Prediction of spatial functional random processes: comparing functional and spatio-temporal kriging approaches

Strandberg, Johan; Luna, Sara Sjöstedt de; Mateu, Jorge

doi:10.1007/s00477-019-01705-y

Cited by 9 publications

(5 citation statements)

References 24 publications

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“…The deterministic component is a constant value for each x i location in each area. As commented before, this stochastic method gives the optimal prediction under the presumption that the process is second-order stationery and normally distributed [31,59].…”

Section: Ordinary Krigingmentioning

confidence: 99%

Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models

et al. 2023

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As far as the knowledge of the seabed is concerned, both for safe navigation and for scientific research, 3D models, particularly digital bathymetric models (DBMs), are nowadays of fundamental importance. This work aimed to evaluate the quality of DBMs according to the interpolation methods applied to obtain grid format 3D surfaces from scattered sample points. Other complementary factors affecting DBM vertical accuracy, such as seabed morphological complexity and surveyed points sampling density, were also analyzed by using a factorial ANOVA experimental design. The experiments were performed on a multibeam dataset provided by the Italian Navy Hydrographic Institute (IIM) with an original resolution of 1 m × 1 m grid spacing, covering a surface of 0.24 km2. Six different sectors comprising different seabed morphologies were investigated. Eight sampling densities were randomly extracted from every sector, each with four repetitions. Finally, four different interpolation methods were tested, including: radial basis multiquadric function (RBMF), ordinary kriging (OK), universal kriging (UK) and Gaussian Markov random fields (GMRF). The results demonstrated that both RBMF and OK produced very accurate DBM in areas characterized by low levels of seabed ruggedness at sampling densities of only 0.0128 points/m2 (equivalent grid spacing of 8.84 m). In contrast, a higher density of 0.1024 points/m2 (3.13 m grid spacing) was required to produce accurate DBM in areas with more complex seabed topography. On the other hand, UK and GMRF were strongly influenced by morphology and sampling density, yielding higher vertical random errors and more prone to slightly overestimate seabed depths. In addition, sampling density and morphology were the factors that most influenced the vertical accuracy of the interpolated DBM. In this sense, the highly statistically significant influence of the interaction between sampling density and morphology on the vertical accuracy of the interpolated DBM confirms the need to perform a preliminary analysis of seabed morphological complexity in order to increase, if necessary, the number of surveyed points in cases of complex morphologies.

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Section: Ordinary Krigingmentioning

confidence: 99%

Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models

et al. 2023

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“…7 Computational concerns make it difficult to deploy an otherwise interesting, functional variant of kriging called GP regression (GPR). 50 However, even plain GPs can be troubled within the same setting. The aforementioned approximations can be useful, but they require tuning of some sort.…”

Section: Literature Reviewmentioning

confidence: 99%

Separable spatio‐temporal kriging for fast virtual sensing

Miniato

Bellio

Grassetti

et al. 2022

Appl Stoch Models Bus & Ind

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Environmental monitoring is a task that requires to surrogate system-wide information with limited sensor readings. Under the proximity principle, an environmental monitoring system can be based on the virtual sensing logic and then rely on distance-based prediction methods, foremostly spatio-temporal kriging. The last one is cumbersome with large datasets, but we show that a suitable separability assumption reduces its computational cost to an extent broader than considered typically. Only spatial interpolation needs to be performed in a centralized way, while forecasting can be delegated to each sensor. This simplification is related to the fact that two separate models are involved, one in time and one in the space domain. Any of the two models can be replaced without re-estimating the other under a composite likelihood (CL) approach. Moreover, the use of convenient spatial and temporal models eases up computation, not only in the CL approach, but also in maximum likelihood estimation. We show that this perspective on kriging allows to perform virtual sensing even in the case of tall datasets.

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“…The total the total cost of the methods after running the optimization problem described in section 2.3 in equations (35)- (42), for an arbitrary selected day, are listed in Table 9. As shown, the cost of the deterministic approach is lower than that of the other methods before the real wind power is dispatched.…”

Section: Case 2: Ieee-24 Bus Test Systemmentioning

confidence: 99%

“…Kriging or Gaussian Process Regression is a common kernel-based regression model capable of modeling complex functions [41]. It is often referred to as the Best Linear Unbiased Estimator (BLUE) and, as the name implies, is a linear estimator [42]. It determines the values at points of interest as a weighted sum of values at other points, and its variations are primarily based on assumptions about the underlying mean function of the data distribution [42].…”

Section: Introductionmentioning

confidence: 99%

“…It is often referred to as the Best Linear Unbiased Estimator (BLUE) and, as the name implies, is a linear estimator [42]. It determines the values at points of interest as a weighted sum of values at other points, and its variations are primarily based on assumptions about the underlying mean function of the data distribution [42]. The interpolation error is minimized by studying and modelling the spatio-temporal distribution of the points already measured.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spatio-Temporal Kriging Based Economic Dispatch Problem Including Wind Uncertainty

Cuenca¹,

Flórez²,

Patiño³

et al. 2020

Preprint

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The incorporation of wind generation introduces challenges to the operation of the power system due to its uncertain characteristics. Therefore, the development of methods to accurately model the uncertainty is necessary. In this paper, the spatio-temporal Kriging and analog approaches are used to forecast wind power generation and used as input to solve an economic dispatch problem, considering the uncertainties of wind generation. Spatio-temporal Kriging takes into account the spatial and temporal information given by the database to enhance wind forecasts. We evaluate the performance of using the spatio-temporal Kriging, and comparisons are carried out versus other approaches in the framework of the economic power dispatch problem, for which simulations are developed on the modified IEEE 3-bus and IEEE 24-bus test systems. The results show that the use of Kriging-based spatio-temporal models in the context of economic power dispatch can provide an opportunity for lower operating costs in the presence of uncertainty when compared to other approaches.

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Prediction of spatial functional random processes: comparing functional and spatio-temporal kriging approaches

Cited by 9 publications

References 24 publications

Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models

Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models

Separable spatio‐temporal kriging for fast virtual sensing

Spatio-Temporal Kriging Based Economic Dispatch Problem Including Wind Uncertainty

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