How do you evaluate the accuracy of the air conditioning data measured with a remote sensing device? ~ Accuracy verification depending on the regression coefficient and determined coefficient-

September 29, 2023

1. At the beginning

Doppler rider (doppler rider () in order to obtain the wind situation of sites that are difficult to observe with observation masts in the wind -style observation aimed at wind development.Doppler LidarThe use of remote sensing equipment represented by) is rapidly expanding. Guidelines, etc. about domestic and overseas style surveys, etc.^1)2)3)4)As an index that quantifies the accuracy of the wind direction and wind speed measured by a remote sensing device, the statistical amount (regression coefficient and determined coefficient) obtained by referring to the wind direction and wind speed measured by the observation mast. Masu. It is known that there are various definitions in regression coefficients and determined coefficients in statistics, but in this paper, guidelines, etc.^1)2)3)4)While referring to, we will explain the statistical quantity used in the wind situation, showing mathematical formulas and specific examples.

2. Fixed wind direction data

The wind direction is as the wind blows,0° from °360Take the value of the range up to °, but if each data is used for accuracy verification, reference datalingering(Example: Observation mast data) and target datay(Example: Doppler riders data)2From the positional relationship on the dimension, the figure1Data that deviates greatly from the straight line y = x as shown inRaw Data) The statistical amount is not calculated correctly because it may be included. So before the accuracy evaluation2Data is straightY = xWe make corrections as shown below as follows.

here,lingeringAnd 𝑦i( =1,2,3,…,N)Shows individual data. figure1As shown in, by fixingRaw DataInstead ofModified DataYou will be able to calculate the wind direction statistics correctly.

figure1Operation of wind direction data

3. Return coefficient and determined coefficient

The wind direction and wind speed of the remote sensing equipment are the data of the observation mastlingering_iDescription variables, data of remote sensing equipmenty_iIs evaluated by linear regression as a purpose variable.

The straight line of the wind direction has a cuty = lingering+bIt is represented as. That regression straight piecebteeth,ROADMAP FOR THE COMMERCIAL ACCEPTANCE OF FLOATING LIDAR TECHNOLOGY¹⁾According to the definition oflingering_iandy_iThe average difference is represented by the following equation.

here,lingering ̅teethlingering _iAverage value,y ̅teethy_iIndicates the average value. Return straight lineaIs a piece of cutbIt can be obtained by the following equation based on the minimum square method.

The regression straight line of the wind speed is represented as 𝑦 = 𝑎'𝑥 without cutting. The tilt of the regression straight line is calculated from the following equation based on the minimum square method.

formula(4)(5)As shown in, the inclination of the recurrent coefficient, which has a cut and none, has different definitions.

Determined coefficientR²How much is the regression straight line, that is, the explanatory variablexThis is an index that describes the purpose of the purpose variable Y.TARALD O. KVALSETH⁵⁾teeth,R²about8Definition (R²₁~R²₈)⁶⁾It is published inR²₁Is shown in the following equation.

here,f_iIs an estimated value due to the regression straight line, if it is a wind directionf_i= lingering_i+bIf it is a wind speedf_i= 𝑎'𝑥_iWill be.R²teeth0from1Take the value betweenR²When = 1,lingering_ibuty_iIs completely explained,lingering_iandy_iIf you draw on a graph, all points will be on a straight line.

4. important point

When calculating statistical volume in practical work, it is a spreadsheet software (Microsoft Excel) And programming languages (Python, RI guess there are many opportunities to use languages. The regression analysis functions implemented in these are very convenient for calculating statistics, but it is necessary to understand and use how the statistics derived from functions are defined. there is.

For example, a regression straight line obtained in spreadsheet software and programming languagesy = lingering+bSince the interface is defined by the next equation based on the minimum square method, the formula is defined by the average difference.(3)It does not match.

AlsoR²The formula is based on the difference between the spreadsheet software and programming language and the presence or absence of cutting.(6)It has been pointed out that the definition is different, specifically,ExcelWith a regression straight line without cuttingR²When calculatingR²₇Is calculated,R²₁It has been confirmed that it will be a larger value compared to⁷⁾⁸⁾。

Therefore, the formula using a spreadsheet software or programming language(4)〜(6)When calculating statistics based on, it is recommended that you build a program that is faithful to the definition using your own functions, etc. instead of regression analysis functions.

5. Concrete example

As a specific example of accuracy verification, Windfarm Certified and Athletics Power Station edition²⁾(below,NKGuidelines) and offshore style observation guidebooks⁴⁾Here are the requirements shown in.

In the NK guidelines, the following conditions(1)(2)It is required to confirm the correlation of observation data by observation mast and remote sensing device.³⁾。

(1) When the observation data from the observation mast and the remote sensing device is treated as an observation data at the hub height, it is used as an airflow analysis input data.

(2) When observing data of the observation mast is used as an input data for airflow analysis, and only for verification of the validity of airflow analysis, observation data with remote sensing devices is used.

table1 Observation mast and remote sensing device correlation between observation data³⁾

Fundamental studies suggest that the accuracy of wind direction and wind speed measured by remote sensing devices on complex terrain such as mountainous areas is more accurate than those measured on flat terrain.⁹⁾¹⁰⁾It is imagined that some cases will not be satisfied with the above requirements (figure).2) If you are not satisfied with the requirements, you need to quantitatively indicate the reasons using the results such as airflow analysis (table)1) In connection with this, there is also a method of correcting the error of the data of remote sensing devices in complex terrain using airflow analysis results.¹¹⁾¹²⁾。

figure2The horizontal axis is a windbound mast, the vertical axis is a vertical rider (vector average) (left) wind direction.(right)Wind speed spray map⁹⁾

Global style observation guidebook⁴⁾Then, the accuracy of wind direction and wind speedKPI（Key Performance Indicator; Important evaluation indicators) and tolerance are defined (table)2) If the error of the wind direction and wind speed measured with a remote sensing device is below the minimum minimum, the measured value must be used as an accuracy equivalent to the observatory mast cup wind speed meter or arrow -shaped wind direction. It is judged that you can. Here, the wind speed range4m/sthat's all16m/sThe reason is that it is less than that of the power generation prediction and the purpose of calculating the wind conditions, because it is determined that the amount of power generation and the load on the load is large.

table2 AccurateKPIAnd tolerance criteria

5. in conclusion

In this paper, we explained the regression coefficient and determined coefficient used to evaluate the air conditioning data measured by remote sensing devices. If you have any questions about technical contents,RTIPlease feel free to contact us.

Reference

CARBON Trust Offshore Wind Accelerator (OWA), Roadmap for the Commercial ACCEPTANCE OF FLOATING LIDAR TECHNOLOGY, 2018, URL:
https://www.carbontrust.com/our-work-and-impact/guides-reports-and-tools/roadmap-for-commercial-acceptance-of-floating-lidar,
access:2023/.
Japan Sea Association, Wind Farm Certificate Land Wind Power Station Edition, 2023,
URL: https://www.classnk.or.jp/hp/pdf/authentication/renewableenergy/ja/windfarm/NKRE-GL-WFC01_March2023_Jpn_20230331.pdf,
access:2023/08/07
Burovolo Veritas Japan, Technical Standards for Confirmation Confirmation Confirmation, 2023, URL:
https://www.bureauveritas.jp/sites/g/files/zypfnx696/files/media/document/windfirm_gijutsukijun_Rev0_0.pdf,
Access: 2023/08/07
New Energy / Industrial Technology Development Organization, Global Wind Statement Observation Guidebook, 2023, URL:
https://www.nedo.go.jp/content/100948288.pdf,
Access: 2023/08/07
Tarald O. KVALSETH, CAUTIONARY NOTE ABOUT R2, The American Statistician Vol.39, No. 4, Part 1 (Nov., 1985), pp.279-285.
University of Tokyo Faculty of Liberal Arts Statistics Class, Introduction to statistics (Basic Statistics II), University of Tokyo Publishing.
Memorandum, RofLMCutting coefficientR^2I tried to plot what the difference between the definition formula is, URL:
https://indenkun.hatenablog.com/entry/2020/03/11/180921,
access:2023/08/07.
Biology Research Institute Iguchi Laboratory, Determined coefficient R²The difference of: Excel, OpenOffice, LibreOffice And statistical analysis software R Using, URL:
https://biolab.sakura.ne.jp/r-squared.html,
access:2023/08/07.
Achievements and issues of wind status observation using Doppler riders in the powerless and complex terrain, Mizuki Mito, Mizuki Kohana, Hideki Kato, Susumu Shimada, Hisori Tanaka, powerless terrain.41Wind energy usage symposium props collection, 2019, pp.199-202.
Toshiari Mito, Shogo Uchiyama, Apparently Apparent, Mizuki Kasei, Kazuhei Ito, Study on observation accuracy of vertical doppler rider in complex terrain (Examination of differences due to average and correction methods), First43Winding energy usage symposium props collection, 2021, pp.184-187.
Meissner, C. and Boquet, m.: Correction of Lidar Remote Measing Measurements by CFD Simulations, in: EWEA 2011, Brussels, 2011.
Kim, H.-G. and Meissner, C.: Correction of Lidar Measurement Error in Complex Terrain by CFD: Case Study of the Yangang Pumped Storage Plant. , 226 --234,
https://doi.org/10.1177/0309524X17709725, 2017.