Furze, j. n., zhu, q. m., hill, j. (2012) 'facilitating description of fuzzy control algorithms...

Facilitating description of fuzzy control algorithms by linking

online models.

James Furze1, Quan Min Zhu1, Feng Qiao2, Jennifer Hill1

1Faculty of Environment and Technology University of the West of England

Frenchay Campus, Coldharbour Lane Bristol, BS16 1QY, UK

2Faculty of Information and Control EngineeringShenyang Jianzhu University

9 Hunnan East Road, Hunnan New DistrictShenyang, 110168, China

Presented in 2012 at 4th International Conference on Modelling, Identification and Control, Wuhan, China June 24-26 ©

Introduction

• What are the variables that we need to model in order to construct algorithms to ordinate the occurrence of plant species?

Energy

Dynamic

300 000+ Plant Species- what are the categories?

• Competitive (C)High potential growth rate, tall stature, vigourous above / below ground

• Stress Tolerant (S)Low growth rate, high storage of minerals (not edible), multilayered canopies

• Ruderal (R)High growth rate, short life, early onset of reproduction, small stature, various canopy forms

• Pure / combined strategies:(C); (C-R); (S); (S-R); (R); (C-S); (C-S-R)

Some examples: Competitive Plant Species

Phalaris arundinacea - Reed Canary Grass

Chamerion angustifolium - Rosebay Willow Herb

Epilobium hirsutum - Great Willow Herb

Petasites hybridus - Butterburr

Urtica dioica - Stinging Nettle

Reynoutria japonica - Japanese Knotweed

Sambucus nigra - Elder

Pinus sylvestris - Scotts Pine

Stress Tolerating Species

• Species shown specific to the stress they tolerate

Koeleria macrantha - Crested Hair Grass (Calcium Rich Soils)

Primula veris - Primula (Calcium Rich Soils)

Juncus squarrosus - Heath Rush (Acidic Soils)

Nardus stricta - Mat Grass (Acidic Soils)

Sedum acre - Biting Stonecrop (Very Dry Habitats)

Thymus praecox - Creeping Thyme (Very Dry Habitats)

Carex panicea - Carnation Sedge (Damp Wetland)

Sucissa pratensis - Devils Bit Scabious (Damp Wetland)

Sanicula europaea - Wood Sanicle (Shaded Habitats)

Viola riviana - Dog Violet (Shaded Habitats)

Minuarta verna - Spring Sandwort (Heavy Metal Contaminated Soils)

Ruderal Species

• The most opportunistic!

Matricaria matricariodes - Pineapple Weed

Polygonum aviculare - Knotgrass

Senecio vulgaris - Groundsel

Stellaria media - Chickweed

Fig. 1. Computer Simulated Competitors, Stress Tolerators, Ruderal Species taken from Bornhofen et al., 2011

Fig. 2. Global Mean Precipitation July 1961-90 (New et al., 1999)Showing the Distribution of Water on a Global Scale

Fig. 3. Global Mean Temperature July 1961-90 (New et al., 1999)Showing the Distribution of Energy on a Global Scale

Fig. 4. Global Ground Frost Frequency July 1961-90Showing a Variable causing Disturbance on a Global Scale

Fig. 5. Fuzzy Logic – defined Union of Singletons (Zadeh, 1973)

U A yyA /)(

Fuzzy singletons are climatic and elevational values

Table 1. Variable partitioning

Objectives• Construct Maps of global locations showing topographical / elevation details

at high resolution scales sourced from publicly accessible files; • Display climatic data using scales of defined resolution; • Implement Fuzzy Algorithms; • Quantify Plant Strategies; • Model Spatial Distribution of Plant Species with climatic and elevation

variables. • Objectives query the distribution of plant strategies amongst more than 300

000 plant species and their individual occurrence.

Fig. 6. Sourcing of elevation data at 1Km resolution from USGS website

Application of Fuzzy Logic – Basic framework of Rule Base

• IF A THEN B • Variables A are climatic or altitude • Consequences B are categorized environments (plant life history

strategies 1- 7 inferred through occurrence of individuals in modelled environments sourced from Global Biodiversity Information Facility (Yesson et al., 2007)

• IF A1(n) – A1(n) AND A2(n) – A2(n) AND A3(n) – A3(n) AND A4(n) – A4(n)

THEN B(n) = E1, …, E7

Fig. 7. Guyana quarterly precipitation 1961-90 mean at 10-minute (18.5km) resolution.

Figure 1 shows example data, where Guyana mean precipitation is 0.75 (January, April, July) 0 – 100 Kg m2 to 200 – 300 Kg m2, and 0.25 (October) 0 – 100 Kg m2 to 300-400 Kg m2. The quantity of precipitation is shown in colours from low (dark blue), to high (dark red). Presented in 2012 at 4th International Conference on Modelling, Identification and Control, Wuhan, China June 24-26 ©

Fig. 8. Guyana digital elevation data / topography at 30-second (1km) resolution.

Figure 2 is a representation of Guyana, situated between latitude 60o – 55o West, longitude 0o-7.5o North with an elevation from 0 – 1500 metres above sea level. Sea level is shown in blue, low elevation is in dark green and low-medium elevation in lighter green to white.

Fig. 9. Fuzzy control algorithm integrating climate variables and digital elevation model data for Guyana

IF Variables A = - Temperature = 80-100 % to 80-100 % (A1(5))- Precipitation = 0.75 x 0-100 Kg m2 (A2(1)) to 200-300 Kg m2 (A2(3)), 0.25 x 0-100 Kg m2 (A2(1)) to 300-400 Kg m2 (A2(4))

- Ground Frost frequency = 0-6 days to 0-6 days (A3(1))- Altitude = -30-1366 m (A4(1)) to 1366-1500 m (A4(2)) THEN B(51847) = E2

Fig. 10. Approximation of Plant Strategy Ordination

Table 2. Categorisation of environments and plant life history strategies

Summary• ‘Real life’ examples of plant strategies were shown• Examples of Computer simulated representations of modelled plant

strategies were shown• Climatic / Elevation (water – energy dynamic) variables sourced online at

increased resolution• Use of fuzzy categorization of singletons to express numerical dispersion

of individual occurrences.• Illustration of graphics / online data display via technical computing

Global locations enhancing climatic prediction• Future work facilitates 13 categories of life-form (growth habit) and

metabolic patterning• Extension to simulation based studies• Formation of novel generational algorithms

References[1] Bamber, J. L., Ekholm, S., Krabill, W. B. (2001). A new, high resolution digital elevation model of Greenland fully validated with laser altimeter data. Journal of Geophysical Research, vol. 106, pp.6733-6745.[2] Barreto, L. S. (2008). The reconciliation of the r-K, and C-S-R-models for life history strategies. Silva Lusitana, vol. 16 (1), pp. 97-103.[3] Barthlott, W., Mutke, J., Rafiqpoor, D., Kier, G., Kreft, H. (2005). Global Centers of Vascular Plant Diversity. Nova Acta Leopoldina NF, vol. 92 (342), pp. 61–83.[4] Bornhofen, S., Barot, S., Lattaud, C. (2011). The evolution of CSR life-history strategies in a plant model with explicit physiology and architecture. Ecological Modelling, vol. 222, pp. 1-10.[5] Craine, J. M. (2005). Reconciling plant strategy theories of Grime and Tilman. J. of Ecology, vol. 93, pp. 1041-1052.[6] Furze, J. N., Zhu, Q. M., Qiao, F., Hill, J. (2011). Species area relations and information rich modelling of plant species variation. Automation and Computing (ICAC), 2011 17th International Conference on, vol., no.,

pp.63-68,10-10 Sept. 2011URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6084902&isnumber=6084889

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521-529.[15] Mitchell, T. D., Jones, P. D. (2005). An improved method of constructing a database of monthly climate observations and associated high resolution grids. Int. J. of Climatology, vol. 25, pp. 693-712.[16] Mustard, J. M., Standing, D. B., Aitkenhead, M. J., Robinson, S., McDonald, J. S. (2003). The emergence of primary strategies in evolving virtual-plant populations. Evolutionary Ecology Research, vol. 5, pp. 1067-

1081.[17] New, M., Hulme, M., Jones, P. (1999). Representing twentieth century space-time climate variability. Part I- Development of a 1961–90 mean monthly terrestrial climatology. J. Climate, vol. 12, pp. 829–856.[18] Pianka, E. (1970). On r and k selection. American Naturalist, vol. 104, pp. 592-597.[19] Raunkier, C. (1934). The Life Forms of Plants and Statistical Plant Geography. Oxford University Press, Oxford.[20] Silvera, K., Santiago, L. S., Cushman, J. C., Winter, K. (2009). Crassulacean acid metabolism and epiphytism linked to adaptive radiations in the orchidaceae. Plant Physiol., vol. 149, pp. 1838-1847.[21] Silvert, W. (2000). Fuzzy indices of environmental conditions. Ecological Modelling, vol.130, pp. 111-119.[22] Sivanandam, S. N. Sumathi, S. Deepa, S. N. (2007). Introduction to fuzzy logic using matlab. Springer-Verlag.[23] Taheriyoun, M. Karamouz, M., Baghvand, A. (2010). Development of an entropy-based fuzzy eutrophication index for reservoir water quality evaluation. Iran. J. Environ. Health. Sci. Eng., vol. 7, (1), pp. 1-14.[24] Trauth, M. H., Gebbers, R., Marwen, N. (2010). MATLAB ® Recipes for Earth Sciences 3rd edition. Springer.[25] URL: http://www.gbif.org[26] URL: http://www.ipcc-data.org[27] URL: http://www.http://eros.usgs.gov/#/Find_Data/Products_and_Data_Available/GTOPO30[28] Yesson, C., Brewer, P. W., Sutton, T., Caithness, N., Pahwa, J. S., Burgess, M., Gray, W. A., White, R. J., Jones, A. C., Bisby, F. A., Culham, A. (2007). How global is the global biodiversity information facility? Plos One,

vol. 11, pp. 1-10.[29] Zadeh, L. S. (1965). Fuzzy sets. Information and Control, vol. 8, pp. 338-353.[30] Zadeh, L. S. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man and Cybernetics, vol. SMC-3 (1), pp. 28-44.Presented in 2012 at 4th International Conference on Modelling, Identification and Control, Wuhan, China June 24-26 ©

Author Contact details:

James. N. FurzeFaculty of Environment and TechnologyUniversity of the West of EnglandFrenchay Campus, Coldharbour Lane,Bristol, BS16 1QY, UK *email: James.Furze@uwe.ac.uk

Paper Reference:

Furze, J. N., Zhu, Q. M., Qiao, F. and Hill, J. (2012) ‘Facilitating description of fuzzy control algorithms to ordinate plant species by linking online models’, Modelling, Identification and Control (ICMIC), 2012 Proceedings of International Conference on, Vol., No., pp. 933-938. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6260180&contentType=Conference+Publications&queryText%3Dfurze

Presented in 2012 at 4th International Conference on Modelling, Identification and Control, Wuhan, China June 24-26 © IEEE

Furze, j. n., zhu, q. m., hill, j. (2012) 'facilitating description of fuzzy control algorithms...

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