Resilience Analysis And Optimal Control Of Complex Water Resources Stochastic Dynamical Systems

As the global economics and society develop rapidly,the interconnections across water,energy,food,and environment systems are increasingly tight,such that the water resources systems have the characteristics of high complexity and strong stochasticity.Because of the intrinsic cascading and bullwhip effects within the Complex,Stochastic,Dynamical,Water Resources Systems(CSDWRS),the uncertainties originated from climate change and human activities may incur the frequent occurrence of unexpected failure,which can induce great damages to the economics and society.Thus,the resilience analysis and optimal control of CSDWRS is urgent for the prevention of system failure and mitigation of involved damages.To solve the “evolution-disruption-control” problems involved in the CSDWRS,this thesis proposes a generic theoretical framework for the resilience analysis applicable to the“simulation-evaluation-optimization” of water resources systems with different complexities,and further applies this framework to three cases:(1)a soil moisture dynamical system(single system),(2)a water supply-environment system(two subsystems),and(3)a water supplypower generation-environment system(multiple subsystems).The main work includes the following five aspects:(1)A generic theoretical framework of resilience analysis is proposed for the CSDWRS,including three parts: stochastic simulation,resilience metrics,and optimal control strategies.First,a generic stochastic dynamical system is adopted to simulate the variation of system state,and further the Fokker-Planck Equation(FPE)is introduced to describe the evolution of the joint probabilistic density function(pdf)of system states.Next,for a single system,the concepts of Engineering(ENG-)and Ecological(ECO-)resilience are re-defined from the perspective of stochastic dynamical systems;for a complex system that consists of multiple subsystems,the propagation matrix,accumulation ratio(AR),risk contribution ratio and system bottleneck are defined for the resilience analysis.Furthermore,the centralized,decentralized,and hybrid control models are established to improve the system resilience and averse the system risk.(2)The resilience analysis for a single water resources system is illustrated by applying the ENG-and ECO resilience metrics to the soil moisture dynamical system in the crop root zone.The ENG-resilience quantifies the recovery rate from a non-stationary to stationary state,which is shown to be a convex function of the stationary expected soil moisture(ESM);the ECO-resilience quantifies the maximum withstandable changes in infiltration condition without undergoing soil moisture regime(SMR)shifts,which is driven to zero when the infiltration condition approaches its thresholds.The regimes shifts are depicted by the phenomena of staganation and hysteresis,both of which are characterized by two distinct thresholds of infiltration condition.This implies that the restoration of the SMR to a better status is more difficult than its degredation,such as the SMR shifts between vegation and desert.(3)The resilience analysis for a water resources system that consists of two subsystems is illustrated by applying the propagation matrix,ARs,risk contribution ratios and system bottleneck to the water supply and environment(WE)systems in the Hehuang Region,China.The propagation matrix can be regulated by human decisions(water delivery rate and biomass harvest rate)and affected by the input stochasticity(variability from streamflow and biomass growth).The abrupt changes in ARs can be characterized by thresholds of human decisions and input stochasticity,which quantifies the maximum withstandable levels of resources utilization rate and system interruption.The bottleneck shift is characterized by another set of thrsholds,which are smaller than those for the abrupt changes of ARs.This implies that the occurrence of bottleneck shift is earlier than that of abrupt changes in ARs.(4)The resilience analysis for a water resources system that consists of multiple subsystems is illustrated by applying ARs,risk contribution ratios,and system bottleneck to the water supply,power generation,and environment(WPE)systems in the Hehuang Region,China.When the involved uncertainties are low,the WPE system can be modelled as deterministic and the coevolution process can be divided into four stages: exploitation,degradation,depression,and recovery;when the involved uncertainties are high,the system can be modelled as stochastic such that the system state can be described as a stationary probabilistic density function(pdf);meanwhile,the responses of ARs to human decisions(water delivery ratio,biomass harvest rate,and etc.)can be superimposed.Further,for the risk contribution ratios,the influences of water delivery ratio,designed capcity of solar power plant,and wealth investigation ratio can be superimposed whereas the influences of other decisions cannot be superimposed.Based on above,the bottleneck shift processes are detected,indicating that water and energy agents are more likely to be the bottleneck at the beginning stage while the society and environment agents are more likely to be the bottleneck at the stationaty stage.(5)Based on above resilience analysis,the optimal control of the CSDWRS is illustrated by applying the centralized,decentralized,and hybrid control models to the WPE system in the Hehuang Region.The objective is to minimize the risks of holistic system or individual agents and also the control cost,and the constraint is the thresholds of system states identified from resilience analysis.Results show that the involved five agents can be classified into two categories: “generous” agents(water,energy,and environment),which are more willing to sacrifice their own security to decrease the risks of other agents;“selfish” agents(society and biology),which are more willing to sacrifice the other agents’ security to decrease their own risks.The hybrid control has higher applicability since it pushes the selfish agents to sacrifice part of their own security for the purpose of reducing the risks of generous agents,such that risks of different agents may be closer to each other.The manager plays a role of adjusting the risk aversion factors of different agents,such that the risks of the most dangerous agents are decreased while the risks of the safest agents are increased.