Journal of Wind Engineering and Industrial Aerodynamics, 38 (1991) 101-108 101 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

Wind data generator: A knowledge-based expert system

Edmond D.H. Cheng Department of Civil Engineering, University o[ Hawaii at Manoa, Honolulu, HI 96822, USA

Summary

Research was undertaken to improve the methods of utilizing short-term wind records to esti- mate long-term extreme winds for design purposes. Recent approaches to the problem include the Markov models developed at the University of Hawaii for extreme wind simulation applicable to a well behaved climate and to typhoon-prone regions.

Recently, it has been realized that the application of these simulation models, is tedious, pain- staking and time consuming for inexperienced users. Therefore, the current effort is to utilize an expert system shell to facilitate the application of the simulation models in a microcomputer environment. An application of this approach is illustrated.

Notation

m

P~j

PM PM(s,r) R S s

SCR

Vh, Vs V.V +I

state of wind speeds number of states of wind speeds of a data base conditional transition probability Pij of period r in season s a matrix ofpij a matrix ofp~f

number of periods in a day number of seasons in a year a given season of S standard deviation of the inherent sampling error of historical records historical and simulated annual extreme wind speeds hourly wind speeds at hour z and hour z+ 1

1. I n t r o d u c t i o n

Recent efforts have been made to improve the methods of utilizing short- term wind records [ 1-4 ]. The contribution made by research at the University

0167-6105/91/$03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.

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of Hawaii is the development of stochastic simulation models which generate hourly wind data in a well behaved climate and in typhoon-prone regions [5-9].

Recently, it has been realized that application of these simulation models is tedious, painstaking and time consuming for inexperienced users. The purpose of this paper is to demonstrate that a knowledge-based exert system approach can be utilized to facilitate the application of the simulation models developed at the University of Hawaii in a microcomputer environment. A brief descrip- tion of the simulation model is presented in the next section.

2. T h e m o d e l

The simulation model presented here has the capability of generating hourly wind data in a well behaved climate in which hurricanes or typhoons may not be expected to occur, as well as in typhoon-prone regions.

The simulation model consists of three components. The first component is the wind simulator (WSR) which is capable of generating non-storm wind data. The second component is the storm simulator (SSR) which is for simu- lating tropical cyclones or other extratropical winds. The last component is a cyclone occurrence simulation program called the storm occurrence simulator (SOR). Basic elements in simulators WSR, SSR, and SOR are briefly de- scribed as follows.

2.1. Wind simulator (WSR)

2.1.1. State of wind speeds In the simulation process for a given wind site, the first step is to divide the

entire range of observed wind speeds into a finite number of states. This is performed with reference to the probability histogram derived from the ob- served wind data for that site. A computer program called WSTAT was devel- oped for performing this task.

2.1.2. Distribution functions The second basic element involves the wind speed distribution functions, i.e.

the probability density functions (PDF) and the cumulative distribution func- tions (CDF) of wind speeds in various states. In this paper, three types of PDFs are utilized to fit a wind speed histogram: uniform, linear and exponen- tial functions. The exponential PDF is exclusively reserved for the last state in which extreme winds are involved.

2.1.3. Transition probability matrices The transition probability Pij is defined as the probability of a wind speed in

state j which will occur in the next hour, given that a wind speed in state i has

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occurred in this hour. For a wind field of m finite states, Plj is actually a con- ditional transition probability of wind speed V~ going from one state i at hour T to wind speed V~+ 1 of state j at hour T+ 1 or

pii=p(V~+l=jlv,=i) (1)

With m states determined, an m × m transition probability matrix P M can be determined.

If the number of periods in a day and the number of seasons in a year are R and S respectively, then there will be R X S transition probability matrices in the simulation process. A typical transition probability matrix for a given period r and season s can be expressed as

PM(s , r ) = [p~f] (2)

where s= 1,2,...,S, and r= 1,2,...,R. Computer programs called W T P M and WSIM were developed for calculating the P M (s,r), and generating the hourly wind data respectively.

2.2. Storm simulator (SSR) In the SSR, the PDF of storms, collected from historical data at a given site,

is the essential element. Calculations of the storm histogram and the PDFs are performed through a computer subroutine called SSTATE. With this infor- mation, a Monte Carlo method based computer program can be developed for storm simulation.

2.3. Storm occurrence simulator (SOR) In the SOR, the interarrival t ime between occurrences of storms in a strong

wind season is the key element. The CDF of the interarrival times may be expressed by a time dependent shifted exponential function. In addition, the probability distributions of the arrival times of the first and the last storms of each strong wind season and probability distributions of the duration of storm seasons are parameters needed in the SOR.

3. Markov property and stationarity tests

In order to substantiate the major assumptions made earlier, a test must be performed of the Markov property, i.e. the existence of dependency between two adjacent hourly wind speeds. Furthermore, this simulation technique is only applicable to stationary time series; the intended simulation model is a stationary first-order Markov chain. Consequently, a test of stationarity of the historical wind speed times series is necessary prior to acceptance of the sim- ulated results. Anderson and Goodman's method [ 10 ] was used in performing these tests (Section 5).

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4. EXSYS-Profess ional

The simulation model is written in FORTRAN with more than 5000 state- ments. The master program consists of four interactive subprograms, 17 sub- routines and uses mathematical and statistical functions from the Interna- tional Mathematical and Statistical Libraries [11].

It is realized that the application of our simulation models by inexperienced users, is tedious, painstaking and time consuming. Therefore, the current ef- fort is to utilize an expert system shell to facilitate the application of the sim- ulation models in a microcomputer environment. In other words, an expert system shell is used to manipulate the master program in the decision making process on input data and parameter selection, linkage mechanism among in- teractive sub-programs, and smooth execution of information flow. This task can be accomplished by decomposing the master program into a network of external programs (executable version) which will be called by an expert sys- tem shell.

The chosen system is a rule-based system called EXSYS-Professional [12] which is coded in C language. Although this system, like many other PC tools, represents knowledge as IF-THEN rules and uses backward chaining to pro- cess these rules, it is capable of executing external programs and can also pass its results to external programs. Furthermore, the EXSYS-Professional has a convenient command language. This language is utilized to control the direc- tion and flow of our knowledge-based expert system (KBES), while the rules provide the logic, inference and chaining capabilities. The EXSYS-Profes- sional was selected because of these powerful features.

5. Application

A schematic block diagram of the KBES simulation model is illustrated in Fig. 1. This KBES simulation technique is applied to wind data at Taipei sta- tion in Taiwan which is situated in a typhoon-prone region. The second 5-year out of the 22-year (January 1961 to December 1982 ) hourly wind records avail- able at Taipei station were used in the test run. Historical wind data at the Taipei station indicated that more than 80% of the annual extreme wind speeds were attributable to typhoons. Therefore, in this test run, the storm occurrence simulator SOR is developed for tropical cyclone occurrences only (Fig. 2). In this paper, tropical cyclones are classified as tropical storms or typhoons whose maximum sustained 10 min mean surface winds are 15-28 m s-1 or 29 m s- and greater respectively. In this illustration, four periods (1 a.m.-8 a.m., 9 a.m.-noon, 1 p.m.-5 p.m. and 6 p.m.-midnight) in a day and three seasons (December-May, June-August and September-November) in a year were chosen. The periods of the day were decided from the averaged diurnal wind speeds, and the selection of seasons was based on the seasonal variation of wind

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TABLE 1

Results ofMarkov property and stationaritytestin X 2 values for Taipeistation historical wind data 1966-1970

Markov Property Test StationarityTest

Season 1 Season 2 Season 3 Season I Season 2 Season 3

Period 1 6842 2352 3524 1001 447 499 2 2988 1156 1649 991 410 497 3 3443 1384 1913 1159 482 589 4 6234 2488 2906 969 426 578

Degrees of freedom 49 49 49 1624 784 784 Z 2 table 66 66 66 1719 850 850

speeds at Taipei station. Therefore, using eqn. (2), 12 transition probability matrices were generated. The tests of Markov property and stationarity of historical records used in the test run were performed and passed (Table 1 ). The model was executed in a 16 MHz IBM PS2/80 microcomputer. It only took 22 and 25 s to execute WSTAT and WTPM respectively. However, to generate 100 years of hourly wind data from WSIM, 37 min were needed.

It was observed that the annual extremes of the simulated (100-year) as well

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Fig. 3. Type I dmtribution of historical and simulated annual extreme wind speeds, 10 m above ground level, at Taipei station.

T A B L E 2

Estimated annual extreme wind speeds from historical records and from simulation method at Taipei, in meters per second at 10 m above ground level

Data Recurrence Vh SCR V, Vh -- V8 period interval SCR

(years)

1897-1984

1966-1970

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100 29.1 1.9 25 23.9 - 0.07 50 26.3 0.06

100 28.6 0.26

as the historical (1897-1984) hourly wind speeds 17, and Vh, are closely fitted by the Gumbel distribution of extreme values (Fig. 3). Using the Gumbel line obtained from the historical annual extreme wind speeds as the reference, the deviations of simulated 25-year, 50-year or 100-year wind speeds from the ref- erence Gumbel line are less than 0.5ScR (Table 2). ScR is the standard deviation of the inherent sampling error of the historical records [ 13,14]. This result is very encouraging.

6. Conclusion

A KBES simulation model for generating long-term wind data, on the basis of short-term wind records, has been demonstrated. The results obtained from

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the appl ica t ion of this knowledge-based technique are very encouraging. Fur- the r research is needed to generalize the p roposed K B E S Simula t ion model.

A c k n o w l e d g m e n t

Par t ia l suppor t of this s tudy by the Na t iona l Science Founda t ion th rough gran t INT-85-1153 is grateful ly acknowledged.

References

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