Search Results (16)

To ensure the safety of nuclear power production, nuclear power plants deploy numerous sensors to monitor various physical indicators during production, enabling the early detection of anomalies. Efficient anomaly detection relies on complete sensor data. However, compared to conventional energy sources, the extreme physical environment of nuclear power plants is more likely to negatively impact the normal operation of sensors, compromising the integrity of the collected data. To address this issue, we propose an anomaly detection method for nuclear power data: Neural Normal Stochastic Process (NNSP). This method does not require imputing missing sensor data. Instead, it directly reads incomplete monitoring data through a sequentialization structure and encodes it as continuous latent representations in a neural network. This approach avoids additional “processing” of the raw data. Moreover, the continuity of these representations allows the decoder to specify supervisory signals at time points where data is missing or at future time points, thereby training the model to learn latent anomaly patterns in incomplete nuclear power monitoring data. Experimental results demonstrate that our model outperforms five mainstream baseline methods—ARMA, Isolation Forest, LSTM-AD, VAE, and NeutraL AD—in anomaly detection tasks on incomplete time series. On the Power Generation System (PGS) dataset with a 15% missing rate, our model achieves an F1 score of 83.72%, surpassing all baseline methods and maintaining strong performance across multiple industrial subsystems. Full article

The rates of continuous evolution plays a crucial role in understanding the pace at which species evolve. Various statistical models have been developed to estimate the rates of continuous trait evolution for a group of related species evolving along a phylogenetic tree. Existing models often assume the independence of the rate parameters; however, this assumption may not account for scenarios where the rate of continuous trait evolution correlates with its evolutionary history. We propose using the autoregressive–moving-average (ARMA) model for modeling the rate of continuous trait evolution along the tree, hypothesizing that rates between two successive generations (ancestor–descendant) are time-dependent and correlated along the tree. We denote PhyRateARMA$(p,q)$ as a phylogenetic rate-of-continuous-trait-evolution ARMA(p,q) model in our framework. Our algorithm begins by utilizing the tree and trait data to estimate the rates on each branch, followed by implementing the ARMA process to infer the relationships between successive rates. We apply our innovation to analyze the primate body mass dataset and plant genome size dataset and test for the autoregressive effect of the rates of continuous evolution along the tree. Full article

The expected acceleration in sea level rise (SLR) throughout this century poses significant threats to coastal cities and low-lying regions. Since the early 1990s, high-precision multi-mission satellite altimetry (SA) has enabled the routine measurement of sea levels, providing a continuous 30-year record from which the mean sea level rise (global and regional) and its variability can be computed. The latest reprocessed product from CMEMS span the period from 1993 to 2020, and have enabled the acquisition of accurate sea level data within the coastal range of 0–20 km. In order to fully utilize this new dataset, we establish a global virtual network consisting of 184 virtual SA stations. We evaluate the impact of different stochastic noises on the estimation of the velocity of the sea surface height (SSH) time series using BIC_tp information criterion. In the second step, the principal component analysis (PCA) allows the common mode noise in the SSH time series to be mitigated. Finally, we analyzed the spatiotemporal characteristics and accuracy of sea level change derived from SA. Our results suggest that the stochasticity of the SSH time series is not well described by a combination of random, flicker, and white noise, but is best described by an ARFIM/ARMA/GGM process. After removing the common mode noise with PCA, about 96.7% of the times series’ RMS decreased, and most of the uncertainty associated with the computed SLR decreased. We confirm that the spatiotemporal correlations should be accounted for to yield trustworthy trends and reliable uncertainties. Our estimated SLR is 2.75 ± 0.89 mm/yr, which aligns closely with recent studies, emphasizing the robustness and consistency of our method using virtual SA stations. We additionally introduce open-source software (SA_Tool V1.0) to process the SA data and reduce noise in surface height time series to the community. Full article

Estimating the height component of Global Navigation Satellite System (GNSS) stations is widely known to be more challenging than estimating the horizontal position. In this study, we utilized height time series data from 37 continuous GNSS stations that were part of the Turkish RTK CORS Network called TUSAGA-Active (Turkish National Permanent GNSS Network Active). The data covered the period from 2014 to 2019, and the selection of stations focused on the Eastern Anatolia region of Turkey due to its topographic characteristics and the pronounced influence of seasonal changes, which facilitated the interpretation of the effects on the height component. The daily coordinates of the GNSS stations were derived using the GAMIT/GLOBK software solution. We identified statistically significant trends, periodic variations, and stochastic components associated with the stations by applying time series analysis to these daily coordinate values. As a result, the vertical velocities of the GNSS stations were determined, along with their corresponding standard deviations. Furthermore, examining the height components of the continuous GNSS stations revealed seasonal effects. We aimed to investigate the potential relationship between these height components and meteorological parameters. The study provides evidence of the interconnectedness between the height components of continuous GNSS stations and various meteorological parameters. Simple linear regression analysis and ARMA time series modeling were utilized to establish this relationship. Full article

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time differences are described. ARMA-type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown. Full article

Under the influence of variable sea conditions, a ship will have an oscillating motion comprising six degrees of freedom, all of which are connected to each other. Among these degrees of freedom, rolling and pitching motions have a severe impact on a ship’s maritime operations. An accurate and effective ship motion attitude prediction method that makes the prediction in a short period of time is required to guarantee the safety and stability of the ship’s maritime operations. Traditional methods are based on time domain analysis, such as the autoregressive moving average (ARMA) models. However, these models have limitations when it comes to predicting the nonlinear and nonstationary characteristics of real ship motion attitude data. Many intelligent algorithms continue to be applied in nonlinear and nonstationary ship attitude prediction, such as extreme learning machines (ELMs) and the long short-term memory (LSTM) neural network, as well as other deep learning methods, showing promising results. By using the sliding window approach, the time-varying dynamic characteristics of the ship’s motion attitude can be preserved better. The simulation results demonstrate that the proposed model performs well in terms of predicting the nonlinear and nonstationary ship motion attitude. Full article

With the continuous development of financial markets worldwide to tackle rapid changes such as climate change and global warming, there has been increasing recognition of the importance of financial time series forecasting in financial market operation and management. In this paper, we propose a new financial time series forecasting model based on the deep learning ensemble model. The model is constructed by taking advantage of a convolutional neural network (CNN), long short-term memory (LSTM) network, and the autoregressive moving average (ARMA) model. The CNN-LSTM model is introduced to model the spatiotemporal data feature, while the ARMA model is used to model the autocorrelation data feature. These models are combined in the ensemble framework to model the mixture of linear and nonlinear data features in the financial time series. The empirical results using financial time series data show that the proposed deep learning ensemble-based financial time series forecasting model achieved superior performance in terms of forecasting accuracy and robustness compared with the benchmark individual models. Full article

Ordinal pattern-based approaches have great potential to capture intrinsic structures of dynamical systems, and therefore, they continue to be developed in various research fields. Among these, the permutation entropy (PE), defined as the Shannon entropy of ordinal probabilities, is an attractive time series complexity measure. Several multiscale variants (MPE) have been proposed in order to bring out hidden structures at different time scales. Multiscaling is achieved by combining linear or nonlinear preprocessing with PE calculation. However, the impact of such a preprocessing on the PE values is not fully characterized. In a previous study, we have theoretically decoupled the contribution of specific signal models to the PE values from that induced by the inner correlations of linear preprocessing filters. A variety of linear filters such as the autoregressive moving average (ARMA), Butterworth, and Chebyshev were tested. The current work is an extension to nonlinear preprocessing and especially to data-driven signal decomposition-based MPE. The empirical mode decomposition, variational mode decomposition, singular spectrum analysis-based decomposition and empirical wavelet transform are considered. We identify possible pitfalls in the interpretation of PE values induced by these nonlinear preprocessing, and hence, we contribute to improving the PE interpretation. The simulated dataset of representative processes such as white Gaussian noise, fractional Gaussian processes, ARMA models and synthetic sEMG signals as well as real-life sEMG signals are tested. Full article

The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, the interrelations between systems defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions of the continuous and discrete transfer functions. Simple transformations are presented to allow interconversions between both systems, recovering formulae obtained with the impulse invariant method. These transformations are also used to formulate a covariance equivalence. The spectral correspondence implied by the bilinear (Tustin) transformation is used to study the equivalence between the two types of systems. The general fractional CT/DT ARMA systems are also studied by considering two DT differential fractional autoregressive-moving average (FARMA) systems based on the nabla/delta and bilinear derivatives. The interrelations CT/DT are also considered, paying special attention to the systems defined by the bilinear derivatives. Full article

This study aims to use remote sensing (RS) time-series data to explore the intrinsic relationship between crop growth and yield formation at different fertility stages and construct a high-precision winter wheat yield estimation model applicable to short time-series RS data. Sentinel-2 images were acquired in this study at six key phenological stages (rejuvenation stage, rising stage, jointing stage, heading stage, filling stage, filling-maturity stage) of winter wheat growth, and various vegetation indexes (VIs) at different fertility stages were calculated. Based on the characteristics of yield data continuity, the RReliefF algorithm was introduced to filter the optimal vegetation index combinations suitable for the yield estimation of winter wheat for all fertility stages. The Absolutely Objective Improved Analytic Hierarchy Process (AOIAHP) was innovatively proposed to determine the proportional contribution of crop growth to yield formation in six different phenological stages. The selected VIs consisting of MTCI(RE2), EVI, REP, MTCI(RE1), RECI(RE1), NDVI(RE1), NDVI(RE3), NDVI(RE2), NDVI, and MSAVI were then fused with the weights of different fertility periods to obtain time-series weighted data. For the characteristics of short time length and a small number of sequences of RS time-series data in yield estimation, this study applied the multiplexed delayed embedding transformation (MDT) technique to realize the data augmentation of the original short time series. Tucker decomposition was performed on the block Hankel tensor (BHT) obtained after MDT enhancement, and the core tensor was extracted while preserving the intrinsic connection of the time-series data. Finally, the resulting multidimensional core tensor was trained with the Autoregressive Integrated Moving Average (ARIMA) model to obtain the BHT-ARIMA model for wheat yield estimation. Compared to the performance of the BHT-ARIMA model with unweighted time-series data as input, the weighted time-series input significantly improves yield estimation accuracy. The coefficients of determination (R²) were improved from 0.325 to 0.583. The root mean square error (RMSE) decreased from 492.990 to 323.637 kg/ha, the mean absolute error (MAE) dropped from 350.625 to 255.954, and the mean absolute percentage error (MAPE) decreased from 4.332% to 3.186%. Besides, BHT-ARMA and BHT-CNN models were also used to compare with BHT-ARIMA. The results indicated that the BHT-ARIMA model still had the best yield prediction accuracy. The proposed method of this study will provide fast and accurate guidance for crop yield estimation and will be of great value for the processing and application of time-series RS data. Full article

The latest studies have compellingly argued that Neural Networks (NN) classification and prediction are the right direction for forecasting. It has been proven that NN are suitable models for any continuous function. Moreover, these methods are superior to conventional methods, such a Box–Jenkins, AR, MA, ARMA, or ARIMA. The latter assume a linear relationship between inputs and outputs. This assumption is not valid for skimmed milk powder (SMP) forecasting, because of nonlinearities, which are supposed to be approximated. The traditional prediction methods need complete date. The non-AI-based techniques regularly handle univariate-like data only. This assumption is not sufficient, because many external factors might influence the time series. It should be noted that any Artificial Neural Network (ANN) approach can be strongly affected by the relevancy and “clarity” of its input training data. In the proposed Convolutional Neural Networks based methodology assumes price series data to be sparse and noisy. The presented procedure utilizes Compressed Sensing (CS) methodology, which assumes noisy trends are incomplete signals for them to be reconstructed using CS reconstruction algorithms. Denoised trends are more relevant in terms of NN-based forecasting models’ prediction performance. Empirical results reveal robustness of the proposed technique. Full article

Covariance function modeling is an essential part of stochastic methodology. Many processes in geodetic applications have rather complex, often oscillating covariance functions, where it is difficult to find corresponding analytical functions for modeling. This paper aims to give the methodological foundations for an advanced covariance modeling and elaborates a set of generic base functions which can be used for flexible covariance modeling. In particular, we provide a straightforward procedure and guidelines for a generic approach to the fitting of oscillating covariance functions to an empirical sequence of covariances. The underlying methodology is developed based on the well known properties of autoregressive processes in time series. The surprising simplicity of the proposed covariance model is that it corresponds to a finite sum of covariance functions of second-order Gauss–Markov (SOGM) processes. Furthermore, the great benefit is that the method is automated to a great extent and directly results in the appropriate model. A manual decision for a set of components is not required. Notably, the numerical method can be easily extended to ARMA-processes, which results in the same linear system of equations. Although the underlying mathematical methodology is extensively complex, the results can be obtained from a simple and straightforward numerical method. Full article

To solve the soft sensor modeling (SSMI) problem in a nonlinear chemical process with dynamic time variation and multi-rate data, this paper proposes a dynamic SSMI method based on an autoregressive moving average (ARMA) model of weighted process data with discount (DSSMI-AMWPDD) and optimization methods. For the sustained influence of auxiliary variable data on the dominant variables, the ARMA model structure is adopted. To reduce the complexity of the model, the dynamic weighting model is combined with the ARMA model. To address the weights of auxiliary variable data with different sampling frequencies, a calculation method for AMWPDD is proposed using assumptions that are suitable for most sequential chemical processes. The proposed method can obtain a discount factor value (DFV) of auxiliary variable data, realizing the dynamic fusion of chemical process data. Particle swarm optimization (PSO) is employed to optimize the soft sensor model parameters. To address the poor convergence problem of PSO, ω-dynamic PSO (ωDPSO) is used to improve the PSO convergence via the dynamic fluctuation of the inertia weight. A continuous stirred tank reactor (CSTR) simulation experiment was performed. The results show that the proposed DSSMI-AMWPDD method can effectively improve the SSM prediction accuracy for a nonlinear time-varying chemical process. The AMWPDD proposed in this paper can reflect the dynamic change of chemical process and improve the accuracy of SSM data prediction. The ω dynamic PSO method proposed in this paper has faster convergence speed and higher convergence accuracy, thus, these models correlate with the concept of symmetry. Full article

The prediction of mold level is a basic and key problem of continuous casting production control. Many current techniques fail to predict the mold level because of mold level is non-linear, non-stationary and does not have a normal distribution. A hybrid model, based on empirical mode decomposition (EMD) and support vector regression (SVR), is proposed to solve the mold level in this paper. Firstly, the EMD algorithm, with adaptive decomposition, is used to decompose the original mold level signal to many intrinsic mode functions (IMFs). Then, the SVR model optimized by genetic algorithm (GA) is used to predict the IMFs and residual sequences. Finally, the equalization of the predict results is reconstructed to obtain the predict result. Several hybrid predicting methods such as EMD and autoregressive moving average model (ARMA), EMD and SVR, wavelet transform (WT) and ARMA, WT and SVR are discussed and compared in this paper. These methods are applied to mold level prediction, the experimental results show that the proposed hybrid method based on EMD and SVR is a powerful tool for solving complex time series prediction. In view of the excellent generalization ability of the EMD, it is believed that the hybrid algorithm of EMD and SVR is the best model for mold level predict among the six methods, providing a new idea for guiding continuous casting process improvement. Full article

Rainfall prediction is a fundamental process in providing inputs for climate impact studies and hydrological process assessments. Rainfall events are, however, a complicated phenomenon and continues to be a challenge in forecasting. This paper introduces novel hybrid models for monthly rainfall prediction in which we combined two pre-processing methods (Seasonal Decomposition and Discrete Wavelet Transform) and two feed-forward neural networks (Artificial Neural Network and Seasonal Artificial Neural Network). In detail, observed monthly rainfall time series at the Ca Mau hydrological station in Vietnam were decomposed by using the two pre-processing data methods applied to five sub-signals at four levels by wavelet analysis, and three sub-sets by seasonal decomposition. After that, the processed data were used to feed the feed-forward Neural Network (ANN) and Seasonal Artificial Neural Network (SANN) rainfall prediction models. For model evaluations, the anticipated models were compared with the traditional Genetic Algorithm and Simulated Annealing algorithm (GA-SA) supported by Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA). Results showed both the wavelet transform and seasonal decomposition methods combined with the SANN model could satisfactorily simulate non-stationary and non-linear time series-related problems such as rainfall prediction, but wavelet transform along with SANN provided the most accurately predicted monthly rainfall. Full article