Non-synchronous Sampling Research Articles

Superimposed multi-harmonic interference frequency and phase measurements based on non-synchronous sampling quantization and all-phase spectrum correction

As a non-destructive detection technique for measuring parallel transparent optics, wavelength-shifting interferometry provides a separation basis for multiple measured surfaces by assigning different frequencies to the interference harmonics based on their optical-path-difference. However, the non-synchronous sampling and spectral aliasing can decrease the measurement accuracy. Therefore, an approximate entropy algorithm is utilized to determine the sampling performance. Then the frequency search accuracy is guaranteed by the zero-padding method, and the all-phase Fourier transform method is introduced to correct the harmonic frequencies and amplitudes, where the spectral aliasing problem is solved by the relative amplitude analysis. So efficient surface measurement combining the above advantages is realized, and the validity is verified by simulation analysis of different profile features and de-tuning errors. The effectiveness of the proposed method is fully confirmed by the repetitive measurements on two parallel plates in the experiments.

Toward Learning Joint Inference Tasks for IASS-MTS Using Dual Attention Memory With Stochastic Generative Imputation.

Irregularly, asynchronously and sparsely sampled multivariate time series (IASS-MTS) are characterized by sparse and uneven time intervals and nonsynchronous sampling rates, posing significant challenges for machine learning models to learn complex relationships within and beyond IASS-MTS to support various inference tasks. The existing methods typically either focus solely on single-task forecasting or simply concatenate them through a separate preprocessing imputation procedure for the subsequent classification application. However, these methods often ignore valuable annotated labels or fail to discover meaningful patterns from unlabeled data. Moreover, the approach of separate prefilling may introduce errors due to the noise in raw records, and thus degrade the downstream prediction performance. To overcome these challenges, we propose the time-aware dual attention and memory-augmented network (DAMA) with stochastic generative imputation (SGI). Our model constructs a joint task learning architecture that unifies imputation and classification tasks collaboratively. First, we design a new time-aware DAMA that accounts for irregular sampling rates, inherent data nonalignment, and sparse values in IASS-MTS data. The proposed network integrates both attention and memory to effectively analyze complex interactions within and across IASS-MTS for the classification task. Second, we develop the stochastic generative imputation (SGI) network that uses auxiliary information from sequence data for inferring the time series missing observations. By balancing joint tasks, our model facilitates interaction between them, leading to improved performance on both classification and imputation tasks. Third, we evaluate our model on real-world datasets and demonstrate its superior performance in terms of imputation accuracy and classification results, outperforming the baselines.

Data-driven based cross-coupling compensation method for the piezoelectric tube scanner of atomic force microscopes

In this work, a data-driven based cross-coupling compensation (DD-CCC) method is proposed to suppress the cross-coupling effect of the scanner in atomic force microscopy (AFM). Firstly, the phase difference method is employed to accurately estimate the frequencies, amplitudes and phases of the harmonic components of the periodic compensation signal obtained from the fractional model-free repetitive control with the nonsynchronized sampling. Afterwards, the compensation signal is constructed analytically via summing the harmonic components, which requires very little memory units. In AFM scanning, the constructed compensation signal is applied in a feedforward manner, which is combined with a baseline tracking controller to follow the desired staircase trajectories. A series of scanning and imaging tests are conducted on an AFM with a fixed sampling frequency and different scanning rates. The results demonstrate that high performance AFM scanning and imaging can be achieved under the scanning rate of 120 Hz with the DD-CCC method.

Distribution Network Topology Identification Using Asynchronous Transformer Monitoring Data

The topology of a distribution network with a high penetration of fluctuating renewable energy is usually adjusted frequently for the reliable and economical operation. This paper proposes an automatic topology identification method based on measurements from widely distributed transformer terminal units (TTUs) to align the topology model in the management system with the actual topology of the distribution network. The proposed method formulates the topology identification problem as an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L2$</tex-math></inline-formula> -norm minimization problem. The challenge lies in the absence of phase angle measurements and the sampling errors caused by the non-synchronous sampling time of different TTUs. Adding variables into the minimization problem for the unavailable phase angles introduces nonlinearity and non-convexity, and the non-synchronous sampling time can cause significant sampling errors when measuring the fluctuating power injections. The non-convexity is addressed by proposing a novel linearization and convex relaxation approach to convert the formulated minimization problem into a convex mixed integer quadratically constrained program (MIQCP) problem. The significant sampling error is addressed by generating pseudo measurements from Lagrange interpolation to be used as alternatives to the actual power measurements having significant errors. Case studies conducted in test systems demonstrate the effectiveness and efficiency of the proposed method.

Test for Non-Synchronized Errors of State Estimation Using Real Data

This letter discusses performance degradation of traditional supervisory control and data acquisition (SCADA)-based static state estimation (SSE) caused by violation of the static assumption. The sensitivity of non-synchronized sampling errors against oscillations is tested through real measurement data and grid model from a subsystem of the North American power gird. The test results show that as an important reason leading to the failure of SCADA-based SSE, the non-synchronized sampling error of SCADA is sensitive to oscillations in that the error rapidly increases when oscillations occur and vanishes when the oscillations cease.

Efficient Capacitor Voltage Balancing Method for Modular Multilevel Converter Under Carrier-Phase-Shift Pulsewidth Modulation

The modular multilevel converter (MMC) is an attractive converter topology for medium-/high-voltage applications. The voltage balancing for floating capacitors of submodules in MMC under carrier-phase-shift pulsewidth modulation (CPS-PWM), is an important research focus. However, the existing capacitor voltage balancing methods under this modulation mode have limited robustness and may not be applied to different working conditions. In this article, the disturbance and unbalance mechanisms of capacitor voltages in MMC system under CPS-PWM are theoretically revealed and solved. The disturbance metrics for capacitor voltage are extracted by using a proposed asynchronized sampling mode. Based on the characteristics of the extracted disturbances in nonsynchronized sampling mode, a novel capacitor voltage balancing method is proposed. The proposed balancing method is highly efficient for different working conditions of MMC, and is easy to be designed/realized. Finally, a flexible mission-profile emulator for the test of MMC is designed and built, with comprehensive validations to verify the effectiveness of the proposed capacitor balancing method under different operating conditions of MMC.

Analytic Mode Decomposition and Windowed Three-Point Interpolated Chirp-Z Transform for Voltage Flicker Components Detection

The extensive development and applications of new energy and power electronics technologies have a significant impact on grid voltage fluctuations and flicker. This paper proposes an accurate method based on analytic mode decomposition (AMD) and windowed three-point interpolated Chirp-Z transform (WICZT) to detect voltage flicker components. The voltage flicker envelope signal is extracted by AMD through the multiplicative result of voltage flicker signal and synchronizing voltage signal to avoid spectrum aliasing, without the analog filter. Then, WICZT based on six-term cosine window is presented to obtain the voltage flicker parameters, which can enhance the frequency resolution and effectively reduce the error caused by the spectral leakage due to the non-synchronous sampling and constraints of fence effect. Based on the proposed method a voltage flicker parameter detection system is developed and implemented in a PXI platform, using LabVIEW. The simulation and experimental results show that the proposed algorithm can effectively provide accurate detection and analysis in cases of single frequency modulation, multi-frequency modulation, harmonic contamination, fundamental frequency deviation and noise interference.

A Novel Technique for Fundamental and Harmonic Parameter Estimation Using Nonergodic $S$ -Transform

Modern power systems produce nonstationary harmonics which bring harm to the electric equipment. Real-time and accurate parameter estimation is the key step of the harmonic elimination. This paper proposes a novel technique of the parameter estimation for fundamental and harmonic using nonergodic $S$ -transform (NEST), which can effectively eliminates the estimated parameter error caused by nonsynchronous sampling. First, the signal is decomposed into the fundamental and harmonics NEST vectors (NESTVs) by NEST, and the amplitudes are detected accurately by extracting the magnitude of NESTVs, which are optimized by the Gaussian window width coefficient of the NEST kernel function. Second, the overlapping and abandoning method is used to remove the end effect of NESTVs so as to obtain the effective and complete data for the parameter estimation. Then, the estimated instantaneous frequency and phase are obtained using the linear phase characteristic of NESTVs. Finally, simulations and experiments prove that the proposed method can not only estimate the stationary signal parameters accurately but also trace the nonstationary signal parameters in the real time under the spectrum leakage condition.

A Minimum Side-Lobe Optimization Window Function and Its Application in Harmonic Detection of an Electricity Gird

Several window functions are currently applied to improve the performance of the discrete Fourier transform (DFT) harmonic detection method. These window functions exhibit poor accuracy in measuring the harmonic contents of a signal with high-order and weak-amplitude components when the power frequency fluctuates within a small range. In this paper, a minimum side-lobe optimization window function that is aimed at overcoming the abovementioned issue is proposed. Moreover, an improved DFT harmonic detection algorithm based on the six-term minimum side-lobe optimization window and four-spectrum-line interpolation method is proposed. In this context, the minimum side-lobe optimization window is obtained by optimizing the conventional cosine window function according to the optimization rules, and the characteristics of the new proposed window are provided to analyze its performance. Then, the proposed optimization window function is employed to improve the DFT harmonic detection algorithm based on the six-term minimum side-lobe optimization window and four-spectrum-line interpolation method. The proposed technique is used to detect harmonics of an electricity gird in which the six-term minimum side-lobe optimization window is utilized to eliminate the influence of spectrum leakage caused by nonsynchronous sampling of signal processing. The four-spectrum-line interpolation method is employed to eliminate or mitigate the fence effect caused by the inherent measurement error of the DFT method. Simulation experiments in two complex conditions and an experiment test are carried out to validate the improved performance of the proposed window. Results reveal that the six-term minimum side-lode optimization window has the smallest peak side lobe when compared with existing windows, which can effectively reduce the interaction influence of spectrum leakage, improve the measurement accuracy of the DFT harmonic detection method, and meet the standard requirement of harmonic measurement in complex situations.

Fractional repetitive control of nanopositioning stages for tracking high-frequency periodic inputs with nonsynchronized sampling.

The repetitive control (RC) has been employed for high-speed tracking control of nanopositioning stages due to its abilities of precisely tracking periodic trajectories and rejecting periodic disturbances. However, in digital implementation, the sampling frequency should be integer multiple of the tracking frequency of the desired periodic trajectory. Otherwise, the rounding error would result in a significant degradation of the tracking performance, especially for the case of high input frequencies. To mitigate this rounding effect, the fractional repetitive control (FRC) technique is introduced to control the nanopositioning stage so as to precisely track high-frequency periodic inputs without imposing constraints on the sampling frequency of the digital control system. The complete procedure of controller design and implementation is presented. The techniques to deal with the problems of non-minimum phase system and fractional delay points number are described in detail. The proposed FRC is plugged into the proportional-integral control, and implemented on a custom-built piezo-actuated nanopositioning stage. Validation experiments are conducted, and the results show that the tracking errors caused by the rounding effect in the traditional RC approach are almost completely eliminated, when tracking sinusoidal waveforms with frequencies from 1000 Hz to 1587.3 Hz under the sampling frequency of 50 kHz, where the fractional parts being rounded vary from 0 to 0.5.

Application of FFT Interpolation Correction Algorithm Based on Window Function in Power Harmonic Analysis

In the power harmonic detection algorithm, the disadvantages of Fast Fourier Transform (FFT) are difficult to accurately detect in non-synchronous sampling and non-integer periodic truncation to need be solved. Therefore, this paper considers various advantages and disadvantages of traditional window functions such as Hanning window and new window function, for example: Blackman-Harris window and Nuttall window. Four three-order Nuttall window functions was adopted, which are more suitable for power harmonic analysis. Meanwhile, the double-line interpolation analysis and algorithm correction of the Nuttall window function are carried out. Finally, the algorithm is compared and simulated. By using this algorithm the phase error is stable at 0.00001°, and the amplitude error is almost 0, which fully meets the requirements of harmonic measurement standards.

DOA Estimation Using Single or Dual Reception Channels Based on Cyclostationarity

This paper addresses the problem of direction-of-arrival (DOA) estimation for cyclostationary signals using less reception channel in comparison with the number of sensors. The system is considered to be realized by using the reception channel(s) to receive the signal reached each sensor in turn. Such simplification results in a cost reduction of the system and the effect of inconsistency among different channels are removed. However, non-synchronized sampling also makes the traditional DOA estimation algorithms ineffective. To cope with the problem, the signal models for DOA estimation using a single channel and dual channels are formulated based on signal cyclostationary, and the single channel cyclic MUSIC (SC-Cyclic-MUSIC) algorithm and the dual channels cyclic MUSIC (DC-Cyclic-MUSIC) algorithm are proposed correspondingly. This paper shows that both SC-Cyclic-MUSIC algorithm and DC-Cyclic-MUSIC algorithm work well when the switching interval is known, and a satisfied performance can also be obtained by DC-Cyclic-MUSIC algorithm when the uncertainty of the switching interval exists. Moreover, the proposed estimators are suitable for both narrow-band and wide-band signals. The computer simulations are provided to verify the effectiveness of the proposed algorithms.

A Fourier Transform-Based Frequency Estimation Algorithm

Nonsynchronous sampling conditions are the source of leakage errors in measurements based on digital signal processing. The optimal method to avoid such errors is to generate a synchronous sampling clock, whenever the input signal shows enough period stability to allow this. Such method, however, does not yield a straightforward evaluation of the input signal frequency, which is required in several applications. This paper proposes a modified synchronous clock generator that together with a modified frequency interpolation algorithm provides an accurate measurement of the input signal frequency when the only available information about the sampling clock is a given integer multiple of the input signal fundamental frequency.

Power harmonic and interharmonic detection method in renewable power based on Nuttall double‐window all‐phase FFT algorithm

Harmonics and interharmonics adversely affect power grids. The fast Fourier transform (FFT) algorithm is one of the most commonly used methods for harmonic analysis. However, in practical applications, the accuracy of harmonic analysis can be seriously affected by fence effect and spectral leakage, which are undesired characteristics inherent to discrete Fourier transforms. Moreover, when non-synchronous sampling is carried out, the phase measurement is not accurate enough, and there is a large error in the identification of interharmonics. In order to improve the measurement precision, the method of all-phase spectrum analysis is used, since it has the characteristics of phase invariance and good spectral leakage suppression. A novel method based on improved Nuttall double-window all-phase FFT is proposed by improving the window function and the spectrum correction method for achieving higher precision. Through simulation and experimental verification, the proposed algorithm has proven to perform better than the traditional algorithms both for the detection of harmonics and interharmonics. In addition, the computation burden is not considerably increased when compared to such algorithms, which allows the on-line use of the proposed algorithm.

An adaptive three-phase reclosure scheme for shunt reactor-compensated transmission lines based on the change of current spectrum

In this paper, a new three-phase adaptive reclosing scheme for transmission lines with shunt reactors is proposed to identify fault nature and determine the arc extinction time under the single and double-phase-to-ground faults. According to the fact that the faulted phase currents of shunt reactors contain only one oscillating frequency before the fault extinction and contain other two different oscillating frequencies when the fault is extinguished, this change of current frequency can be used to distinguish transient faults. When sampling rate is an integral multiple of the faulted phase current frequency of shunt reactors under permanent faults, an abrupt increase of currents even harmonics which is caused by spectral leakage of the DFT algorithm under non-synchronous sampling can lead to identify transient faults and three-phase reclosing. Electromagnetic Transient Program simulation results verify the correctness of the frequency spectrum characteristic analysis of the faulted currents of shunt reactor. The feasibility of the proposed scheme is also tested under different fault condition.

A Digital Power Quality Monitoring Equipment Designed for Digital Substation

Taking into account both current status and development trend of digital substation, this paper proposed a design of a new multi-channelled digital power quality monitoring equipment with high compatibility. The overall functional structure, hardware architecture, software architecture, interface architecture and some key techniques such as IEC 61850 modelling of transient event and harmonic measurement method under the condition of non-synchronous sampling are described in this paper.

An improved optimize method for power harmonics analysis based on windowed double-spectrum-line interpolation

Double-spectrum-line interpolation could effectually decrease the frequency spectral leakage caused by non-synchronized sampling and non-integral period truncation in harmonics analysis; however, this algorithm is not complicated and facilitates the realization in embedded system. Some parameters of interpolation polynomials in windowed Double-spectrum-line interpolation are given along with a developed formula of phase. An optimized method is also proposed which enhances real-time performance by decreasing periods of sample. A program flow chart is provided in this paper. The precision range is obviously inhibited under frequency variation. The simulation of a complex signal with 21 order harmonics verifies the effectiveness of the method.

Distinguishing CPFSK from QAM and PSK Modulations

Digital modulation classification is important for many civilian as well as military applications. In this paper, we propose a simple and robust feature to distinguish continuous-phase FSK from QAM and PSK modulations. The feature is based on product of two consecutive signal values and on time averaging of imaginary part of the product. Conditional probability density functions of the feature given modulation type are determined. In order to overcome the complexity of calculating probability density functions, central limit theorem for strictly stationary m-dependent sequences is used to obtain Gaussian approximations. After calculating probability density functions, thresholds are determined based on minimization of total probability of misclassification. Since threshold-based results are valid for special cases requiring knowledge of some parameters, we resort to usage of support vector machines for classification, which require little training and no a priori information except for carrier frequency. Following that joint effects on the performance of carrier offset, fast fading, and non-synchronized sampling are studied in the presence of additive white Gaussian noise. For comparison purposes, rectangular pulse shape is used. To prove practical usefulness, not only the performance is analyzed for root-raised cosine pulses but also for quite less oversampling of symbols than what is found in other approaches. In the course of doing that, the performance is compared with wavelet-based feature that uses support vector machines for modulation separation.

Adaptive Repetitive Control With Two Nonsynchronized Sampling

Repetitive controllers have been shown to be effective for tracking periodic reference commands with known period. For a reference with fixed period, its implementation can be done with time fixed sampling where an integer number of samples in each period can be required. With variable periodic signal tracking with real-time realization, the number of samples per period may be a noninteger with a fixed sample rate. This paper presents an adaptive repetitive control scheme for reducing tracking errors due to variable periodic reference signals with two nonsynchronized sampling. Aside from time sampling, a position pulse signal generated by optical encoder is used to produce another fixed sampling. This technique can accommodate the variable periodic signal and variable samples per period for synchronization can be achieved by the position sampling. Experimental studies of a twin linear motor control system which comes up with variable periodic references are given. The experimental results illustrate the validity of the proposed implementation method in that adaptive repetitive control with two nonsynchronized sampling can effectively eliminate steady-state errors within a few cycles that are caused by variable periodic references.

Quasi-likelihood analysis for nonsynchronously observed diffusion processes

We consider nonsynchronous sampling of parameterized stochastic regression models, which contain stochastic differential equations. Constructing a quasi-likelihood function, we prove that the quasi-maximum likelihood estimator and the Bayes type estimator are consistent and asymptotically mixed normal when the sampling frequency of the nonsynchronous data becomes large.