A water resource system risk multi-link conduction method

Abstract

The application discloses a water resource system risk multi-link conduction method, mainly comprising the following steps. Firstly, risk element data in a researched area are collected and standardized processing is conducted; then, water resource system risk links are constructed by using the correlation between risk elements; then, a risk conduction mechanism is defined: ①risk opening stage: simple mechanism of risk conduction and opening condition of risk are described; ②resistance threshold effect: the resistance ability of a system in risk conduction is described, according to the conduction characteristics of the risk link, the risk conduction mechanism and the resistance threshold effect of risk links with different structures are revealed; ③recovery threshold effect: natural and social repair forces make the risk not exist all the time, therefore, the risk recovery effect is defined; ④threshold value updating calculation: the resistance and recovery abilities are increased by risk prevention and control, therefore, the threshold value is updated; ⑤risk termination stage: the risk termination condition is deduced according to the risk conduction mechanism; ⑥risk intensity and conduction speed relationship: the greater the risk disturbance intensity is, the faster the risk conduction speed is. By exploring the risk link conduction mechanism, the water resource risk evaluation system under complex conditions is improved.

Description

Technical Field

[0001] This invention belongs to the field of hydrological risk analysis, specifically relating to a multi-link transmission method for risks in water resource systems. Background Technology

[0002] Under the combined influence of global climate change and human activities, extreme drought events are becoming more frequent in my country, exacerbating the risks of hydrological, meteorological, and socio-economic disasters. Risk assessment is the most effective scientific basis for risk prevention and control; however, risk is not static. Given the coupling of multiple systems including hydrology, society, and economy, risk analysis focuses not only on risk assessment indicators and levels but also on the changes in risk, especially the relationships between risk factors. How to establish a mathematical model to describe the dynamic transmission mechanism of risk is a pressing issue in risk analysis. Risk transmission is a dynamic process of risk change based on energy release theory. It mainly treats risk as a form of energy, describing its changes in the stages of generation, release, transmission, and termination during risk events, thus extending to the evaluation of risk's spatiotemporal evolution. Facing the connections between risk events caused by extreme drought in meteorological, hydrological, and socio-economic systems, this paper establishes a risk transmission model to explore the transmission mechanism of risk in the water resource system. Summary of the Invention

[0003] The technical problem to be solved by this invention is to explore the transmission mechanism of risk in water resource systems in order to address the relationship between risk events caused by extreme drought in systems such as meteorology, hydrology, and socio-economics. This invention provides a multi-link transmission method and system for risk in water resource systems, aiming to improve the risk assessment technology of water resource systems under extreme drought and provide theoretical support for the formulation of risk prevention and control measures.

[0004] To address the above technical problems, this invention provides the following technical solution: a method for multi-link transmission of risks in a water resource system, comprising the following steps:

[0005] S1. Collect risk factors of disaster events in the water resource system of the target area under extreme drought conditions, and standardize the sample data according to the nature of the risk factors.

[0006] S2. For different risk factors, use Copula function correlation analysis to analyze the degree of correlation between risk factors, and construct the risk link of water resource system based on the degree of correlation;

[0007] S3. Define the period during which the current risk factor affects the next risk factor as the risk transmission stage. During the risk transmission stage, for different risk links, determine the state of risk transmission based on the initial disturbance value of the risk factor in the water resource system, the activation threshold of the risk factor, the known effects of natural and social restorative forces, and the recovery threshold of the risk factor. At the same time, update the risk activation threshold and the risk factor recovery threshold based on preset conditions.

[0008] S4. Extract the maximum disturbance value of risk elements in each risk transmission stage, combine it with the initial disturbance value of risk elements, calculate the instantaneous transmission time and instantaneous transmission speed of each risk element, and then calculate the disturbance value received by the risk elements in each transmission stage.

[0009] S5. Based on the disturbance values ​​received by the risk element at each transmission stage and the maximum disturbance value of the risk element, calculate the stable transmission speed at which the disturbance value received by the risk element at each stage reaches the maximum disturbance value, and the corresponding transmission time; finally, calculate the total transmission time of the risk element.

[0010] Furthermore, the aforementioned step S1 specifically includes:

[0011] (1) For risk factors that are stable and whose indicator values ​​are directly proportional to risk, the Min-Max standardization method is adopted, as shown in the following formula:

[0012]

[0013] (2) For risk factors that are stable and whose indicator values ​​are inversely proportional to risk, the Min-Max standardization method is adopted, as shown in the following formula:

[0014]

[0015] In the formula, x represents the numerical value of the risk factor; x max The maximum value of the risk factor; x min The minimum value of the risk factor; x * These are the standardized values ​​for risk factors;

[0016] (3) For unstable elements among the risk factors, the Z-score standardization method is adopted, as shown in the following formula:

[0017]

[0018] In the formula, x represents the numerical value of the risk factor; x * denoted as the standardized risk factor value; μ and σ are the mean and variance of the risk factor, respectively, and Φ(·) is the standard normal distribution function.

[0019] Furthermore, the aforementioned step S2 specifically includes:

[0020] Using the Gumbel Copula function:

[0021]

[0022]

[0023]

[0024] In the formula: x1 and x2 are the standardized risk element values, respectively; and u1, u1 and u2 are the distribution functions of variables x1 and x2, respectively; C θ (·) is the constructed Gumbel Copula function, where θ is one of the parameters and τ is the rank correlation coefficient of the variable.

[0025] Introduce the confidence levels α for elements i and j. i,j The following equation is satisfied:

[0026] τ(i,j)≥α i,j

[0027] Then, it is determined that risk element i and risk element j are correlated, and a chain structure is established between risk element i and risk element j.

[0028] Furthermore, in step S3 above, during the risk transmission phase, the current risk factor affects the next risk factor specifically as follows:

[0029] R j =D i,j (N i +R i )

[0030] In the formula, R i R j N represents the disturbance values ​​of risk element i and risk element j; i Let D be the initial value of the i-th risk element; i,j (·) is the consequence function of the disturbance value of risk element j with respect to the state of risk element i.

[0031] Further, in the aforementioned step S3, the risk links include: single-source single-sink structure, multi-source single-sink structure, single-source multi-sink structure, and multi-source multi-sink structure;

[0032] The single-source, single-sink structure is: information from a single risk element is transmitted to another risk element;

[0033]

[0034] In the formula, N i Ri These are the initial value and disturbance value of risk element i, respectively; D i,j (·) is the consequence function of the disturbance value of risk element j with respect to the state of risk element i; T i,j Let be the activation threshold of risk element i for risk element j;

[0035] The multi-source single-sink structure: information from several risk factors is transmitted to another risk factor;

[0036] R k,i =D k,i (N k +R k )

[0037]

[0038] In the formula, Ω1 is the set of all source risk elements of risk element i; N k R k Let D be the initial value and disturbance value of the k-th risk element in Ω1, respectively; k,i (·) is the consequence function of the disturbance value of risk element i with respect to the state of the k-th risk element in Ω1; T i ω is the activation threshold for risk element i; k,i Let be the weight of the influence of the k-th risk element in Ω1 on risk element i;

[0039] The single-source, multi-sink structure: information from a single risk element is transmitted to several other risk elements.

[0040]

[0041] In the formula, Ω2 represents the set of all exchange risk elements of risk element i; N i R i These are the initial value and disturbance value of risk element i, respectively; R l D represents the disturbance value of the l-th exchange rate risk element in Ω2. i,l (·) is the consequence function of the l-th risk element disturbance value in Ω2 with respect to the state of risk element i; T l is the activation threshold for the l-th risk element in Ω2;

[0042] The multi-source, multi-sink structure: several risk factors are transmitted to several other risk factors;

[0043]

[0044] In the formula, Ω1 and Ω2 are the sets of source risk elements and the set of sink risk elements, respectively; Let be the initial value and disturbance value of the m-th risk element in level i; Let be the disturbance value of the nth risk element in level i+1; D(x) is the nonlinear function that transmits the source risk element to the sink risk element; T n The activation threshold for the nth exchange rate risk element; The weight of the influence of the m-th source risk element related to the n-th exchange risk element on the n-th exchange risk element.

[0045] Furthermore, in step S3 above, when determining the risk transmission status, if the disturbance value of the current risk element exceeds the risk element activation threshold, the risk element is activated and its status changes; if the disturbance value of the current risk element is less than the risk element activation threshold, the risk element status remains unchanged, and risk transmission ceases. If all risk elements are activated, risk transmission ceases when the status of all risk elements in the entire risk network returns to normal; if not all risk elements are activated, risk transmission ceases when the disturbance value at the end of the risk link fails to cause a change in the status of the next risk element. That is:

[0046] R n ≤T n

[0047] In the formula, R n The risk disturbance value at the end of the activated risk link; T n This is the activation threshold for its next risk factor.

[0048] Furthermore, in the aforementioned method for multi-link risk transmission in a water resource system, when determining the risk transmission status, risk transmission ceases when the status value of a risk element decreases to the recovery threshold. That is, for the i-th risk element:

[0049]

[0050] In the formula, t is the time period value; R i (t) represents the disturbance value of risk element i at time period t; Re i (t) is an increasing function of time for the repair value of the i-th risk factor by natural or social restorative forces; C i Let be the recovery threshold for the i-th risk element.

[0051] Further, in the aforementioned step S3, updating the risk activation threshold and risk element recovery threshold based on preset conditions specifically involves: based on the improvement of the risk resistance and recovery capabilities caused by objective factors, i.e., decreasing the activation threshold and increasing the risk recovery threshold, as shown in the following formula:

[0052] T i (t+1)=α i (t)T i (t)

[0053] Ci (t+1)=β i (t) -1 C i (t)

[0054] In the formula, t is the time period value; T i (t) represents the risk activation threshold of risk element i; C i (t) represents the risk recovery threshold of risk element i; α i (t), β i (t) is the adjustment parameter, where 0 < α < 1 and 0 < β < 1.

[0055] Furthermore, the aforementioned step S4 includes the following sub-steps:

[0056] S401. Extract the maximum disturbance value of each risk element. And the risk propagation time T under the maximum disturbance value. i max Based on the initial disturbance values ​​of the risk factors, the instantaneous propagation time of each risk factor is calculated as follows:

[0057]

[0058]

[0059]

[0060] In the formula, R i Let be the initial disturbance value of the i-th risk element; Let the disturbance value of the i-th risk element be R i The instantaneous transmission time f for the (i+1)th risk element. i+1 (·) represents the function relating t and R. R represents the disturbance value of the i-th risk element. i The instantaneous transmission speed r towards the (i+1)th risk element ij This represents the transmission disturbance value of the i-th risk element in the j-th stage;

[0061] S402. Based on the inverse proportional relationship of f(·), let f(x) = -ax + b (x > 0, a > 0, b > 0).

[0062] According to the risk transmission chain structure, when the state of the environment changes, the instantaneous risk transmission time for risk element N1 is t1, then:

[0063] T1=t1=f1(1)=b1-a1

[0064] In the formula, T1 is the risk transmission time from risk element N1 to N2;

[0065] S403, according to formula For risk factor N2:

[0066]

[0067]

[0068] In the formula, R1 is the disturbance value of risk element N1 at a certain moment; These are the maximum risk disturbance values ​​for risk elements N1 and N2, respectively, i.e., the upper limit of risk disturbance. Let R be the instantaneous velocity at which risk element N1 propagates to risk element N2 when the disturbance intensity is R1. a1 represents the time required for risk element N1 to propagate to risk element N2 when the disturbance intensity is R1; a2 and b2 are parameters related to risk element N2.

[0069] S404. Calculate the disturbance value received by the risk factor: instantaneous velocity. In the 0-T1 phase:

[0070]

[0071] In the formula, r 21 This represents the disturbance value received by risk element N2 during the 0-T1 phase.

[0072] Furthermore, the aforementioned step S5 specifically refers to: during the T1-T2 stage, risk factor N1 reaches the upper limit of risk disturbance. At this point, the rate at which risk factor N1 is transmitted to risk factor N2 stabilizes at v2:

[0073]

[0074] The disturbance value received by risk factor N2 during the T1-T2 phase is:

[0075]

[0076] In the formula, r 22 Let N2 be the disturbance value received by risk element N2 during the T1-T2 stage, where the risk intensity and velocity v2 are constant.

[0077]

[0078] Finally, the total risk transmission time T2 of risk factor N2 is obtained as follows:

[0079] T2 = T1 + t2

[0080]

[0081] Compared with the prior art, the beneficial technical effects of the present invention using the above technical solution are as follows:

[0082] This invention considers the risk evolution of hydrology, meteorology, society, economy, and ecosystems under extreme drought conditions, identifies multiple risk factors, and highlights the diversity and systematic nature of risk transmission. The risk factors used in this invention include: disaster-causing factors such as rainfall, temperature, and upstream water inflow; and risk factors such as regional runoff, water resources, groundwater level, urban area, population, arable land area, vegetation coverage, and GDP.

[0083] This invention starts from different risk factors and transmission links in the water resources system from a macro perspective, and explores the transmission mechanism under extreme drought conditions by combining different link structures such as series, parallel and mixed links, highlighting the diversity and integrity of risk transmission.

[0084] This invention studies the risk transmission mechanism of water resource systems under extreme drought conditions from the perspective of water resource security risk management, based on risk analysis techniques from the fields of economics and computer science, highlighting the interdisciplinary nature and innovation of risk transmission. Attached Figure Description

[0085] Figure 1 This is a flowchart of the method of the present invention.

[0086] Figure 2 The diagram shows the risk chain structure. In the diagram, (a) is a single-source single-sink structure, (b) is a multi-source single-sink structure, (c) is a single-source multi-sink structure, and (d) is a multi-source multi-sink structure.

[0087] Figure 3 This is a diagram illustrating the risk transmission process. Detailed Implementation

[0088] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0089] In this invention, various aspects of the invention are described with reference to the accompanying drawings, in which numerous illustrative embodiments are shown. Embodiments of the invention are not limited to those depicted in the drawings. It should be understood that the invention is implemented through any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed herein are not limited to any particular implementation. Furthermore, some aspects of the invention disclosed may be used alone or in any suitable combination with other aspects of the invention disclosed.

[0090] like Figure 1 The present invention discloses a method for multi-link transmission of risks in water resource systems, comprising the following steps:

[0091] S1. Collect risk factors of disaster events in the water resource system of the target area under extreme drought conditions, and standardize the sample data according to the nature of the risk factors.

[0092] S2. For different risk factors, use Copula function correlation analysis to analyze the degree of correlation between risk factors, and construct the risk link of water resource system based on the degree of correlation;

[0093] S3. Define the period during which the current risk factor affects the next risk factor as the risk transmission stage. During the risk transmission stage, for different risk links, determine the state of risk transmission based on the initial disturbance value of the risk factor in the water resource system, the activation threshold of the risk factor, the known effects of natural and social restorative forces, and the recovery threshold of the risk factor. At the same time, update the risk activation threshold and the risk factor recovery threshold based on preset conditions.

[0094] S4. Extract the maximum disturbance value of risk elements in each risk transmission stage, combine it with the initial disturbance value of risk elements, calculate the instantaneous transmission time and instantaneous transmission speed of each risk element, and then calculate the disturbance value received by the risk elements in each transmission stage.

[0095] S5. Based on the disturbance values ​​received by the risk element at each transmission stage and the maximum disturbance value of the risk element, calculate the stable transmission speed at which the disturbance value received by the risk element at each stage reaches the maximum disturbance value, and the corresponding transmission time; finally, calculate the total transmission time of the risk element.

[0096] Furthermore, as a preferred embodiment of the multi-link transmission method for water resource system risks according to the present invention, based on risk events in the water resource system under extreme drought conditions, data on risk sources and disaster-causing factors such as rainfall, temperature, and upstream water inflow in the target area, as well as risk element data such as inter-regional runoff, water resource volume, groundwater level, urban area, population, cultivated land area, vegetation coverage, and GDP are collected and standardized according to the different element properties using the following method:

[0097] (1) For risk factors that are stable and whose indicator values ​​are directly proportional to risk, such as population density and GDP, the Min-Max standardization method is used, as shown in the following formula:

[0098]

[0099] (2) For risk factors that are stable and whose indicator values ​​are inversely proportional to risk, such as water resources, the Min-Max standardization method is adopted, as shown in the following formula:

[0100]

[0101] In the formula, x represents the numerical value of the risk factor; x maxThe maximum value of the risk factor; x min The minimum value of the risk factor; x * These are the standardized values ​​for risk factors;

[0102] (3) For unstable elements among the risk factors, where the variable parameters vary greatly in extreme cases and the data range is not fixed, such as rainfall and upstream water inflow, the Z-score standardization method is adopted, as shown in the following formula:

[0103]

[0104] In the formula, x represents the numerical value of the risk factor; x * denoted as the standardized risk factor value; μ and σ are the mean and variance of the risk factor, respectively, and Φ(·) is the standard normal distribution function.

[0105] Furthermore, as a preferred embodiment of the multi-link transmission method for water resource system risks according to the present invention, in step S2, the Gumbel Copula function is used as follows:

[0106]

[0107]

[0108]

[0109] In the formula: x1 and x2 are the standardized risk element values, respectively; and u1, u1 and u2 are the distribution functions of variables x1 and x2, respectively; C θ (·) is the constructed Gumbel Copula function, where θ is one of the parameters and τ is the rank correlation coefficient of the variable.

[0110] Introduce the confidence levels α for elements i and j. i,j The following equation is satisfied:

[0111] τ(i,j)≥α i,j

[0112] Then, it is determined that risk element i and risk element j are correlated, and a chain structure is established between risk element i and risk element j.

[0113] In step S3, during the risk transmission phase, changes in the state of the risk source will affect the risk elements, causing changes in the state of other risk elements in the system link. Specifically, the current risk element affects the next risk element as follows:

[0114] R j =D i,j (N i +Ri )

[0115] In the formula, R i R j N represents the disturbance values ​​of risk element i and risk element j; i Let D be the initial value of the i-th risk element; i,j (·) is the consequence function of the disturbance value of risk element j with respect to the state of risk element i.

[0116] For different risk links such as Figure 2 As shown, the risk chains include: single-source single-sink structure, multi-source single-sink structure, single-source multi-sink structure, and multi-source multi-sink structure.

[0117] like Figure 2 As shown in (a), the single-source single-sink structure is: information of a single risk element is transmitted to another risk element;

[0118]

[0119] In the formula, N i R i These are the initial value and disturbance value of risk element i, respectively; D i,j (·) is the consequence function of the disturbance value of risk element j with respect to the state of risk element i; T i,j Let be the activation threshold of risk element i for risk element j;

[0120] like Figure 2 As shown in (b), the multi-source single-sink structure involves the transfer of information from several risk factors to another risk factor.

[0121] R k,i =D k,i (N k +R k )

[0122]

[0123] In the formula, Ω1 is the set of all source risk elements of risk element i; N k R k Let D be the initial value and disturbance value of the k-th risk element in Ω1, respectively; k,i (·) is the consequence function of the disturbance value of risk element i with respect to the state of the k-th risk element in Ω1; T i ω is the activation threshold for risk element i; k,i Let be the weight of the influence of the k-th risk element in Ω1 on risk element i;

[0124] like Figure 2 As shown in (c), the single-source multi-sink structure involves the transmission of information from a single risk element to several other risk elements.

[0125]

[0126] In the formula, Ω2 represents the set of all exchange risk elements of risk element i; N i R i These are the initial value and disturbance value of risk element i, respectively; R l D represents the disturbance value of the l-th exchange rate risk element in Ω2. i,l (·) is the consequence function of the l-th risk element disturbance value in Ω2 with respect to the state of risk element i; T l is the activation threshold for the l-th risk element in Ω2;

[0127] like Figure 2 As shown in (d), the multi-source, multi-sink structure involves several risk factors being transmitted to several other risk factors.

[0128]

[0129] In the formula, Ω1 and Ω2 are the sets of source risk elements and the set of sink risk elements, respectively; Let be the initial value and disturbance value of the m-th risk element in level i; is the disturbance value of the nth risk element in level i+1; D(x) is the nonlinear function that transmits the source risk element to the sink risk element; The activation threshold for the nth exchange rate risk element; The weight of the influence of the m-th source risk element related to the n-th exchange risk element on the n-th exchange risk element.

[0130] Combination Figure 3 Considering the resistance of risk elements to risk transmission, a risk activation threshold is introduced. When determining the risk transmission status, if the disturbance value of the current risk element exceeds the risk element activation threshold, the risk element is activated and its status changes; if the disturbance value of the current risk element is less than the risk element activation threshold, the risk element's status remains unchanged, and risk transmission ceases. If all risk elements are activated, risk transmission ceases when the status of all risk elements in the entire risk network returns to normal; if not all risk elements are activated, risk transmission ceases when the disturbance value at the end of the risk link fails to cause a change in the status of the next risk element.

[0131] R n ≤T n

[0132] In the formula, R n The risk disturbance value at the end of the activated risk link; T n This is the activation threshold for its next risk factor.

[0133] When determining the risk transmission status, risk transmission will stop at this node when the state value of a certain risk element decreases to the recovery threshold C. That is, for the i-th risk element:

[0134]

[0135] In the formula, t is the time period value; R i (t) represents the disturbance value of risk element i at time period t; Re i (t) is an increasing function of time for the repair value of the i-th risk factor by natural or social restorative forces; C i Let be the recovery threshold for the i-th risk element.

[0136] The specific update of risk activation threshold and risk element recovery threshold based on preset conditions is as follows: Based on the improvement of risk resistance and recovery capabilities caused by objective factors, such as the construction of disaster relief projects, the introduction of prevention and control policies, and the enhancement of risk prevention awareness after a risk event, all of these factors lead to an increase in risk resistance and recovery capabilities, i.e., a decrease in the activation threshold and an increase in the risk recovery threshold, as shown in the following formula:

[0137] T i (t+1)=α i (t)T i (t)

[0138] C i (t+1)=β i (t) -1 C i (t)

[0139] In the formula, t is the time period value; T i (t) represents the risk activation threshold of risk element i; C i (t) represents the risk recovery threshold of risk element i; α i (t), β i (t) is the adjustment parameter, where 0 < α < 1 and 0 < β < 1.

[0140] As a preferred embodiment of the multi-link transmission method for water resource system risks proposed in this invention, step S4 includes the following sub-steps:

[0141] S401. Extract the maximum disturbance value of each risk element. And the risk propagation time T under the maximum disturbance value. i max Based on the initial disturbance values ​​of the risk factors, the instantaneous propagation time of each risk factor is calculated as follows:

[0142]

[0143]

[0144]

[0145] In the formula, R i Let be the initial disturbance value of the i-th risk element; Let the disturbance value of the i-th risk element be R i The instantaneous transmission time f for the (i+1)th risk element. i+1 (·) represents the function relating t and R. R represents the disturbance value of the i-th risk element. i The instantaneous transmission speed r towards the (i+1)th risk element ij This represents the transmission disturbance value of the i-th risk element in the j-th stage;

[0146] S402. Based on the inverse proportional relationship of f(·), let f(x) = -ax + b (x > 0, a > 0, b > 0).

[0147] According to the risk transmission chain structure, when the state of the environment changes, the instantaneous risk transmission time for risk element N1 is t1, then:

[0148] T1=t1=f1(1)=b1-a1

[0149] In the formula, T1 is the risk transmission time from risk element N1 to N2;

[0150] S403, according to formula For risk factor N2:

[0151]

[0152]

[0153] In the formula, R1 is the disturbance value of risk element N1 at a certain moment; These are the maximum risk disturbance values ​​for risk elements N1 and N2, respectively, i.e., the upper limit of risk disturbance. Let R be the instantaneous velocity at which risk element N1 propagates to risk element N2 when the disturbance intensity is R1. a1 represents the time required for risk element N1 to propagate to risk element N2 when the disturbance intensity is R1; a2 and b2 are parameters related to risk element N2.

[0154] S404. Calculate the disturbance value received by the risk factor: instantaneous velocity. In the 0-T1 phase:

[0155]

[0156] In the formula, r 21 This represents the disturbance value received by risk element N2 during the 0-T1 phase.

[0157] As a preferred embodiment of the multi-link risk transmission method for water resource systems proposed in this invention, step S5 specifically involves: during the T1-T2 stage, risk element N1 reaches the upper limit of risk disturbance. At this point, the rate at which risk factor N1 is transmitted to risk factor N2 stabilizes at v2:

[0158]

[0159] The disturbance value received by risk factor N2 during the T1-T2 phase is:

[0160]

[0161] In the formula, r 22 Let N2 be the disturbance value received by risk element N2 during the T1-T2 stage, where the risk intensity and velocity v2 are constant.

[0162]

[0163] Finally, the total risk transmission time T2 of risk factor N2 is obtained as follows:

[0164] T2 = T1 + t2

[0165]

[0166] While the present invention has been described above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for multi-link transmission of risks in a water resources system, characterized in that, Includes the following steps: S1. Collect risk factors of disaster events in the water resource system of the target area under extreme drought conditions, and standardize the sample data according to the nature of the risk factors. S2. For different risk factors, use Copula function correlation analysis to analyze the degree of correlation between risk factors, and construct the risk link of water resource system based on the degree of correlation. S3. Define the period during which the current risk factor affects the next risk factor as the risk transmission stage. During the risk transmission stage, for different risk links, determine the state of risk transmission based on the initial disturbance value of the risk factor in the water resource system, the activation threshold of the risk factor, the known effects of natural and social restorative forces, and the recovery threshold of the risk factor. At the same time, update the risk activation threshold and the risk factor recovery threshold based on preset conditions. Risk chains include: single-source single-sink structure, multi-source single-sink structure, single-source multi-sink structure, and multi-source multi-sink structure. The source risk element is defined as its parent node element, and the sink risk element is defined as its child node element. The single-source, single-sink structure is: information from a single risk element is transmitted to another risk element; ， In the formula, , These are the initial value and disturbance value of risk element i, respectively; Let be the consequence function of the perturbation value of risk element j with respect to the state of risk element i; Let be the activation threshold of risk element i for risk element j; The multi-source single-sink structure: information from several risk factors is transmitted to another risk factor; ， ， In the formula, Let i be the set of all source risk elements; , They are respectively The initial value and disturbance value of the k-th risk element; The disturbance value of risk element i is related to The consequence function of the state of the k-th risk element; , where i is the activation threshold for risk element i; for The weight of the influence of the k-th risk factor on risk factor i; The single-source, multi-sink structure: information from a single risk element is transmitted to several other risk elements. ， In the formula, Let i be the set of all exchange risk elements; , These are the initial value and disturbance value of risk element i, respectively; for The disturbance value of the l-th exchange rate risk factor; for The consequence function of the disturbance value of the l-th risk element with respect to the state of risk element i; for The activation threshold of the l-th risk element; The multi-source, multi-sink structure: several risk factors are transmitted to several other risk factors; ， In the formula, , These are the sets of source risk elements and sink risk elements, respectively. , Let be the initial value and disturbance value of the m-th risk element in level i; This represents the disturbance value of the nth risk element in level i+1; It is a nonlinear function that transmits source risk factors to exchange risk factors; The activation threshold for the nth exchange rate risk element; The weight of the influence of the m-th source risk element related to the n-th exchange rate risk element on the n-th exchange rate risk element; S4. Extract the maximum disturbance value of risk elements in each risk transmission stage, combine it with the initial disturbance value of risk elements, calculate the instantaneous transmission time and instantaneous transmission speed of each risk element, and then calculate the disturbance value received by the risk elements in each transmission stage. S5. Based on the disturbance values ​​received by the risk element at each transmission stage and the maximum disturbance value of the risk element, calculate the stable transmission speed at which the disturbance value received by the risk element at each stage reaches the maximum disturbance value, and the corresponding transmission time; finally, calculate the total transmission time of the risk element.

2. The method for multi-link risk transmission in a water resources system according to claim 1, characterized in that, Step S1 is as follows: (1) For risk factors that are stable and whose indicator values ​​are directly proportional to risk, the Min-Max standardization method is adopted, as shown in the following formula: ； (2) For risk factors that are stable and whose indicator values ​​are inversely proportional to risk, the Min-Max standardization method is adopted, as shown in the following formula: ； In the formula, The numerical values ​​of the risk factors; This represents the maximum value of the risk factor. This represents the minimum value of the risk factors. These are the standardized values ​​for risk factors; (3) For unstable elements among the risk factors, the Z-score standardization method is adopted, as shown in the following formula: ； In the formula, The numerical values ​​of the risk factors; These are the standardized values ​​for risk factors; and These are the mean and variance of the risk factors, respectively. It is the standard normal distribution function.

3. The method for multi-link risk transmission in a water resources system according to claim 1, characterized in that, Step S2 is as follows: Using the Gumbel Copula function: ， ， ， In the formula: , These are the standardized risk factor values; and , and They are variables , The distribution function; For the constructed Gumbel Copula function, One of the parameters, The rank correlation coefficient of the variables; Introduce the confidence levels of element i and element j The following equation is satisfied: ， Then, it is determined that risk element i and risk element j are correlated, and a chain structure is established between risk element i and risk element j.

4. The method for multi-link risk transmission in a water resource system according to claim 3, characterized in that, In step S3, during the risk transmission phase, the current risk factor affects the next risk factor specifically as follows: ， In the formula, , Let i be the disturbance values ​​of risk element i and risk element j; Let be the initial value of the i-th risk element; Let be the consequence function of the disturbance value of risk element j with respect to the state of risk element i.

5. The method for multi-link risk transmission in a water resources system according to claim 4, characterized in that, In step S3, when determining the risk transmission status, if the disturbance value of the current risk element exceeds the risk element activation threshold, the risk element is activated and the risk element status changes. When the disturbance value of the current risk element is less than the risk element activation threshold, the state of the risk element does not change and the risk transmission stops. If all risk elements are activated, the risk transmission stops when the state of all risk elements in the entire risk network returns to normal. If not all risk factors are activated, risk transmission ceases when the disturbance value at the end of the risk chain fails to cause a change in the state of the next risk factor. ， In the formula, The risk disturbance value at the end of the activated risk link; This is the activation threshold for its next risk factor.

6. The method for multi-link risk transmission in a water resource system according to claim 5, characterized in that, When determining the risk transmission status, risk transmission ceases when the status value of a risk element drops to the recovery threshold. That is, for the i-th risk element: ， In the formula, t is the time period value; Let be the disturbance value of risk element i during time period t; Let be the time-increasing function of the restoration value of the i-th risk factor by natural or social restorative forces; Let be the recovery threshold for the i-th risk element.

7. The method for multi-link risk transmission in a water resource system according to claim 6, characterized in that, In step S3, updating the risk activation threshold and risk element recovery threshold based on preset conditions specifically involves: based on the improvement of the risk resistance and recovery capabilities caused by objective factors, i.e., decreasing the activation threshold and increasing the risk recovery threshold, as shown in the following formula: ， ， In the formula, t is the time period value; The risk activation threshold for risk element i; The risk recovery threshold for risk element i; , To adjust the parameters, where , .

8. The method for multi-link risk transmission in a water resource system according to claim 7, characterized in that, Step S4 includes the following sub-steps: S401. Extract the maximum disturbance value of each risk element. and the risk transmission time under the maximum disturbance value. Based on the initial disturbance values ​​of the risk factors, the instantaneous propagation time of each risk factor is calculated as follows: ， ， ， In the formula, Let be the initial disturbance value of the i-th risk element; Let the disturbance value of the i-th risk element be R i The instantaneous transmission time of the transmission to the (i+1)th risk element. Let t be a function relating t and R. R represents the disturbance value of the i-th risk element. i The instantaneous transmission speed at the (i+1)th risk element. This represents the transmission disturbance value of the i-th risk element in the j-th stage; S402, according to Inversely proportional, making , According to the risk transmission chain structure, when the state of the environment changes, the risk factors... The instantaneous risk transmission time is ,but: ， In the formula, Risk factors Towards The risk transmission time; S403, according to formula For risk factors have: ， ， In the formula, Risk factors The disturbance value at a certain moment; , Risk factors , The maximum risk disturbance value, i.e., the upper limit of risk disturbance; For the disturbance strength is Time risk factors Towards risk factors The instantaneous velocity of conduction; Risk factors When the disturbance strength is Time-related risk factors The time required for conduction; , Regarding risk factors Parameters; S404. Calculate the disturbance value received by the risk factor: instantaneous velocity. In 0- The stages include: ， In the formula, Risk factors In 0- The disturbance value received during the stage.

9. A method for multi-link risk transmission in a water resources system according to claim 8, characterized in that, Step S5 specifically involves: in - Stage, risk factors Reaching the upper limit of risk disturbance At this time, risk factors Towards risk factors The conduction speed stabilizes at : ， Risk factors exist - The disturbance value received during the stage is: ， In the formula, Risk factors exist - The disturbance value received at each stage, at which point the risk intensity is constant, and the speed... must, ; Finally, the risk factors are obtained. Total risk transmission time for: ， 。

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