CN111091283A - Power data fingerprint evaluation method based on Bayesian network - Google Patents
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Abstract
The invention provides a power data fingerprint evaluation method based on a Bayesian network, which comprises the following three parts: establishing a power data fingerprint evaluation index system, and establishing a Bayesian network evaluation model and Bayesian network reasoning. Analyzing a specific flow of the power data fingerprint, screening evaluation indexes from all indexes by using an entropy weight method, and constructing a power data fingerprint evaluation index system; the dependency relationship of each index node is distinguished, a Bayesian network structure is given, and the reasonable Bayesian network structure is beneficial to accurate inference evaluation; the security of the power data is high, and in order to solve the problem that only small sample data exist, according to the characteristics of the power data, the Beta distribution is equivalently approximate to the normal distribution, and then the maximum posterior probability method of Bayesian estimation is used for calculating the estimated value of the parameter, so that the Bayesian network parameter learning is completed; and the accurate reasoning of the Bayesian network is carried out by utilizing the clique tree propagation algorithm, so that the reasoning time is saved, and the reasoning accuracy is improved.
Description
Technical Field
The invention relates to a power data fingerprint evaluation method, in particular to a power data fingerprint evaluation method based on a Bayesian network, and belongs to the technical field of index evaluation.
Background
With the wide application of information technology in the power industry, the informatization level of power is higher and higher, the amount of managed service data is increased, the data sharing requirement among power services is higher and higher, the directly shared data is subject to illegal forwarding, and once the data is leaked, it is often difficult to trace the data leakage source. The core data of the power industry distributes the data to other application systems through various ways according to the related requirements of national networks and provincial companies, and the other application systems can have the condition of data distribution at the same time, so that the problem of secondary data distribution is caused. In order to guarantee the safety of data, data fingerprint technology is applied to control the distribution of data in the power data. The power data containing the data fingerprints is distributed in an uncertain environment, so that the performance indexes of the power data fingerprints need to be evaluated, useful information is obtained, and a proper data fingerprint technology is selected.
Digital fingerprints are a special case of digital watermarking technology, and have many commonalities in evaluation. The robustness of the watermark information, the watermark capacity of the carrier and the fidelity of the carrier work are 3 basic characteristics of the digital watermark system. Robustness refers to the ability of a watermarked work to detect the watermark after some signal processing or channel attack. Watermark capacity refers to the number of bits that are effectively encoded in a watermark in a unit of time or in a work under certain scenarios. Fidelity refers to the perceptual similarity between the original carrier and the watermarked work, also referred to as imperceptibility. In practical applications, the digital watermark should also satisfy the security of the embedding position, the universality of the algorithm and the high efficiency of calculation as much as possible. The current attacks faced by data fingerprints in the streaming process include single-user attacks and multi-user attacks. How to properly evaluate the performance of the attack in diversified attacks.
In view of this, a suitable method for evaluating the power data fingerprint must be found.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a power data fingerprint evaluation method based on a Bayesian network, which can improve the security of power data, and overcome the defects of the prior art.
The invention provides a power data fingerprint evaluation method based on a Bayesian network, which comprises the following steps of:
step 1, obtaining evaluation data in a safety evaluation result, selecting an alternative index set according to the evaluation data and daily use conditions of electric power data, and screening the alternative index set by using an entropy weight method so as to evaluate the safety of electric power data fingerprints from the aspects of robustness, fidelity, utilization prevention, capacity and the like; turning to the step 2;
step 2, carrying out hierarchical analysis on each evaluation index which is screened out in the step 1 and influences the fingerprint security of the power data, determining the dependency relationship and relationship strength among nodes, and constructing a structure of the Bayesian network; turning to the step 3;
step 3, selecting a proper evaluation method, and quantitatively giving the prior probability of each node index according to the performance of the data on a plurality of indexes; turning to the step 4;
step 4, according to the Bayesian network structure determined in the step 2, parameters are given by utilizing a Bayesian network parameter learning method integrating power data distribution characteristics; the method comprises the steps of utilizing Beta distribution to approximate normal distribution, combining a virtual sample statistic value with an existing small sample data set after calculating coefficients, and then utilizing a maximum posterior probability method of Bayesian estimation to calculate an estimated value of a parameter; turning to step 5;
step 5, converting the Bayesian network into a clique tree; turning to step 6;
and 6, accurately reasoning the Bayesian network by using a cluster tree propagation algorithm.
The method of the invention comprises the following three parts: establishing a power data fingerprint evaluation index system, establishing a Bayesian network evaluation model and carrying out Bayesian network reasoning. Analyzing a specific flow of the power data fingerprint, screening evaluation indexes from all indexes by using an entropy weight method, and constructing a simple and reasonable power data fingerprint evaluation index system; the dependency relationship of each index node is distinguished, according to the characteristics of power data, after the Beta distribution is equivalently approximated to the normal distribution, the estimated value of the parameter is calculated by using a maximum posterior probability method of Bayesian estimation, the Bayesian network parameter learning is completed, a Bayesian network structure is given, and the reasonable Bayesian network structure is beneficial to accurate inference evaluation; the confidentiality of the power data is high, and in order to solve the problem that only small sample data exists, parameter learning is carried out by quantitatively giving the prior probability of each node index by using an expert scoring method; and the accurate reasoning of the Bayesian network is carried out by utilizing the cluster tree propagation algorithm, so that the reasoning time is saved, and the reasoning accuracy is improved.
As a further technical solution of the present invention, the following is specifically described:
further, the specific method of step 1 is as follows:
step 1.1, constructing an alternative index set, setting x evaluated objects and t indexes, standardizing index data to form a standardized alternative index set, wherein the standardized alternative index set R is as follows:
step 1.2, screening the alternative index set by using an entropy weight method, namely defining entropy and entropy weight, calculating the weight of each index, screening out evaluation indexes according to the index weight, and screening out the entropy h of the jth evaluation indexjComprises the following steps:
wherein
k＝1/ln(x)
Wherein f satisfies 0 ≦ f ≦ 1, and Σ f ≦ 1, and when f is 0, flnf is 0; i is an evaluated object, and j is an evaluation index; entropy weight W of jth evaluation indexjComprises the following steps:
in step 1, the basic performance of the power data fingerprint comprises fidelity, effectiveness, safety, robustness, capacity, high efficiency and utilization prevention. Wherein the fidelity comprises imperceptibility; robustness is established on the basis of attacks, the faced attacks comprise individual attacks and multi-person attacks, the single attack comprises removal attacks, synchronization attacks and protocol attacks, the synchronization attacks comprise geometric distortion attacks, mosaic attacks, jitter attacks and Oracle attacks, and the protocol attacks comprise explanation attacks and copy attacks; the reliability comprises false detection rate, missed detection rate, traceability and verifiability; the anti-utilization property comprises communication secrecy, encryption algorithm secrecy, embedded safety and the like.
Further, the specific method of step 2 is as follows: performing hierarchical analysis on each evaluation index which is screened out in the step 1 and influences the fingerprint security of the power data, and dividing the factors into a plurality of groups according to attributes and domination relations to form different levels; and determining the dependency relationship and relationship strength among the nodes to construct the structure of the Bayesian network. The next layer, such as robustness, contains the degree of identity and the bit error rate. The next layer, such as robustness, contains the degree of identity and the bit error rate.
Further, the specific method of step 3 is as follows:
step 3.1, selecting a qualitative and quantitative evaluation method, and combining the performances of a plurality of electric power data on each index to give a numerical representation, namely a prior probability; go to step 3.2;
and 3.2, determining a value range and a weight jump value for each node by using an expert survey method, compiling a weight coefficient selection table and a selection description, and weighting the result given by combining the opinion of an expert in the power aspect to give the prior probability of each node in order to make the coefficient more objective and moderate.
Further, the specific method of step 4 is as follows:
step 4.1, aiming at the characteristics of the power data, expressing the possibility of parameter values given by expert knowledge by using a normal distribution model; go to step 4.2;
step 4.2, constructing a target optimization model, adopting Beta distribution to approximate normal distribution representing priori knowledge, and calculating parameter values of the Beta distribution, namely virtual sample statistical values; go to step 4.3;
and 4.3, combining the virtual sample statistic with the existing small sample data set, and calculating the estimated value of the parameter by using a maximum posterior probability method of Bayesian estimation.
Further, in the step 4.1, a value range of a normal distribution standard deviation is calculated and determined, the priori knowledge follows the normal distribution, a probability density function of the normal distribution is an expected value thereof and is marked as mu, and a variance thereof is sigma2Two parameters of normal distribution, mu and sigma, determine the position and amplitude of distribution, respectively, and random variables X-N (mu, sigma)2) The probability density function is as follows:
calculating the integral of the probability density function over the interval 0-1 yields the expected EN(X), calculating
The following variance D was obtainedN(X)：
The Beta distribution is convenient to calculate, so that the Beta distribution is used for approximating the normal distribution, and under the condition that the normal distribution and the Beta distribution are equal to each other, an objective function to be solved for approximating the distribution is written by taking the expectation, the variance and α and β of the Beta distribution as variables;
in step 4.2, the expectation, variance and mean expression of the Beta distribution are as follows:
wherein α and β respectively represent the shape parameter and the position parameter of the Beta distribution, EB(X) expectation of Beta distribution, DB(X) represents the variance of the Beta distribution, and mode (X) represents the mean of the Beta distribution;
under the condition that the normal distribution and the Beta distribution are expected to be equal, an objective function required to be solved by the simulation distribution is written by taking α and β of the expectation, the variance and the Beta distribution of the normal distribution as variables, and the objective function is as follows:
min[(DN(X)-DB(X))2+(μ-Mode(X))2]
and (3) bringing known parameter values into the objective function and simplifying the objective function, wherein β of the Beta distribution is used as an argument, and the simplified objective function is as follows:
judging whether the target function has a minimum value, deriving the simplified functional expression, solving a zero point, if the zero point exists, the target function has the minimum value, and continuing to solve the target function, otherwise, finely adjusting coefficients in the target function within a range of ensuring that the calculation result is not greatly influenced, specifically, expressing the relation between α and β by a variable t (β t α), rounding t in the simplified target function, and because the processed coefficients are in decimal places, the functional expression is derived again, and the process is continued.
Solving the corresponding independent variable value when the target function takes the minimum value, namely substituting β of the corresponding Beta distribution into the functional relation of α and β to obtain α of the Beta distribution.
In the step 4.3, the obtained Beta parameter is added into a Bayesian estimation method, and Bayesian parameter estimation models fusing coefficients α and β are as follows:
in the formula, NijkIndicates that pi (X) is satisfied in the observed sample Di) The number of samples where Xj is k is given as j. And reading a small sample data set of the Bayesian network, and calculating the estimated value of the parameter by using a maximum posterior probability method of Bayesian estimation according to the existing network structure and the parameter estimation model to complete Bayesian network parameter learning.
Further, the specific method of step 5 is as follows:
step 5.1, establishing a Bayesian network moral graph and triangulating the Bayesian network moral graph; go to step 5.2;
and 5.2, determining the cluster nodes and generating a cluster tree.
Further, in the step 5.1, all nodes and edges in the original bayesian network are reserved, and if a certain node in the original bayesian network has more than two father nodes, all father nodes of the node are connected in pairs in the moral graph to establish a bayesian network moral graph;
when the Bayesian network moral graph is triangulated, if the moral graph has more than 3 nodes, adding an undirected edge to connect two non-adjacent nodes in the graph, and if the moral graph has more than 3 nodes, continuing to subdivide until a triangulated graph is formed;
in the step 5.2, determining a group node, wherein the group node is a maximum complete subgraph in the triangularization graph;
and generating a group tree, wherein each node in the group tree corresponds to one group node, and the intersection of the two group nodes is used as a separation node.
Further, the specific method of step 6 is as follows:
step 6.1, initializing algorithm parameters and absorbing messages; go to step 6.2;
and 6.2, calculating the marginal probability and giving a final result.
Further, in step 6.1, when initializing the algorithm parameters, defining each clique node and the separation node in step 5.2 as σ (x), setting the initial value of σ (x) to 1, and for each node V in the bayesian network, if yes, setting the initial value of σ (x) to 1
Then order
σ(x)＝σ(x)*P(V|P(V))
Wherein p (v) represents edge probability;
when absorbing the message, the clique node x transmits the message to the adjacent clique node y, and the middle part passes through the separation node B, then:
in step 6.2, if V is a node in the bayesian network, the edge probability p (V) can be calculated by the following formula:
in conclusion, the method provided by the invention has the advantages that the basic flow of the data fingerprint structure is analyzed, the entropy weight method is utilized to screen the alternative index set, so that the power data fingerprint evaluation index system is constructed, the index system is simpler and more reasonable, and the efficiency is greatly improved; the Bayesian network parameter learning method fusing expert prior knowledge is utilized to carry out parameter learning of the Bayesian network, so that the usability is greatly improved; the accurate reasoning of the Bayesian network is carried out by utilizing the clique tree propagation algorithm, the reasoning time is saved, and the reasoning accuracy is improved.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Drawings
FIG. 1 is a basic flow diagram of power data fingerprint evaluation according to the present invention.
Fig. 2 is an exemplary diagram of a bayesian network structure in accordance with the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection authority of the present invention is not limited to the following embodiments.
The embodiment provides a power data fingerprint evaluation method based on a Bayesian network, which comprises the following steps:
the method comprises the steps of 1, obtaining evaluation data in a safety evaluation result, selecting an alternative index set according to the evaluation data and daily use conditions of electric power data, and screening the alternative index set by using an entropy weight method so as to evaluate the safety of electric power data fingerprints from the aspects of robustness, fidelity, utilization prevention, capacity and the like. The specific method comprises the following steps:
step 1.1, constructing an alternative index set; setting x evaluated objects and t indexes, forming a standardized alternative index set after the index data is standardized, wherein the standardized alternative index set R is as follows:
step 1.2, screening the alternative index set by using an entropy weight method, namely defining entropy and entropy weight, calculating the weight of each index, screening out evaluation indexes according to the index weight, and screening out the entropy h of the jth evaluation indexjComprises the following steps:
wherein
k＝1/ln(x)
Wherein f satisfies 0 ≦ f ≦ 1, and Σ f ≦ 1, and when f is 0, flnf is 0; i is an evaluated object, and j is an evaluation index; entropy weight W of jth evaluation indexjComprises the following steps:
in step 1, the basic performance of the power data fingerprint comprises fidelity, effectiveness, safety, robustness, capacity, high efficiency and utilization prevention. Wherein the fidelity comprises imperceptibility; robustness is established on the basis of attacks, the faced attacks comprise individual attacks and multi-person attacks, the single attack comprises removal attacks, synchronization attacks and protocol attacks, the synchronization attacks comprise geometric distortion attacks, mosaic attacks, jitter attacks and Oracle attacks, and the protocol attacks comprise explanation attacks and copy attacks; the reliability comprises false detection rate, missed detection rate, traceability and verifiability; the anti-utilization property comprises communication secrecy, encryption algorithm secrecy, embedded safety and the like.
And 2, performing hierarchical analysis on each evaluation index which is screened out in the step 1 and influences the fingerprint security of the power data, determining the dependency relationship and relationship strength among the nodes, and constructing the structure of the Bayesian network. The specific method comprises the following steps: and (3) performing hierarchical analysis on each evaluation index which is screened out in the step (1) and influences the fingerprint security of the power data, and dividing the factors into a plurality of groups according to attributes and domination relations to form different hierarchies. And determining the dependency relationship and relationship strength among the nodes to construct the structure of the Bayesian network. The next layer, such as robustness, contains the degree of identity and the bit error rate.
And 3, selecting a proper evaluation method, and quantitatively giving the prior probability of each node index according to different performances of the data on each index. The specific method comprises the following steps:
3.1, selecting a qualitative and quantitative evaluation method, representing according to different performances of a plurality of electric power data on each index, and giving prior probability; go to step 3.2;
and 3.2, determining a value range and a weight jump value for each node by using an expert survey method, compiling a weight coefficient selection table and a selection description, and weighting the result given by combining the opinion of an expert in the power aspect to give the prior probability of each node in order to make the coefficient more objective and moderate.
And 4, according to the Bayesian network structure determined in the step 2, providing parameters by using a Bayesian network parameter learning method integrating power data distribution characteristics. The method comprises the steps of reading a small sample data set of the Bayesian network by utilizing the characteristic that Beta distribution is approximate to normal distribution of power data, combining a virtual sample statistic value with an existing small sample data set after calculating coefficients, and calculating an estimated value of a parameter by utilizing a maximum posterior probability method of Bayesian estimation according to an existing network structure and the parameter estimation model to finish parameter learning of the Bayesian network. The specific method comprises the following steps:
and 4.1, aiming at the characteristics of the power data, expressing the possibility of parameter dereferencing given by expert knowledge by using a normal distribution model, and calculating and determining the dereferencing range of the normal distribution standard deviation. The priori knowledge follows normal distribution, the probability density function of the normal distribution is the expected value thereof and is marked as mu, and the variance thereof is sigma2Normally distributedTwo parameters mu and sigma determine the position and amplitude of the distribution, respectively, and the random variables X-N (mu, sigma)2) The probability density function is as follows:
calculating the integral of the probability density function over the interval 0-1 yields the expected EN(X), calculating
The following variance D was obtainedN(X)：
The Beta distribution is convenient to calculate, so that the Beta distribution is used for approximating the normal distribution, and under the condition that the normal distribution and the Beta distribution are expected to be equal, an objective function required to be solved by approximating the distribution is written by taking the expectation, the variance and α and β of the Beta distribution as variables.
In step 4.2, the expectation, variance and mean expression of Beta distribution are as follows:
wherein α and β respectively represent the shape parameter and the position parameter of the Beta distribution, EB(X) expectation of Beta distribution, DB(X) represents the variance of the Beta distribution, and mode (X) represents the mean of the Beta distribution.
Under the condition that the normal distribution and the Beta distribution are expected to be equal, an objective function to be solved by the simulation distribution is written by taking α and β of the expectation, the variance and the Beta distribution of the normal distribution as follows:
min[(DN(X)-DB(X))2+(μ-Mode(X))2]
and (3) bringing known parameter values into the objective function and simplifying the objective function, wherein β of the Beta distribution is used as an argument, and the simplified objective function is as follows:
judging whether the target function has a minimum value, deriving the simplified functional expression, calculating a zero point, if the zero point exists, the target function has the minimum value, and continuously calculating the target function, otherwise, finely adjusting coefficients in the target function within a range of ensuring that the calculation result is not greatly influenced, specifically, expressing the relation between α and β by a variable t (β t α), rounding the t in the simplified target function, and because the processed coefficients are in decimal places, the functional expression is derived again, and the process is continuously calculated.
Solving the corresponding independent variable value when the target function takes the minimum value, namely substituting β of the corresponding Beta distribution into the functional relation of α and β to obtain α of the Beta distribution.
In the step 4.3, the obtained Beta parameter is added into a Bayesian estimation method, and Bayesian parameter estimation models fusing coefficients α and β are as follows:
in the formula, NijkRepresenting observationSatisfies pi (X) in sample Di) The number of samples where Xj is k is given as j. And reading a small sample data set of the Bayesian network, and calculating the estimated value of the parameter by using a maximum posterior probability method of Bayesian estimation according to the existing network structure and the parameter estimation model to complete Bayesian network parameter learning.
And 5, converting the Bayesian network into a clique tree. The specific method comprises the following steps:
step 5.1, establishing a Bayesian network route graph and triangulating the Bayesian network route graph
Reserving all nodes and edges in the original Bayesian network, if a certain node in the original Bayesian network has more than two father nodes, connecting every two father nodes of the node in a moral graph, and establishing a Bayesian network moral graph;
when the Bayesian network moral graph is triangulated, if the moral graph has more than 3 nodes, adding an undirected edge to connect two non-adjacent nodes in the graph, and if the moral graph has more than 3 nodes, continuing to subdivide until a triangulated graph is formed;
step 5.2, determining the cluster nodes and generating a cluster tree
Determining a group node, wherein the group node is a maximum complete subgraph in a triangularization graph;
and generating a group tree, wherein each node in the group tree corresponds to one group node, and the intersection of the two group nodes is used as a separation node.
And 6, accurately reasoning the Bayesian network by using a cluster tree propagation algorithm. The specific method comprises the following steps:
step 6.1, initialize algorithm parameter, absorb message
When initializing the algorithm parameters, defining each clique node and the separation node in step 5.2 as sigma (x), setting the initial value of sigma (x) as 1, and for each node V in the Bayesian network, if
Then order
σ(x)＝σ(x)*P(V|P(V))
Wherein p (v) represents edge probability;
when absorbing the message, the clique node x transmits the message to the adjacent clique node y, and the middle part passes through the separation node B, then:
step 6.2, calculating the marginal probability and giving a final result
Calculating an edge probability, and if V is a node in the bayesian network, calculating the edge probability p (V) by:
the above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.
Claims (10)
1. A power data fingerprint evaluation method based on a Bayesian network is characterized by comprising the following steps:
step 1, obtaining evaluation data in a safety evaluation result, selecting an alternative index set according to the evaluation data and the daily use condition of power data, and screening the alternative index set by using an entropy weight method; turning to the step 2;
step 2, carrying out hierarchical analysis on each evaluation index which is screened out in the step 1 and influences the fingerprint security of the power data, determining the dependency relationship and relationship strength among nodes, and constructing a structure of the Bayesian network; turning to the step 3;
step 3, selecting a proper evaluation method, and quantitatively giving the prior probability of each node index; turning to the step 4;
step 4, according to the Bayesian network structure determined in the step 2, parameters are given by utilizing a Bayesian network parameter learning method integrating power data distribution characteristics; turning to step 5;
step 5, converting the Bayesian network into a clique tree; turning to step 6;
and 6, accurately reasoning the Bayesian network by using a cluster tree propagation algorithm.
2. The Bayesian network-based power data fingerprint estimation method as recited in claim 1, wherein the specific method in step 1 is as follows:
step 1.1, setting x evaluated objects and t indexes, forming a standardized alternative index set after index data are standardized, wherein the standardized alternative index set R is as follows:
step 1.2, defining entropy and entropy weight, calculating the weight of each index, screening out evaluation indexes according to the index weight, and screening out the entropy h of the jth evaluation indexjComprises the following steps:
wherein
k＝1/ln(x)
Wherein f satisfies 0 ≦ f ≦ 1, and Σ f ≦ 1, and when f is 0, fn f is 0; i is an evaluated object, and j is an evaluation index; entropy weight W of jth evaluation indexjComprises the following steps:
3. the Bayesian network-based power data fingerprint estimation method as recited in claim 2, wherein the step 2 comprises the following specific steps:
performing hierarchical analysis on each evaluation index which is screened out in the step 1 and influences the fingerprint security of the power data, and dividing the factors into a plurality of groups according to attributes and domination relations to form different levels; and then determining the dependency relationship and relationship strength among the nodes to construct the structure of the Bayesian network.
4. The Bayesian network-based power data fingerprint estimation method as recited in claim 3, wherein the specific method in the step 3 is as follows:
step 3.1, selecting a qualitative and quantitative evaluation method, and presenting numerical value representation on each index by combining the electric power data; go to step 3.2;
and 3.2, determining a value range and a weight jump value for each node by using an expert survey method, compiling a weight coefficient selection table and a selection description, and weighting the result given by combining the opinion of an expert in the power aspect to give the prior probability of each node in order to make the coefficient more objective and moderate.
5. The Bayesian network-based power data fingerprint estimation method as recited in claim 4, wherein the specific method of the step 4 is as follows:
step 4.1, aiming at the characteristics of the power data, expressing the possibility of parameter values given by expert knowledge by using a normal distribution model; go to step 4.2;
step 4.2, constructing a target optimization model, adopting Beta distribution to approximate normal distribution representing priori knowledge, and calculating parameter values of the Beta distribution, namely virtual sample statistical values; go to step 4.3;
and 4.3, combining the virtual sample statistic with the existing small sample data set, and calculating the estimated value of the parameter by using a maximum posterior probability method of Bayesian estimation.
6. The Bayesian network-based power data fingerprint estimation method as recited in claim 5, wherein in the step 4.1, a value range of a normal distribution standard deviation is calculated and determined, and a priori knowledge is givenSubject to normal distribution, the probability density function of normal distribution is its expected value, denoted as mu, and its variance is sigma2Two parameters of normal distribution, mu and sigma, determine the position and amplitude of distribution, respectively, and random variables X-N (mu, sigma)2) The probability density function is as follows:
calculating the integral of the probability density function over the interval 0-1 yields the expected EN(X), calculating
The following variance D was obtainedN(X)：
α, β writing an objective function needed to be solved by approximating distribution for variables;
in step 4.2, the expectation, variance and mean expression of the Beta distribution are as follows:
wherein α and β respectively represent the shape parameter and the position parameter of the Beta distribution, EB(X) expectation of Beta distribution, DB(X) the variance, Mod, of the Beta distributione (X) represents the mean of the Beta distribution;
under the condition that the normal distribution and the Beta distribution are expected to be equal, an objective function to be solved by the simulation distribution is written by taking α and β of the expectation, the variance and the Beta distribution of the normal distribution as follows:
min[(DN(X)-DB(X))2+(μ-Mode(X))2]
and (3) bringing known parameter values into the objective function and simplifying the objective function, wherein β of the Beta distribution is used as an argument, and the simplified objective function is as follows:
judging whether the objective function has a minimum value, deriving the simplified functional expression, solving a zero point, if the zero point exists, determining that the objective function has the minimum value, and continuously solving the objective function; otherwise, finely adjusting the coefficients in the objective function within a range of ensuring that the calculation result is not greatly influenced;
in the step 4.3, the obtained Beta parameter is added to a bayesian estimation method, and a bayesian parameter estimation model fusing the coefficients α and β is as follows:
in the formula, NijkIndicates that pi (X) is satisfied in the observed sample Di) The number of samples where Xj is k is given as j.
7. The Bayesian network-based power data fingerprint estimation method as recited in claim 6, wherein the specific method in the step 5 is as follows:
step 5.1, establishing a Bayesian network moral graph and triangulating the Bayesian network moral graph; go to step 5.2;
and 5.2, determining the cluster nodes and generating a cluster tree.
8. The Bayesian network-based power data fingerprint estimation method according to claim 7, wherein in the step 5.1, all nodes and edges in the original Bayesian network are retained, and if a certain node in the original Bayesian network has more than two father nodes, all the father nodes of the node are connected in pairs in a moral graph, so as to establish a Bayesian network moral graph;
when the Bayesian network moral graph is triangulated, if the moral graph has more than 3 nodes, adding an undirected edge to connect two non-adjacent nodes in the graph, and if the moral graph has more than 3 nodes, continuing to subdivide until a triangulated graph is formed;
in the step 5.2, determining a group node, wherein the group node is a maximum complete subgraph in the triangularization graph;
and generating a group tree, wherein each node in the group tree corresponds to one group node, and the intersection of the two group nodes is used as a separation node.
9. The Bayesian network-based power data fingerprint estimation method as recited in claim 8, wherein the step 6 comprises the following specific steps:
step 6.1, initializing algorithm parameters and absorbing messages; go to step 6.2;
and 6.2, calculating the marginal probability and giving a final result.
10. The bayesian network based power data fingerprinting method according to claim 9, characterized in that in step 6.1, when initializing algorithm parameters, each clique node and separation node in step 5.2 is defined as σ (x), the initial value of σ (x) is set as 1, and for each node V in the bayesian network, if yes, the algorithm parameters are initialized
Then order
σ(x)＝σ(x)*P(V|P(V))
Wherein p (v) represents edge probability;
when absorbing the message, the clique node x transmits the message to the adjacent clique node y, and the middle part passes through the separation node B, then:
in step 6.2, if V is a node in the bayesian network, the edge probability p (V) can be calculated by the following formula:
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