Assessment Methods for Water-Energy-Food Stochastic Systems

Abstract

The present disclosure relates to a method for evaluating a water-energy-food stochastic system. The method includes: constructing a water-energy-food stochastic system under the influence of risk, and constructing a corresponding stochastic differential equation for the water-energy-food stochastic system; using the stochastic differential equation, stochastically simulating multiple state variables in the water-energy-food stochastic system using a stochastic simulation method to obtain instantaneous probabilities and steady-state probabilities; deriving elasticity indicators based on the instantaneous and steady-state probabilities, and evaluating the water-energy-food stochastic system based on the elasticity indicators. According to embodiments of the present disclosure, the accuracy of risk-based assessment and analysis can be improved.

Description

Technical Field

[0001] The present disclosure relates to the technical field of water resource management, and in particular to an evaluation method for a water-energy-food stochastic system. Background Art

[0002] The impacts of low flow and high water temperatures are increasingly embedded in the water-energy-food nexus, making system resilience assessment a new perspective for water resources management. The complexity of the water-energy-food system is reflected in two aspects: first, the random nature of extreme weather and climate conditions in the context of global warming; second, the interconnectedness of the water, energy, and food subsystems, driven by human activities. The rare low flow and high water temperature event in the XX River Basin in the summer of 2022 posed unprecedented challenges to water supply, agricultural production, and energy security. Drought caused lakes to shrink and rivers to dry up, while the accompanying high temperatures increased evapotranspiration from vegetation and water bodies, leading to a sharp decline in water resources. Drought dried up rivers, significantly reducing hydropower generation, while high temperatures triggered a surge in electricity demand, creating an imbalance between electricity supply and demand and leading to an energy crisis. During droughts, irrigation areas could no longer secure water supplies, and high temperatures significantly reduced crop yields, causing agricultural losses. Water, energy, and food crises are closely linked to climate change. Resilience reflects the ability of a system to withstand risks and return to a stable state. Faced with severe threats from extreme climate events such as high temperatures and droughts, climate resilience has become a research focus. Assessing the resilience of the water-energy-food system can improve our understanding of the interconnected and complex water resource system, which is crucial to maintaining the normal state and stable operation of the system.

[0003] However, existing research mainly focuses on the ability of low-dimensional systems to cope with risks, and ignores the transmission and transfer of risks within high-dimensional systems. Summary of the Invention

[0004] In order to solve the above technical problems, the present disclosure provides an evaluation method for a water-energy-food stochastic system.

[0005] In a first aspect, the present disclosure provides an evaluation method for a water-energy-food stochastic system, comprising:

[0006] Constructing a water-energy-food stochastic system under risk influence, and constructing a corresponding stochastic differential equation for the water-energy-food stochastic system;

[0007] Based on the stochastic differential equation, a stochastic simulation method is used to perform stochastic simulation on multiple state variables in the water-energy-food stochastic system to obtain instantaneous probability and steady-state probability;

[0008] A elasticity index is derived according to the instantaneous probability and the steady-state probability, and the water-energy-food stochastic system is evaluated based on the elasticity index.

[0009] In a second aspect, the present disclosure provides an evaluation device for a water-energy-food stochastic system, comprising:

[0010] An equation construction module is used to construct a water-energy-food stochastic system under the influence of risk, and to construct a corresponding stochastic differential equation for the water-energy-food stochastic system;

[0011] A simulation processing module is used to perform random simulation on multiple state variables in the water-energy-food random system based on the stochastic differential equation using a stochastic simulation method to obtain instantaneous probability and steady-state probability;

[0012] A system evaluation module is used to deduce a elasticity index according to the instantaneous probability and the steady-state probability, and to evaluate the water-energy-food stochastic system based on the elasticity index.

[0013] In a third aspect, the present disclosure provides an evaluation device for a water-energy-food random system, comprising:

[0014] processor;

[0015] a memory for storing executable instructions;

[0016] The processor is used to read executable instructions from the memory and execute the executable instructions to implement the evaluation method of the water-energy-food random system of the first aspect.

[0017] In a fourth aspect, the present disclosure provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor implements the evaluation method of the water-energy-food random system of the first aspect.

[0018] The technical solution provided by the embodiments of the present disclosure has the following advantages over the prior art:

[0019] The evaluation method of the water-energy-food random system of the embodiment of the present disclosure can construct a water-energy-food random system under the influence of risks, and construct a corresponding random differential equation for the water-energy-food random system. Then, based on the random differential equation, a random simulation method is used to randomly simulate multiple state variables in the water-energy-food random system to obtain instantaneous probability and steady-state probability. Then, elasticity indicators are deduced based on the instantaneous probability and the steady-state probability, and the water-energy-food random system is evaluated based on the elasticity indicators. Thus, a water-energy-food random system under the influence of risks and a corresponding random differential equation are constructed. By randomly simulating multiple state variables, instantaneous probability and the steady-state probability are obtained, thereby deducing elasticity indicators, and the water-energy-food random system is evaluated in combination with the elasticity indicators, thereby improving the accuracy of evaluation and analysis under the influence of risks. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The above and other features, advantages, and aspects of the various embodiments of the present disclosure will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. Throughout the drawings, the same or similar reference numerals represent the same or similar elements. It should be understood that the drawings are schematic and that the originals and elements are not necessarily drawn to scale.

[0021] Figure 1 A schematic flow chart of an evaluation method for a water-energy-food stochastic system provided in an embodiment of the present disclosure;

[0022] Figure 2 A schematic diagram of the structure of a water-energy-food random system provided by an embodiment of the present disclosure;

[0023] Figure 3 A schematic diagram of the structure of a water-energy-food random system variable provided in an embodiment of the present disclosure;

[0024] Figure 4 A flow chart of another method for evaluating a random water-energy-food system provided by an embodiment of the present disclosure;

[0025] Figure 5 A schematic diagram of the structure of an evaluation device for a water-energy-food random system provided by an embodiment of the present disclosure;

[0026] Figure 6 A schematic diagram of the structure of an evaluation device for a water-energy-food random system provided in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0027] The following describes embodiments of the present disclosure in more detail with reference to the accompanying drawings. Although certain embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be construed as limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are for illustrative purposes only and are not intended to limit the scope of protection of the present disclosure.

[0028] It should be understood that the various steps described in the method embodiments of the present disclosure may be performed in different orders and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present disclosure is not limited in this respect.

[0029] As used herein, the term "including" and its variations are open-ended, i.e., "including but not limited to." The term "based on" means "based, at least in part, on." The term "one embodiment" means "at least one embodiment," the term "another embodiment" means "at least one additional embodiment," and the term "some embodiments" means "at least some embodiments." Other terms are defined in the following description.

[0030] It should be noted that the concepts of "first" and "second" mentioned in this disclosure are only used to distinguish different devices, modules or units, and are not used to limit the order or interdependence of the functions performed by these devices, modules or units.

[0031] It should be noted that the modifications of "one" and "multiple" mentioned in the present disclosure are illustrative rather than restrictive, and those skilled in the art should understand that unless otherwise clearly indicated in the context, they should be understood as "one or more".

[0032] The names of the messages or information exchanged between the multiple devices in the embodiments of the present disclosure are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0033] In order to solve the above problems, the present disclosure provides an evaluation method for a water-energy-food random system. Figures 1-4 The evaluation method of the water-energy-food random system provided by the embodiment of the present disclosure is described in detail.

[0034] Figure 1 A flow chart of an evaluation method for a water-energy-food stochastic system provided by an embodiment of the present disclosure is shown.

[0035] In an embodiment of the present disclosure, the water-energy-food stochastic system evaluation method may be performed by an electronic device, which may include but is not limited to devices such as a computer device, a cloud server, or a cloud server cluster.

[0036] like Figure 1 As shown, the evaluation method of the water-energy-food stochastic system may include the following steps.

[0037] S110. Construct a water-energy-food stochastic system under the influence of risk, and construct a corresponding stochastic differential equation for the water-energy-food stochastic system.

[0038] In an embodiment of the present disclosure, the electronic device can construct a water-energy-food stochastic system under the influence of risk, and construct a corresponding stochastic differential equation for the water-energy-food stochastic system.

[0039] Alternatively, the water-energy-food stochastic system can be used to characterize the complex water resource system in a certain region.

[0040] Alternatively, the stochastic differential equation may be a differential equation containing random terms or random processes, and these random terms may include random parameters, random initial values ​​or random boundary values.

[0041] Specifically, the electronic device can construct a water-energy-food stochastic system under the influence of risk, and construct a corresponding stochastic differential equation for the water-energy-food stochastic system.

[0042] Figure 2 A schematic structural diagram of a water-energy-food random system provided by an embodiment of the present disclosure is shown.

[0043] like Figure 2As shown, electronic devices can construct a stochastic water-energy-food system under risk. This system can be summarized into four main components: the water supply system, the energy system, the food system, and the social system. The XX Economic Belt can be summarized as a virtual reservoir with water storage capacity, storing water resources necessary for human production and life. Water flows through the water supply system to agricultural irrigation and industrial power generation. The water supply system provides water resources for the energy and food systems. Only a small portion of this water is non-consumable, while the majority is consumptive. After use, it carries pollutants and returns to the ecological environment as return water. The energy system primarily considers power plants, including hydropower plants and non-hydropower plants (such as thermal power plants, wind power plants, and photovoltaic power plants). The power generation of hydropower plants is significantly affected by flow, while the power generation of thermal power plants is significantly affected by water temperature. Hydropower plants convert the potential energy of water into electricity and can therefore be summarized as a clustered power plant located in the center of the XX Economic Belt. The water used by hydropower plants is non-consumable, and water used upstream can be reused by downstream users. Some cooling water used in thermal power plants is consumable. Common cooling methods include once-through cooling, recirculating cooling, and air cooling. Once-through cooling is often used in areas with abundant water resources, such as along rivers. Its water intake and withdrawal processes disrupt the natural flow patterns of water sources, emit thermal pollution, and impact aquatic populations. Human activities related to power generation, including reservoir construction and the combustion of fossil fuels, have an impact on the environment. The food system primarily focuses on agricultural and aquatic products. Agricultural production is significantly affected by flow, while aquatic production is significantly affected by water temperature. Agricultural production requires irrigation water, which is supported by freshwater resources provided by rivers, lakes, and underground aquifers. When precipitation decreases in a river basin or drought persists, the flow of the main stream of the XX River decreases, the water level in the two lake basins drops, and small reservoirs in some areas become severely insufficient, leading to reduced grain production. Fisheries rely on water, and water temperature is a key hydrological factor affecting fish survival. When water temperature exceeds critical limits, it can disrupt fish metabolism and, in severe cases, even cause mortality. The social system is closely related to the water-energy-food system. Human policy adjustments such as the construction of cascade reservoirs, low-carbon transformation of thermal power, the xx fishing ban plan, and water diversion for irrigation have affected the water-energy-food nexus.

[0044] S120. Based on the stochastic differential equation, a stochastic simulation method is used to perform stochastic simulation on multiple state variables in the water-energy-food stochastic system to obtain instantaneous probability and steady-state probability.

[0045] In an embodiment of the present disclosure, the electronic device can use a random simulation method to perform random simulation on multiple state variables in the water-energy-food random system based on the stochastic differential equation to obtain instantaneous probability and steady-state probability.

[0046] Alternatively, the stochastic simulation method (Monte Carlo) may be a numerical simulation method that takes probabilistic phenomena as a research object.

[0047] Alternatively, the state variables can be used to describe the complex relationships within the water-energy-food system.

[0048] Optionally, the instantaneous probability may be a probability value representing a probability density function at a specific point.

[0049] Alternatively, the steady-state probability can be the probability distribution of a random variable taking a specific value in a system over a long period of time.

[0050] Specifically, after constructing the stochastic differential equation, the electronic device can use a stochastic simulation method to perform stochastic simulation on multiple state variables in the water-energy-food stochastic system according to the stochastic differential equation to obtain instantaneous probability and steady-state probability.

[0051] S130. Derivation of elasticity indicators based on the instantaneous probability and the steady-state probability, and evaluation of the water-energy-food stochastic system based on the elasticity indicators.

[0052] In an embodiment of the present disclosure, the electronic device can deduce a elasticity index according to the instantaneous probability and the steady-state probability, and evaluate the water-energy-food stochastic system based on the elasticity index.

[0053] Optionally, the elasticity index may be a pre-set index for evaluation.

[0054] Specifically, after obtaining the instantaneous probability and the steady-state probability, the electronic device can deduce a elasticity index according to the instantaneous probability and the steady-state probability, and evaluate the water-energy-food stochastic system based on the elasticity index.

[0055] Therefore, in the embodiment of the present disclosure, a water-energy-food random system under the influence of risk can be constructed, and a corresponding random differential equation can be constructed for the water-energy-food random system. Then, based on the random differential equation, a random simulation method is used to randomly simulate multiple state variables in the water-energy-food random system to obtain instantaneous probability and steady-state probability. Then, elasticity indicators are deduced based on the instantaneous probability and the steady-state probability, and the water-energy-food random system is evaluated based on the elasticity indicator. Thus, a water-energy-food random system under the influence of risk and a corresponding random differential equation are constructed. By randomly simulating multiple state variables, instantaneous probability and the steady-state probability are obtained, thereby deducing elasticity indicators, and the water-energy-food random system is evaluated in combination with the elasticity indicator, thereby improving the accuracy of evaluation and analysis under the influence of risk.

[0056] Optionally, the multiple state variables introduced into the water-energy-food stochastic system to describe the complex relationships within the water-energy-food system may include water resources, per capita water consumption, per capita electricity generation, per capita food production, population and climate risks.

[0057] Optionally, multiple auxiliary variables introduced into the water-energy-food stochastic system to describe regional socio-economic conditions may include regional GDP, technological level, and total wastewater discharge.

[0058] Optionally, multiple intermediate variables introduced into the water-energy-food stochastic system to describe the connection between the water-energy-food system and socio-economic conditions may include flow, water temperature, inflow, outflow, rainfall, evapotranspiration, hydropower generation, thermal power generation, agricultural product output and aquatic product output.

[0059] Figure 3 A schematic diagram of the structure of a water-energy-food random system variable provided by an embodiment of the present disclosure is shown.

[0060] like Figure 3 As shown in Figure 2, in order to describe the complex relationship within the water-energy-food system in the study area, six state variables are introduced, such as Figure 3 The middle rectangle includes: water resources (S), which represents the amount of water resources stored in the xx economic zone; per capita water consumption (W), which represents the per capita water consumption intensity of the water supply system, separating the impact of total water consumption and population; per capita electricity generation (E), which represents the per capita power supply level of the energy system, separating the impact of total power generation of hydropower plants and thermal power plants and population; per capita food supply (F), which represents the per capita food supply level of the food system, separating the impact of total output of agricultural products and aquatic products and population; population (N), which represents the scale of human society in the region; climate risk (A), which represents climate disasters that can be perceived by human society and may cause system collapse. The research focuses on the threats of extreme events such as low flow and high water temperature.

[0061] In order to describe the socio-economic conditions of the study area, three auxiliary variables are introduced, such as Figure 3 The circle in the figure includes: gross regional product (G), which represents the total benefits obtained from the energy and food systems and can be estimated through market water prices; technological level (K), which represents the ability of mankind to control and repair the natural environment, scientific and technological research and development, and technological innovation; total wastewater discharge (C), which represents pollutants discharged into the ecosystem, which will affect regional water quality and disrupt the survival of plants and animals.

[0062] In order to describe the connection between the water-energy-food system and socioeconomic conditions in the study area, 10 intermediate variables were introduced, such as Figure 3The hexagons in the diagram include: the flow (Q) and water temperature (T) at a certain station, which, as environmental variables, can describe the hydrological conditions of the xx economic zone; the inflow (I), outflow (O), rainfall (P) and evapotranspiration (ET), which can describe the storage capacity of water resources in the xx economic zone; and the hydropower generation (Eq), thermal power generation (Et), agricultural product output (Fq) and aquatic product output (Ft), which can describe the impact of environmental variables on the energy and food systems.

[0063] Figure 3 The interactive diagram of the water-energy-food system under the influence of risks is displayed, including positive feedback and negative feedback paths. The energy and food systems play similar roles: on the one hand, human society invests water resources for electricity production and food output, creating more resources to accumulate wealth and increasing regional GDP; the accumulation of wealth can encourage scientific and technological workers to invest more funds in education, research and other fields, thereby promoting the improvement of scientific and technological levels; the continuous improvement of technological levels, such as the increase in the proportion of wind and solar power generation and water-saving irrigation, will promote the development of energy and food systems in a better direction, forming a positive feedback path. On the other hand, the accumulation of wealth can promote regional economic development and promote the continuous growth of population; the increase in population stimulates the level of local water resource exploitation, resulting in a lack of sufficient water resources in the energy and food systems, thereby inhibiting the development of energy and food systems; the scale of low flow and high water temperature extreme events under the climate crisis continues to escalate, and climate risks pose a serious threat to the security of energy and food systems, forming a negative feedback path. Similarly, it can be explained from the perspective of feedback paths. Figure 3 The changes of other variables in .

[0064] Optionally, the stochastic differential equations include a hydrological equation, an energy equation, a food equation, a water use equation, a population equation, and a climate risk equation.

[0065] Optionally, S110 may specifically include: determining an ordinary differential equation of the water-energy-food stochastic system; introducing Gaussian white noise of risk impact into the ordinary differential equation to construct the stochastic differential equation.

[0066] In an embodiment of the present disclosure, the electronic device may determine the ordinary differential equation of the water-energy-food stochastic system.

[0067] Among them, the ordinary differential equation corresponding to the deterministic dynamic model can be:

[0068]

[0069] Here, x is a multidimensional state variable that evolves over time t (for example, per capita water supply, per capita electricity generation, and population). The parameter λ is a multidimensional vector that describes the deterministic changes in the system (for example, population growth rate and technology wealth ratio are used as economic and social parameters, respectively). The function f(·) is a multidimensional matrix that describes the dynamic evolution law of the system. Here, x, λ, and f(·) are all multidimensional, that is, x = (x1, x2, …, x n ) T ∈R n ,λ∈R s and f:R n ×R s →R n , n is the number of variables, and s is the number of parameters.

[0070] Furthermore, the electronic device may introduce Gaussian white noise of risk influence into the ordinary differential equation to construct the stochastic differential equation.

[0071] Specifically, the above ordinary differential equation ignores the external interference that the system may suffer. This interference can be understood as randomness. The electronic device can introduce Gaussian white noise of risk influence as randomness into the ordinary differential equation to construct the stochastic differential equation.

[0072] Among them, the Ito integral form of the stochastic differential equation is:

[0073] dX t =f(X t )dt+g(X t )·dW t ,X(0)=X0;0≤t≤T (2).

[0074] Where X is a multidimensional random variable that evolves over time t. Parameter r is a multidimensional vector that describes the random disturbance to the system (the impact of climate risk events). The larger r is, the greater the random disturbance is. t is Gaussian white noise, which can be understood as the formal derivative of the Wiener process.

[0075] Gaussian white noise can simply and effectively describe the random interference to the system. The function f(·) is a multidimensional matrix that describes the dynamic evolution of the system. The function g(·) is also a multidimensional matrix that describes the magnitude of the interference to the system. Similar to the deterministic dynamic equation, r, W, and g(·) are all multidimensional, that is, r∈R 1 , W∈R n and g:R n ×R s →R n 1 is the number of parameters. The symbol “·” indicates that the equation is solved using the Ito integral form. t. X(0)=X0 is the initial condition, and [0,T] is the time interval.

[0076] It should be noted that when g(·)=c, that is, g(·) is a constant, the random term is simplified to additive noise; when g(X t ; r) = R·X t , that is, when g(·) is not a constant, the random term is represented by multiplicative noise. R is a diagonal matrix, and the diagonal elements satisfy the condition R ii =r i Both additive and multiplicative noise can be used to describe random processes. Generally speaking, multiplicative noise is more widely used in population dynamics, biological processes, and environmental systems, especially when the system is subject to external environmental disturbances. Therefore, this study chose multiplicative noise to explain sudden climate risk events.

[0077] It is worth noting that deterministic variables are generally represented by lowercase letters (for example, x), while random variables are usually represented by uppercase letters (for example, X). Deterministic variables are described by ordinary differential equations, usually in the form of derivatives, that is, Random variables are described by stochastic differential equations, which are generally expressed in the form of differentials, i.e. dX t =….

[0078] The Euler-Maruyama algorithm (EM) is a numerical method for solving stochastic differential equations. It is a generalization of the Euler algorithm, which is only suitable for solving ordinary differential equations. To apply the EM algorithm to equation (2), we first discretize the interval Δt = T / L, where L is an integer. The recursive formula of the equation is as follows:

[0079]

[0080] Δt=Rδt (4).

[0081] Among them, the time step Δt is an integer multiple R of the Wiener process step δt. i -W i-1 is the variation of the Wiener process, and the formula is as follows:

[0082]

[0083] Where ΔW j Is of the form The independent random variables are: -8 , R=4.

[0084] Optionally, when constructing a water-energy-food stochastic system under risk influence, it includes: describing the mutual relationships, using stochastic differential equations to describe the uncertainties outside the system and the linkages within the system; determining the constitutive relationships, and estimating the socioeconomic relationships, driving functions and basic parameters in the stochastic differential equations through actual data.

[0085] In some embodiments of the present disclosure, six stochastic differential equations are used to describe the interrelationships of the water-energy-food stochastic dynamic system, respectively characterizing the evolution of water resources (S), per capita electricity generation (E), per capita food production (F), per capita water consumption (W), population (N) and climate risk (A).

[0086] The hydrological equation describes the dynamic balance of water resources (S) in the XX Economic Zone. Water resources are replenished by precipitation and inflow, with most returning to the atmosphere through evapotranspiration. A small amount is consumed by agriculture, industry, and domestic use, and ultimately discharged to downstream areas and estuaries as outflow. Specifically, it can be expressed as:

[0087] dS=[I+P-ET-O-WN·10 -4 ]·dt+r S S·dW s (6).

[0088] Where I is the inflow; P is precipitation; ET is soil evaporation and vegetation transpiration; O is the outflow, which is linearly related to the inflow I according to the linear reservoir assumption, with a linear coefficient of 1.5; WN is the product of per capita water consumption (W) and population (N), representing the total amount of consumable water used for residential life, industrial and agricultural production.

[0089] Per capita electricity generation and per capita food production are closely related to water resources. * It is a standardized value that stimulates humans to use water resources for production and life, which can be expressed as:

[0090]

[0091] Among them, S * The amount of water resources is lower than the critical value S crit The critical water resource level is the maximum level of water resources that stimulates human use for production and life. When water resources fall below the critical water level, water resources are insufficient, and irrigation and power generation are restricted. In this case, an increase in water resources will promote an increase in food production and power generation. When water resources are above the critical water level, water resources are sufficient, and food production and power generation are not affected.

[0092] The energy equation describes the dynamic changes in per capita electricity generation (E). Increased water resources and improved technology have a positive impact on the growth of per capita electricity generation. The study considers hydropower generation and thermal power generation. Since hydropower generation is affected by flow and thermal power generation is affected by water temperature, per capita electricity generation will be affected by climate risk. Increased climate risk has a negative inhibitory effect on the growth of per capita electricity generation. The energy equation can be specifically expressed as:

[0093] dE=[e S (S * )+e K (K)+e A (A * )]·dt+r e E·dW e (8).

[0094] Among them, S * is the standardized value below the critical value of water resources; K is the level of science and technology; A * It is a normalized value above the climate risk threshold. When the amount of water resources is below the threshold S crit When water resources are insufficient, water for power generation is restricted. The per capita power generation will increase with the increase of water resources. This kind of impact is represented by the driving function e S (S * ). The improvement of scientific and technological level, for example, increasing the proportion of wind and solar power generation, will promote the increase of per capita power generation. This kind of impact is represented by the driving function e K (K) indicates that with climate change, the extreme risk of low flow and high water temperature will increase. Drought will reduce river flow, which is not conducive to hydropower production; high temperature will increase river water temperature, reducing the power generation efficiency of thermal power plants. In general, only when the climate risk is higher than the critical value A crit The impact of climate on the energy system will only appear when the climate changes. This impact is driven by the driving function e A (A * )express.

[0095] The food equation describes the dynamic changes in per capita food production (F). Increased water resources and improved technology have a positive impact on the growth of per capita food production. The study considers agricultural and aquatic product output. Since agricultural product output is affected by flow and aquatic product output is affected by water temperature, per capita food production is affected by climate risk. Increased climate risk has a negative inhibitory effect on per capita food production growth. The food equation can be expressed as:

[0096] dF=[f S (S * )+f K (K)+f A (A *)]·dt+r f F·dW f (9).

[0097] Among them, S * is the standardized value below the critical value of water resources; K is the level of science and technology; A * It is a normalized value above the climate risk threshold. When the amount of water resources is below the threshold S crit When water resources are insufficient and irrigation water is restricted, per capita grain production will increase with the increase of water resources. This type of impact is represented by the driving function e S (S * ). The improvement of scientific and technological level, for example, increasing the proportion of water-saving irrigation, will promote the increase of per capita food production. This kind of impact is represented by the driving function e K (K) indicates that with climate change, the extreme risk of low flow and high water temperature will increase. Drought will reduce river flow, which is not conducive to food production; high temperature will increase river water temperature, affecting the growth and reproduction of aquatic organisms. In general, only when the climate risk is higher than the critical value A crit The impact of climate on the food system will only appear when the climate changes, and this impact is driven by the driving function e A (A * )express.

[0098] The water use equation describes the dynamic changes in per capita water consumption (W). Advances in science and technology have a negative inhibitory effect on the growth of per capita water consumption. Increases in per capita electricity generation and per capita grain production will increase the development and utilization of water resources, positively promoting the growth of per capita water consumption. Per capita water consumption can be specifically expressed as:

[0099] dW=[w K (K)+w E (E)+w F (F)]·dt+r w W·dW w (10).

[0100] Among them, K is the level of science and technology; E is the average power generation; F is the average grain production per capita. The positive effects of average power generation and average grain production on average water consumption are respectively represented by the driving function w E (E) and w F (F) indicates that the improvement of scientific and technological level can improve the efficiency of human use of water resources and curb the growth of per capita water consumption. This kind of impact is represented by the driving function w K(K) stated that technological progress has a wide-ranging impact on water use. On the one hand, improvements in water efficiency and wastewater purification and treatment can reduce water consumption. On the other hand, mechanization will promote the development of industrial and agricultural activities, further increasing water consumption. Overall, the increase in water use caused by intensified human activities far exceeds the water savings from wastewater treatment and improved water efficiency. Therefore, the study assumes that technological progress will significantly reduce per capita water consumption.

[0101] The population equation describes the dynamics of the population (N) in the xx economic zone. In the classic logistic model, the total population tends to approach the capacity of the environment. Population growth is determined not only by the natural growth rate but also by economic and environmental factors. Integrating these two influences into the logistic model yields the following:

[0102]

[0103] Among them, G is the gross regional product; C is the total amount of wastewater discharged; N max is the environmental carrying capacity of the population of the xx economic zone. The regional GDP will stimulate population growth, which is determined by the driving function n G (G) represents the total amount of wastewater discharge, which limits the growth of population, and is represented by the driving function n C (C) indicates.

[0104] The climate risk equation describes the dynamic changes of low flow-high water temperature risk (A), which can be expressed as:

[0105] dA=k a A·dt+r a A·dW a (7).

[0106] Among them, k a is the growth rate of climate risk, which can be calculated using formulas (8)-(12).

[0107]

[0108] Among them, Q obs and T obs are the multi-year average flow and multi-year average water temperature observed at a certain station from 20yy to 20yy; k q and k t Q is the flow rate change slope and water temperature change slope obtained by performing MK trend analysis on the flow rate and water temperature of a station under the RCP4.5 scenario; crit and T critare the thresholds calculated based on the flow rate and water temperature at a certain station. The threshold can be understood as the sum of the mean term and the trend term. The threshold will change over time. When the flow rate (or water temperature) has an upward (or downward) trend, the flow rate (or water temperature) threshold will also increase (or decrease) accordingly.

[0109]

[0110] Among them, A q The risk of low flow is only when the flow Q is less than the threshold Q crit , it will be triggered, otherwise the risk of low flow is 0; similarly, A t The risk of high water temperature is only when the water temperature T is higher than the threshold T crit It will be triggered only when the water temperature reaches 0. q and r t are the noise intensities of flow and water temperature, respectively, which represent the uncertainty of flow and water temperature changes and can be obtained by calculating the ratio of the standard deviation and mean of flow and water temperature observed at a certain station from 20yy to 20yy.

[0111]

[0112] Among them, k a is the growth rate of climate risk; a is the climate attenuation factor. When a low flow-high water temperature extreme event occurs, the growth rate of climate risk increases with the low flow risk A. q and high water temperature risk A t When there is no low flow-high water temperature extreme event, the growth rate of climate risk is a fixed negative value (i.e., ζ a ), indicating that climate risk is decreasing.

[0113] Among them, A * Is above the climate risk threshold A crit The standardized value of crit The impact of climate change on energy and food systems will only become apparent when the

[0114] The constitutive relationship refers to the transformation relationship between the internal variables of the water-energy-food stochastic dynamic system of the xx economic zone, which can reflect the long-term evolution characteristics of the system. The constitutive relationship determines the evolution direction of the water-energy-food stochastic dynamic system and can be fitted and estimated using historical observation data. The study divides the constitutive relationship into two categories: (1) social-economic relationship, which describes the mutual transformation relationship between various economic and social elements in the xx economic zone; (2) driving function relationship, which characterizes the driving or inhibitory effect of economic and social elements or auxiliary variables on state variables. Finally, the basic parameters in the stochastic differential equation are estimated using actual data.

[0115] Socioeconomic relationships are the transformational relationships between basic economic and social elements and state variables, or between economic and social elements themselves. They can be reasonably estimated using measured data. The socioeconomic relationships of the water-energy-food stochastic dynamic system are represented by three descriptive equations, corresponding to the dynamic changes in three auxiliary variables: gross regional product (G), technological level (K), and total wastewater discharge (C).

[0116]

[0117] Among them, G * is the standardized regional GDP; the regional GDP (G) can be expressed as a function of per capita water consumption (W) and population (N). An increase in any of these two variables will lead to an increase in the regional GDP.

[0118]

[0119] Among them, K * It is the standardized scientific and technological level; the scientific and technological level (K) is determined by the economic investment in technological development. The larger the regional GDP (G), the higher the scientific and technological level.

[0120]

[0121] Among them, C * is the standardized total wastewater discharge; total wastewater discharge (C) can be expressed as a function of per capita water consumption (W), population (N), and technological level (K). Total wastewater discharge is influenced by two factors: first, pollutants generated by food and energy systems increase total wastewater discharge with increases in per capita water consumption and population size; second, continuous advancements in technology significantly enhance pollutant treatment capacity and reduce pollution levels, resulting in a decreasing trend in total wastewater discharge.

[0122] The steps for deriving the driving function are summarized as follows: First, calculate the total growth rate TR (X i ); Secondly, according to the weight coefficient w i,j (d i,j 0 distributes the total growth rate to different driving factors d i,j The weight of the driving factor can be determined based on measured data and expert experience. i For example, if the total growth rate is TR(X i ), then the driving factor d i,j The state variable X caused by i The growth rate can be expressed as:

[0123]

[0124] Among them, Λ i,j (d i,j ) is the sign function, reflecting the driving factor d i,j For the state variable X i The promoting (or inhibiting) effect of i,j (d i,j ) is the weight function, reflecting the driving factor d i,j For the state variable X i The weight of the total growth rate. Note that the sum of the weights of all driving factors is 1; v i,j (d i,j ) is a scaling function that can convert the driving factor d i,j The range of variation is scaled to [0,1]; n is the number of driving factors. Usually, the total growth rate TR (X i ) will change over time, which invisibly increases the difficulty of modeling. Therefore, to simplify the model, this study uses the multi-year average of the growth rate to characterize the evolution trajectory of the water-energy-food stochastic dynamic system.

[0125] The study sets the observation data of each state variable and auxiliary variable in 20yy as the initial value of the stochastic differential equation. In order to explore the full state space of the system, the initial value of the system should be randomly distributed, so the initial value of the variable can be expressed as:

[0126] X0=X obs ·(1+r·ξ) (21).

[0127] Among them, X0 is a vector composed of the initial values ​​of each variable. obs is the actual observed value of each variable in 20yy; ξ is a randomly generated Gaussian white noise with mean 0 and variance 1; r is the scaling factor of the noise intensity.

[0128] Optionally, S130 may specifically include: calculating the Euclidean norm between the instantaneous probability and the steady-state probability; and when the Euclidean norm approaches zero, deriving the elasticity index through the steady-state probability density and the probability potential function.

[0129] In the embodiment of the present disclosure, the electronic device may calculate the Euclidean norm between the instantaneous probability and the steady-state probability.

[0130] Specifically, a discrete Wiener process is randomly generated to simulate the Gaussian white noise that affects the state variables; the EM algorithm is used to derive the numerical solutions of the six stochastic differential equations. It should be noted that once the discrete Wiener process is given at the same time, a simulation of the system is achieved. In order to obtain reliable numerical results, this step is repeated many times, and the kernel density estimation method is used to simulate the instantaneous and steady-state probabilities; the Euclidean norm (L2 norm) between the instantaneous and steady-state probabilities is calculated. When the L2 norm tends to zero, the system is usually considered to have reached a stable state. The L2 norm of the random variable at each time cutoff is defined as follows:

[0131] ‖X‖2=(|X1| 2 +|X2| 2 +|X3| 2 +…+|X n | 2 ) 1 / 2 (28).

[0132] Where X represents a random variable, n represents the number of discrete simulated values ​​of the random variable, and ‖X‖2 represents the L2 norm of the random variable, which is obtained by taking the square root of the sum of the squares of the elements that make up the random variable.

[0133] X n =p s (x n )-p(x n ,t) (29).

[0134] Among them, X n Indicates p s (x n ) and p(x n ,t). X n It should tend to zero as time goes by. s (x n ) represents the steady-state probability density, p(x n ,t) represents the instantaneous probability density.

[0135] Figure 4 A flow chart of another water-energy-food random system evaluation method provided by an embodiment of the present disclosure is shown.

[0136] like Figure 4As shown, the electronic device can construct a water-energy-food stochastic system under risk influence and construct a corresponding stochastic differential equation for the water-energy-food stochastic system, that is, determining the ordinary differential equation of the water-energy-food stochastic system. Gaussian white noise influenced by risk is introduced into the ordinary differential equation to construct the stochastic differential equation. Based on the stochastic differential equation, a stochastic simulation method (Monte Carlo) is then used to perform stochastic simulation of multiple state variables in the water-energy-food stochastic system, obtaining instantaneous probabilities and steady-state probabilities. Finally, a resilience index is derived based on the instantaneous and steady-state probabilities, namely, the Euclidean norm (L2 norm) between the instantaneous and steady-state probabilities is calculated. When the Euclidean norm approaches zero, the resilience index is derived using the steady-state probability density and probability potential function, and the water-energy-food stochastic system is evaluated based on the resilience index.

[0137] Figure 5 A schematic structural diagram of an evaluation device for a water-energy-food random system provided by an embodiment of the present disclosure is shown.

[0138] like Figure 5 As shown, the evaluation device 500 for the water-energy-food stochastic system may include an equation building module 510 , a simulation processing module 520 and a system evaluation module 530 .

[0139] The equation construction module 510 can be used to construct a water-energy-food stochastic system under risk influence, and construct a corresponding stochastic differential equation for the water-energy-food stochastic system.

[0140] The simulation processing module 520 can be used to perform random simulation on multiple state variables in the water-energy-food random system based on the stochastic differential equation using a random simulation method to obtain instantaneous probability and steady-state probability.

[0141] The system evaluation module 530 can be used to derive a resilience index according to the instantaneous probability and the steady-state probability, and evaluate the water-energy-food stochastic system based on the resilience index.

[0142] Therefore, in the embodiment of the present disclosure, a water-energy-food random system under the influence of risk can be constructed, and a corresponding random differential equation can be constructed for the water-energy-food random system. Then, based on the random differential equation, a random simulation method is used to randomly simulate multiple state variables in the water-energy-food random system to obtain instantaneous probability and steady-state probability. Then, elasticity indicators are deduced based on the instantaneous probability and the steady-state probability, and the water-energy-food random system is evaluated based on the elasticity indicator. Thus, a water-energy-food random system under the influence of risk and a corresponding random differential equation are constructed. By randomly simulating multiple state variables, instantaneous probability and the steady-state probability are obtained, thereby deducing elasticity indicators, and the water-energy-food random system is evaluated in combination with the elasticity indicator, thereby improving the accuracy of evaluation and analysis under the influence of risk.

[0143] In some embodiments of the present disclosure, the multiple state variables in the water-energy-food stochastic system include water resources, per capita water consumption, per capita power generation, per capita food production, population and climate risk.

[0144] In some embodiments of the present disclosure, the stochastic differential equations include hydrological equations, energy equations, food equations, water use equations, population equations, and climate risk equations.

[0145] In some embodiments of the present disclosure, the equation construction module 510 may specifically include an equation determination unit and an equation construction unit.

[0146] The equation determination unit can be used to determine the ordinary differential equation of the water-energy-food stochastic system.

[0147] The equation construction unit can be used to introduce Gaussian white noise of risk influence into the ordinary differential equation to construct the stochastic differential equation.

[0148] In some embodiments of the present disclosure, the system evaluation module 530 may specifically include a data calculation unit and an indicator derivation unit.

[0149] The data calculation unit may be configured to calculate a Euclidean norm between the instantaneous probability and the steady-state probability.

[0150] The index derivation unit can be used to derive the elasticity index through steady-state probability density and probability potential function when the Euclidean norm tends to zero.

[0151] It should be noted that Figure 5 The water-energy-food random system evaluation device 500 shown can perform Figures 1-4 The various steps in the method embodiment shown are implemented Figures 1-4The various processes and effects in the illustrated method embodiment are not described in detail here.

[0152] Figure 6 A schematic structural diagram of an evaluation device for a water-energy-food random system provided by an embodiment of the present disclosure is shown.

[0153] In some embodiments of the present disclosure, Figure 6 The evaluation device of the water-energy-food random system shown can be an electronic device. Specifically, the electronic device can include but is not limited to devices such as computer devices, cloud servers or cloud server clusters.

[0154] like Figure 6 As shown, the evaluation device for the water-energy-food random system may include a processor 601 and a memory 602 storing computer program instructions.

[0155] Specifically, the processor 601 may include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or may be configured to implement one or more integrated circuits of the embodiments of the present application.

[0156] Memory 602 may include a large-capacity memory for information or instructions. By way of example, and not limitation, memory 602 may include a hard disk drive (HDD), a floppy disk drive, flash memory, an optical disk, a magneto-optical disk, magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 602 may include removable or non-removable (or fixed) media. Where appropriate, memory 602 may be internal or external to the integrated gateway device. In certain embodiments, memory 602 is non-volatile solid-state memory. In certain embodiments, memory 602 includes read-only memory (ROM). Where appropriate, the ROM may be mask-programmed ROM, programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable PROM (EEPROM), electrically alterable ROM (EAROM), or flash memory, or a combination of two or more of these.

[0157] The processor 601 reads and executes the computer program instructions stored in the memory 602 to perform the steps of the water-energy-food random system evaluation method provided by the embodiment of the present disclosure.

[0158] In one example, the evaluation device of the water-energy-food random system may further include a transceiver 603 and a bus 604. Figure 6 As shown, the processor 601 , the memory 602 and the transceiver 603 are connected via a bus 604 and communicate with each other.

[0159] The bus 604 includes hardware, software, or both. By way of example and not limitation, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a Hyper Transport (HT) interconnect, an Industrial Standard Architecture (ISA) bus, an InfiniBand interconnect, a Low Pin Count (LPC) bus, a memory bus, a MicroChannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local Bus (VLB) bus, or other suitable buses, or a combination of two or more of these. Where appropriate, the bus 604 may include one or more buses. Although embodiments herein describe and illustrate a particular bus, this application contemplates any suitable bus or interconnect.

[0160] The embodiments of the present disclosure also provide a computer-readable storage medium, which can store a computer program. When the computer program is executed by a processor, the processor implements the evaluation method of the water-energy-food random system provided by the embodiments of the present disclosure.

[0161] The above-mentioned storage medium may, for example, include a memory 602 of computer program instructions, and the above-mentioned instructions may be executed by the processor 601 of the water-energy-food stochastic system evaluation device to complete the water-energy-food stochastic system evaluation method provided by the embodiment of the present disclosure. Alternatively, the storage medium may be a non-transitory computer-readable storage medium, for example, a non-transitory computer-readable storage medium may be a ROM, a random access memory (RAM), a compact disc read-only memory (CD-ROM), a magnetic tape, a floppy disk, an optical data storage device, etc.

[0162] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising" is intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a list of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article or apparatus.

[0163] The foregoing description is intended only to provide specific embodiments of the present disclosure, intended to enable those skilled in the art to understand and implement the present disclosure. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present disclosure. Therefore, the present disclosure is not intended to be limited to the embodiments described herein, but rather to be construed in the broadest manner consistent with the principles and novel features disclosed herein.

Claims

1. A method for evaluating a water-energy-food stochastic system, characterized in that: include: Constructing a water-energy-food stochastic system under risk influence, and constructing a corresponding stochastic differential equation for the water-energy-food stochastic system; Based on the stochastic differential equation, a stochastic simulation method is used to perform stochastic simulation on multiple state variables in the water-energy-food stochastic system to obtain instantaneous probability and steady-state probability; A elasticity index is derived according to the instantaneous probability and the steady-state probability, and the water-energy-food stochastic system is evaluated based on the elasticity index, wherein the stochastic differential equation includes a hydrological equation, an energy equation, a food equation, a water use equation, a population equation, and a climate risk equation, and the multiple state variables in the water-energy-food stochastic system include water resources, per capita water use, per capita power generation, per capita food production, population, and climate risk; Based on the stochastic differential equation, a stochastic simulation method is used to perform stochastic simulation on multiple state variables in the water-energy-food stochastic system to obtain instantaneous probabilities and steady-state probabilities, including: computing a numerical solution to the stochastic differential equation using the Euler-Maruyama algorithm; Based on the numerical solution, a random simulation method is used to randomly simulate multiple state variables in the water-energy-food random system, and the instantaneous probability and steady-state probability are simulated by the kernel density estimation method.

2. The method according to claim 1, characterized in that The stochastic differential equation corresponding to the water-energy-food stochastic system is constructed, including: determining ordinary differential equations for the water-energy-food stochastic system; Gaussian white noise of risk influence is introduced into the ordinary differential equation to construct the stochastic differential equation.

3. The method according to claim 1, characterized in that The deducing a linear indicator according to the instantaneous probability and the steady-state probability includes: calculating a Euclidean norm between the instantaneous probability and the steady-state probability; When the Euclidean norm approaches zero, the elastic index is derived through steady-state probability density and probability potential function.

4. An evaluation device for a water-energy-food random system, characterized in that: include: An equation construction module is used to construct a water-energy-food stochastic system under the influence of risk, and to construct a corresponding stochastic differential equation for the water-energy-food stochastic system; A simulation processing module is used to perform random simulation on multiple state variables in the water-energy-food random system based on the stochastic differential equation using a stochastic simulation method to obtain instantaneous probability and steady-state probability; a system evaluation module, configured to derive elasticity indicators based on the instantaneous probability and the steady-state probability, and evaluate the water-energy-food stochastic system based on the elasticity indicators, wherein the stochastic differential equations include a hydrological equation, an energy equation, a food equation, a water use equation, a population equation, and a climate risk equation, and the plurality of state variables in the water-energy-food stochastic system include water resources, per capita water use, per capita power generation, per capita food production, population, and climate risk; Among them, the simulation processing module is also used to calculate the numerical solution of the stochastic differential equation using the Euler-Maruyama algorithm; based on the numerical solution, a random simulation method is used to randomly simulate multiple state variables in the water-energy-food random system, and the kernel density estimation method is used to simulate the instantaneous probability and steady-state probability.

5. The device according to claim 4, characterized in that The equation building module includes: an equation determination unit, for determining an ordinary differential equation of the water-energy-food stochastic system; The equation construction unit is used to introduce the Gaussian white noise of risk influence into the ordinary differential equation to construct the stochastic differential equation.

6. The device according to claim 4, characterized in that The system evaluation module includes: a data calculation unit, configured to calculate the Euclidean norm between the instantaneous probability and the steady-state probability; An index derivation unit is used to derive the elasticity index through steady-state probability density and probability potential function when the Euclidean norm tends to zero.

7. An evaluation device for a water-energy-food random system, characterized in that: include: processor; a memory for storing executable instructions; Wherein, the processor is used to read the executable instructions from the memory and execute the executable instructions to implement the evaluation method of the water-energy-food random system described in any one of claims 1-3.

8. A non-volatile computer-readable storage medium, characterized in that The storage medium stores a computer program, and when the computer program is executed by the processor, the processor implements the evaluation method of the water-energy-food random system according to any one of claims 1 to 3.

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