A robustness assessment method, apparatus, and storage medium for power system integrated tree applications.

Abstract

This invention discloses a robustness evaluation method for power system integrated tree applications, comprising the following steps: S1. Transforming the infinite norm robustness evaluation problem for integrated trees into a minimum adversarial sample problem for each data point, modeling it as a mixed-integer linear programming problem; S2. Abstracting the relationships between data attributes and the value constraints of data attributes from the physical rules of the power system; S3. Representing the Boolean variables in step S1 with continuous variables; S4. Incorporating the relationships between data attributes and the value constraints of data attributes in step S2 into the mixed-integer linear programming problem in step S3 using variable transformation; S5. Solving for the robustness of each data point in step S1 using the method in step S4, obtaining the robustness of integrated tree applications considering the physical constraints of the power system, thereby solving the problem that existing technologies cannot analyze the robustness of power systems based on integrated tree models.

Description

Technical Field

[0001] This invention relates to a robustness assessment method, apparatus, and storage medium for power system integrated tree applications, belonging to the field of computer artificial intelligence security technology. Background Technology

[0002] With the ever-increasing energy demand of modern society, the operation and management of power systems have become increasingly complex and challenging. Traditional methods and technologies are no longer sufficient to meet the growing electricity demand and improve the reliability, efficiency, and sustainability of power systems. Against this backdrop, modern power systems deeply integrate information technologies such as control, communication, and computers, resulting in an exponential increase in the amount of data generated during daily operation. As a powerful data-driven approach, machine learning has been gradually introduced into power system operation, providing new directions and solutions for decision-makers and operators. The massive amounts of data provide the foundation for the application of machine learning in power systems, and data-driven predictive technologies have been widely applied in frequency control, data acquisition and monitoring, state estimation, and electricity markets.

[0003] With the widespread application of machine learning in power systems, power companies are increasingly outsourcing complex machine learning tasks to cloud services. However, this shift has also brought a series of cybersecurity issues that urgently need to be addressed. The operation of power systems relies on raw data collected from end-user sites and transmitted through communication networks. However, this data is vulnerable to cyberattacks during transmission. Attackers may steal, tamper with, or destroy this data, interfering with the power system's predictive output and leading to safety hazards such as equipment failure, financial losses, and widespread power outages.

[0004] Furthermore, the threat of adversarial attacks on power systems should also be taken seriously. Attackers may attempt to disrupt the normal operation of the power system by intentionally interfering with its data and operational processes. Such adversarial attacks could lead to power system instability or even large-scale blackouts, causing serious impacts on society. To ensure the stable and safe operation of the power system, it is urgent to address the cybersecurity issues related to machine learning within the power system.

[0005] Ensemble tree methods have attracted significant attention in power systems as an efficient machine learning approach due to their ability to balance accuracy, complexity, and interpretability. This method can handle complex problems in power systems and provide high-precision predictions and decision support. This makes ensemble tree-based methods a popular choice for machine learning applications in power systems.

[0006] However, while communication networks provide services to power systems and ensemble tree-based machine learning applications, they are vulnerable to adversarial attacks. Attackers may use adversarial techniques to disrupt communication networks, such as tampering with data or engaging in other malicious activities. Such disruption can severely impact the performance and reliability of ensemble tree-based machine learning applications. Therefore, it is necessary to analyze the robustness of ensemble tree-based power systems to ensure their resilience against adversarial attacks.

[0007] Only by ensuring the robustness of power systems based on integrated trees can we effectively respond to adversarial attacks and guarantee the normal operation and reliability of power systems. This will provide reliable decision support for power companies and operators, and drive further innovation and development in power systems. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a robustness evaluation method, device and storage medium for power system integrated tree applications, so as to overcome the shortcomings of the prior art.

[0009] The technical solution of this invention is as follows:

[0010] The first aspect: provides a robustness evaluation method for power system integration tree applications, including the following steps:

[0011] S1. Applying an integrated tree to power system physical constraints. The norm robustness evaluation problem is transformed into a minimum adversarial example problem for solving the data. Combining the structure and properties of ensemble trees, the adversarial example generation problem is formally described and represented, and the ensemble tree's... Norm robustness evaluation is modeled as a mixed-integer linear programming problem;

[0012] S2. Abstract the equality constraints between data attributes and the inequality constraints on the values ​​of data attributes from the physical laws, variable ranges and detection rules of the power system.

[0013] S3. Associate the discrete variables in the mixed-integer linear programming problem in step S1 with the continuous power data in S2, and represent the continuous power data using Boolean discrete variables that describe the decision tree structure;

[0014] S4. Integrate the equality and inequality constraints between power data attributes from step S2 into the ensemble tree. Norm robustness evaluation in mixed-integer linear programming problems;

[0015] S5. Use the global optimization method to solve the robustness of the mixed integer linear programming problem in step S4, and obtain the robustness of the power system based on the ensemble tree model.

[0016] Specifically, step S1 includes: the robustness evaluation of the ensemble tree can be measured using the minimum adversarial perturbation of the ensemble tree, and... The discriminative problem of robustness evaluation of ensemble trees under norm is transformed into the problem of finding the minimum adversarial sample of the ensemble tree. This problem is then modeled as a mixed integer linear programming problem.

[0017] The constraints for the mixed-integer linear programming problem are:

[0018]

[0019] l1+l2+…+l N =1

[0020]

[0021]

[0022]

[0023] Where, x j <α1、x j <α2、x j <α3、…、x j <α M (α1<α2<…<α M ) represents the result extracted from the ensemble tree node along with attribute x. j The corresponding predicate; Indicates about attribute x j Boolean predicate variable, corresponding to predicate x j <α j α k Indicates feature x j The boundary value of the corresponding k-th predicate, where the predicate variable is 1 to represent attribute x. j Satisfying the predicate, setting it to 0 indicates that attribute x j The predicate is not satisfied; N This represents a Boolean leaf variable corresponding to the Nth leaf node. A leaf variable of 1 indicates that the leaf node takes a value, and a leaf variable of 0 indicates that the leaf node does not take a value. This represents the Boolean leaf variable of the k-th leaf node under the pseudo-subtree; p represents the m-th leaf variable in the proper subtree. root The predicate variable representing the root node; p node The predicate variable represents a non-root node of the tree; v i This represents the value stored in the i-th leaf node;

[0024] The objective function of the mixed-integer linear programming problem is: Adversarial perturbations of norms:

[0025]

[0026] in, Indicates feature x j The i-th predicate variable corresponds to this, where i is a positive integer from 1 to n, j is a positive integer from 1 to M, n represents the maximum number of predicates corresponding to the feature, M represents the total number of features, and C represents a constant. Indicates feature x j The weight of the i-th predicate variable.

[0027] Furthermore, in step S2, the relationships between data attributes include load balancing equations and power flow equations between nodes; the value constraints of data attributes include the voltage range of nodes and the load range of lines.

[0028] The load balancing equation is as follows:

[0029] 1 T ΔLD=0

[0030] The power flow equation is:

[0031] ΔFL=-SCH -1 ΔLD

[0032] The load range is:

[0033]

[0034] Where ΔFL represents the power flow disturbance vector, ΔLD represents the load disturbance vector, and ΔLD d LD represents the value of the d-th row of the load disturbance vector. d Indicates ΔLD d The corresponding original load value, τ is a parameter, SCH -1 represents the power transfer factor matrix, where 1 represents a column vector of all 1s, 0 represents a column vector of all 0s, and q represents the number of features of the LD.

[0035] Specifically, in step S3, the range of values ​​for the predicates corresponding to the predicate variables of the ensemble tree is represented using continuous variables:

[0036]

[0037]

[0038] in, Indicates the value in x j A continuous variable within the range of values ​​of the k-th digit. x representsj The k-th predicate variable, z k express and Whether the values ​​are consistent, adversarial examples represent:

[0039]

[0040]

[0041] in, Represents the adversarial sample vector. It consists of the power flow disturbance vector ΔFL, the power generation disturbance vector ΔPG, and the load disturbance vector ΔLD, where Y represents a continuous variable. The matrix consists of x, which represents the original data vector, and ∈, which represents the adversarial perturbation vector.

[0042]

[0043]

[0044] The equality and inequality constraints between power data attributes in step S4 are incorporated into the integration tree. Norm robustness evaluation of mixed-integer linear programming problems is as follows:

[0045] Obtain the original variables and constraints of the mixed integer linear programming problem in step S1, add continuous variables and physical constraints from step S2 to the mixed integer linear programming problem, establish the relationship constraints between continuous variables and Boolean variables using the method in step S3, add the mixed integer linear programming problem in step S4, use continuous variables to represent the objective function, and solve the mixed integer linear programming problem.

[0046] An integrated tree incorporating equality and inequality constraints between power data attributes The mixed-integer linear programming problem with norms is as follows:

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] 1 T ΔLD=0

[0054] ΔFL=-SCH -1 ΔLD

[0055]

[0056]

[0057] l1+l2+…+l N =1

[0058]

[0059]

[0060]

[0061] in, Indicates the value in x j A continuous variable within the range of values ​​of the k-th digit. x represents j The k-th predicate variable, z k express and Whether the values ​​are consistent, B is a defined non-negative continuous variable. Let Y represent the adversarial sample vector, and Y represent a continuous variable. The matrix consists of x, which represents the original data vector, and ∈, which represents the adversarial perturbation vector.

[0062] Specifically, in step S5, the global optimization method for solving the mixed-integer linear programming problem includes:

[0063] Global optimization methods include branch and bound and cutting plane methods.

[0064] Specifically, the global optimization method for solving the mixed-integer linear programming problem in step S5 includes:

[0065] Global optimization methods include branch and bound and cutting plane methods.

[0066] Furthermore, considering the robustness evaluation results of all data points, the robustness evaluation results of the entire ensemble tree model are obtained.

[0067] The second aspect: providing a robustness assessment apparatus for power system integrated tree applications, characterized in that: the apparatus includes: a processor and a memory, wherein the memory stores computer program instructions suitable for execution by the processor, the computer program instructions being executed by the processor causing the processor to execute a robustness assessment method for power systems based on integrated trees as described in any of the first aspects.

[0068] Third aspect: A storage medium is provided, including computer program instructions stored on the storage medium, wherein the computer program instructions are executed by a processor to perform a robustness evaluation method for a power system based on an integrated tree, as described in any of the first aspects.

[0069] The beneficial effects of this invention are: compared with the prior art,

[0070] 1) This invention integrates the tree... The robustness assessment of the norm is modeled as a mixed-integer linear programming problem, and the equality constraint relationship between data attributes is abstracted from the physical rules, variable ranges and detection rules in the power system. Then, by solving the robustness of the mixed-integer linear programming problem, the robustness assessment result of the power system based on the ensemble tree model is obtained.

[0071] 2) This invention uses binary variables to process complex tree structures. By deriving the key relationships between tree nodes and converting significant physical constraints into binary variables, the robustness evaluation problem subject to physical constraints is solved as a mixed-integer linear programming problem.

[0072] 3) This invention is intended to... To address the robustness assessment problem under the norm, a variable-changing method is proposed to keep the physical constraints unchanged. Then, by describing all constraints using binary variables and modifying the objective function, a general solution for physical constraint robustness assessment is developed. Attached Figure Description

[0073] Figure 1 This is a flowchart of the present invention;

[0074] Figure 2 A schematic block diagram of a robustness evaluation apparatus for a power system based on an integrated tree, provided for at least one embodiment of this disclosure;

[0075] Figure 3 A schematic block diagram of a storage medium provided for at least one embodiment of this disclosure. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings.

[0077] Example 1: As shown in the attached document Figure 1 As shown, the first aspect is to provide a robustness evaluation method for power system integration tree applications, including the following steps:

[0078] S1. Applying an integrated tree to power system physical constraints. The norm robustness evaluation problem is transformed into a minimum adversarial example problem for solving the data. Combining the structure and properties of ensemble trees, the adversarial example generation problem is formally described and represented, and the ensemble tree's... Norm robustness evaluation is modeled as a mixed-integer linear programming problem;

[0079] Specifically, step S1 includes: treating the structure of the ensemble tree as a constraint on the model, considering the minimum distance norm of the adversarial examples as an optimization variable, and restricting both the constraints and the optimization objective to the minimum distance norm. The optimization problem obtained by generating adversarial examples is as follows:

[0080]

[0081] stf(x)≠f(x+δ)

[0082] g(x+δ)=0

[0083] ψ(x+δ)≥0

[0084] For the constraint problem in the structure of ensemble trees, the relationship between predicate variables and leaf variables is described to generate examples of adversarial ensemble tree models. For attribute x... i Suppose the predicate extracted from the tree corresponding to it is x. i <α1、x i <α2、x i <α3、…、x i <α M and α1<α2<…<α M Then, given the perturbed variable, it will be located at x. i <α1、x i <α2、x i <α3、…、x i <α M Within the interval. Below are the predicate constraints:

[0085]

[0086] Indicates about attribute x j Boolean predicate variable, corresponding to predicate x j <α j Consider a single decision tree with leaf variables l1, l2, ..., l N So we have:

[0087] l1+l2+…+l N =1

[0088] Furthermore, we described the correlation between predicate variables and leaf variables:

[0089]

[0090]

[0091] To construct adversarial examples, the misclassification constraint must be satisfied:

[0092]

[0093] Where, x j <α1、x j <α2、x j <α3、…、x j <α M (α1<α2<…<α M ) represents the result extracted from the ensemble tree node along with attribute x. j The corresponding predicate; Indicates about attribute x j Boolean predicate variable, corresponding to predicate x j <α j α k Indicates feature x j The boundary value of the corresponding k-th predicate, where the predicate variable is 1 to represent attribute x. j Satisfying the predicate, setting it to 0 indicates that attribute x j The predicate is not satisfied; N This represents a Boolean leaf variable corresponding to the Nth leaf node. A leaf variable of 1 indicates that the leaf node takes a value, and a leaf variable of 0 indicates that the leaf node does not take a value. This represents the Boolean leaf variable of the k-th leaf node under the pseudo-subtree; p represents the m-th leaf variable in the proper subtree. root The predicate variable representing the root node; p node The predicate variable represents a non-root node of the tree; v i This represents the value stored in the i-th leaf node;

[0094] For the objective function, the inherent characteristic of constructing adversarial examples is changing the prediction path to terminate at different leaf nodes; the key computation is determining the values ​​of the predicate variables. Once the predicate variables are determined, the distance between the adversarial example and the original input is calculated. Therefore, the objective function can be:

[0095]

[0096] in, Indicates feature x j The i-th predicate variable corresponds to this, where i is a positive integer from 1 to n, j is a positive integer from 1 to M, n represents the maximum number of predicates corresponding to the feature, M represents the total number of features, and C represents a constant. Indicates feature x j The weight of the i-th predicate variable.

[0097] S2. Abstract the equality constraints between data attributes and the inequality constraints on the values ​​of data attributes from the physical rules, variable ranges and detection rules of the power system.

[0098] Based on the physical rules governing the various attributes in the power grid, we can establish relationships between data attributes, such as load balancing equations and power flow equations between nodes. Simultaneously, we can also derive the value constraints for each attribute based on the physical rules, such as the voltage range of a node and the maximum load of a line. The following are the equations and constraints to consider in a power system: relationships between data attributes include load balancing equations and power flow equations between nodes; value constraints for data attributes include the voltage range of a node and the load range of a line.

[0099] The relationship between data attributes: The load balancing equation between nodes is:

[0100] 1 T ΔLD=0

[0101] The power flow equation is:

[0102] ΔFL=-SCH -1 ΔLD

[0103] Data attribute value constraints: Node load range is...

[0104]

[0105] Where ΔFL represents the power flow disturbance vector, ΔLD represents the load disturbance vector, and ΔLD d LD represents the value of the d-th row of the load disturbance vector. d Indicates ΔLD d The corresponding original load value, τ is a parameter, SCH -1 represents the power transfer factor matrix, where 1 represents a column vector of all 1s, 0 represents a column vector of all 0s, and q represents the number of features of the LD.

[0106] S3. Associate the discrete variables in the mixed-integer linear programming problem in step S1 with the continuous power data in S2, and represent the continuous power data using Boolean discrete variables that describe the decision tree structure;

[0107] Specifically, the range of values ​​for the predicates corresponding to the predicate variables in the ensemble tree is represented using continuous variables:

[0108]

[0109]

[0110] in, Indicates the value in x j A continuous variable within the range of values ​​of the k-th digit. x represents j The k-th predicate variable, z k express and Whether the values ​​are consistent. Therefore, adversarial examples can be represented as:

[0111]

[0112]

[0113] in, Represents the adversarial sample vector. It consists of the power flow disturbance vector ΔFL, the power generation disturbance vector ΔPG, and the load disturbance vector ΔLD. Y represents a continuous variable. The matrix consists of x, which represents the original data vector, and ∈, which represents the adversarial perturbation vector.

[0114]

[0115]

[0116] S4. The relationships between data attributes and the value constraints of data attributes in step S2 are expressed using continuous variables in step S3 and then added to the mixed integer linear programming problem;

[0117] Specifically, the equality and inequality constraints between power data attributes in step S4 are integrated into the ensemble tree. Norm robustness evaluation of mixed-integer linear programming problems is as follows:

[0118] Although equality and inequality constraints can be described using predicate variables, this makes solving the robustness evaluation problem more complex. Therefore, our goal is to preserve the constraints given in step S2.

[0119] To solve this problem, the key is to change the objective function. The method transforms discrete expressions into continuous expressions. The description of this method is as follows. For The optimization problem of norm can be expressed as:

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] 1 T ΔLD=0

[0127] ΔFL=-SCH -1 ΔLD

[0128]

[0129]

[0130] l1+l2+…+l N =1

[0131]

[0132]

[0133]

[0134] in, Indicates the value in x j A continuous variable within the range of values ​​of the k-th digit. x represents j The k-th predicate variable, z k express and Whether the values ​​are consistent, B is a defined non-negative continuous variable. Let Y represent the adversarial sample vector, and Y represent a continuous variable. The matrix consists of x, which represents the original data vector, and ∈, which represents the adversarial perturbation vector.

[0135] S5. The robustness of the mixed-integer linear programming problem in step S4 is solved using global optimization methods to obtain the robustness of the power system based on the ensemble tree model. Global optimization methods for solving mixed-integer linear programming problems include branch and bound, and cutting plane methods. Branch and bound is one of the commonly used methods for solving mixed-integer linear programming problems. It finds the optimal solution by continuously decomposing the problem into smaller subproblems and solving these subproblems using linear programming methods. Simultaneously, upper and lower bounds are used to limit the search space to reduce the solution time. Some commercial and open-source optimization software packages, such as CPLEX, Gurobi, and GLPK, provide efficient tools for solving mixed-integer linear programming problems based on optimized branch and bound methods. These solvers are then used to solve the problem. The norm of mixed-integer linear programming problems can improve the solution efficiency.

[0136] The robustness of solving mixed-integer linear programming problems using the Gurobi solver to individual data in the test sample is obtained, leading to an ensemble tree application of the sample considering power system physical constraints. Norm robustness.

[0137] Furthermore, considering the robustness evaluation results of all samples, the robustness evaluation results of the entire ensemble tree model are obtained.

[0138] • Test results:

[0139] The test dataset used takes into account the susceptibility of data collected in power system scenarios to noise interference, such as sudden fluctuations in power load and sensor failures. Appropriate preprocessing and cleaning are necessary to improve the accuracy and reliability of subsequent analysis. Our data is obtained by injecting 12,000 load configurations sampled from the publicly available New York State Real Load Data Tracking dataset into the IEEE 14-node power system. Default parameters for the IEEE 14-node power system provided by MATPOWER are used. If the stability condition is violated, the corresponding data is labeled "0"; otherwise, the data is labeled "1". In total, we use 12,000 labeled data points to train and test xgboost (a commonly used ensemble tree model) and verify its robustness under different parameter settings. Next, we will use misclassification constraint C1, inequality constraint C2, and equality constraint C3 to evaluate the physical constraint robustness of xgboost.

[0140] For each data point, its minimum adversarial sample and corresponding perturbation can be obtained, thereby determining the robustness of that data point.

[0141] Table 1: Variation of robustness evaluation values ​​based on xgboost under different constraints

[0142]

[0143] The constraint used is misclassification (C1), inequality (C2), and equality (C3). Table 1 shows that the constraints of the robustness evaluation problem increase with the property value. Given a specific property value, there may not be any feasible solution to the robustness evaluation problem. For this property value, an attacker cannot interfere with it and change its prediction. This property value is then defined as a robust property value, measured by the robustness RP value.

[0144]

[0145] Table 2: Variation of robustness RP value based on xgboost under different constraints

[0146]

[0147]

[0148] As shown in Table 2, the number of robust attribute values ​​increases with the increase of constraints. Different norms do not affect the number of robust attribute values.

[0149] Table 3: By adjusting the parameter min_child, in Robustness evaluation value of static security assessment based on xgboost under the norm.

[0150]

[0151] The above results indicate that the lower bound of adversarial perturbations is affected by model parameters, and the physical constraints of the power system increase the difficulty for attackers to mislead the static security assessment results based on ensemble trees.

[0152] Example 2:

[0153] At least one embodiment of this disclosure also provides a schematic block diagram of a robustness evaluation apparatus for a power system integration tree application. The robustness evaluation apparatus for the power system integration tree application includes a processor and a memory, wherein the memory stores computer program instructions suitable for execution by the processor, the computer program instructions, when executed by the processor, causing the processor to perform a robustness evaluation method for a power system integration tree application as described in any one of the embodiments.

[0154] For example, the processor may be a central processing unit (CPU), a graphics processing unit (GPU), a tensor processor (TPU), or other processing units with data processing and / or instruction execution capabilities. For instance, the processor can be implemented as a general-purpose processor, or as a microcontroller, microprocessor, digital signal processor, dedicated image processing chip, or field-programmable logic array, etc. For example, the memory may include at least one type of volatile memory and non-volatile memory, such as read-only memory (ROM), hard disk, flash memory, etc. Accordingly, the memory can be implemented as one or more computer program products, which may include various forms of computer-readable storage media on which one or more computer program instructions may be stored. The processor can execute the program instructions to perform a robustness evaluation method for any power system integrated tree application provided in at least one embodiment of this disclosure. The memory can also store various other applications and various data, such as various data used and / or generated by the applications.

[0155] Example 3:

[0156] At least one embodiment of this disclosure also provides a storage medium (e.g., a non-transitory storage medium). Figure 3 This is a schematic block diagram of a storage medium provided in at least one embodiment of this disclosure. Figure 3 As shown, the storage medium includes computer program instructions stored on the storage medium. When executed by a processor, the computer program instructions perform a robustness evaluation method for a power system integration tree application provided in at least one embodiment of this disclosure.

[0157] For example, storage media can take many forms, including tangible storage media, carrier media, or physical transmission media. Stable storage media can include optical discs or magnetic disks, and other storage systems used in computers or similar devices that enable the system components described in the figure. Unstable storage media can include dynamic memory, such as the main memory of a computer platform. Tangible transmission media can include coaxial cables, copper cables, and optical fibers, such as the lines that form a bus within a computer system. Carrier transmission media can transmit electrical signals, electromagnetic signals, acoustic signals, or optical signals. These signals can be generated by radio frequency or infrared data communication methods. Typical storage media (e.g., computer-readable media) include hard disks, floppy disks, magnetic tapes, and any other magnetic media; CD-ROMs, DVDs, DVD-ROMs, and any other optical media; punched cards and any other physical storage media containing a punch pattern; RAM, PROMs, EPROMs, FLASH-EPROMs, and any other memory chips or magnetic tapes; carrier waves for transmitting data or instructions, cables or connection devices for transmitting carrier waves, and any other data that can be read using computer program instructions (e.g., program code) and / or by a computer.

[0158] Computer program instructions (e.g., program code) for performing the operations of this disclosure can be written in one or more programming languages ​​or a combination thereof, including but not limited to object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0159] In some examples, the functionality described in at least one embodiment of this disclosure may also be performed at least in part by one or more hardware logic components. For example, without limitation, exemplary types of hardware logic components that may be used include: field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), system-on-a-chip (SoCs), complex programmable logic devices (CPLDs), and so on.

[0160] All aspects not detailed herein are well-known to those skilled in the art. Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of this invention and not intended to limit it. Although the invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of this invention without departing from the spirit and scope of the invention, and all such modifications and substitutions should be covered within the scope of the claims of this invention.

Claims

1. A robustness evaluation method for power system integration tree applications, characterized in that, Includes the following steps: S1. Applying an integrated tree to power system physical constraints. The norm robustness evaluation problem is transformed into a minimum adversarial example problem for solving the data. Combining the structure and properties of ensemble trees, the adversarial example generation problem is formally described and represented, and the ensemble tree's... Norm robustness evaluation is modeled as a mixed-integer linear programming problem; S2. Abstract the equality constraints between data attributes and the inequality constraints on the values ​​of data attributes from the physical laws, variable ranges and detection rules of the power system. S3. Associate the discrete variables in the mixed-integer linear programming problem in step S1 with the continuous power data in S2, and represent the continuous power data using Boolean discrete variables that describe the decision tree structure; S4. Integrate the equality and inequality constraints between power data attributes from step S2 into the mixed integer linear programming problem; S5. Use the global optimization method to solve the robustness of the mixed integer linear programming problem in step S4, and obtain the robustness of the power system based on the ensemble tree model; In step S2, the relationships between data attributes include load balancing equations and power flow equations between nodes; the constraints on the values ​​of data attributes include the voltage range of nodes and the load range of lines. The load balancing equation is as follows: ， The power flow equation is: ， The load range is: ， in, This represents the vector of disturbances in the power flow. This represents the vector of disturbances in the load. This represents the value of the d-th row of the load disturbance vector. Indicates and The corresponding value of the original load, For parameters, Represents the power transfer factor matrix. This represents a column vector consisting entirely of 1s. This represents a column vector consisting entirely of zeros. express The number of features; In step S3, the range of values ​​for the predicates corresponding to the predicate variables of the ensemble tree is represented using continuous variables: ， ， in, , , , , This represents the attributes extracted from the ensemble tree node. The corresponding predicates, among which ; Representation of features The boundary value corresponding to the k-th predicate; n represents the maximum number of predicates corresponding to the feature, and M represents the total number of features. Indicates the value in A continuous variable within the range of its kth value interval. express The k-th predicate variable, express and Are the values ​​consistent? Adversarial examples are represented as: ， ， in, Represents the adversarial sample vector. The disturbance vector of the tidal current The disturbance vector of power generation and the disturbance vector of the load composition, Representing continuous variables The matrix formed Represents the original data vector. Represents the adversarial perturbation vector; ， 。 2. The robustness evaluation method for the application of power system integration tree according to claim 1, characterized in that, Step S1 specifically includes: The robustness evaluation of the ensemble tree is measured using the minimum adversarial perturbation of the ensemble tree, and... The discriminative problem of robustness evaluation of ensemble trees under norm is transformed into the problem of finding the minimum adversarial sample of the ensemble tree. This problem is then modeled as a mixed integer linear programming problem. The constraints for the mixed-integer linear programming problem are: ， ， ， ， ， in, , , , , This represents the attributes extracted from the ensemble tree node. The corresponding predicates, among which ; Indicates about attributes Boolean predicate variables, corresponding to the predicate , Representation of features The boundary value of the corresponding k-th predicate, where the predicate variable is 1 to represent the attribute. Satisfying the predicate, taking 0 indicates an attribute. The predicate is not satisfied; This represents a Boolean leaf variable corresponding to the Nth leaf node. A leaf variable of 1 indicates that the leaf node takes a value, and a leaf variable of 0 indicates that the leaf node does not take a value. This represents the Boolean leaf variable of the k-th leaf node under the pseudo-subtree; This represents the Boolean leaf variable of the m-th leaf node in the proper subtree; The predicate variable representing the root node; Predicate variables representing non-root nodes of the tree; This represents the value stored in the i-th leaf node; The objective function of the mixed-integer linear programming problem is: Adversarial perturbations of norms: ， in, Representation of features The i-th predicate variable corresponds to this, where i is a positive integer from 1 to n, j is a positive integer from 1 to M, n represents the maximum number of predicates corresponding to the feature, M represents the total number of features, and C represents a constant. Representation of features The weight of the i-th predicate variable.

3. The robustness evaluation method for the application of power system integration tree according to claim 2, characterized in that, In step S4, the equality and inequality constraints between power data attributes are incorporated into the mixed integer linear programming problem as follows: Obtain the original variables and constraints of the mixed integer linear programming problem in step S1, add continuous variables and physical constraints from step S2 to the mixed integer linear programming problem, establish the relationship constraints between continuous variables and Boolean variables using the method in step S3, add the constraint relationship to the mixed integer linear programming problem in step S4, use continuous variables to represent the objective function, and solve the mixed integer linear programming problem. An integrated tree incorporating equality and inequality constraints between power data attributes The mixed-integer linear programming problem with norms is as follows: ， ， ， ， ， ， ， ， ， ， ， ， ， ； Here, B is a defined non-negative continuous variable.

4. The robustness evaluation method for the application of power system integration tree according to claim 3, characterized in that, In step S5, the global optimization method for solving the mixed-integer linear programming problem includes: Global optimization methods include branch and bound and cutting plane methods.

5. The robustness evaluation method for the application of power system integration tree according to claim 1, characterized in that, By considering the robustness evaluation results of all data points, the robustness evaluation results of the entire ensemble tree model are obtained.

6. A robustness evaluation device for integrated trees considering physical constraints of power systems using the infinite norm, characterized in that: The device includes a processor and a memory, wherein the memory stores computer program instructions suitable for execution by the processor, the computer program instructions being executed by the processor causing the processor to perform the robustness evaluation method for the power system integrated tree application as described in any one of claims 1-5.

7. A storage medium comprising computer program instructions stored on the storage medium, wherein, The computer program instructions are executed by the processor to perform the robustness evaluation method for the power system integration tree application as described in any one of claims 1-5.

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