Comprehensive relative toughness model construction method

Abstract

The invention relates to a method for constructing a comprehensive relative toughness model. The method comprises the following steps: S1, constructing a basic relative toughness model for describing the toughness of a dynamic network; s2, a relative time scale is introduced for the basic relative toughness model, so that the basic relative toughness model is corrected for the first time, and a relative toughness model based on the relative time scale is obtained; and S3, introducing a toughness change rate for the relative toughness model based on the relative time scale so as to carry out secondary correction on the relative toughness model based on the relative time scale and obtain a comprehensive relative toughness model. According to the scheme, the relative toughness index is creatively designed, so that the scheme has the real-time characteristic matched with the dynamic change process, and the scheme is more suitable for toughness analysis of a dynamic network / system.

Description

Technical Field

[0001] The present invention relates to a method for constructing a comprehensive relative toughness model, and in particular to a method for constructing a comprehensive relative toughness model. Background Art

[0002] Resilience is defined as a system's ability to resist, absorb, adapt, and return to its original state after experiencing a disturbance. Current resilience research focuses on the entire resilience process: experiencing a shock, experiencing performance degradation, recovering and adapting, and finally maintaining stable operation. Calculations and analyses based on this resilience process describe a system's "resilience capacity" over a specific time period. As a system property, resilience assumes that resilience is present and available at every moment, meaning that resilience is available at every moment. Therefore, the concept of relative resilience has been proposed. It describes a system's ability to resist, absorb, adapt, and recover at a specific moment in time.

[0003] Relative resilience represents the system's immediate resilience at the current moment. Relative resilience is independent of previous or subsequent moments and only considers the initial state, the reference state (which can be the lowest performance moment), and the current state. It measures the system's resilience at the current moment. Relative resilience is used to assess the system's immediate resilience at a specific moment in real time relative to a reference moment, including its ability to resist, absorb, adapt, and recover. Its core is to dynamically reflect the system's immediate state before and after a disturbance by using the current performance value, the reference performance value, and the rate of change. Relative resilience reflects the system's immediate capabilities at a given moment, expressed as the relative ratio of the performance difference (current to reference moments), combined with the combined effects of time efficiency and rate of change. It is essentially a "snapshot" of the system's dynamic response, rather than a cumulative effect over time.

[0004] In physics, the concept of relative resilience is related to system dynamics and nonlinear dynamics. It concerns how a system, after a transient disturbance, returns to a stable state or a new equilibrium through internal dynamic processes. This recovery process may involve energy dissipation, system reorganization, or self-organization. For example, in ecosystems, relative resilience can be associated with rapid niche filling, restoration of species diversity, and maintenance of ecosystem function.

[0005] Therefore, how to construct a widely applicable relative toughness model based on the instantaneous characteristics and advantages of relative toughness is an urgent problem that needs to be solved. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for constructing a comprehensive relative toughness model.

[0007] To achieve the above-mentioned object of the invention, the present invention provides a method for constructing a comprehensive relative toughness model, comprising the following steps: S1. Construct a basic relative resilience model to describe dynamic network resilience; S2. introducing a relative time scale into the basic relative toughness model to modify the basic relative toughness model and derive a relative toughness model based on the relative time scale; S3. Introducing the toughness change rate into the relative toughness model based on the relative time scale, so as to make a secondary correction to the relative toughness model based on the relative time scale and obtain a comprehensive relative toughness model.

[0008] According to one aspect of the present invention, in step S1, in the step of constructing a basic relative resilience model for describing dynamic network resilience, the basic relative resilience model is expressed as:

[0009] in, Relative toughness, Indicates that the dynamic network The performance size of the moment, Indicates that the dynamic network The performance size of the moment, Indicates the performance of the dynamic network at the initial moment, Indicates the current moment, represents the reference time, Indicates that the dynamic network Performance at all times The performance difference at the moment, Represents the performance of the dynamic network at the initial moment and The performance difference at that moment.

[0010] According to one aspect of the present invention, in step S2, a relative time scale is introduced into the basic relative toughness model to perform a correction on the basic relative toughness model and obtain a relative toughness model based on the relative time scale. The relative toughness model based on the relative time scale is expressed as:

[0011]

[0012] in, express Moment and The difference between moments is the relative time scale.

[0013] According to one aspect of the present invention, in step S2, the step of introducing a relative time scale into the basic relative toughness model to perform a correction on the basic relative toughness model and derive a relative toughness model based on the relative time scale includes: S21. Obtaining a resilience process regarding the dynamic network resilience based on the basic relative resilience model; S22. Introducing a time reference parameter based on the toughness process and performance reference parameters , used to divide the toughness process into intervals; S23. Introducing the relative time scale into the intervals divided by the toughness process to modify the basic relative toughness model and obtain a relative toughness model based on the relative time scale.

[0014] According to one aspect of the present invention, in step S21, in the step of obtaining the resilience process of the dynamic network resilience based on the basic relative resilience model, the resilience process includes four stages, and the four stages included in the resilience process are: an impact stage, a performance degradation stage, a performance recovery stage, and a performance stabilization stage; In step S22, a time reference parameter is introduced based on the toughness process and performance reference parameters , the step of dividing the toughness process into intervals includes: A reference moment for analyzing the performance change trend during the toughness process is selected based on the toughness process. , and based on the reference moment Obtaining performance change trend results during the toughness process; Introduce time reference parameters based on the performance change trend results and performance reference parameters , in order to divide the toughness process into intervals.

[0015] According to one aspect of the present invention, in step S22, based on the reference time In the step of obtaining the performance change trend result during the toughness process, the reference time Before and the reference moment Then the analysis results are divided; wherein, at the reference time Previously, there were two types of analysis results, namely: The performance change trend is an upward trend, then at the reference time Previously in the performance recovery phase, reference time The performance is the best, among which The value is negative, indicating that the reference time The closer, the better the performance; The performance change trend is a downward trend, then at the reference time Previously, it was in the performance degradation stage, reference time The performance is the worst, among which The value is positive, indicating that The further away, the better the performance; At the reference time Afterwards, there are two types of analysis results, which are: The performance change trend is an upward trend, then at the reference time After that, it is in the performance recovery phase, with reference to the time The performance is the worst, among which The value is positive, indicating that The further away, the better the performance; The performance change trend is a downward trend, then at the reference time After that, it is in the stage of performance degradation, reference time The performance is the best, among which The value is negative, indicating that the reference time The closer, the better the performance.

[0016] According to one aspect of the present invention, in step S22, a time reference parameter is introduced based on the performance change trend result. and performance reference parameters In the step, the time reference parameter Expressed as: ; The performance parameters are expressed as: ; Then, in the step of dividing the toughness process into intervals, four intervals are obtained and expressed as: At the reference time Before, there were two intervals, and they were: Interval three, and expressed as: ; Interval 2, and expressed as: ; At the reference time After that, there are two intervals, which are: Interval 1, and is expressed as: ; Interval four, and expressed as: .

[0017] According to one aspect of the present invention, in step S23, the step of introducing the relative time scale into the intervals divided by the toughness process to modify the basic relative toughness model and obtain a relative toughness model based on the relative time scale includes: S231. Based on the current moment of the resilience process and reference time The relative time scale is constructed and expressed as:

[0018] ; in, express Moment and The difference between moments is the relative time scale; S232. The constructed relative time scale is introduced into the interval divided for the toughness process, and is respectively: At the reference time Before, there were two intervals, and they were: Interval three, and expressed as: ; Interval 2, and expressed as: ; At the reference time After that, there are two intervals, which are: Interval 1, and is expressed as: ; Interval four, and expressed as: ; S233. Based on each interval with the relative time scale correction, an exponential function is introduced for functional description to construct a functional form of the relative time scale, which is expressed as: ; S234. Introduce the functional form of the relative time scale into the basic relative toughness model to obtain a relative toughness model based on the relative time scale.

[0019] According to one aspect of the present invention, in step S3, the step of introducing the toughness change rate into the relative toughness model based on the relative time scale to perform a secondary correction on the relative toughness model based on the relative time scale and derive a comprehensive relative toughness model includes: S31. Obtain the toughness change rate of the dynamic network toughness, and the toughness change rate is expressed as:

[0020] in, Indicates the rate of change of toughness; S32. Based on the intervals divided in step S22, the positive and negative changes of the basic relative toughness model and the positive and negative changes of the toughness change rate are introduced, and they are: At the reference time Before, there were two intervals, and they were: Interval three, and expressed as: ; Interval 2, and expressed as: ; At the reference time After that, there are two intervals, which are: Interval 1, and is expressed as: ; Interval four, and expressed as: ; S33. Based on the positive and negative changes of the basic relative toughness model and the positive and negative changes of the toughness change rate, an exponential function is introduced to perform functional description to construct a functional form of the toughness change rate, which is expressed as: ; S34. Introducing the toughness change rate into a relative toughness model based on a relative time scale to derive the comprehensive relative toughness model; wherein the comprehensive relative toughness model is expressed as: .

[0021] According to one aspect of the present invention, it also includes: S4. Introducing a scaling factor into the comprehensive relative resilience model to adjust the sensitivity interval of the comprehensive relative resilience model so as to take into account the relative time scale and toughness change rate The comprehensive relative toughness calculated when has practical significance within the range of all real numbers; the comprehensive relative toughness model with the introduction of scaling factors is expressed as:

[0022] in, are scaling factors, and .

[0023] According to a solution of the present invention, a relative resilience index is creatively designed in this solution to enable this solution to have real-time characteristics that match the dynamic change process, making this solution more suitable for resilience analysis of dynamic networks / systems.

[0024] According to a solution of the present invention, the free selection of the reference moment in this solution can make the constructed comprehensive relative resilience model applicable to different scenarios and show different meanings, which greatly expands the scope of application and flexibility of this solution.

[0025] According to a solution of the present invention, this solution is based on relative resilience and not only considers the stage of the resilience process of the dynamic network and whether it can recover, but also considers the speed and efficiency of change (resistance, absorption, adaptation, recovery), that is, the length of time the dynamic network changes (resistance, absorption, adaptation, recovery) from interference and the rate of change at the current moment.

[0026] According to a solution of the present invention, the traditional resilience calculation based on time integration can be considered as an increasing function of time, the accumulation of performance functions over time. In the solution of this application, the resilience capacity at a certain moment is focused on through relative resilience, and different descriptions are proposed according to different stages of the resilience process, considering the different resilience capacities displayed - resistance, absorption, recovery, and adaptation. Taking performance as the main metric, different interpretations are given to time and the size of the rate of change at different stages. Moreover, compared with the traditional resilience value which is always positive, the relative resilience value in this solution can be negative, indicating that it is in a relatively declining stage. The relationship between the two, resilience as a property of the system, relative resilience focuses on the resilience capacity at a certain moment, and process resilience focuses on the resilience capacity during the entire resilience process, which makes this solution easier to analyze the resilience capacity of the dynamic network at each moment, and realizes the accuracy and reliability of the resilience process analysis.

[0027] According to a solution of the present invention, traditional resilience is based on a time integral method, which is a cumulative performance value and reflects the overall performance of a time period; while the relative resilience of this solution is based on a real-time value calculation method, which is more suitable for real-time monitoring and rapid adjustment of dynamic systems, and has higher real-time performance than traditional resilience.

[0028] According to a solution of the present invention, this solution realizes multi-dimensional consideration of resilience. Among them, on the basis of considering performance value, time and change rate are further considered, which can more comprehensively reflect the dynamic characteristics of the system, combine the three dimensions of performance, time and rate, break through the limitations of traditional single indicators, and achieve the effect of multi-dimensional fusion.

[0029] According to a solution of the present invention, this solution fully considers the different stages of the resilience process, and the value can be positive or negative. The positive and negative values ​​are used to distinguish whether the system is in the "recovery" or "decline" stage, which more intuitively and accurately reflects the corresponding trend, where positive values ​​represent recovery ability and negative values ​​represent resistance ability.

[0030] According to a solution of the present invention, this solution can capture system state changes in real time, effectively ensuring the sensitivity of its application, thereby enabling this solution to be extended to fields with higher sensitivity requirements, such as transient response during voltage drops.

[0031] According to a solution of the present invention, this solution can integrate performance differences, time dimensions and change rates, effectively avoiding single-dimensional deviations. In addition, it can support multi-scenario analysis. In particular, by introducing the time reference parameter γ and the performance reference parameter δ The fine division of the toughness process is achieved, which can fully support the targeted optimization of different stages.

[0032] According to a solution of the present invention, this solution has the capability and advantage of real-time decision support. Its real-time decision support capability makes this solution easier to apply in the power system to monitor the relative resilience of grid nodes in real time, quickly locate vulnerable links, and guide whether to start the backup power supply or adjust the load.

[0033] According to a solution of the present invention, this solution has the ability of dynamic adjustment and can dynamically allocate bandwidth according to the relative toughness value to improve local recovery efficiency.

[0034] According to a solution of the present invention, this solution has the characteristics of being quantitative and intuitive, and directly reflects the performance trend through positive and negative values ​​(positive value means recovery, negative value means decline), thereby realizing a flexible display of the toughness process.

[0035] According to one solution of this invention, this solution can also be extended to intelligent manufacturing. For example, in the event of a production line failure, the robot's operating mode can be adjusted based on its relative resilience to reduce downtime. It can also be extended to ecosystem management, for example, by dynamically assessing the relative resilience of coral reefs and formulating short-term protective measures (such as artificial cooling). BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flowchart of a method for constructing a comprehensive relative resilience model according to an embodiment of the present invention; Figure 2 Schematic diagram of the principle of basic relative toughness according to an embodiment of the present invention, wherein (a) represents a positive relative toughness and (b) represents a negative relative toughness; Figure 3 A schematic diagram of a toughening process according to an embodiment of the present invention; Figure 4 Schematic diagram of the partitioning of the basic relative toughness model according to one embodiment of the present invention, wherein ① represents interval 1, ② represents interval 2, ③ represents interval 3, and ④ represents interval 4; Figure 5 Schematic diagram of the partitioning of the basic relative resilience model considering relative time scales according to one embodiment of the present invention, wherein ① represents interval 1, ② represents interval 2, ③ represents interval 3, and ④ represents interval 4; Figure 6FIG. 1 is a schematic diagram of the partitioning of a basic relative resilience model considering the rate of change according to an embodiment of the present invention, wherein (a) represents different situations of trend changes within interval three, and Indicates the selected moments under different trend changes The slope of the point at the position, (b) represents the different situations of trend changes in interval 2, and Indicates the selected moments under different trend changes The slope of the point at the position, where ① represents interval one, ② represents interval two, ③ represents interval three, and ④ represents interval four.

[0037] Figure 7 FIG. 1 is a schematic diagram of the partitioning of a basic relative resilience model considering the rate of change according to an embodiment of the present invention, wherein (a) represents different situations of trend change within interval 1, and Indicates the selected moments under different trend changes The slope of the point at the position, (b) represents the different situations of trend changes in interval four, and Indicates the selected moments under different trend changes The slope of the point at the position, where ① represents interval one, ② represents interval two, ③ represents interval three, and ④ represents interval four. DETAILED DESCRIPTION

[0038] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described one by one here, but the embodiments of the present invention are not limited to the following embodiments.

[0039] like Figure 1 As shown, according to one embodiment of the present invention, a method for constructing a comprehensive relative toughness model of the present invention includes the following steps: S1. Construct a basic relative resilience model to describe dynamic network resilience; S2. Introducing a relative time scale into the basic relative resilience model to make a correction to the basic relative resilience model and derive a relative resilience model based on the relative time scale; S3. The toughness change rate is introduced into the relative toughness model based on relative time scale to make a secondary correction to the relative toughness model based on relative time scale and obtain a comprehensive relative toughness model.

[0040] According to one embodiment of the present invention, in step S1, in the step of constructing a basic relative resilience model for describing the resilience of a dynamic network, the dynamic network may be a dynamic network of drones; wherein, for a drone cluster, the control of the cluster is achieved through a communication network, and a scientific and reasonable information interaction model can ensure the normal movement of the cluster individuals and the cluster as a whole, as well as the accurate execution of the task. In the process of executing the task, the drone is in motion, the distance between the cluster individuals is changing, and the corresponding communication network is dynamic and conforms to the characteristics of a scale-free network. Through analysis, it can be found that the movement of the cluster individuals themselves and the attack loss of the cluster are mapped on the cluster information interaction network as the movement and removal of network nodes. At the same time, due to the connection rules of the communication network, network reconstruction will occur, making it highly dynamic, adaptive, and self-recovering, and possessing a certain degree of resilience.

[0041] Therefore, we can define resilience in dynamic networks within clusters as the ability of a system to resist, absorb, adapt, and recover to its original state after a disturbance. Resilience research focuses on the entire resilience process: shock exposure, performance degradation, recovery and adaptation, and stable operation. Calculations and analysis based on this resilience process can then describe the system's "resilience" over a specific time period. Therefore, as a system property, resilience is considered to be present and available at every moment, meaning that "resilience" is available at every moment. Therefore, this proposal further proposes the concept of relative resilience to describe the system's relative resistance, absorption, adaptation, and recovery capabilities at a given moment.

[0042] Building on this foundation, relative resilience represents the system's immediate resilience compared to a reference moment. Relative resilience is independent of previous and subsequent moments, considering only the initial, reference, and current states. It measures the system's resilience at the current moment. Furthermore, relative resilience can be used to assess a system's immediate resilience at a specific moment in real time, including its ability to resist, absorb, adapt, and recover. Its core principle is to dynamically reflect the system's immediate state before and after a disturbance by using current performance values, reference performance values, and the rate of change.

[0043] In this implementation, relative resilience reflects the instantaneous capability of the system at a certain moment, and is expressed as the relative ratio of the performance difference (current moment to reference moment). Its essence is an instantaneous snapshot of the system's dynamic response, rather than a cumulative effect over time. Figure 2 As shown, in step S1, in the step of constructing a basic relative resilience model for describing dynamic network resilience, the basic relative resilience model is expressed as:

[0044] in, Relative toughness, Indicates that the dynamic network The performance size of the moment, Indicates that the dynamic network The performance size of the moment, Indicates the performance of the dynamic network at the initial moment, Indicates the current moment, represents the reference time, Indicates that the dynamic network Performance at all times The performance difference at the moment, Represents the performance of the dynamic network at the initial moment and The performance difference at that moment.

[0045] According to one embodiment of the present invention, in step S2, a relative time scale is introduced into the basic relative toughness model to perform a correction on the basic relative toughness model and obtain a relative toughness model based on the relative time scale. The relative toughness model based on the relative time scale is expressed as:

[0046]

[0047] in, express Moment and The difference between moments is the relative time scale.

[0048] According to one embodiment of the present invention, in step S2, the step of introducing a relative time scale into the basic relative toughness model to perform a correction on the basic relative toughness model and derive a relative toughness model based on the relative time scale includes: S21. Obtain the resilience process of dynamic network resilience based on the basic relative resilience model; in this embodiment, the resilience process includes four stages, and the four stages included in the resilience process are: impact stage, performance degradation stage, performance recovery stage and performance stabilization stage; for details, see Figure 3 As shown in Figure 2, the entire resilience process can be described as: suffering shock - performance degradation - recovery and adaptation - stable operation. Therefore, the change process between its various stages can be obtained based on the four stages included: Impact Phase - Performance Degradation Phase: During this process, system performance gradually declines due to the impact. Resilience, as a system property, demonstrates its ability to absorb the impact, effectively resisting the changes caused by the impact. This phase demonstrates a state where losses outweigh recovery. Furthermore, based on the changes during this phase, relative resilience is related to the performance value at that moment, the initial performance value, and the performance value at the reference moment. A higher relative resilience value indicates higher relative resilience and greater absorption capacity, resulting in smaller performance changes and, in other words, less performance degradation.

[0049] Performance Degradation Phase - Performance Recovery Phase: After performance drops to its lowest value during this process, the system gradually recovers due to its resilience. This phase demonstrates resilience, eliminating the changes caused by the shock. In other words, recovery outweighs losses. Furthermore, based on the changes during this phase, it can be seen that a larger relative resilience value indicates higher relative resilience and recovery capacity at that moment, indicating a greater degree of recovery compared to the reference moment.

[0050] Performance Recovery Phase - Performance Stabilization Phase: During this phase, after experiencing performance degradation caused by the shock, losses and recovery are balanced, with recovery exceeding losses. The system maintains a relatively stable performance level. This stable state may or may not be the same as the initial state, but the system maintains stable operation within this state. Therefore, during this phase, the system demonstrates adaptability, adapting to changes caused by the shock. In other words, recovery equals loss. Furthermore, based on the changes during this phase, it can be seen that a larger relative resilience value indicates better performance after stabilization, indicating greater adaptability.

[0051] S22. Introducing time reference parameters based on toughness process and performance reference parameters , used to divide the toughness process into intervals; in this embodiment, a time reference parameter is introduced based on the toughness process and performance reference parameters , used to divide the toughness process into intervals, including: Based on the resilience process, a reference moment is selected to analyze the performance change trend during the resilience process. , and based on the reference moment Obtain the performance change trend results during the toughness process; in this embodiment, the reference time It is a custom time. It makes the reference time There are also differences in the selection. In this embodiment, for the drone cluster, the reference time You can select the change position of the performance degradation phase and performance recovery phase of the dynamic network; for details, see Figure 3 As shown in the figure, the switching between the performance degradation stage and the performance recovery stage shows the turning point of the system resilience change trend. Therefore, the reference time The intersection of the performance degradation phase and the performance recovery phase can be selected. This makes it easier to accurately analyze the performance change trend during the performance resilience process and accurately divide the intervals.

[0052] See also Figure 4 As shown, in this embodiment, the reference time Previous and reference moments The analysis results are then divided; at the reference time Previously, there were two types of analysis results, namely: If the performance change trend is upward, then at the reference moment Previously in the performance recovery phase, reference time The performance is the best, among which The value is negative, indicating that the reference time The closer, the better the performance; If the performance change trend is downward, then at the reference moment Previously, it was in the performance degradation stage, reference time The performance is the worst, among which The value is positive, indicating that The further away, the better the performance; At the reference time Afterwards, there are two types of analysis results, which are: If the performance change trend is upward, then at the reference moment After that, it is in the performance recovery phase, with reference to the time The performance is the worst, among which The value is positive, indicating that The further away, the better the performance; If the performance change trend is downward, then at the reference moment After that, it is in the stage of performance degradation, reference time The performance is the best, among which The value is negative, indicating that the reference time The closer, the better the performance.

[0053] Based on the above partitioning, we know that the reference time The choice of directly affects the calculation direction and value of relative toughness: As mentioned above, the reference moment The change position of the performance degradation phase and performance recovery phase of the dynamic network can be selected, and the reference time That is, when the performance is at its lowest point, this setting method focuses on the recovery moment.

[0054] In other settings, the reference time If it is the initial state / arbitrary state, then this setting mode focuses on the degree to which the system deviates from the reference state; among them, different reference moments The choice of will affect the analysis of the toughness stage and the calculation of the relative toughness value. It affects the positive and negative magnitude of the numerator in the relative toughness model; if the numerator is close to the value of the two moments, the denominator value is small, which will cause the relative toughness value to be more sensitive to performance fluctuations. Specifically, if the reference moment Relative resilience is used to assess the efficiency of a system in recovering from a shock. For example, in an ecosystem, if a coral reef is selected as a reference time in the recovery phase , relative resilience can quantify its repair speed and guide dynamic management. It can be used to monitor the recovery progress in real time and optimize resource allocation (such as repairing damaged network nodes). In the stable phase, relative resilience reflects the system's ability to adapt to new equilibrium states. For example, in the stable phase of a communication network, it can be used to detect whether performance deviates from expectations due to structural changes. It can be used to warn of potential risks (such as secondary collapse) and verify whether the system has achieved long-term stability goals. If the reference time In the later stages of decline (e.g., region 4), relative resilience is negative, indicating continued deterioration in system performance. For example, when a power grid experiences overload in the later stages, relative resilience quantifies its ability to withstand secondary disturbances, enabling timely triggering of emergency mechanisms (e.g., load shedding) to prevent system collapse.

[0055] Introducing time reference parameters based on performance trend results and performance reference parameters , to divide the toughness process into intervals; in this embodiment, the time reference parameter Expressed as: ; The performance parameters are expressed as: ; Therefore, in the step of dividing the entire toughness process into intervals, four intervals are obtained and expressed as: At the reference time Before, there were two intervals, and they were: Interval three: A negative value indicates the initial stage of growth. A larger value (negative size) indicates greater relative resilience. Within this range, a larger value indicates a smaller absolute value, meaning the performance difference between that moment and the reference moment is smaller, indicating better performance.

[0056] Interval 2: ; A positive value indicates that it is in the pre-decline stage. The larger the value, the greater the relative toughness, which means the smaller the loss at that moment.

[0057] At the reference time After that, there are two intervals, which are: Interval 1: A positive value indicates that it is in the post-recovery stage. The larger the value, the greater the relative toughness, which means the better the recovery at that moment.

[0058] Interval 4: A negative value indicates the post-decline stage; larger values ​​(negative numbers) indicate greater relative toughness. Within this range, larger values ​​and smaller absolute values ​​indicate a performance value close to the reference moment, with a smaller decline and a greater relative toughness.

[0059] S23. Introducing a relative time scale for the intervals divided by the toughness process to modify the basic relative toughness model and obtain a relative toughness model based on the relative time scale. In this embodiment, the step of introducing a relative time scale for the intervals divided by the toughness process to modify the basic relative toughness model and obtain a relative toughness model based on the relative time scale includes: S231. Based on the current moment in the resilience process and reference time Construct a relative time scale, where, when considering the time scale, it is sufficient to obtain its relative time, and then the relative time can be expressed as the relative resilience moment and reference time The relative difference between Indicates; further, based on the relative difference and time reference parameters The description of the time scale can be realized and expressed as:

[0060] ; in, express Moment and The difference between moments is the relative time scale; S232. Introduce the constructed relative time scale into the intervals divided for the resilience process. Based on the aforementioned division of intervals in the entire resilience process, further combine the time scales of the corresponding intervals to achieve further description of each interval, which are respectively: See also Figure 5 As shown, at the reference time Before, there were two intervals, and they were: Interval three: ; A negative value indicates that it is in the pre-rising stage; Larger values ​​(negative numbers) and smaller absolute values ​​indicate a smaller distance from the reference time. For the same performance increase, the shorter the time required, the faster the increase, and the greater the resilience (adaptability).

[0061] Interval 2: ; A negative value indicates that it is in the front descending stage; Larger values ​​(negative numbers) and smaller absolute values ​​indicate a smaller distance from the reference time. For the same degree of performance degradation, a shorter time and a faster decline indicate lower resilience (resistance).

[0062] At the reference time After that, there are two intervals, which are: Interval 1: ; A positive value indicates that it is in the post-recovery stage; The larger the value, the longer the time required for the same recovery level, and the worse the resilience (recovery) ability.

[0063] Interval 4: ; A positive value indicates that it is in the post-decline stage; The smaller the value, the closer the distance to the reference time. For the same degree of decline, the shorter the time required, the faster the decline, and the worse the resilience (adaptability).

[0064] S233. Based on each interval with relative time scale correction, an exponential function is introduced for functional description to construct a functional form of relative time scale, which is expressed as: ; S234. The relative time scale function is introduced into the basic relative toughness model to obtain a relative toughness model based on relative time scale. Thus, the relative toughness model based on relative time scale can be expressed as:

[0065]

[0066] in, express Moment and The difference between moments is the relative time scale.

[0067] In this embodiment, based on the relative resilience model based on relative time scale, it can be seen that the time taken for a certain degree of performance change relative to the reference time is large, and the increase or decrease is large. The value of is positive or negative. In the performance improvement stage, the shorter the relative time used, the better the resilience; in the performance degradation stage, the shorter the relative time used, the faster the degradation and the worse the resilience.

[0068] Therefore, the relative resilience model based on relative time scale can be obtained: when When , the function is about The increasing function of is a decreasing function. The increase, Increase, Reduce, , so Reduce, The value range is (0, 1); thus, , , ; , , 0, so the value range of the relative resilience model based on relative time scale is .

[0069] when When , the function is about The increasing function of As The increase, Increase, Reduce, , so Increase, The value range is (0, 1); thus, , , ; , , 0, so the value range of the relative resilience model based on relative time scale is .

[0070] when When , the function value is 0.

[0071] In summary, the function The value range depends on Value: When calculating Normalizing to (-5, 5), we can achieve (Region 1 and Region 4), (Region 2 and Region 3).

[0072] According to one embodiment of the present invention, in step S3, the step of introducing the toughness change rate into the relative toughness model based on the relative time scale to perform a secondary correction on the relative toughness model based on the relative time scale and derive the comprehensive relative toughness model includes: S31. Obtain the resilience change rate of the dynamic network resilience, and the resilience change rate is expressed as:

[0073] in, Represents the rate of change of resilience, that is, the dynamic network The slope of the performance at the moment; On this basis, we can know that the rate parameter is the selected moment in the performance change trend of the toughness process The slope of the point at the location indicates the speed of absorption / adaptation / recovery. The rate of change of relative resilience focuses on the speed of change in resilience at that moment, that is, the faster / slower the recovery rises, and the faster / slower the resistance falls. This gives this solution better resilience calculation performance and better adaptability to smaller relative resilience, making this solution highly compatible with relative resilience calculations.

[0074] S32. Based on the intervals divided in step S22, the positive and negative changes of the basic relative toughness model and the positive and negative changes of the toughness change rate are introduced, and they are: See also Figure 6 As shown, at the reference time Before, there were two intervals, and they were: Interval three: ; In the pre-ascending stage, the rate parameter is a positive value. The larger the rate parameter value is, the faster the rising speed of this point is, which means that the resilience shown at this moment is better.

[0075] Interval 2: ; In the pre-decline stage, the rate parameter is a negative value. The larger the value, the smaller the absolute value, the smoother it is, and the slower the decline speed at the corresponding point, indicating that the resilience and resistance adaptability presented at this moment are better.

[0076] See also Figure 7 As shown, at the reference time After that, there are two intervals, which are: Interval 1: ; In the post-recovery stage, the rate parameter is a positive value. The larger the value, the faster the rising speed of the point, indicating that the resilience at this moment is on an upward trend and the recovery is better.

[0077] Interval 4: ; In the post-decline stage, the rate parameter is negative. The larger the value, the smaller the absolute value, the smoother it is, and the slower the decline speed at the corresponding point, which means that the resilience shown at this moment is better and the decline is slower.

[0078] S33. Based on the positive and negative changes of the basic relative toughness model and the positive and negative changes of the toughness change rate, an exponential function is introduced to describe the functional form of the toughness change rate, which is expressed as: .

[0079] In this embodiment, the functional form of the toughness change rate is described by introducing an exponential function based on its value and increase and decrease. For this purpose, the toughness change rate has a value range of (-0.5, 0.5) and increases monotonically within the real number range. When the value is 0, , the value approaches The range of the change rate is defined as (-0.5, 0.5), which means that the change rate has a general influence on the relative toughness calculation. Normalization (-5, 5) can achieve , , control the amplitude of change.

[0080] S34. Introduce the toughness change rate into the relative toughness model based on the relative time scale to obtain a comprehensive relative toughness model; wherein the comprehensive relative toughness model is expressed as: .

[0081] In this embodiment, the comprehensive relative toughness model Indicates the consideration of relative performance size (performance recovery rate), represents the consideration of relative time scales, Indicates the consideration of the rate of change of resilience. Therefore, the comprehensive relative resilience expression can be used to characterize the "resilience capacity" of the system at a certain moment, the degree and ability of resistance, absorption, adaptation, recovery in the dimensions of performance, time, and rate of change. Among them, the comprehensive relative resilience value range of the comprehensive relative resilience model is When the performance degree changes slightly, the influence of relative time change on the comprehensive relative toughness change is small, while the change rate has a greater impact on the comprehensive relative toughness change. As the performance degree change increases, the influence of the performance change degree plays a decisive role, indicating that the performance difference dominates the overall trend, and the time and rate terms are secondary influencing factors.

[0082] According to one embodiment of the present invention, the method for constructing a comprehensive relative toughness model of the present invention further includes: S4. Introduce a scaling factor to the comprehensive relative resilience model to adjust the sensitivity range of the comprehensive relative resilience model so that the relative time scale is taken into account. and toughness change rate The comprehensive relative toughness calculated when has practical significance within the range of all real numbers; the comprehensive relative toughness model with the introduction of scaling factors is expressed as:

[0083] in, are scaling factors, and .

[0084] In this embodiment, the scaling factor Its value can be adjusted according to actual application scenarios and data to ensure that the model response is reasonable within the expected parameter range and in line with the actual situation, and to ensure that the model can still sensitively reflect the relative resilience of the system under extreme values. At the same time, normalization can also be performed. In this embodiment, the scaling factor The recommended value range is (0.1, 0.3), and the scaling factor The recommended value range is (0.3, 0.7).

[0085] The above contents are merely examples of specific solutions of the present invention. For devices and structures not described in detail, it should be understood that they can be implemented by adopting general devices and methods available in the art.

[0086] The above description is merely one embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for constructing a comprehensive relative resilience model, characterized in that: The following steps are involved: S1. Construct a basic relative resilience model to describe dynamic network resilience; S2. introducing a relative time scale into the basic relative toughness model to modify the basic relative toughness model and derive a relative toughness model based on the relative time scale; S3. Introducing the toughness change rate into the relative toughness model based on the relative time scale, so as to make a secondary correction to the relative toughness model based on the relative time scale and obtain a comprehensive relative toughness model.

2. The method for constructing a comprehensive relative resilience model according to claim 1, characterized in that: In step S1, in the step of constructing a basic relative resilience model for describing dynamic network resilience, the basic relative resilience model is expressed as: in, Relative toughness, Indicates that the dynamic network The performance size of the moment, Indicates that the dynamic network The performance size of the moment, Indicates the performance of the dynamic network at the initial moment, Indicates the current moment, represents the reference time, Indicates that the dynamic network Performance at all times The performance difference at the moment, Represents the performance of the dynamic network at the initial moment and The performance difference at that moment.

3. The method for constructing a comprehensive relative toughness model according to claim 2, characterized in that: In step S2, a relative time scale is introduced into the basic relative toughness model to perform a correction on the basic relative toughness model and obtain a relative toughness model based on the relative time scale. The relative toughness model based on the relative time scale is expressed as: in, express Moment and The difference between moments is the relative time scale.

4. The method for constructing a comprehensive relative toughness model according to claim 3, characterized in that: In step S2, the step of introducing a relative time scale into the basic relative toughness model to correct the basic relative toughness model and obtain a relative toughness model based on the relative time scale includes: S21. Obtaining a resilience process regarding the dynamic network resilience based on the basic relative resilience model; S22. Introducing a time reference parameter based on the toughness process and performance reference parameters , used to divide the toughness process into intervals; S23. Introducing the relative time scale into the intervals divided by the toughness process to modify the basic relative toughness model and obtain a relative toughness model based on the relative time scale.

5. The method for constructing a comprehensive relative toughness model according to claim 4, characterized in that: In step S21, in the step of obtaining a resilience process of the dynamic network resilience based on the basic relative resilience model, the resilience process includes four stages, and the four stages included in the resilience process are: an impact stage, a performance degradation stage, a performance recovery stage, and a performance stabilization stage; In step S22, a time reference parameter is introduced based on the toughness process and performance reference parameters , the step of dividing the toughness process into intervals includes: A reference moment for analyzing the performance change trend during the toughness process is selected based on the toughness process. , and based on the reference moment Obtaining performance change trend results during the toughness process; Introduce time reference parameters based on the performance change trend results and performance reference parameters , in order to divide the toughness process into intervals.

6. The method for constructing a comprehensive relative toughness model according to claim 5, characterized in that: In step S22, based on the reference time In the step of obtaining the performance change trend result during the toughness process, the reference time Before and the reference moment Then the analysis results are divided; wherein, at the reference time Previously, there were two types of analysis results, namely: The performance change trend is an upward trend, then at the reference time Previously in the performance recovery phase, reference time The performance is the best, among which The value is negative, indicating that the reference time The closer, the better the performance; The performance change trend is a downward trend, then at the reference time Previously, it was in the performance degradation stage, reference time The performance is the worst, among which The value is positive, indicating that The further away, the better the performance; At the reference time Afterwards, there are two types of analysis results, which are: The performance change trend is an upward trend, then at the reference time After that, it is in the performance recovery phase, with reference to the time The performance is the worst, among which The value is positive, indicating that The further away, the better the performance; The performance change trend is a downward trend, then at the reference time After that, it is in the stage of performance degradation, reference time The performance is the best, among which The value is negative, indicating that the reference time The closer, the better the performance.

7. The method for constructing a comprehensive relative toughness model according to claim 6, characterized in that: In step S22, a time reference parameter is introduced based on the performance change trend result. and performance reference parameters In the step, the time reference parameter Expressed as: ； The performance parameters are expressed as: ； Then, in the step of dividing the toughness process into intervals, four intervals are obtained and expressed as: At the reference time Before, there were two intervals, and they were: Interval three, and expressed as: ; Interval 2, and expressed as: ; At the reference time After that, there are two intervals, which are: Interval 1, and is expressed as: ; Interval four, and expressed as: .

8. The method for constructing a comprehensive relative toughness model according to claim 7, characterized in that: In step S23, the step of introducing the relative time scale into the intervals divided by the toughness process to modify the basic relative toughness model and obtain a relative toughness model based on the relative time scale includes: S231. Based on the current moment of the resilience process and reference time The relative time scale is constructed and expressed as: ； in, express Moment and The difference between moments is the relative time scale; S232. The constructed relative time scale is introduced into the interval divided for the toughness process, and is respectively: At the reference time Before, there were two intervals, and they were: Interval three, and expressed as: ; Interval 2, and expressed as: ; At the reference time After that, there are two intervals, which are: Interval 1, and is expressed as: ; Interval four, and expressed as: ; S233. Based on each interval with the relative time scale correction, an exponential function is introduced for functional description to construct a functional form of the relative time scale, which is expressed as: ； S234. Introduce the functional form of the relative time scale into the basic relative toughness model to obtain a relative toughness model based on the relative time scale.

9. The method for constructing a comprehensive relative toughness model according to claim 8, characterized in that: In step S3, the step of introducing the toughness change rate into the relative toughness model based on the relative time scale to perform a secondary correction on the relative toughness model based on the relative time scale and obtain a comprehensive relative toughness model includes: S31. Obtain the toughness change rate of the dynamic network toughness, and the toughness change rate is expressed as: in, Indicates the rate of change of toughness; S32. Based on the intervals divided in step S22, the positive and negative changes of the basic relative toughness model and the positive and negative changes of the toughness change rate are introduced, and they are: At the reference time Before, there were two intervals, and they were: Interval three, and expressed as: ; Interval 2, and expressed as: ; At the reference time After that, there are two intervals, which are: Interval 1, and is expressed as: ; Interval four, and expressed as: ; S33. Based on the positive and negative changes of the basic relative toughness model and the positive and negative changes of the toughness change rate, an exponential function is introduced to perform functional description to construct a functional form of the toughness change rate, which is expressed as: ； S34. Introducing the toughness change rate into a relative toughness model based on a relative time scale to derive the comprehensive relative toughness model; wherein the comprehensive relative toughness model is expressed as: 。 10. The method for constructing a comprehensive relative toughness model according to claim 9, characterized in that: Also includes: S4. Introducing a scaling factor into the comprehensive relative resilience model to adjust the sensitivity interval of the comprehensive relative resilience model so as to take into account the relative time scale and toughness change rate The comprehensive relative toughness calculated when has practical significance within the range of all real numbers; the comprehensive relative toughness model with the introduction of scaling factors is expressed as: in, are scaling factors, and .

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