High-order Taylor series expansion methods for error propagation in geographic information systems

Xue, Jie; Leung, Yee; Ma, Jun

doi:10.1007/s10109-014-0207-x

Cited by 20 publications

(10 citation statements)

References 17 publications

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“…2, with a threshold value for identification of the steady-state, I ee , both normalized (Mejia et al, 2010). information systems (Xue et al, 2015) and spatial explorations (Sun e Zhang, 2016).…”

Section: Denoising and Steady-state Detectionmentioning

confidence: 99%

“…However, it requires a high computational cost, and every modification in the model and/or in the input values requires a new execution of the method, being prohibitive in iterative processes . Another disadvantage, according to Xue et al (2015), is that this method does not have an analytical relationship between the uncertainties of inputs and outputs. Additional information about the Monte Carlo method can be found in Kuo and Uppuluri (1983), Helton (1993), Helton and Davis (2003), and Yan et al 2015.…”

Section: Denoising and Steady-state Detectionmentioning

confidence: 99%

“…The use of the TS method for the propagation of errors is well consolidated in the literature and has as its main idea the determination of an analytical expression for the uncertainties of the outputs due to inputs, whose effects can be explained and analyzed through this relation (Xue et al, 2015).…”

Section: Denoising and Steady-state Detectionmentioning

confidence: 99%

“…The first order series approach offers, in general, significant results and ease in its application, being recommended for linear and polynomial functions. However, for non-linear functions the results may be less accurate, suggesting truncation of the series with higher order terms Xue et al, 2015).…”

Section: Error Propagationmentioning

confidence: 99%

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Statsscandleplot: A New Way of Monitoring Operational Performance Indicators

Giaquinto

Trierweiler

Teixeira³

et al. 2019

Braz. J. Chem. Eng.

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Operational KPIs play an extremely important role in the process industry, aiding in decision making. However, they need to be reliably calculated to be representative. The present work presents a schematic methodology for the calculation of these KPIs, including techniques of steady-state detection, denoising, error propagation and sensitivity analysis, presented, as far as it is known, in the form of a new graphical tool proposed by the authors named StatSSCandlePlot. The methodology was applied in a real case study of a gas fired boiler in which the indicator studied was its efficiency evaluated by the Stack Loss Method. From the StatSSCandlePlot it was possible to identify the trends of the indicator, the portion of each window in the steady-state, the values to be considered from the indicator and, in a complementary way, to identify the variable that most influences the variation of the indicator, through the sensitivity analysis.

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Section: Denoising and Steady-state Detectionmentioning

confidence: 99%

Section: Denoising and Steady-state Detectionmentioning

confidence: 99%

Section: Denoising and Steady-state Detectionmentioning

confidence: 99%

Section: Error Propagationmentioning

confidence: 99%

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Statsscandleplot: A New Way of Monitoring Operational Performance Indicators

Giaquinto

Trierweiler

Teixeira³

et al. 2019

Braz. J. Chem. Eng.

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“…Two common methods to determine the propagation of errors through GIS operations are the Taylor series method and the Monte Carlo method (Xue et al 2015). The former is analytical and establishes mathematical functions that portray the uncertainty propagation, while the latter is a numerical simulation method.…”

Section: Introductionmentioning

confidence: 99%

Propagation of positional error in 3D GIS: estimation of the solar irradiation of building roofs

Biljecki

Heuvelink

Ledoux

et al. 2015

International Journal of Geographical Information Science

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While error propagation in GIS is a topic that has received a lot of attention, it has not been researched with 3D GIS data. We extend error propagation to 3D city models using a Monte Carlo simulation on a use case of annual solar irradiation estimation of building rooftops for assessing the efficiency of installing solar panels. Besides investigating the extension of the theory of error propagation in GIS from 2D to 3D, this paper presents the following contributions. We (1) introduce varying XY/Z accuracy levels of the geometry to reflect actual acquisition outcomes; (2) run experiments on multiple accuracy classes (121 in total); (3) implement an uncertainty engine for simulating acquisition positional errors to procedurally modelled (synthetic) buildings; (4) perform the uncertainty propagation analysis on multiple levels of detail (LODs); and (5) implement Solar3Dcity -a CityGML-compliant software for estimating the solar irradiation of roofs, which we use in our experiments. The results show that in the case of the city of Delft in the Netherlands, a 0.3/0.6 m positional uncertainty yields an error of 68 kWh/m 2 /year (10%) in solar irradiation estimation. Furthermore, the results indicate that the planar and vertical uncertainties have a different influence on the estimations, and that the results are comparable between LODs. In the experiments we use procedural models, implying that analyses are carried out in a controlled environment where results can be validated. Our uncertainty propagation method and the framework are applicable to other 3D GIS operations and/ or use cases. We released Solar3Dcity as open-source software to support related research efforts in the future.

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