Nonstationary Variables Research Articles

Adaptive prediction model for effective electrical machine maintenance

Purpose The purpose of this paper is to propose an optimal predictive model for the short-term forecast of real-time non-stationary machine variables by combining time series prediction with adaptive algorithms to minimize the error and to improve the prediction accuracy. Design/methodology/approach The proposed model is applied for prediction of speed and controller set point of three-phase induction motor operating on closed loop speed control with AC drive and PI controller. At Stage 1, the trend of the machine variables has been extracted and added to auto-regressive moving average (ARMA) time series prediction. ARMA prediction has been carried out using different combinations of AR and MA methods in order to make prediction with less Mean Squared Error (MSE). Findings The prediction error indicates the inadequacy of the model to estimate the data characteristics, which has been resolved at the subsequent stage by cascading an adaptive least mean square finite impulse response filter to the time series model. The adaptive filter receives the predicted output including training data and iteratively adjusts its coefficients for zero error convergence. Research limitations/implications The componentized data prediction based on time series and cascade adaptive filter algorithm decomposes the non-stationary data characteristics for predictive maintenance. Evaluation of the model with different combination of time series algorithms and parameter settings of adaptive filter has been carried out to illustrate the performance of the prediction model. This prediction accuracy is compared with existing linear adaptive filter prediction using MSE as comparison index. The wide margin in the MSE values substantiates the prediction efficiency of the proposed model for machine data. Originality/value This model predicts the dynamic machine data with component decomposition at high accuracy, which enables to interpret the system response under dynamic conditions efficiently.

Spectrum Anomaly of the Supernova Remnant 3C58

We measured the instantaneous spectra of the supernova remnant 3C58 for the epochs: 2003.4, 2004.4, and 2013.2 with the RTF-32 radio telescope of the “Svetloe” IAA RAS observatory at four frequencies from 1550 to 8450 MHz. The spectra of 3C58 for the time intervals: 1963–1971, 1981–1998, and 2004–2010 were obtained from the published data allowing us to compare the intensity of 3C58 and standard sources. To reduce all the data to a unified system and build the spectra, we used the “artificial moon” flux scale. Comparison of the spectra according to the data obtained in 1963–2013 revealed non-stationary frequency-dependent variations of flux densities, as well as local deviations of the 3C58 spectra from the frequency power law. Possible causes of the detected anomalies are discussed.

ROBUST INFERENCE IN STRUCTURAL VECTOR AUTOREGRESSIONS WITH LONG-RUN RESTRICTIONS

Long-run restrictions are a very popular method for identifying structural vector autoregressions, but they suffer from weak identification when the data is very persistent, i.e., when the highest autoregressive roots are near unity. Near unit roots introduce additional nuisance parameters and make standard weak-instrument-robust methods of inference inapplicable. We develop a method of inference that is robust to both weak identification and strong persistence. The method is based on a combination of the Anderson-Rubin test with instruments derived by filtering potentially nonstationary variables to make them near stationary using the IVX instrumentation method of Magdalinos and Phillips (2009). We apply our method to obtain robust confidence bands on impulse responses in two leading applications in the literature.

Non-stationary variability in accreting compact objects

Accreting compact objects show variations in source flux over a broad range of timescales and in all wavebands. The light curves typically show a lognormal distribution of flux and a linear relation between flux and rms. It has been demonstrated that an exponential transform of an underlying (and unobserved) Gaussian stochastic process provides a very good description of the light curves with these observed properties. Recently, a non-stationary power spectrum was observed on fast timescales (~ days) in the active galaxy, IRAS 13224--3809, as well as a non-lognormal flux distribution and non-linear rms-flux relation. Here, we investigate the affects of piecewise non-stationary power spectra on the resultant flux distribution and rms-flux relation. We demonstrate that the simple "exponentiation" model successfully reproduces the observed quantities, even when the light curves are non-stationary. We also demonstrate how non-lognormal flux distributions and rms-flux relations inconsistent with a linear model can be erroneously produced from poorly sampled PSDs. This is of particular importance for AGN surveys where very long baselines are required to sample the PSD down to low enough frequencies.

Modeling Depth of the Redox Interface at High Resolution at National Scale Using Random Forest and Residual Gaussian Simulation

AbstractThe management of water resources needs robust methods to efficiently reduce nitrate loads. Knowledge on where natural denitrification takes place in the subsurface is thereby essential. Nitrate is naturally reduced in anoxic environments and high‐resolution information of the redox interface, that is, the depth of the uppermost reduced zone is crucial to understand the variability of the denitrification potential. In this study we explore the opportunity to use random forest (RF) regression to model redox depth across Denmark at 100‐m resolution based on ~13,000 boreholes as training data. We highlight the importance of expert knowledge to guide the RF model in areas where our conceptual understanding is not represented correctly in the training data set by addition of artificial observations. We apply random forest regression kriging in which sequential Gaussian simulation models the RF residuals. The RF model reaches a R2 score of 0.48 for an independent validation test. Including sequential Gaussian simulation honors observations through local conditioning, and the spread of 800 realizations can be utilized to map uncertainty. Emphasis is put on adequate handling of nonstationarities in variance and spatial correlation of the RF residuals. The RF residuals show no spatial correlation for large parts of the modeling domain, and a local variance scaling method is applied to account for the nonstationary variance. Moreover, we present and exemplify a framework where newly acquired field data can easily be integrated into random forest regression kriging to quickly update local models.

Incipient Fault Detection for Multiphase Batch Processes With Limited Batches

Sufficient batches are in general, required for fault detection of batch processes. However, sometimes, it is difficult and may be impractical to conduct multiple cycles and wait until enough batches are available. Without batch-wise normalization step, the nonstationary cannot be efficiently removed by time-wise normalization. The mean values of the nonstationary variables are still time varying and the interval of fault-free data is very wide in each phase. Therefore, the incipient fault, which has a small magnitude including early changing and the slow developing, may be buried by nonstationary trends resulting in low fault detection rate. To address the above issue, a two-layer fault detection method is proposed to detect the incipient fault for multiphase batch processes with limited batches. First, a concurrent variable separation strategy is proposed to distinguish nonstationary variables from stationary variables for multiple batches in each phase. Second, a two-layer fault detection model is constructed to detect the incipient fault. Cointegration analysis-based fault detection model is built to investigate the relationship between nonstationary variables, which can effectively distinguish the incipient fault from the normal trend of the nonstationary variables. Principal component analysis is adopted to describe the correlation of stationary variables. Afterward, a total fault detection model is constructed to monitor the relation between nonstationary variables and stationary variables. To illustrate the feasibility and effectiveness, the proposed algorithm is applied to two multiphase batch processes including fed-batch penicillin fermentation process and semiconductor etch process.

Quantification of Tidal Asymmetry and Its Nonstationary Variations

AbstractTidal wave deformation and tidal asymmetry widely occur in tidal estuaries and lagoons. Tidal asymmetry has been intensively studied because of its controlling role on residual sediment transport and large‐scale morphological evolution. There are several methods available to characterize tidal asymmetry prompting the need for an overview of their applicability and shortcomings. In this work we provide a brief review and evaluation of two methods, namely, the harmonic method and the statistical method. The latter comprises several statistical measures that estimate the probability density function and various forms of skewness. We find that both the harmonic and statistical methods are effective and have complementary advantages. The harmonic method is applicable to predominantly semidiurnal or diurnal regimes, while the statistical methods can be used in mixed tidal regimes. Assisted by harmonic data, a modified skewness measure can isolate the contribution of different tidal interactions on net tidal asymmetry and also reveal its subtidal variations. The application of the skewness measure to nonstationary river tides reveals stronger tidal asymmetry during spring tides than neap tides, and the nonlinear effects of river discharges on tidal asymmetry in the upper and lower regions of long estuaries.

Meticulous Assessment of Operating Performance for Processes with a Hybrid of Stationary and Nonstationary Variables

Due to the changes of external environment, unpredictable disturbances, etc., the industrial processes often have nonstationary characteristics. Assessment of operating performance for industrial processes with a hybrid of stationary and nonstationary variables is rather challenging since the statistical properties are time-variant. To solve this problem, a meticulous model for feature extracting to assess the operating performance of nonstationary processes is proposed in this paper. After distinguishing the stationary and nonstationary variables, the stationary variables are characterized by principal component analysis (PCA) to obtain the principal variation information, and the nonstationary variables are characterized by co-integration analysis (CA) to obtain the long term equilibrium relationship. Hence the inner features of both stationary variables and nonstationary variables are meticulously extracted. Next, to characterize the correlations between the stationary and nonstationary variables, a gl...

Monitoring nonstationary and dynamic trends for practical process fault diagnosis

This article introduces a revised common trend framework to monitor nonstationary and dynamic trends in industrial processes and shows needs for each improvement on the basis of three application studies. These improvements relate to (i) the extension of the common trend framework to include sets that contain stationary and nonstationary variables, (ii) handling cases where residuals are not drawn from multivariate normal distributions and (iii) the application of the framework to larger variable sets. Existing work does not adequately address these practically important issues. Industrial application studies highlight the needs for (i) the extended framework to model data sets containing stationary and nonstationary variables, (ii) handling statistics that are not based on normally distributed residuals and (iii) the use of Chigira procedure to robustly extract common trends. The extended framework is compared to traditional approaches.

Error-adaptive modeling of streaming time-series data using radial basis functions

Abstract We propose an error-adaptive method for constructing time-series models for novelty detection using radial basis functions. The optimization problem is implemented in an incremental, or online manner, and permits the balancing of the quality of the data fit and the sparsity of the model in the objective function of a linear program. The resulting algorithm is applied to several examples of streaming time-series data. Novel data points are identified using an infeasibility criterion while feasible data points are not used for training and may be discarded. In practice, only a small fraction of observed streaming data points are actually required to update the model. The sparsity promoting term in the objective function serves to determine the location and number of RBFs required to fit the data. Balancing sparsity with the accuracy of the model allows the user to adjust model complexity. It appears that the ability to adapt the error bound in the optimization problem may help to prevent over-fitting. We illustrate the approach with several examples and show that the fitting procedure is robust to additive Gaussian noise with non-stationary variance. We compare the proposed algorithm with several other methods in the literature, including both online and batch algorithms.

Methods of Analyzing Nonstationary Variability of the Black Sea Wave Climate

Methods of Analyzing Nonstationary Variability of the Black Sea Wave Climate

Hydraulic heterogeneity and its impact on kinematic porosity in Swedish coastal terrains

Hydrogeology in crystalline rock aquifers is often problematic due to the heterogeneity and anisotropy in the fracture network. Kinematic porosity of the host rock is exceedingly important for municipal decision makers in assessing sustainably extractable water supply volumes and assessing contaminant transport behavior within the matrix. This study explores heteroscedasticity in the hydrogeological characteristics of the fracture network and estimation of kinematic porosity from superficial fracture measurements. Estimates were based on the geometrical properties of the fractures including: fracture frequency, aperture and orientation. The estimates were adjusted for aperture changes with depth, connectivity of the fracture network, fracture continuity and measurement orientation bias. The results were compared with well archive data and correlations were found to be significant with more than 95% confidence. Erratic behaviour of well data relative to fracture measurements indicates that well orientation with respect to the fracture network gives incomplete hydrogeological data. Spatial heterogeneity of the bedrock was examined using spatial statistics and geographic information systems. The results from the spatial statistical analyses of well data showed that the heterogeneity within the bedrock is sufficiently high that spatial correlations cease to exist in nearly all investigated rock types at distances greater than 500 m, and in some rocks, particularly sedimentary gneisses, no spatial correlations were observed. Arbitrarily grouped samples with similar geology and topography showed evidence of non-stationary variance. Results indicate that regional generalizations based on sparse point measurements are highly error prone and potential exists in complementary field-based estimates.

Population composition and financial markets: evidence from Japan

PurposeThis study aims to examine the relation between population composition and financial market variables in post-war Japan.Design/methodology/approachCointegration and Granger causality tests are applied to annual data for the period 1948-2015.FindingsAccounting for nonstationarity, this study finds long-run equilibrium relations between real financial price (stock and house) indices and the proportion of population in the prime earning (45-64) or retirement (65+) age. Granger causality tests that account for possibly nonstationary variables find some evidence of dynamic causation running from the 45-64 cohort to the real financial price indices. No such evidence is found for the 65+ cohort.Originality/valueThis study complements the existing literature primarily based on US data with analysis of Japanese data that has some unique population composition features.

Metody analiza nestatsionarnoy izmenchivosti volnovogo klimata Chernogo morya

Metody analiza nestatsionarnoy izmenchivosti volnovogo klimata Chernogo morya

A Unified Approach in Sieve Estimation for Nonparametric Time Series Models with Diverse Variables

A novel and unified approach is proposed in sieve estimation to tackle the issue of unbounded support of variables in nonparametric regression models. The model em- braces time trend and both stationary and nonstationary variables that are allowed to be correlated. This approach is introduced via weighted least squares, and it im- proves the existing methodology and alleviates the requirement of related moments. As a byproduct, the requirement on the α-mixing coefficients for stationary process is reduced to the least in comparison with the literature. Central limit theorems are established for the sieve estimator and other related quantities. Monte Carlo simulation confirms the theoretical results and an empirical study is provided.

Assessing temporal variations of Ammonia Nitrogen concentrations and loads in the Huaihe River Basin in relation to policies on pollution source control

To assess the quality of a water environment, an in-depth analysis of temporal patterns of contaminant concentrations in water body should be carried out based on unbiased water quality datasets. In this study, we developed a modified log-linear model to account for non-stationary seasonal variations of contaminant concentrations over multiple periods. The model was applied to analyze temporal changes of the Ammonia Nitrogen (AN) concentration at Middle Reaches of Huaihe River (MRHR) and two major tributaries, Shaying River (SR) and Guo River (GR). The modified model outperformed the original models and fitted the data well with Pearson correlation coefficients ranging from 0.67 to 0.86. Temporal patterns of AN concentrations, loads and sources were identified from 1998 to 2015 in connection to the implementation of Five-Year Plans (FYPs, policies for controlling water pollution) in the Huaihe River Basin (HRB). The results show that the AN concentration experienced a significant decrease. Since FYPs focused on controlling AN point sources, the proportion of AN loads derived from point sources decreased from 48–86% to 1–17% in the MRHR and from 66–92% to 2–56% in the SR and GR. However, rebounds of AN concentration occurred in the first year of each FYP period possibly due to discontinuity of the policy implementation over the transition between two consecutive FYPs. High AN concentration anomalies were found in flood seasons, related to pollution discharge beyond limits and/or irrational regulation of sluices. These results have implications for future pollution control policies in the HRB, particularly, the need to reduce the upper limits of contaminant loads for flood seasons, continuity of the policies implementation, reduction of non-point source pollution, rational sluice regulation and integrated pollution prevention programs. The developed model and approach are applicable to other polluted river basins to facilitate water quality assessment and evaluation of pollution control policies.

The role of the AFA coefficient as a new criterion in the long-run liaison between corporate liquidity and bank credit

PurposeThis paper aims to focus on the absence of a direct criterion for the ideal level of net working capital (NWC) for which Acikgoz (2014) theoretically demonstrates that this NWC can be treated in a manner that allows the assessment of repayments. The study presents and discusses a new multiplier (i.e. the afa coefficient), defined as the ratio of cash equivalents ratio to NWC, measured as the percentage of short-term liabilities (Acikgoz, 2014). In other words, the study explores whether NWC could be an indicator of the ratios of corporate short-term bank credit to STL and of bank credit to total assets.Design/methodology/approachSectoral panel regressions are used in the case of Turkey, spanning the period 1996-2013, on data obtained from the Central Bank of Turkey. Through second-generation panel unit root tests for cross-section dependence and panel cointegration methodologies, the results illustrate the statistical significance of the CD statistics, indicating the presence of cross dependence, the presence of non-stationary variables and the presence of a long-run association for the variables under study.FindingsThe findings document that a transformed variable of NWC is more substantive than the explicatory quality of the current ratio and may potentially be used in the prediction of bank credit in corporate liabilities.Originality/valueThe afa coefficient shows the ratio of liquid assets to NWC as a percentage of STL. The results illustrate that this coefficient plays a significant role for corporate bank credit usage in the case of the Turkish sectoral analysis.

Clustering and Standard Error Bias in Fixed Effects Panel Data Regressions

We address several issues concerning standard error bias in pooled time-series cross-section regressions. These include autocorrelation, problems with unit root tests, nonstationarity in levels regressions, and problems with clustered standard errors. We conduct unit root test for crimes and other variables. We use Monte Carlo procedures to illustrate the standard error biases caused by the above issues in pooled studies. We replicate prior research that uses clustered standard errors with difference-in-differences regressions and only a small number of policy changes. Standard error biases in the presence of autocorrelation are substantial when standard errors are not clustered. Importantly, clustering greatly mitigates bias resulting from the use of nonstationary variables in levels regressions, although in some circumstances clustering can fail to correct for standard error biases due to other reasons. The “small number of policy changes” problem can cause extreme standard error bias, but this can be corrected using “placebo laws”. Other biases are caused by weighting regressions, having too few units, and having dissimilar autocorrelation coefficients across units. With clustering, researchers can usually conduct regressions in levels even with nonstationary variables. They should, however, be leery of pitfalls caused by clustering, especially when conducting difference-in-differences analyses.

Uncertainty quantification in multiscale simulation of woven fiber composites

Woven fiber composites have been increasingly employed as light-weight materials in aerospace, construction, and transportation industries due to their superior properties. These materials possess a hierarchical structure that necessitates the use of multiscale simulations in their modeling. To account for the inherent uncertainty in materials, such simulations must be integrated with statistical uncertainty quantification (UQ) and propagation (UP) methods. However, limited advancement has been made in this regard due to the significant computational costs and complexities in modeling spatially correlated structural variations coupled at different scales. In this work, a non-intrusive approach is proposed for multiscale UQ and UP to address these limitations. We introduce the top-down sampling method that allows to model non-stationary and continuous (but not differentiable) spatial variations of uncertainty sources by creating nested random fields (RFs) where the hyperparameters of an ensemble of RFs is characterized by yet another RF. We employ multi-response Gaussian RFs in top-down sampling and leverage statistical techniques (such as metamodeling and dimensionality reduction) to address the considerable computational costs of multiscale simulations. We apply our approach to quantify the uncertainty in a cured woven composite due to spatial variations of yarn angle, fiber volume fraction, and fiber misalignment angle. Our results indicate that, even in linear analysis, the effect of uncertainty sources on the material’s response could be significant.

Accounting for non-stationary variance in geostatistical mapping of soil properties

Simple and ordinary kriging assume a constant mean and variance of the soil variable of interest. This assumption is often implausible because the mean and/or variance are linked to terrain attributes, parent material or other soil forming factors. In kriging with external drift (KED) non-stationarity in the mean is accounted for by modelling it as a linear combination of covariates. In this study, we applied an extension of KED that also accounts for non-stationary variance. Similar to the mean, the variance is modelled as a linear combination of covariates. The set of covariates for the mean may differ from the set for the variance. The best combinations of covariates for the mean and variance are selected using Akaike's information criterion. Model parameters of the selected model are then estimated by differential evolution using the Restricted Maximum Likelihood (REML) in the objective function. The methodology was tested in a small area of the Hunter Valley, NSW Australia, where samples from a fine grid with gamma K measurements were treated as measurements of the variable of interest. Terrain attributes were used as covariates. Both a non-stationary variance and a stationary variance model were calibrated. The mean squared prediction errors of the two models were somewhat comparable. However, the uncertainty about the predictions was much better quantified by the non-stationary variance model, as indicated by the mean and median of the standardized squared prediction error and by accuracy plots. We conclude that the non-stationary variance model is more flexible and better suited for uncertainty quantification of a mapped soil property. However, parameter estimation of the non-stationary variance model requires more attention due to possible singularity of the covariance matrix.