Nonlinear Dynamics Part 14 potx

Nonlinear Dynamics 318 Pooled Peak Period p=1,q=1 p=1,q=1 Degree of differentiation d m 0.24 0.46 ψ 1 0.66 0.02 AR polynomial coefficients ψ 2 - - θ 1 0.52 0.55 MA polynomial coefficients θ 2 - - θ 3 - θ 4 - θ 5 - Log-likelihood -2622.36 -1079.26 JB Test Null: normality 2.02 1.42 Q 2 (7) Null: serial independence 136.25** 66.18** LM ARCH (1) Null: no ARCH effect 1.41 1.32 * rejection at 5% significance level ** rejection at 1% significance level Table 1. Estimation Results for the ARFIMA(p,d m ,q) models for the Heraklion airport. Pooled Peak Period p=1,q=1 p=1,q=1 Degree of differentiation d m 0.15 0.31 ψ 1 0.66 0.05 AR polynomial coefficients ψ 2 - - θ 1 0.35 0.48 MA polynomial coefficients θ 2 - - θ 3 - θ 4 - θ 5 - Log-likelihood -2588.14 -1002.80 JB Test Null: normality 4.43 1.24 Q 2 (7) Null: serial independence 145.25** 64.54** LM ARCH (1) Null: no ARCH effect 1.65 0.03 * rejection at 5% significance level ** rejection at 1% significance level Table 2. Estimation Results for the ARFIMA(p,d m ,q) models for the Kerkyra airport. Advanced Computational Approaches for Predicting Tourist Arrivals: the Case of Charter Air-Travel 319 Pooled Peak Period p=1,q=1 p=1,q=1 Degree of differentiation d m 0.34 0.37 ψ 1 0.67 0.05 AR polynomial coefficients ψ 2 - - θ 1 0.43 0.58 MA polynomial coefficients θ 2 - - θ 3 - θ 4 - θ 5 - Log-likelihood -2689.31 -1017.48 JB Test Null: normality 3.48 2.48 Q 2 (7) Null: serial independence 122.52** 75.67** LM ARCH (2) Null: no ARCH effect 0.82 0.10 * rejection at 5% significance level ** rejection at 1% significance level Table 3. Estimation Results for the ARFIMA(p,d m ,q) models for Rhodes airport. Specifications DATA TR–CV–TE *: 60%-20%-20% Structure Input layer: Gamma memory (genetically optimized memory depth) 1 hidden layer (genetically optimized number of hidden units h) Learning Back-propagation Chromosome [5,15] , [0.01-0.1], [0.5-0.9], τ [1,5], m [1,12]h γ μ ∈ ∈∈∈∈ ** Fitness function Mean square error (cross-validation set) Selection Roulette Cross-over Two point (p=0.9) Genetic algorithm optimization Mutation Probability p=0.09 * Training - Cross-validation - Testing ** h: neurons in hidden layer, γ: learning rate, μ: momentum, τ: time delay, m:dimension Table 4. Data and neural network specifications for iterative short-term prediction. Pooled NSI Arrivals τ m Heraklion 1 6 Kerkyra 1 4 Rhodes 1 4 Table 5. Estimates of the depth of the Gamma memory (parameters τ and m) of the genetically-optimized TLNNs for the three cases. Nonlinear Dynamics 320 Pooled Data Peak Demand Period GA-TLNN* Heraklion Kerkyra Rhodes 17% 26% 18% 2.8 3.4 3.2 ARFIMA (average over cases tested) 37% 8.2 *genetically optimized TLNN Table 6. Mean Absolute Percent Error of predictions using ARFIMA and genetically optimized TLNN. 0 5 10 15 20 25 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Pasengers Millions Total Arrivals NSI Arrivals SI Arrivals Fig. 1. Yearly evolution of the total arrivals, non-scheduled international arrivals (NSI Arrivals) and scheduled international arrivals (SI Arrivals) for the Greek airports. Advanced Computational Approaches for Predicting Tourist Arrivals: the Case of Charter Air-Travel 321 0 1 1 2 2 3 3 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Passengers Millions NSI Arrivals Total International Arrivals Domestic Arrivals Total Arrivals 0 5 10 15 20 25 30 35 40 45 50 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Flights Thousands NSI Flights International Flights Domestic Flights Total Flights Heraklion (Crete) 0 0 0 1 1 1 1 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Passengers Millions NSI Arrivals Total International Arrivals Domestic Arrivals Total Arrivals 0 2 4 6 8 10 12 14 16 18 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Flights Thousands NSI Flights International Flights Domestic Flights Total Flights Kerkyra 0 1 1 2 2 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Passengers Millions NSI Arrivals Total International Arrivals Domestic Arrivals Total Arrivals 0 5 10 15 20 25 30 35 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Flights Thousands NSI Flights International Flights Domestic Flights Total Flights Rhodes Fig. 2. Evolution of arrivals (passengers per year) and flights per year for the period of 1999- 2006. Nonlinear Dynamics 322 39 8214 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec NSI Arrivals Hundreds 1999 2002 2004 2006 Average of 1999-2006 (%) Heraklion (Crete) 5 1935 0 500 1,000 1,500 2,000 2,500 Jan Feb Mar Apr May Jun Jul Aug Sept Oct N ov Dec NSI Arrivals Hundreds 1999 2002 2004 2006 Average of 1999-2006 (%) Kerkyra 9 2646 0 500 1,000 1,500 2,000 2,500 3,000 3,500 Jan Feb Mar Apr May Jun Jul Aug Sept Oct N ov Dec NSI Arrivals Hundreds 1999 2002 2004 2006 Average of 1999-2006 (%) Rhodes Fig. 3. Monthly variation of non-scheduled international arrivals in Rhodes for the period between 1999 and 2006. Advanced Computational Approaches for Predicting Tourist Arrivals: the Case of Charter Air-Travel 323 R² = 0.7764 -100000 0 100000 200000 300000 400000 500000 0 100000 200000 300000 400000 500000 Preidcted NSI Arrivals NSI Arrivals Heraklion R² = 0.6784 0 50000 100000 150000 200000 250000 0 50000 100000 150000 200000 250000 Preidcted NSI Arrivals NSI Arrivals Kerkyra R² = 0.7894 -100000 -50000 0 50000 100000 150000 200000 250000 300000 350000 0 50000 100000 150000 200000 250000 300000 350000 Preidcted NSI Arrivals NSI Arrivals Rhodes Fig. 4. Scatter plots of actual versus predicted values of NSI arrivals for the three airports. Nonlinear Dynamics 324 0 100 200 300 400 500 600 700 Jul-05 Aug-05 Sep-05 Oct-05 Nov-05 Dec-05 Jan-06 Feb-06 Mar-06 Apr-06 May-06 Jun-06 Jul-06 Aug-06 Sep-06 Oct-06 Nov-06 T h ousan d s NSI Arrivals Predicted NSI Arrivals (TLNN) Predicted NSI Arrivals (ARFIMA) 0 500 1000 1500 2000 2500 3000 Nov-05 Dec-05 Jan-06 Feb-06 Mar-06 NSI Arrivals Predicted NSI Arrivals (TLNN) Predicted NSI Arrivals (ARFIMA) Fig. 5. Predictions using the ARFIMA and genetically optimized TLNN. Results from the three case study airports are aggregated both for ARFIMA and TLNN. 14 A Nonlinear Dynamics Approach for Urban Water Resources Demand Forecasting and Planning Xuehua Zhang, Hongwei Zhang and Baoan Zhang 1 Department of Environmental Economics, Tianjin Polytechnic University 2 School of Environmental Science and Technology, Tianjin University China 1. Introduction Over the past decades, controversial and conflict-laden water allocation issues among competing domestic, industrial and agricultural water use as well as urban environmental flows have raised increasing concerns (Huang & Chang, 2003); Particularly, Such competition has been exacerbated by the growing population, rapidly economic growth, deteriorating quality of water resources, and shrinking water availability due to a number of natural and human-induced impacts. A sounding strategy for water resources allocation and management can help to reduce or avoid the losses which are caused by water resources scarcity. However, in the water management system, many components and their interactions are uncertain. Such uncertainties could be multiplied not only by fasting changes of socioeconomic boundary conditions but also by unpredictable extreme weather events which caused by climate change. Thus, water resources management should be able to deal with all challenges above. Therefore, an effective integrated approach is desired for urban water adaptive management. Many methods, such as stochastic, fuzzy, and interval-parameter programming techniques, have been employed to counteract uncertainties in different fields of water management and have made great progresses in managing uncertainties in model scale. Water resource is an integral part of the socio-economic-environmental (SEE) system, which is a complex system dominated by human. In order to reach a sounding decision, it is necessary for decision- makers to obtain a better understanding of the significant factors that shape the urban and the way the water resources system reacting to certain policy. Therefore, study of sustainable water resource management should be based on general system theory that addresses dynamic interactions amongst the related social-economic, environmental, and institutional factors as well as non-linearity and multi-loop feedbacks. System dynamics (SD) aims at solving of complex systems problems by simulating development trends of the system and identifying the interrelations of each factor in the system. This will help to explore the hidden mechanism and thus improve the performance of the whole system. Hence, after proposed by W. Forrester (Forrester, 1968), SD model has been widely used in global, national, and regional scales for sustainability assessment and system development programme (Meadows 1973; Mashayekhi, 1990; Saeed, 1994). Due to Nonlinear Dynamics 326 the complexity of problems in the water system, the use of dynamic simulation models in water management has a long tradition (Biswas 1976; Roberts et al., 1983; Abbott and Stanley, 1999; Ahmad & Simonovic, 2004). The development journaey of several sections of applying system dynamics as a tool for integrated water management system analysis can be traced as from focusing on water system itself, to having a strong economic examinations on feedback relationships between industry and water availability, and then to having interaction with population growth (Liu et al., 2007). The above development make SD model has the flexibility and capability to support deliberative-analytical processes effectively. Meanwhile, SD and Multi Objective Programme (MOP) integrated model as an extension of the previous SD applications has been presented and used in urban water management in recent years, which takes into account both optimization and simulation (Guo et al, 1999; Zhang & Guo, 2002). This chapter will introduce a nonlinear dynamics approach for urban water resources demand forecasting and planning based on SD-MOP integrated model. 2. Uncertainties in Urban water system 2.1 Urban water system analysis Generally, urban water system could be divided into four subsystems, i.e., social subsystem, economic subsystem, environmental subsystem and water resources subsystem. The relationships and interactions are complicate, as Fig. 1. Fig. 1. Urban water management subsystems and relations 2.2 Uncertainties of urban water management system analysis Urban water resources demand forecasting and planning are two important parts of urban water integrated management. Commonly, integrated water management should provide a framework for integrated decision-making and could be consists of system analysis, action results forecast, planning formulate and implementation, and evaluation and monitoring the goals and effects of implementation. At the system analysis stage, information collection and investigation are the basic work. A system structure is built based on a careful consideration of interactions among factors and subsystems. Long-term and short-term goals, problems, and priority focused will then are identified with both experts and stakeholders take part in. At the forecast stage, simulation model and evaluation model will be set up. Fixing on parameters and variable values of models and listing alternative solutions are the key process of the stage, based on field investigation, literature review and interviews with local stakeholders. Then according to the simulation and evaluation results of the alternatives, the selected solution can be identified and the corresponding desired actions can be determined. Urban flow Consumptio n Labor Environmental capacity Wastewater discharge Production flow Wastewater discharge Municipal flow Water resources subsystem Environmental subsystem Economic subsystem Social subsystem A Nonlinear Dynamics Approach for Urban Water Resources Demand Forecasting and Planning 327 Implementation and re-evaluation can’t be separated completely. Management and re- evaluation is the mechanism that improves management goals and practices constantly. Uncertainties limit the forecasting ability of and thus influence the quality of decision making. They can be categorized into four types : (1) intransience uncertainties caused by fasting changes of urban socioeconomic conditions; (2) external uncertainties caused by the stress of factors beyond the urban boundary (Liu, 2007); (3) uncertainties associated with raw data and model parameters driven from outdated or absent issues news, events, or statistic data; and (4) uncertainties arising from multiple frames (e.g. people’s cognizing/ perceiving technique/ability advance, world and ethical view change) (Jamieson, 1996; Pahl-Wostl, 2009). The above uncertainties are associated with all four stages, the details as Fig. 2. Fig. 2. The uncertainties in urban water management system We can find that all above uncertainties are raised from the cognitive dimension (e.g. limited understanding system behavior and interactions among composing factors, uncertainty from fasting changes of socioeconomic conditions and change of natural conditions) and technical dimension (e. g. outdated or absent issues news/events/data, absent specific to techniques and countermeasures, limited of forecasting method) two aspects. 2.3 Overlook of counteracting measures to water system uncertainties Whether we recognize it or not, socioeconomic laws and the natural laws are located in the objective world. So we can say that uncertainty is raised from the limitations of human cognition. Due to human cognitive abilities change, their understanding of the current world and their forecast of the future world will change over time. Furthermore, SEE system System analysis Forecasting and planning Implement and Re- evaluation Outdated or absent informations Limited understanding system behavior and interactions Absent specific to techniques and countermeasures Limited recognizing priorities focused and ke y p roblems Uncertainty of system structure Uncertainty of and parameter’ and variable’ value Uncertainty of alternative solutions Limitation of forecast methods Uncertainty of forecast results Uncertainty from fasting changes of socioeconomic conditions and natural conditions Uncertainty of selected solution Uncertainty of desired action Uncertainty of available techniques and countermeasures Uncertainty of Implement and re-evaluation results Uncertainty of external driving force (e.g. global change in general and climate change in particular) [...]... 250 2005 2008 2011 2 014 2017 2020 2005 2008 2011 2 014 2017 2020 year b a year 1 water S-B index(/) 1.2 1.2 WP index(/) 1.4 1 0.8 0.6 0.4 optimal original 0.2 0 0.8 0.6 0.4 0.2 optimal original 0 2005 c optimal original 2008 2011 2 014 year 2017 2020 d 2005 2008 2011 2 014 2017 2020 year Fig 7 Main level variable comparing between optimal design and original tendency 340 Nonlinear Dynamics In Fig 7, sub... decreasing the speed of economic development The water resource strategy plan is based on nonlinear dynamics forecasting approach for water resource demand 35 0 SD nonl i ear m hod et 30 0 t r end ext endi ng m hod et 25 0 20 0 15 0 10 0 2005 2004 2003 0 0 2002 5 0 2001 pr edi ct i on er r or ( % ) 5.5 Nonlinear dynamics approach validity test in practice Follow is an example of Qinhuangdao water resource... conclusion : (i) complex system analysis and nonlinear dynamics simulation are very useful for urban water resource demand forecasting and planning, (ii) the integrated model of SD-MOP can avoid the randomness of proposal designed by experiences of planners and decision-makers, which results in the generated planning proposal has high reliability A Nonlinear Dynamics Approach for Urban Water Resources... to the parameter X If there are some departures from the model validity requirement standards, the SD model should be adjusted until fix to the standards Then, SD model could be used in target system behavior simulation 3.3 SD model validity in simulating nonlinear feedback mechanism Although SD equations are linearity, they simulating in computer can describe nonlinear characteristics produced by multi-feedback... (23) 334 Nonlinear Dynamics Ws( t ) = ( 1− 4b + 1)(B-C)+2A ( − 1 + 1 a e 2b 2 b 4b 2 1a 1− 4b )t a (22) 4b − 1)(B-C)+2A ( − 1 + 1 1 − 4b )t ( 1− a + e 2 b 2b a + C 4b 2 1a The equation (22) is the curve of the Water supply capacity From D f ( t ) = bW 's( t ) , then 4b 4b 4b 4b (C-B)+2A(-1+ 1- ) ( − 1 + 1 1- 4b )t (C-B)+2A(1+ 1- ) ( − 1 − 1 a e 2b 2 b a + a a e 2b 2 b Df (t ) = a 4b 4b 4 14 1a a The... was researched by our group during 1998 to 2000 In the plan, we used two methods, nonlinear method and trend extending method, to forecast urban water resources demand Fig 8 shows the comparative errors for forecasting data and actual data between SD nonlinear method and trend extending method From Fig 8, we can know that nonlinear forecasting is more accurate with can give support to water resources... describe nonlinear characteristics produced by multi-feedback when consider temporal dynamic affection 4 Decision-making system based on SD-MOP integrated model for urban water resources demand forecasting and planning From above analysis, we can know that urban water resources demand forecasting is the key procedure of urban water system management In different scenarios, the forecasting A Nonlinear Dynamics. .. Qinhuangdao J Environ Sci, 22, pp 92-97(in Chinese) Zhang Xuehua, Guo Huaichen, Zhang Baoan (2002) Application of System Dynamics- Multi Objedtive Programme integrated model in urban water resources planning of Qinhuangdao.Advance in water seience, 13, pp 351-357(in Chinese) 342 Nonlinear Dynamics Zhang Xuehua, Zhang Hongwei, Zhang Baoan (2010) SD-MOP integrate model and its application in water resources... population subsystem In SD level equation, three time points are denoted as J（past）, K (present), and L (future) The step from J to K is referred to as JK and that from K to L as KL The duration period A Nonlinear Dynamics Approach for Urban Water Resources Demand Forecasting and Planning 329 between successive points is named DT Therefore, a level variable could be referred to as LEVEL.J, LEVEL.K, or LEVEL.L...328 Nonlinear Dynamics is a complexity system reflecting the mutual and complicated functions amongst the internal elements, which can be characterized by the complicated system structure properties far from balance . both for ARFIMA and TLNN. 14 A Nonlinear Dynamics Approach for Urban Water Resources Demand Forecasting and Planning Xuehua Zhang, Hongwei Zhang and Baoan Zhang 1 Department of Environmental. when a b> 4 , 2 14 0 bab −< , then 1,2 114b 1 2b 2b a i λ = −± − The solution of the equation (5) corresponding homogeneous equation is shown as: 1 2b () 1 2 14b 14b (cos sin ) 2b. 1 2b () 1 2 14b 14b (cos sin 2b a 2b a t st WeC tC tC − = −+ −+ (8) W s(0) =B will be into the equation (8). Then, 1 CBC = + , 1 BCC = − From, 1 ' 2b () 2 1 2 2b 114b14b ((B C)cos