Spatio-temporal Random Field Research Articles

Short-term PV energy yield predictions within city neighborhoods for optimum grid management

The global shift towards the exploitation of renewable energy sources is a key aspect in the transition to carbon-free societies. Although harnessing of PV energy disclosed the numerous environmental and economic benefits of PV systems, the ever-increasing share of PV systems in power generation has revealed their adverse effect on the electricity grid due to their dependence on weather conditions. Uncertain environmental parameters, especially cloud cover, can adversely affect the stability of the energy generated by a PV system, causing dynamic changes in PV power generation in a given future time period. Therefore, accurate predictions of PV power output are a major challenge, as they can contribute to the optimal management and flexibility of the power grid, and to the improvement of the operating efficiency of PV power stations, thus enabling the development of flexible green power electricity grids across cities. In addition, precise forecasting can provide system/grid operators with information needed for efficient capacity management and scheduling and ensure grid stability.Most forecasting models provide promising results in terms of error performance; however, they need weather variables or satellite information as inputs that make prognosis significantly challenging. Hence, the current work utilizes a data-driven method for predicting PV power generation from distributed PV systems. The spatio-temporal model Sparse Gaussian Conditional Random Fields was considered. Although this model was used extensively for wind forecasting, in this work, it was used for solar PV power output predictions. Moreover, the effect of varying spatial distribution for aggregated multiple PV systems was investigated on the forecast model performance. The main objective was to provide the solar PV energy sector with important information for building a smart grid for cities or regions.Continuous data from a grid-connected dense network of 21 PV systems was used within a region of 38.485 km2 in Nicosia, Cyprus. It should be noted that the test set includes data only from winter months. The results showed that the predicted power output signal responds to the fluctuation and follows the trend of the actual power signal, even on days with large variations in actual PV power. The average nRMSE of all PV systems in each dataset studied ranges from 0.119 to 0.146, proving that the proposed method delivered significant results that can be compared with existing results from similar studies. Overall, the proposed method can provide important information that can assist in decision-making for the management, optimization, and visualization of grids across cities.

Informational assessment of large scale self-similarity in nonlinear random field models

Large-scale behavior of a wide class of spatial and spatiotemporal processes is characterized in terms of informational measures. Specifically, subordinated random fields defined by nonlinear transformations on the family of homogeneous and isotropic Lancaster–Sarmanov random fields are studied under long-range dependence (LRD) assumptions. In the spatial case, it is shown that Shannon mutual information between random field components for infinitely increasing distance, which can be properly interpreted as a measure of large scale structural complexity and diversity, has an asymptotic power law decay that depends on the underlying LRD parameter scaled by the subordinating function rank. Sensitivity with respect to distortion induced by the deformation parameter under the generalized form given by divergence-based Rényi mutual information is also analyzed. In the spatiotemporal framework, a spatial infinite-dimensional random field approach is adopted. The study of the large-scale asymptotic behavior is then extended under the proposal of a functional formulation of the Lancaster–Sarmanov random field class, as well as of divergence-based mutual information. Results are illustrated, in the context of geometrical analysis of sample paths, considering some scenarios based on Gaussian and Chi-Square subordinated spatial and spatiotemporal random fields.

Test and Visualization of Covariance Properties for Multivariate Spatio-Temporal Random Fields

The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance function plays a key role in modeling, inference, and prediction. For multivariate space-time data, understanding the spatio-temporal variability, within and across variables, is essential in employing a realistic covariance model. Meanwhile, the complexity of generic covariances often makes model fitting very challenging, and simplified covariance structures, including symmetry and separability, can reduce the model complexity and facilitate the inference procedure. However, a careful examination of these properties is needed in real applications. In the work presented here, we formally define these properties for multivariate spatio-temporal random fields and use functional data analysis techniques to visualize them, hence, providing intuitive interpretations. We then propose a rigorous rank-based testing procedure to conclude whether the simplified properties of covariance are suitable for the underlying multivariate space-time data. The good performance of our method is illustrated through synthetic data, for which we know the true structure. We also investigate the covariance of bivariate wind speed, a key variable in renewable energy, over a coastal and an inland area in Saudi Arabia. The supplementary material is available online, including the R code for our developed methods.

Sojourn functionals for spatiotemporal Gaussian random fields with long memory

AbstractThis paper addresses the asymptotic analysis of sojourn functionals of spatiotemporal Gaussian random fields with long-range dependence (LRD) in time, also known as long memory. Specifically, reduction theorems are derived for local functionals of nonlinear transformation of such fields, with Hermite rank $m\geq 1,$ under general covariance structures. These results are proven to hold, in particular, for a family of nonseparable covariance structures belonging to the Gneiting class. For $m=2,$ under separability of the spatiotemporal covariance function in space and time, the properly normalized Minkowski functional, involving the modulus of a Gaussian random field, converges in distribution to the Rosenblatt-type limiting distribution for a suitable range of values of the long-memory parameter.

Discrete-valued time series based on the exponential family with the multidimensional parameter and their probabilistic and statistical analysis.

We propose herein a new parsimonious Markov model for a discrete-valued time series with conditional probability distributions of observations lying in the exponential family with the multidimensional parameter. A family of explicit consistent asymptotically normal statistical estimators is constructed for the parameters of the proposed model for increasing length of observed time series, and asymptotically effective estimator is found within this constructed family. The obtained results can be used for robust statistical analysis of discrete-valued time series,and for statistical analysis of discrete-valued spatio-temporal data and random fields.

Non-Separable Spatio-Temporal Models via Transformed Multivariate Gaussian Markov Random Fields

Abstract Models that capture spatial and temporal dynamics are applicable in many scientific fields. Non-separable spatio-temporal models were introduced in the literature to capture these dynamics. However, these models are generally complicated in construction and interpretation. We introduce a class of non-separable transformed multivariate Gaussian Markov random fields (TMGMRF) in which the dependence structure is flexible and facilitates simple interpretations concerning spatial, temporal and spatio-temporal parameters. Moreover, TMGMRF models have the advantage of allowing specialists to define any desired marginal distribution in model construction without suffering from spatio-temporal confounding. Consequently, the use of spatio-temporal models under the TMGMRF framework leads to a new class of general models, such as spatio-temporal Gamma random fields, that can be directly used to model Poisson intensity for space–time data. The proposed model was applied to identify important environmental characteristics that affect variation in the abundance of Nenia tridens, a dominant species of gastropod in a well-studied tropical ecosystem, and to characterize its spatial and temporal trends, which are particularly critical during the Anthropocene, an epoch of time characterized by human-induced environmental change associated with climate and land use.

New spatio-temporal complex covariance functions for vectorial data through positive mixtures

In the literature, the theory of complex-valued random fields is usually recalled to describe the evolution of vector data in space, without including the temporal dimension. However, as in the real case, the development of the complex formalism in a spatio-temporal context and the construction of some new classes of spatio-temporal complex covariance models are of sure interest for the scientific community partly due to the ongoing explosion in the availability of vector observations in space–time. In this paper, after presenting the fundamental aspects of the complex formalism of a spatio-temporal random field in a complex domain and the extension of some classes of complex-valued covariance models from a spatial domain to a spatio-temporal one, a new family of spatio-temporal complex-valued models obtained through a positive mixture of an infinite number of terms is proposed and various examples are discussed. A case study on modeling the spatio-temporal complex correlation structure of vectorial data is also provided.

Modeling spatio-temporal complex covariance functions for vectorial data

The theory of complex-valued random fields was already used in Geostatistics to describe vector data with two components. However, in the literature, there are various contributions focused only on modeling their spatial evolution, while the temporal perspective was analyzed separately or used to model time-varying complex covariance models. Thus, in this context it is surely challenging to propose some advances in modeling the joint spatial and temporal behavior of vector data with a reasonable representation on a complex domain.In this paper, after introducing the fundamental aspects of the complex formalism of a spatio-temporal random field and some approaches for building new families of spatio-temporal models, the spatio-temporal complex modeling of current data observed in the US East and Gulf Coast is deeply discussed and the results regarding a comparative analysis between two different complex-valued covariance models are also presented.

Supervised linear classification of Gaussian spatio-temporal data

In this article we focus on the problem of supervised classifying of the spatio-temporal Gaussian random field observation into one of two classes, specified by different mean parameters. The main distinctive feature of the proposed approach is allowing the class label to depend on spatial location as well as on time moment. It is assumed that the spatio-temporal covariance structure factors into a purely spatial component and a purely temporal component following AR(p) model. In numerical illustrations with simulated data, the influence of the values of spatial and temporal covariance parameters to the derived error rates for several prior probabilities models are studied.

Predicting abundance indices in areas without coverage with a latent spatio-temporal Gaussian model

Abstract A general spatio-temporal abundance index model is introduced and applied on a case study for North East Arctic cod in the Barents Sea. We demonstrate that the model can predict abundance indices by length and identify a significant population density shift in northeast direction for North East Arctic cod. Varying survey coverage is a general concern when constructing standardized time series of abundance indices, which is challenging in ecosystems impacted by climate change and spatial variable population distributions. The applied model provides an objective framework that accommodates for missing data by predicting abundance indices in areas with poor or no survey coverage using latent spatio-temporal Gaussian random fields. The model is validated, and no violations are observed.

Variation in use of Caesarean section in Norway: An application of spatio-temporal Gaussian random fields.

Aims:Caesarean section (CS) is a medical intervention performed in Norway when a surgical delivery is considered more beneficial than a vaginal. Because deliveries with higher risk are centralized to larger hospitals, use of CS varies considerably between hospitals. We describe how the use of CS varies geographically by municipality. Since indications for CS should have little variation across the relatively homogenous population of Norway, we expect fair use of CS to be evenly distributed across the municipalities.Methods:Data from the Medical Birth Registry of Norway were used in our analyses (810,914 total deliveries, 133,746 CSs, 440 municipalities). We propose a spatial correlation model that takes the location into account to describe the variation in use of CS across the municipalities. The R packages R-INLA and TMB are used to estimate the yearly municipal CS rate and the spatial correlation between the municipalities. We also apply stratified models for different categories of delivering women (Robson groups). Estimated rates are displayed in maps and model parameters are shown in tables.Results:The CS rate varies substantially between the different municipalities. As expected, there was strong correlation between neighbouring municipalities. Similar results were found for different Robson groups.Conclusions:The substantial difference in CS use across municipalities in Norway is not likely to be due to specific medical reasons, but rather to hospitals’ different policies towards the use of CS. The policy to be either more or less restrictive to CS was not specific to any category of deliveries.

Short-Term Time Wind Speed Forecasting Based on Spatio-Temporal Geostatistical Approach and Kriging Method

Short-term wind speed prediction is an essential task for wind resource and wind energy planning. However, most of this literature does not take into account the spatio-termporal correlation of wind data from the geographical field. For this reason, we propose an integrated spatio-temporal kriging and functional kriging strategy to exploit such spatio-temporal correlation into the wind speed prediction. First, the deterministic trend component in wind data is estimated to be removed. The residuals are used for spatio-temporal modeling and prediction. Based on the spatio-temporal kriging framework, four spatio-temporal covariance models (product-sum model, separable exponential product model, separable and nonseparable Gneiting models) are considered which describe the spatio-temporal correlation of wind data. In particular, the flexibility of using the nonseparable Gneiting model is highlighted. More specifically, four spatio-temporal random fields are modeled from the 12 wind monitoring stations over Ireland. We also use an involved weighted least squares method for estimating parameters of the four covariance models involved in the spatio-temporal kriging strategy. We apply the fitted covariance models to generate day-ahead wind speed predictions at both observed and nonobserved locations where wind station already exist but also to nearby locations. Leave-one-out cross-validation is applied to check the significance of the difference among the four models, these spatio-temporal ordinary kriging (STOK), functional ordinary kriging (FOK) and autoregressive integrated moving average (ARIMA) methods are compared for day-ahead wind speed predictions. Forecasting results indicate that the predicting accuracy is improved almost 33.5% using FOK compared with three approaches which confirm the effectiveness of the functional kriging method in the paper.

Classification of Gaussian spatio-temporal data with stationary separable covariances

The novel approach to classification of spatio-temporal data based on Bayes discriminant functions is developed. We focus on the problem of supervised classifying of the spatiotemporal Gaussian random field (GRF) observation into one of two classes specified by different drift parameters, separable nonlinear covariance functions and nonstationary label field. The performance of proposed classification rule is validated by the values of local Bayes and empirical error rates realized by leave one out procedure. A simulation study for spatial covariance functions belonging to powered-exponential family and temporal covariance functions of AR(1) models is carried out. The influence of the values of spatial and temporal covariance parameters to error rates for several label field models are studied. The results showed that the proposed classification methodology can be applied successfully in practice with small error rates and can be a useful tool for discriminant analysis of spatio-temporal data.

In vitro Diagnosis of Exercise Related Skin Trauma based on Spatiotemporal Image Segmentation

In vitro diagnosis is a kind of product and service that can get clinical diagnosis information by detecting human samples (blood, body fluid, tissue, etc.) outside human body and then judge disease or body’s functioning. This paper proposes an in vitro diagnosis method based on spatiotemporal image segmentation. Firstly, the image sequence segmentation method based on spatiotemporal Markov random field is used to segment computed tomography image, then the computed tomography image of exercise related skin trauma is segmented. According to the segmented computed tomography image, the in vitro diagnosis of exercise-related skin trauma is realized by the detection method based on the superpixel spatiotemporal characteristics. The results show that the proposed method can effectively detect skin trauma in vitro and has good segmentation effect on skin computed tomography image, as well as high accuracy in trauma detection. It can also be used in physical examination, chronic disease management and severe disease monitoring. Compared with similar detection methods, this method has significant application value.

Land-Use Regression Variable Selection with Spatiotemporal Dependent Errors and Large Sample Size: A National and Daily Ground-Level NO2 Model

Nitrogen dioxide (NO2) is a primary constituent of traffic-related air pollution and has well established harmful environmental and human health impacts. Knowledge of the spatiotemporal distribution of NO2 is critical for assessing exposure and subsequent risk assessment. A common approach for assessing exposure to outdoor air pollution is linear regression involving spatially referenced covariates, known as land-use regression (LUR). While LURs have undoubtedly been useful for many exposure and risk assessment studies, the typical assumption of independent errors is usually violated because the spatial dependence in the response cannot be captured fully by the covariates, resulting in biased covariate estimates and decreased sensitivity and specificity in the model-selection process. Here, we develop an approach for simultaneous variable selection and estimation of LUR models with spatiotemporal correlated errors that is feasible with large sample sizes. We employ a general-Vecchia approximation, which is highly accurate and guarantees linear complexity with respect to the sample size. We demonstrate this new approach with spatiotemporal random field simulations and with the case study of daily ground-level NO2 in the United States. The simulations show that our approach results in consistently better prediction as measured by the cross-validation mean squared error (MSE) compared to the competing methods. Additionally, the model selection false positive and negative rates are lower across most simulation scenarios. For NO2, our approach has at least a 10 percent improvement in prediction MSE over all of the competing methods and results in significantly more sparse models. US-wide, daily NO2 predictions and R-code are freely available for use.

Large-scale modelling and forecasting of ambulance calls in northern Sweden using spatio-temporal log-Gaussian Cox processes

Although ambulance call data typically come in the form of spatio-temporal point patterns, point process-based modelling approaches presented in the literature are scarce. In this paper, we study a unique set of Swedish spatio-temporal ambulance call data, which consist of the spatial (GPS) locations of the calls (within the four northernmost regions of Sweden) and the associated days of occurrence of the calls (January 1, 2014–December 31, 2018). Motivated by the nature of the data, we here employ log-Gaussian Cox processes (LGCPs) for the spatio-temporal modelling and forecasting of the calls. To this end, we propose a K-means clustering based bandwidth selection method for the kernel estimation of the spatial component of the separable spatio-temporal intensity function. The temporal component of the intensity function is modelled by means of Poisson regression, using different calendar covariates, and the spatio-temporal random field component of the random intensity of the LGCP is fitted using the Metropolis-adjusted Langevin algorithm. Spatial hot-spots have been found in the south-eastern part of the study region, where most people in the region live and our fitted model/forecasts manage to capture this behaviour quite well. Also, there is a significant association between the expected number of calls and the day-of-the-week, and the season-of-the-year. A non-parametric second-order analysis indicates that LGCPs seem to be reasonable models for the data. Finally, we find that the fitted forecasts generate simulated future spatial event patterns which quite well resemble the actual future data.

Oscillations of the variable cross beams under seismic and technogenic influences (part II)

The forced transverse oscillations of the variable cross section compressed beams under seismic and technogenic impacts are considered. The source of oscillations is the kinematic perturbations of the beam ends in the form of a harmonic or random vector process. The mathematical model of oscillations is presented as a boundary value problem from the basic partial differential equation of the fourth order hyperbolic type in spatial coordinate and the second order in time, which is supplemented by the boundary conditions. The beam fluctuations are interpreted as the spatiotemporal random fields inhomogeneous in space and stationery in time. In the deterministic case, the amplitudes of the forced oscillations are determined, the influence of the kinematic disturbances’ frequency and the beam oscillations’ shift of their phases is studied. In the stochastic problem, the standard deviations for the deflections are calculated, the influence of the characteristic frequency and correlation of the components of the vector perturbation process on the deflections’ output function is studied. The problem is solved by the methods of the variables’ separation, finite differences and the theory of random processes. The examples are considered, the conclusions are drawn from the calculations results in the Matlab computing complex environment.

Detection of Local Differences in Spatial Characteristics Between Two Spatiotemporal Random Fields

Comparing the spatial characteristics of spatiotemporal random fields is often at demand. However, the comparison can be challenging due to the high-dimensional feature and dependency in the data. We develop a new multiple testing approach to detect local differences in the spatial characteristics of two spatiotemporal random fields by taking the spatial information into account. Our method adopts a two-component mixture model for location wise p-values and then derives a new false discovery rate (FDR) control, called mirror procedure, to determine the optimal rejection region. This procedure is robust to model misspecification and allows for weak dependency among hypotheses. To integrate the spatial heterogeneity, we model the mixture probability as well as study the benefit if any of allowing the alternative distribution to be spatially varying. An EM-algorithm is developed to estimate the mixture model and implement the FDR procedure. We study the FDR control and the power of our new approach both theoretically and numerically, and apply the approach to compare the mean and teleconnection pattern between two synthetic climate fields. Supplementary materials for this article are available online.

Flow of Spatiotemporal Turbulentlike Random Fields

We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence-free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and multifractal, both in space and time, as it is demanded by the phenomenology of turbulence at infinite Reynolds numbers. We then solve numerically the flow equations for a differentiable version of this field. We observe that trajectories get also rough, characterized by nearly the same Hurst exponent as the one of our prescribed advecting field. Moreover, even when considering the simplest situation of the advection by a fractional Gaussian field, we evidence in the Lagrangian framework additional intermittent corrections. The present approach involves properly defined random fields, and asks for a rigorous treatment that would explain our numerical findings and deepen our understanding of this long lasting problem.

Experimental investigation of chirped amplitude modulation heterodyne ghost imaging.

We have constructed a chirped amplitude modulation heterodyne ghost imaging (CAM-HGI) experimental system that demonstrates a robust ability against background light in experiments. In the experiments, the background light is simulated by irradiating a spatiotemporal random modulated light field onto the target. The effects of background light, modulation depth and modulation duration of the signal light source on CAM-HGI are investigated experimentally. The results show that the quality of CAM-HGI can be improved by increasing the modulation depth and the modulation duration of the signal light source, and more importantly, an image with a good signal-to-noise ratio (SNR) can be achieved even when the irradiation SNR is lower than -30 dB. This technique of CAM-HGI has an important application prospect for laser imaging in strong background light environments.