Sampled Data Sequence Research Articles

Markov-based genetic algorithm with [formula omitted]-greedy exploration for Indian classical music composition

Recent technological advancements have made it possible to automate some of the intricate activities involved in music production. In this paper, a heuristic method is proposed for automatic composition of Indian Classical Music (ICM). Composing ICM necessitates consideration of raga constraints which distinguishes it from other genres of music. The raga-based music cannot be generated through random exploration of search space. More specifically, certain disordering in note combinations can violate the raga constraints. To address the aforesaid issue, the paper proposes a novel method by combining genetic algorithm with Markov chain model attuned to ICM sequences. Moreover, the proposed method uses ϵ-greedy strategy to balance the exploration and exploitation of musical search space. In order to preserve the musical characteristics, domain-specific genetic operators (i.e., crossover and mutation) are defined. The evaluation function based on music theory is used to direct the search to favorable tracks. The Kullback Liebler (KL) divergence metric is used to analyze the probability distribution of output and sample data sequence. The results indicate that by regulating the exploration rate, the method is capable of generating melodic sequences while maintaining the desired musical note distribution. Moreover, the method converges faster than the conventional genetic algorithm.

Dynamic Forecasting Algorithm of Inbound Ice and Snow Tourism in China Based on Improved Deep Confidence Network

Ice and snow-based tourism is getting popular around the world and it is one of the major sources of revenue for a region with required facilities. According to a report by China Daily, China was expected to witness 230 million tourist visits in 2020-2021 with a total revenue generation surpassing 390 billion yuan. In order to promote the ice and snow tourism, proper arrangements such as accommodation, transport facility, and energy provision for heating and food need to be arranged as per the demand of the visitors at a certain period of time. A tourist prediction system can help in this regard for good estimation but considering the problems of traditional ice and snow tourism systems, specifically the prediction accuracy and long forecasting time, a dynamic forecasting algorithm for ice and snow inbound tourism based on an improved deep confidence network is proposed. The system analyzes the relationship between the demand for ice and snow inbound tourism and the level of national economic development, people’s living standards, demographic characteristics, traffic conditions, and tourism supply capacity. It then takes the influencing factors of ice and snow inbound tourism demand as sample data and arranges the sample data sequence. The inbound tourism demand dynamic prediction model uses an improved deep confidence network to learn and train the prediction model, input test data into the trained model, and output the dynamic prediction value of ice and snow inbound tourism demand in the output layer to obtain the prediction result. The simulation results show that the proposed algorithm has improved accuracy in predicting the demand of inbound tourism for ice and snow, whereas the forecasting time is reduced.

Frequency-Domain Prony Method for Autoregressive Model Identification and Sinusoidal Parameter Estimation

In this study, the weighted integral method for identifying differential equation models is extended to a discrete-time system with a difference equation (DE) model and a finite-length sampled data sequence, and obtain a frequency-domain algorithm for short-time signal analysis and frequency estimation. The derivation consists of three steps. 1) Provide the DE (autoregressive model) with unknown coefficients, which is satisfied in a finite observation interval. 2) Discrete Fourier transform (DFT) the DE to obtain algebraic equations (AEs) among the Fourier coefficients. Two mathematical techniques are introduced to maintain the circulant nature of time shifts. 3) Simultaneously solve a sufficient number of AEs with least squares criterion to obtain unknowns exactly when the driving term is absent, or to obtain unknowns that minimize the driving power when it is present. The methods developed enable a decomposed processing of identification and estimation in the frequency domain. Thus, they will be suitable for maximizing statistical efficiency (smallness of estimation error variance), reducing the computational cost, and use in a resolution-enhanced time-frequency analysis of real-world signals. The performance of the proposed methods are compared with those of several DFT-based methods and Cramer–Rao lower bound. Also, the interference effect and its reduction in frequency-decomposed processing are examined.

Exact FFT-based identification of autoregressive (AR) model

In this study, we extend the weighted integral method (WIM) based on differential equation modeling and finite duration observation [IEEE Trans. SP 57, 9 (2009); Inverse Problems 26, 015011 (2010); and JASA 134(4) (2013)] to a discrete WIM with difference equation (DE) modeling and finite length sampled data sequence, and obtain a novel theory and algorithm for short-time signal analysis and spectral estimation.The discrete WIM is composed of three steps: (1) provide the DE (AR model) with unknown coefficients which is satisfied in finite observation interval. (2) Weighted sum the DE with orthogonal sequences (FFT) to obtain algebraic equations (AEs) among the weighted sums in the interval (discrete Fourier coefficients). A mathematical technique is introduced to maintain circulantness of the time shifts. (3) Solve simultaneously a sufficient number of AEs with least squares criterion to obtain the unknowns exactly when the driving term is absent, or to obtain the ones minimizing the driving power when it is present.This approach will be important both in theoretical aspects and in practical usage for resolution-enhanced time-frequency analysis in multi-harmonics and multi-resonance mixture conditions. We compare the performance with other methods and CRLB, and show several experiments using speech and music signals.

Deep Sequential Models for Suicidal Ideation From Multiple Source Data.

This paper presents a novel method for predicting suicidal ideation from electronic health records (EHR) and ecological momentary assessment (EMA) data using deep sequential models. Both EHR longitudinal data and EMA question forms are defined by asynchronous, variable length, randomly sampled data sequences. In our method, we model each of them with a recurrent neural network, and both sequences are aligned by concatenating the hidden state of each of them using temporal marks. Furthermore, we incorporate attention schemes to improve performance in long sequences and time-independent pre-trained schemes to cope with very short sequences. Using a database of 1023 patients, our experimental results show that the addition of EMA records boosts the system recall to predict the suicidal ideation diagnosis from 48.13% obtained exclusively from EHR-based state-of-the-art methods to 67.78%. Additionally, our method provides interpretability through the t-distributed stochastic neighbor embedding (t-SNE) representation of the latent space. Furthermore, the most relevant input features are identified and interpreted medically.

A Virtual Sample Generation Method Based on Differential Evolution Algorithm for Overall Trend of Small Sample Data: Used for Lithium-ion Battery Capacity Degradation Data

Considering the wide application of lithium-ion battery in life, the prediction of the remaining life of lithium-ion battery has become a research hotspot. Studies show, due to the improvement of the technology level of lithium-ion battery, its life is getting longer and longer. Even under the condition of accelerated life test, it is difficult to obtain enough available data for research in a short term. In order to solve the problem of how to accurately predict the residual life with the data-driven method under the condition of small sample size, an overall trend virtual sample generation method based on differential evolution (OT-DEVSG) is proposed. This method uses a differential evolution algorithm with better optimization performance, and improves the original mega-trend-diffusion (MTD) method, the range of virtual samples is effectively constrained and the trend of samples can be estimated more accurately. The method can effectively generate a virtual sample data sequence with time parameters, and adapt the virtual sample to the real-life sample trend, which solves the problem of insufficient degradation data of the lithium-ion batteries. Finally, we validate the effectiveness of the OT-DEVSG method with three existing data sets. The experimental results show that the proposed OT-DEVSG method is effective for solving the problem of long-term life prediction of lithium-ion batteries.

Optimal time-distributed fast Fourier transform: Application to online iterative learning control—experimental high-speed nanopositioning example

In this paper, an optimal time-distributed fast Fourier transform algorithm and a time-distributed inverse fast Fourier transform (OTD-FFT/TD-IFFT) algorithm are proposed. This work is motivated by the need to implement FFT/IFFT online on general microprocessors (e.g., Intel’s x86 microprocessors) in control applications and signal processing, for example, online implementation of frequency domain iterative learning control (FD-ILC) techniques. In these applications, the conventional FFT algorithm executes all the calculations within one single sampling period, thereby, becoming the bottleneck in online implementations of signal processing and control algorithms. In the proposed OTD-FFT technique, the FFT computation of an online sampled data sequence is optimally distributed among all the sampling periods without increasing the total computational complexity, arriving at the minimal per-sampling-period computational complexity. As a result, the entire Fourier transformed sequence is obtained without latency. The proposed approach is extended to online IFFT computation, and then applied to online FD-ILC implementation. The computational complexity analysis shows that by using the proposed approach, the per-sampling-period computational complexity is substantially reduced. The efficacy of the proposed OTD-FFT/TD-FFT for online implementation of FD-ILC technique is demonstrated through experiments of high-speed trajectory tracking on a piezoelectric actuator.

Characterization of order statistics in two runs using conditional expectation

The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order statistics of two runs statistics, and obtain their probability mass functions. In addition, the means and variances of the order statistics are derived using traditional conditional expectation.

A New Data Perturbation Method of Reference Control in Statistical Database

Data perturbation is a method of reference control in statistical database. Data modification and data exchange are two methods of data perturbation. Data modification replaces the original data with the sample data sequence after deciding probability distribution function of the original data and generating sample data sequence. Data swapping interchanges attribute values of records. While the algorithm of the former is complex, this paper presents a new method in which the sample sequence generation is skipped. We simply sort the original data, divide them into different groups and exchange attribute values of the same group. Experiments show that the proposed method can effectively simplify the former method and guarantee the safety of the statistical data at the same time.

Pregnant Environment Analysis Model of Earthquake-Induced Underground Engineering Slope Based on Gray Relation and Variation

Complicated and variational relation among the factors of the pregnant environment, resulted that, it was hard to orderly sentence the connection from the pregnant risk factors to the overall slope safety. Through differentiating risk relational factors into the extreme variation, same directional matrix was established for the pregnant environment safety of earthquake-induced underground engineering slope. Gray relation Analysis Model was established on the pregnant environment of earthquake-induced underground engineering slope, which was integrated with entropy information of same directional matrix. Model calculated out the gray relation degree and variation coefficient among the sample data sequence of the observed units, and finally sentenced the overall safety of underground engineering slope systemically. Example showed that toward the multi-objective decision-making problem for the safety assessment of underground engineering slope, model possessed with a scientific, simple, practical feature, whose outcome revealed the full status of the slope pregnant environment.

Prognostics for drilling process with wavelet packet decomposition

On-line tool condition monitoring is highly needed in drilling production process. Input current has been employed to monitor the drilling tool wear by many researchers. But few cases can represent the wear status and recognize the breakage simultaneously. The remaining life of tool has not been discussed sufficiently. This paper presents a strategy of on-line tool monitoring system for drilling machine using wavelet packet decomposition of spindle current signature. A moving window technique is used to extract the real drilling parts of data from sampled data sequence. The wavelet packet decomposition is used to extract features from non-stationary current signal. Critical features are selected according to their ability of discriminating the wear progress under Fisher criterion. Logistic regression combined with autoregressive moving average models are used to evaluate the failure possibility and remaining life of the drill bit. Experimental results show good performance of the proposed algorithm.

Spectral Analysis of Nonuniformly Sampled Data: A New Approach Versus the Periodogram

We begin by revisiting the periodogram to explain why arguably the plain least-squares periodogram (LSP) is preferable to the ldquoclassicalrdquo Fourier periodogram, from a data-fitting viewpoint, as well as to the frequently-used form of LSP due to Lomb and Scargle, from a computational standpoint. Then we go on to introduce a new enhanced method for spectral analysis of nonuniformly sampled data sequences. The new method can be interpreted as an iteratively weighted LSP that makes use of a data-dependent weighting matrix built from the most recent spectral estimate. Because this method is derived for the case of real-valued data (which is typically more complicated to deal with in spectral analysis than the complex-valued data case), it is iterative and it makes use of an adaptive (i.e., data-dependent) weighting, we refer to it as the real-valued iterative adaptive approach (RIAA). LSP and RIAA are nonparametric methods that can be used for the spectral analysis of general data sequences with both continuous and discrete spectra. However, they are most suitable for data sequences with discrete spectra (i.e., sinusoidal data), which is the case we emphasize in this paper.

Discrete Hilbert transformation and its application to estimate the wind speed in Hong Kong

Discrete Hilbert Transform (DHT) has been applied to estimate the wind speed with the sample data sequence selected from the data record observed by the observatory in Hong Kong in June 1989, during which the data pertain to deep valleys and sharp crests due to manifold weather conditions in this region. To confirm the performance of the discrete Hilbert transformer, two harmonic input sequences were used to inspect the output signals, whether good agreement with the theoretical results is obtained. It was found that the energy spectrum and the outputs for the two different harmonic discrete waves are certainly correct. After the inspection of the DHT filter, the sample data for wind speed in Hong Kong were used for wind speed forecasting. For zero mean input sequence, the variance of the output is the same as that of the input signals, and so is the energy spectrum. The DHT of an individual input sample can really reflect the local variation performance, since it is the convolution with the reciprocal of time and the input data sequence, but there exists phase shift. For harmonic signals, the output signal holds a 90° phase delay.

Autoregression and irregular sampling: Spectral estimation

We describe how to model an irregularly sampled data sequence as a set of observations from a linear stochastic process, permitting data classification and spectral estimation. The technique is a generalisation of the prediction error approach taken by the Burg and Covariance methods, in that a generalised prediction error energy is minimised with respect to the AR coefficients. Various tests on synthetic data, using line and broad-band spectra, show that the method is robust. In a companion paper we show that the generalised prediction error approach permits filtering or signal separation.

A simulation clock-based solution to the frequency domain experiment indexing problem

Frequency domain experiments (FDEs) were introduced to perform system sensitivity analysis for factor screening in complex simulations. Since then, FDEs have been used in simulation optimization, gradient estimation and several other research areas. Central to all FDEs is the Fourier analysis of a sampled data sequence. The choice of an appropriate oscillation index and associated sampling index for the sampled data sequence has been a much researched topic now known in the FDE literature as the indexing problem. In this paper we address the indexing problem by providing some general guidelines on the selection of the oscillation index and considering the implementation of two different indices: the continuous global simulation clock time and an inherently discrete index such as the job index in a simple queuing system. We show that the choice of a discrete oscillation index has to be made in an application-dependent manner and does not generalize well to different discrete-event simulation scenarios. In contrast, because the notion of time underlies all discrete-event simulations, the global simulation clock time is a natural choice for an FDE indexing scheme. Two different schemes for the global simulation clock time are presented. The results are illustrated via different scenarios commonly found in simulations of queuing networks and manufacturing systems.

Comparison of methods for spectral estimation with interrupted data

The problem considered is to match the periodogram (spectrum) of a real sampled data sequence when only the samples outside a gap are available: that is, when the samples in the gap are missing or corrupted. Different arguments lead to three reasonable estimation algorithms. Tests with contrived data records indicate that two of these algorithms are preferable, one when the gap length is less than 15% of the record, and the other for 20%-50% gaps. An algorithm based on an autoregressive model is found to have an estimate performance that is relatively independent of gap length. >

Frequency resolution of Fourier and maximum entropy spectral estimates

An analytic determination of the frequency resolution for maximum entropy and conventional Blackman‐Tukey spectral estimates is made for the case of known autocorrelation. As the signal‐to‐noise ratio decreases, the maximum entropy resolution is no better than that achievable by the Blackman‐Tukey spectral estimate. The mean resolution of an ensemble of spectra constructed from sampled data sequences agrees with the analytic result.

The cepstrum: A guide to processing

This paper is a pragmatic tutorial review of the cepstrum literature focusing on data processing. The power, complex, and phase cepstra are shown to be easily related to one another. Problems associated with phase unwrapping, linear phase components, spectrum notching, aliasing, oversampling, and extending the data sequence with zeros are discussed. The advantages and disadvantages of windowing the sampled data sequence, the log spectrum, and the complex cepstrum are presented. The influence of noise upon the data processing procedures is discussed throughout the paper, but is not thoroughly analyzed. The effects of various forms of liftering the cepstrum are described. The results obtained by applying whitening and trend removal techniques to the spectrum prior to the calculation of the cepstrum are discussed. We have attempted to synthesize the results, procedures, and information peculiar to the many fields that are finding cepstrum analysis useful. In particular we discuss the interpretation and processing of data in such areas as speech, seismology, and hydroacoustics. But we must caution the reader that the paper is heavily influenced by our own experiences; specific procedures that have been found useful in one field should not be considered as totally general to other fields. It is hoped that this review will be of value to those familiar with the field and reduce the time required for those wishing to become so.