Multiple Periodic Signals Research Articles

Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals

In this paper, a discrete-time design of a fractional internal model-based repetitive controller with a sliding mode approach is presented for uncertain linear systems subject to repetitive trajectory and periodic disturbance. The proposed algorithm, named a fractional delay-based repetitive sliding mode controller (FD-RSMC), aims to enhance tracking accuracy, transient response, and robustness against parametric variations beyond what is offered by conventional repetitive controllers. First, a fractional delay-based repetitive controller (FD-RC) that allows the periodic delay steps to be noninteger is presented to improve the trajectory tracking accuracy and good disturbance compensation of multiple periodic signals. Second, a sliding mode control (SMC) with a discrete-time reaching law is systematically incorporated into FD-RC to improve transient response, especially during the learning period of FD-RC, and also to provide system robustness against model uncertainties. Finally, the stability proof of the closed-loop system with the proposed controller is assessed based on a delayed-sliding mode-reaching condition. Finally, comparative simulation studies are presented to demonstrate the superior performance of the proposed controller.

Modeling of servo dynamic stiffness for multiple-periodic repetitive learning control system

Servo dynamic stiffness is a pivotal index in characterizing the rejecting performance for the exogenous periodic disturbances of the repetitive learning control system. In this paper, the mathematical modeling of the servo dynamic stiffness for the well-designed repetitive learning control system with multiple-periodic signals is studied by the frequency analysis method. To analysis the complex form of the servo dynamic stiffness, the magnitudes of the direct (real part) and quadrature (imaginary part) servo dynamic stiffness at harmonics of the disturbance are discussed based on the parameters of the repetitive learning controller. An illustrated example of the two linear servomotors with the mechanical coupling is given in this study. Computer simulation are presented to illustrate the effect of the proposed measurement method of the servo dynamic stiffness for the multiple-periodic repetitive learning control system. The proposed servo dynamic stiffness modeling can be used to accurate design the parameters of the repetitive learning control system, such that the batter control performance of the repetitive learning control system at most of the harmonics of the multi-periodic input signal can be achieved.

Compound faults diagnosis of rotating machinery via enhanced two-layer sliding correlated kurtosis

Compound faults identification from vibration signals is still a challenge for rotating machinery because the multiple periodic impulsive fault signals may oscillate with the same frequency. In this research, a method termed enhanced two-layer sliding correlated kurtosis (TLSCK) is presented for isolating and identifying the compound defects from the monitored data containing strong background noise and compound faults. The method contains two main steps: the dual-tree complex wavelet package transform (DTCWPT) based correlated kurtogram is conducted on the raw monitored data as a frequency filtering step; further, the enhanced TLSCK method is conducted to diagnosis the compound defects from above filtered signals. The output signal of the enhanced TLSCK could locate the occurrence of interested fault impulses, while the unwanted vibration components and residual noise are well eliminated. Both numerically simulated and experimentally measured vibration data of damaged rolling bearings are analyzed via the presented method to test its performance, and the analysis results validate that the proposed method is effective in detecting compound faults of rotating machinery.

Examining the Rotation Period Distribution of the 40 Myr Tucana–Horologium Association with TESS

The Tucana–Horologium association (Tuc-Hor) is a 40 Myr old moving group in the southern sky. In this work, we measure the rotation periods of 313 Tuc-Hor objects with TESS light curves derived from TESS full-frame images and membership lists driven by Gaia EDR3 kinematics and known youth indicators. We recover a period for 81.4% of the sample and report 255 rotation periods for Tuc-Hor objects. From these objects we identify 11 candidate binaries based on multiple periodic signals or outlier Gaia DR2 and EDR3 renormalized unit weight error values. We also identify three new complex rotators (rapidly rotating M dwarf objects with intricate light-curve morphology) within our sample. Along with the six previously known complex rotators that belong to Tuc-Hor, we compare their light-curve morphology between TESS Cycle 1 and Cycle 3 and find that they change substantially. Furthermore, we provide context for the entire Tuc-Hor rotation sample by describing the rotation period distributions alongside other youth indicators such as Hα and Li equivalent width, as well as near-ultraviolet and X-ray flux. We find that measuring rotation periods with TESS is a fast and effective means to confirm members in young moving groups.

Weak signal detection of composite multistable stochastic resonance with Woods–Saxon potential

Abstract Weak signal detection under strong noise is a common problem in many engineering fields. The research on the detection theory and method of stochastic resonance (SR) has very important theoretical significance and application value for the realization of early weak fault diagnosis. In order to further enhance the weak signal processing capability of SR, an improved novel composite multistable potential well model is proposed by combining the tristable model and the Woods–Saxon model. The switching mechanism of the novel model constructed with the fusion of the tristable model and the Woods–Saxon model between different steady states is studied, the output response performance of SR system with the novel composite multistable model is analyzed. The adaptive synchronization optimization method of multiple system parameters adopts the differential brainstorming algorithm to realize the adaptive selection of multiple parameters. Simulation experiments are carried out on single and multiple low-frequency periodic signals and single and multiple high-frequency periodic signals under the Gaussian noise environment, simulation results indicate that the novel composite multistable SR system performs better. On the basis of this model, the composite multistable SR system is applied to the fault detection of rolling bearings, which has a good detection effect.

Classifying Be Star Variability With TESS. I. The Southern Ecliptic

TESS photometry is analyzed for 430 classical Be stars observed in the first year of the mission. The often complex and diverse variability of each object in this sample is classified to obtain an understanding of the behavior of this class as a population. Ninety-seven percent of the systems are variable above the noise level, with timescales spanning nearly the entire range of what is accessible with TESS, from tens of minutes to tens of days. The variability seen with TESS is summarized as follows. Nearly every system contains multiple periodic signals in the frequency regime between about 0.5 and 4 day−1. One or more groups of closely spaced frequencies is the most common feature, present in 87% of the sample. Among the Be stars with brightening events that are characteristic of mass ejection episodes (18% of the full sample, or 31% of early-type stars), all have at least one frequency group, and the majority of these (83%) show a concurrent temporary amplitude enhancement in one or more frequency groups. About one-third (34%) of the sample is dominated by longer-term trends (timescales >2 day). Low-frequency stochastic signals are prominent in about 25% of the sample, with varying degrees of intensity. Higher-frequency signals (6 < f < 15 day−1) are sometimes seen (in 15% of the sample) and in most cases likely reflect p-mode pulsation. In rare cases (∼3%), even higher frequencies beyond the traditional p-mode regime (f > 15 day−1) are observed.

Separable Synchronous Multi-Innovation Gradient-Based Iterative Signal Modeling From On-Line Measurements

This article is aimed to study the modeling problems of combinational signals or periodic signals. To overcome the computation complexity of modeling the signals with plenty of characteristic parameters, a parameter separation scheme is developed based on the different characteristic of the signals to be modeled. For the purpose of achieving high-accuracy performance and reducing complexity, two multi-innovation gradient-based iterative (MIGI) subalgorithms are presented by means of gradient search. In terms of the phenomenon that the coupling parameters lead to the inability of algorithms, a separable synchronous (SS) interactive estimation method is proposed to eliminate the coupling parameters and perform the signal modeling algorithm in accordance with the hierarchical principle. By means of simulation experiments, the proposed SS iterative signal modeling algorithm based on the moving batch data is used for estimating a power signal with three sine waves and a periodic square wave signal. The results demonstrate the effectiveness of the proposed method for modeling the combinational signals with multiple frequencies and other periodic signals. Since the proposed method combines real-time data sampling and iterative estimation, it can be used for on-line identification.

Multiple Person Detection by Footsteps Sounds Using GMRS

This article targets footsteps sounds produced by multiple persons aiming to detect the multiple persons separately contained in the sound. To the best of authors’ knowledge, there have been no research on the detection of multiple persons from the footsteps sounds. For data processing, we propose to apply the geometric mean for real-time serial-to-parallel converter (GMRS). GMRS is a period estimation method applicable to a composite signal consisting of multiple periodic signals, such like a footsteps sound produced by multiple persons. In particular, GMRS is capable of estimating the period of each of the periodic signals while large power differences exist among the periodic signals. This article provides the performance evaluation of GMRS through computer simulations for the detection of multiple persons from the footsteps sounds as well as experimental results. As a result, it is confirmed that GMRS successfully detects 3 persons.

Sequential Multiperiod Repetitive Control Design With Application to Industrial Wide-Format Printing

Repetitive control (RC) enables high control performance for systems subject to periodic disturbances. Many disturbances in mechatronic applications involve the sum of multiple periodic signals, which is not necessarily periodic over a small time interval. The contribution of this article is a design procedure for multiple repetitive controllers, each addressing a single periodic component that achieves high performance with fast convergence in the presence of multiple periodic disturbances. The developed approach involves sequential design of the controllers, and systematically addresses modeling errors and coupling between controllers. An experimental case study on an industrial roll-to-roll printer confirms the benefits of the proposed approach, including superior performance compared to preexisting RC designs.

Vibration Signal Extraction Based on FFT and Least Square Method

Fast Fourier Transform (FFT), widely used in spectrum analysis, is a powerful processing vibration signal to obtain the signal amplitude, frequency, and phase. However, the discrepancy between the FFT derived values and the real values could be introduced due to spectral leakage and spectral interference. This inconsistency is prohibited in some applications, for example, the extraction of vibration characteristics for power machinery and failure diagnostics. Therefore, the methodology to obtain the frequency domain’s exact characteristics becomes one of the most concerning topics in vibration and signal processing. In this paper, a newly developed iterative method is presented in detail for high-accuracy characteristic extraction of multiple frequencies periodic vibration signals based on FFT and least square method. In the situation where the attenuation signal is superposed onto the periodic signal, the accurate characteristics of these two signals are also obtainable. Besides, simulation examples are provided, showing that the proposed method can be applied to the single-frequency signal, multiple frequency signals (including the signals of which the adjacent frequencies are close), and attenuation signal. The experimental results show that using the data processing method in this paper to extract the attenuation signals’ characteristics, and the fitted attenuation curves are in good agreement with the actual attenuation signals. The method shown in this paper can be used for precisely extracting the characteristics of the periodic signal and attenuation signals in engineering.

A Simple Concurrent Parameter Estimation Method Suitable for Noncontact Vital Sensing Using a Doppler Sensor

In this paper, a simple concurrent parameter estimation method for multiple periodic signals is proposed, which provides extensive performance evaluations through computer simulations. This method is suitable for vital sensing using a Doppler sensor. It enables us to simultaneously estimate the number of targets, periods, directions, and fundamental waveforms of each of the multiple targets. Particularly, simulation results clarify that the proposed method allows estimating the directions of multiple targets even if the number of the targets exceeds the degree of freedom of receiver antennas. In addition, it is emphasized that the direction estimation by the proposed method is robust against the coherence among the incoming signals.

Research and application of improved adaptive MOMEDA fault diagnosis method

Abstract In a strong noise environment, vibration signals are easily submerged by noise. In recent years, many scholars have studied a large number of noise reduction methods. In 2017, Multipoint Optimal Minimum Entropy Deconvolution Adjusted (MOMEDA) is applied to the fault diagnosis of gearbox. Although MOMEDA overcomes Maximum correlation kurtosis deconvolution (MCKD) defects and it can extract continuous impulse signal, but it still has the following problems: 1) It can only extract single periodic pulse. If we want to extract the characteristics of multiple periodic pulse signals, we need to further update the algorithm; 2) In a strong noise environment, MOMEDA can also search for a fixed periodic signal, but most of the information is false component, it is easy to cause misdiagnosis, therefore, the signal needs to be preprocessed; 3) The accuracy of MOMEDA noise reduction is affected by the search interval and filter size, and McDondald did not reasonably explain them, so an adaptive selection method is needed. Considering these problems. Firstly the article preprocesses the composite fault with ensemble empirical mode decomposition (EEMD) and then reconstructs the intrinsic mode function with the same time scale. Further, proposing kurtosis spectral entropy as the objective function, the grid search method is used to search the filter length of MOMEDA, and the reconstructed intrinsic mode function is further denominated by MOMEDA. Finally, the proposed method is used to search the complex fault pulse signals in strong noise environment. It proves its reliability.

A New Approach for Joint Parameter Estimation of Continuously and Non-Continuously Phase-Varying Multiple Periodic Signals

This study proposes a new approach for parameter estimation of random-phase varying multiple periodic signals. A phase-varying multiple signal is typically observed in digital communication signals...

Multiple-Period Repetitive Controller for Selective Harmonic Compensation with Three-Phase Shunt Active Power Filter

This paper presents a shunt active power filter (SAPF) for compensating inter-harmonics and harmonics when inter-harmonics content is evident in the grid. The principle of inter-harmonics generation in the grid was analyzed, and the inter-harmonics effect on repetitive controllers was discussed in terms of control performance. Traditional repetitive controllers are not applicable in inter-harmonic compensation. Moreover, the effect of an ideal controller on harmonics signals was analyzed on the basis of the internal model principle. The repetitive controller was improved in the form of a basis function according to theoretical analysis. The finite-dimensional repetitive controller, which is also called the multiple-period repetitive controller, was designed for the control of multiple periodic signals. A selective harmonic compensation system was developed with SAPF. This system can be used to compensate harmonics and inter-harmonics in the grid. Finally, system control performance was verified by simulation and experimental results.

Periods of Excess Energy in Extreme Weather Events

The reconstruction of periodic signals that are embedded in noise is a very important task in many applications. This already difficult task is even more complex when some observations are missed or some are presented irregularly in time. Kolmogorov-Zurbenko (KZ) filtration, a well-developed method, offers a solution to this problem. One section of this paper provides examples of very precise reconstructions of multiple periodic signals covered with high level noise, noise levels that make those signals invisible within the original data. The ability to reconstruct signals from noisy data is applied to the numerical reconstruction of tidal waves in atmospheric pressure. The existence of such waves was proved by well-known naturalist Chapman, but due to the high synoptic fluctuation in atmospheric pressure he was unable to numerically reproduce the waves. Reconstruction of the atmospheric tidal waves reveals a potential intensification on wind speed during hurricanes, which could increase the danger imposed by hurricanes. Due to the periodic structure of the atmospheric tidal wave, it is predictable in time and space, which is important information for the prediction of excess force in developing hurricanes.

Forecast of stock market based on nonharmonic analysis used on NASDAQ since 1985

Although research involving economic time series forecasting based on virtual market models is frequently conducted, long-term forecasting is difficult due to many factors that affect actual markets. However, as exemplified by the business cycle and Elliot Wave theories in economics, it is assumed that fluctuations in economic time series forecasting have various periodicities, ranging from short-term to long-term. Accordingly, we used a new high-resolution frequency analysis (Non-Harmonic Analysis (NHA)) method, which we have recently developed, to conduct analysis of the periodicity of economic time series forecasting. We also attempted a long-term economic time series forecast by combining multiple periodic signals. In the verification experiment, we analysed the National Association of Securities Dealers Automated Quotations (NASDAQ) closing price data for a time period of approximately 20 years using nonharmonic analysis with an analysis window of the previous 2 years, and forecasted price fluctuations for the following 2 years.

Application of Repetitive Control to Eccentricity Compensation in Rolling

Repetitive control is applied here to compensate for roll eccentricity disturbances in thickness control of the cold rolling process. A unique aspect of the process is that the eccentricity disturbance may be from multiple rolls and hence may be composed of multiple periodic components whose periods may not be commensurate, namely, divisible by a common factor an integral number of times. The paper presents a multiple-period repetitive controller structure that can compensate for such a disturbance. The structure proposed is also applicable to other tracking and regulation applications involving multiple periodic signals. Procedures to analyze and design control systems with such a structure, to ensure stability and performance, are presented.