Using Probabilistic Finite Automata to Simulate Hourly series of GLOBAL RADIATION.

Mora-LopezM. Sidrach-de-Cardona

Shah JayeshValentino CrespiCS-594

Overview

• Abstract.• Introduction.• Data Set.• Probabilistic Finite Automata.• Global Radiation.• Generalization of Model.• Result.• Conclusion.• Questions, Comments ??????

Abstract

• Model to generate synthetic series of hourly exposure of the Global Radiation.

• Based on Subclass of Probabilistic Finite Automata (PFA) for Variable-length Marcov Process.

• Check “variable memory” of Cloudiness…………

Introduction

• Traditionally, analysis based on stochastic process theory.

• Should eliminate negative values appears in series.• PFA - Mathematical model developed in Artificial

Intelligent and Machine Learning.

Why Machine Learning Model ?

• Useful for studying system in which goal concept presents Probabilistic behavior.

Global Radiation

• http://earthguide.ucsd.edu/earthguide/diagrams/energybalance/index.html

Data Set

Data of hourly exposure series of global radiation were recordedover several years at 9 Spanish metrological station.

Data Set

• Weather characteristics of locations are very different.

• Moderate Atlantic Climate (Oviedo).• Continental Continental Climate (Madrid, Tortosa).• Costal Mediterranean Climate both in winter

and summer(Malaga, Mallorca).

Probabilistic Finite Automata.

• First application used for universal data compression.• Used for, Analysis of biological sequences, for DNA and

proteins.• Analysis of natural languages, handwriting and speech.

Probabilistic Finite Automata.

Probabilistic Finite Automata.

Building PFA for Hourly Global Radiation

• Hourly Clearness index,Kh = Gh/ Gh,0

Where,

Gh Hourly global radiation.

Gh,0 Extraterrestrial hourly global radiation

Building PFA for Hourly Global Radiation

Why Constructed “Artificial”?

• Data from different days linked together.• Last observation of each day is followed by the

first observation of the following day.

Building PFA for Hourly Global Radiation

Numbers of hours ? • Each series (Month) is constant and equal for

all locations.

10 January, February, November, December.

12 March, April, September, October.14 May, Jun, July, August.

• To Discretize the continuous values of clearness index we have only 8 different discrete values.

Building PFA for Hourly Global Radiation

• Relationship between Values of Clearness index and symbol Of alphabet.

• Don’t having uniform interval. • Lower and upper intervals, frequency of values is less

than other intervals.

Algorithm

1. Compute the series of discrete values.2. Initialize the PDF with a node, with label null sequence.3. The set PSS – Possible Subsequence Set – is initialized

with all sequences of order 1. each element in this set corresponds to a sequence of discrete values. Take o =1 as the initial value of the order – that is, the size if subsequence to consider.

4. If there are elements of order o is PSS, pick any of these elements, Y. Using all discrete sequences in the series, compute the frequency of Y. if 4a and 4b are true, then go to 5, else go to 6.

4a the frequency of this sequence is greater than the threshold frequency.

4b for same, the probability of occurrence of the subsequence is not equal to the probability of the subsequence final(Y)xp, that is

Algorithm

(not equal: when the ratio between the probabilities is significantly greater than one; for instance, greater than 1.2).

5. Do5a Add to the PFA a node, labeled Y, and

compute its corresponding probabilities vector. 5b For each amplified sequence, Yxp; if the

probability of this amplified sequence is greater than the threshold probability, then include it in PSS.

6. Remove the analyzed subsequence, Y, from PSS.7. If there are no elements of order o in PSS, add 1 to the

value of o. if o<= N and there are elements of length o is PSS, then go to 4, else stop.

Generating new series of Hourly Global Radiation.

• Generate a synthetic series.• Tested on null hypothesis that the series have same

mean and variance, with significance level 0.05 .• This series, selected as proxy for recorded one, else

generate another synthetic series until we find a synthetic series which rejected the null hypothesis.

• In all cases, less than 10 synthetic series had to be generated.

Generating new series of Hourly Global Radiation.

• For each selected synthetic series, compare cumulative probability distribution function (cpdf) with cpdf of the recorded series.

• Comparison is based on the Kolmogorov-Smirnov two-sample test-statistic, which focus of the absolute value of the maximum difference between two empirical distribution function.

Generalization of the Simulated Model

• To generate a new series of hourly clearness index uses, input data as

• Mean monthly value of the daily clearness index• Cpdf of the recorded month.

• Most of metrological stations, these values are not available and only mean monthly values of the daily global radiation are usually recorded.

• One of the Aim of Paper: To characterize the observed relationship between

the recorded data and parameter used for the proposed model.

Generalization of the Simulated Model

Generalization of the Simulated Model

• Relationship between these two parameters have computed the correlation coefficient between them and proves to be 0.992 .

• Concluded• Mean monthly daily clearness index which is available

can be used in model instead of the mean monthly hourly clearness index.

Result

• List of Test1. Both series have the same mean and variance have

been tested. (with significant level 0.05). 2. Cpdf of the recorded and simulated series have be

compared with Kolmogorov-Smirnov two-sample test statistic with a bootstrap P-value.

Result

• It is observed that 97.8 % of the month it is same.

Result

Result

Result

Result

Result

Conclusion

• Model only use monthly mean value of global radiation and generate following.

• Constructed PFA.• Proposed standard cpdf.• Generate new series of hourly global radiation similar

to real one.

• Conclude that probabilistic Finite Automata can be used to characterize and predict new series of hourly global solar radiation series.

No Questions ???????????

Thank you……