new Python package simtree is developed with elegant visualization modules that can further facilitate the model interpretation. Numerical results on extensive regression datasets show that SIMTree is an accurate and interpretable machine learning model.

Maximum-likelihood extremum seeking control of microalgae cultures

Abstract This paper proposes a model-free extremum seeking control (ESC) approach to optimize the productivity of continuous cultures of microalgae, considering the dilution rate and the light intensity as manipulated variables, and the biomass concentration as single measurement. The resulting two-input single-output optimization problem is first solved using a recursive least-squares strategy based on the representation of the process by a Hammerstein block-oriented model. In order to face the presence of noise on the regressor variables (input and output signals), the problem is then reformulated as a maximum-likelihood estimation problem, which is solved on a moving horizon. Simulation results demonstrate the method performance.

A Recursive Denoising Learning for Gear Fault Diagnosis Based on Acoustic Signal in Real Industrial Noise Condition

Acoustic-based diagnosis (ABD) is a promising method for machinery fault detection due to its ability to overcome the limitation of vibration measurement through non-contact measurement by air couple. However, most of the ABD approaches are not widely used in real industrial scenario due to the limitation of strong and highly non-stationary background noise interference. To address the shortcoming, a novel ABD method based on recursive denoising learning (RDL) is proposed in this article. In the proposed method, a new multistage attention mechanism is designed as the fundament of RDL for adaptive tracking and estimating non-stationary industrial background noise and automatic suppressing noise. Based on the multistage attention mechanism, a novel recursive learning strategy is introduced to further improve the performance of noise suppression by recursive tracking noise component and gradual denoising in coarse-to-fine manner. Then, an information fusion method, which is based on an improved tiny-shuffle network (TSN), is adopt to increase the discriminative representation of fault feature through fusion of multi-channel denoising information for improving diagnosis accuracy. Afterward, an RDL-based fault diagnosis method is finally obtained by combining with a standard fault diagnosis model, and it eventually achieves good performance for detection gear fault pattern in noise interference environment. The experimental results in both real industrial background noise condition and additive white Gaussian noise (AWGN) condition with different signal-to-noise ratios (SNRs) indicate that the proposed method performs better than all other popular methods in noise suppression and gear fault pattern detection, which verify the effectiveness of the proposed ABD method in dealing with gear fault diagnosis task under noise condition.