An algorithm for non-parametric estimation in state–space models

Chau, Thi Tuyet Trang; Ailliot, Pierre; Monbet, Valérie

doi:10.1016/j.csda.2020.107062

Cited by 9 publications

(5 citation statements)

References 38 publications

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“…They are all based on nearest neighbors of the hidden-state in the reference catalog C weighted thanks to a kernel function. Among the different kernels, Chau et al (2021) propose to use a tricube kernel which has a compact support and is smooth at its boundary. Throughout this article, as selected by Lguensat et al (2017), a radial basis function (also known as Gaussian kernel, squared exponential kernel, or exponentiated quadratic) is considered and defined as:…”

Section: Methodology For Uncertainty Quantificationmentioning

confidence: 99%

Wind turbine quantification and reduction of uncertainties based on a data-driven data assimilation approach

Hirvoas

Prieur

Arnaud

et al. 2022

Journal of Renewable and Sustainable Energy

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In this paper, we propose a procedure for quantifying and reducing uncertainties impacting numerical simulations involved in the estimation of the fatigue of a wind turbine structure. The present study generalizes a previous work carried out by the authors proposing to quantify and to reduce uncertainties affecting the properties of a wind turbine model by combining a global sensitivity analysis and a recursive Bayesian filtering approach. We extend the procedure to include the uncertainties involved in the modeling of a synthetic wind field. Unlike the model properties having a static or slow time-variant behavior, the parameters related to the external sollicitation have a non-explicit dynamic behavior which must be taken into account during the recursive inference. A non-parametric data-driven approach to approximate the non-explicit dynamic of the inflow related parameters is used. More precisely, we focus on data assimilation methods combining a nearest neighbor or analog sampler with a stochastic filtering method such as the ensemble Kalman filter. This so-called data-driven data assimilation approach is evaluated on an industrial case of a wind turbine in operation using in situ measurements from an operating structure. The measured data are used by the method to recursively reduce the uncertainties that affect the parameters related to both model properties and wind field.

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Section: Methodology For Uncertainty Quantificationmentioning

confidence: 99%

Wind turbine quantification and reduction of uncertainties based on a data-driven data assimilation approach

Hirvoas

Prieur

Arnaud

et al. 2022

Journal of Renewable and Sustainable Energy

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“…The disturbance matrix associated to the ambient temperature The disturbance matrix associated to the solar radiation Energies 2021, 14,2551…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…However, literature shows the importance of building a unified simple model to better represent the thermal system dynamics [12]. The state-space method was a subject of development for both linear and non-linear systems [13][14][15][16][17][18]. Furthermore, in thermal dynamics, the method gets interesting for its flexibility and ease-of-implementation in control and optimization models.…”

Section: Introductionmentioning

confidence: 99%

A Substitutive Coefficients Network for the Modelling of Thermal Systems: A Mono-Zone Building Case Study

et al. 2021

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A modelling approach based on the Substitutive Coefficients Network (SCN) is developed to predict the thermal behavior of a system in the dynamic state-space, without requiring knowledge of the thermal mass. The method can apply either to large- (building, combined solar systems, geothermal energy, and thermodynamic installations) or to small-scale systems (heat exchangers, electronic devices cooling systems, and Li-ion batteries). This current method is based on a dimensionless formulation of the simplified dynamic thermal balance model, using relaxation time as a key parameter to establish the model. The introduction of relaxation time reduces the parameters set as guidance coefficients. The parameters are finally expressed by a combination of global heat transfer coefficients related to each layer and/or sub-layer of the system. Advantages of the method are reliability, “non-destructibility”, i.e., it allows a reliable prediction of the thermal behavior which experimentally is inaccessible, and reducibility of the parameters size estimate. Additionally, the method is inexpensive in terms of computation memory. It is also easy to implement in practical numerical schemes. In this paper, the method leads to a simplified mathematical model that predicts the thermal behavior of a mono-zone eco-cottage building installed at Lorraine University (in Longwy, France) as a case study. Thermal performance of the building is estimated under the hourly weather conditions onsite, as obtained from the Meteonorm software. The thermal dynamics within hourly Typical Meteorological Year 2 (TMY2) Meteonorm data disturbances and the internal heating input state in the winter period were simulated with a simplified numerical discretization method. Results provide a general dynamic state of the different sub-components of the system, with limited design of the model parameters.

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“…Subsequently, a large number of scholars have also conducted in-depth research on kernel density estimation methods. Among these scholars, what is more typical is that Chau et al proposed a method combining the Stochastic Expectation-Maximization (SEM) algorithm and Sequential Monte Carlo (SMC) approaches for nonparametric estimation in state-space models in 2021 [14]. According to the probabilistic density estimation method, as long as the kernel function and optimal window width are appropriate, the real probabilistic density function of any random variable can be approximated without restriction.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic En Route Sector Traffic Demand Prediction Based on Quantile Regression Neural Network and Kernel Density Estimation

Tian,

Zhang,

et al. 2024

Applied Sciences

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With the development of civil aviation in China, airspace congestion has become more and more serious and has gradually spread from airport terminal areas to en route networks. Traditionally, most prediction methods that obtain traffic flow data are based on the number of aircraft passing through an en route sector and require flight data to meet strict assumptions and conditions. While these methods are normally used in the actual operation of air traffic flow management departments in China, the results are not satisfactory due to the nonlinearity of traffic demand along en route sectors and the change in high-frequency noise. In order to refine aircraft control in airspace, it is necessary to predict traffic flow accurately. Thus, this paper proposes the quantile regression neural network and kernel density estimation method to obtain some quantiles of continuous traffic demand data in the future, which combines the strong nonlinear adaptive ability of neural networks with the ability of quantile regression to describe explanatory variables. By using these continuous conditional quantiles, we obtain the probability density function and probability density curve of the continuous traffic demand in the future using the kernel density estimation method. In this way, we can obtain not only a specific point prediction value and its change interval but also the probability of each value in the prediction change interval of traffic demand in the en route sector as well as a more accurate point prediction value for a specific day.

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An algorithm for non-parametric estimation in state–space models

Cited by 9 publications

References 38 publications

Wind turbine quantification and reduction of uncertainties based on a data-driven data assimilation approach

Wind turbine quantification and reduction of uncertainties based on a data-driven data assimilation approach

A Substitutive Coefficients Network for the Modelling of Thermal Systems: A Mono-Zone Building Case Study

Probabilistic En Route Sector Traffic Demand Prediction Based on Quantile Regression Neural Network and Kernel Density Estimation

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