CN108762238B - DCD-based hydrometallurgy leaching process fault diagnosis method - Google Patents

DCD-based hydrometallurgy leaching process fault diagnosis method Download PDF

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CN108762238B
CN108762238B CN201810622817.0A CN201810622817A CN108762238B CN 108762238 B CN108762238 B CN 108762238B CN 201810622817 A CN201810622817 A CN 201810622817A CN 108762238 B CN108762238 B CN 108762238B
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CN108762238A (en
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王姝
张思琦
刘秀鹏
常玉清
赵露平
王福利
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Northeastern University China
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Abstract

The invention belongs to the technical field of fault diagnosis in a hydrometallurgical leaching process, and particularly relates to a fault diagnosis method in the hydrometallurgical leaching process based on DCD. A DCD-based leaching process fault diagnosis method is mainly oriented to a hydrometallurgy leaching process, a dynamic causal graph knowledge base is established by extracting expert knowledge and information in process data as prior information, a reasoning diagnosis mechanism is entered after an abnormal condition is observed, the posterior probability of each possible fault reason is calculated by taking the abnormal condition as evidence, and a diagnosis result is obtained by comparing the posterior probabilities. The algorithm mainly comprises the steps of DCD event determination in the leaching process, DCD structure learning, DCD parameter learning, DCD on-line process fault diagnosis and the like. The invention utilizes the DCD fault diagnosis technology to process the uncertainty of the information in the leaching process, reduces the dependence of the diagnosis technology on a large amount of data to a certain extent, can bring more accurate diagnosis results and ensures the economic benefit and the production benefit of enterprises.

Description

DCD-based hydrometallurgy leaching process fault diagnosis method
Technical Field
The invention belongs to the technical field of fault diagnosis in a hydrometallurgical leaching process, and particularly relates to a fault diagnosis method in the hydrometallurgical leaching process based on DCD.
Background
With the gradual reduction of high grade ores, the hydrometallurgical industry has begun to receive high attention from countries around the world. Compared with the traditional pyrometallurgical method, the hydrometallurgical technology has the advantages of high efficiency, cleanness, suitability for recycling low-grade complex metal mineral resources and the like. Especially aiming at the characteristics of low grade, complex symbiosis and high impurity content of gold ore in China, the industrialization of the hydrometallurgy process has great significance for improving the comprehensive utilization rate of the gold ore, reducing the yield of solid waste and reducing environmental pollution. In the face of a complex industrial process such as hydrometallurgy, an abnormal or fault phenomenon occurs in a certain link, which causes huge production and economic losses to the whole process flow and is easy to cause safety accidents. Therefore, the method has great practical significance for effective fault diagnosis in the hydrometallurgical process. The method takes the leaching process of hydrometallurgy as a research background, and carries out real-time monitoring and fault diagnosis on the leaching process. The process flow diagram of the hydrometallurgical leaching process is shown in figure 3.
The cyanidation leaching process is one of the important production processes that determines the final gold yield. And (4) conveying the ore pulp subjected to flotation to a cyaniding leaching process, adding sodium cyanide into each leaching tank and filling air into each leaching tank to enable gold to fully react with the added reagent. Wherein, sodium cyanide is an important reaction reagent for hydrometallurgy, and the charged air provides stirring power and proper oxidation-reduction potential for the reaction to promote the reaction. In addition, in order to prevent sodium cyanide from hydrolysis and release highly toxic hydrogen cyanide gas, calcium oxide needs to be added into the pulp to adjust the pH value.
The reasonable hydrometallurgical process flow is a basic premise for ensuring effective recycling of gold in the ore and high return of income for enterprises. However, when the actual production process is affected by external environmental interference and uncertain factors, the operation variables (such as the flow rate of sodium cyanide, the flow rate of zinc powder, etc.) gradually deviate from the normal working range set at the initial stage of production, which causes abnormal phenomena in the process operation and further causes the operation process to break down. Because the economic value of gold is extremely high, the method has important practical significance for timely discovering and reasonably processing the fault condition in the hydrometallurgy process, improving the production efficiency and the economic benefit of enterprises and reducing potential safety hazards.
In foreign countries, the technology for processing low-grade nonferrous metal resources in a large scale is quite mature. Although China is not behind foreign in the aspect of hydrometallurgical processes, the automatic control technology adapted to the wet metallurgy process is far from the foreign world. Obviously, as the demand for mineral resources continues to increase, it becomes extremely difficult to improve the hydrometallurgical economics and technical targets and economic benefits by means of improved processes alone. Under the guidance of strategic guidelines of sustainable development, in order to economically and effectively utilize low-grade non-ferrous metal mineral resources, how to treat faults occurring in the hydrometallurgical process becomes the focus of research at the present stage. The traditional hydrometallurgical process fault diagnosis technology is mainly a data quantitative analysis-based method represented by PCA, and the method mainly depends on process data. Whereas hydrometallurgical processes are relatively complex, process parameters are high and contain many variables that are difficult to measure directly, and in this context, it is difficult to perform fault diagnosis using data-based methods. The method of combining qualitative information and quantitative information, namely the dynamic causal graph, can avoid the problems to a certain extent, the causal graph mainly depends on the causal relationship between a process mechanism and variables to establish a model for fault diagnosis, and the method has good application prospect for fault diagnosis of a complex production process, such as hydrometallurgy.
Disclosure of Invention
Technical problem to be solved
Aiming at the existing technical problems, the invention provides a DCD-based hydrometallurgy leaching process fault diagnosis method, which carries out online fault diagnosis according to the monitored abnormal phenomenon and gives fault reasons.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that: a DCD-based hydrometallurgical leaching process fault diagnosis method comprises the following steps:
step A: establishing a DCD knowledge base model of a diagnosis object, wherein the model comprises selection and definition of basic event and intermediate event variables, connection and establishment of causal relationship among the variables, and setting of various parameters required by the variables;
and B: and monitoring whether the process is abnormal or not in real time through real-time running data acquired in the actual process, starting an inference process to carry out inference calculation and analysis if the monitored variable is in an abnormal state, and obtaining an inference result according to a quantitative probability numerical value.
Preferably, in the step a, DCD event determination is included, and event variables involved in the hydrometallurgical leaching process are defined;
in the process of determining the DCD events in the leaching process, the process state variables are used as node events of the causal graph, the abnormality or the fault is used as a basic event of the causal graph, and the basic event and the node event of the causal graph need to be determined by analyzing the fault and the cause thereof which are common in the process.
Preferably, after the DCD structure learning is further included in step a, after the node events and the basic events of the causal graph are determined, the causal relationship between the variables is further determined, and the causal relationship between the variables is determined based on a mutual information causal graph structure learning algorithm to establish the causal graph model.
Preferably, the causal graph structure learning algorithm is as follows:
the basic idea of the causal graph structure learning algorithm is that based on expert experience and given sample data, through conditional independence test, edge deletion operation is conducted on a complete potential graph of the causal graph to obtain an optimal causal graph undirected potential graph, and then the direction of directed edges among variables is determined according to causal relationships among the variables to obtain a final causal graph;
the conditional independence between any two node variables X and Y given a set of node variables can be judged by marginal probability and conditional probability in a probability table that can be directly calculated from a given data set;
and gives two definitions as follows:
definition 1: a causal graph model consisting of undirected edges between any two nodes of the causal graph, called a complete potential graph of the causal graph;
definition 2 if there is a relationship between the variable X, Y and the variable set Z, P (X | Z) ═ P (X | Y, Z), i.e. the state and probability of the variable Y do not affect the state of the variable X under the condition that the variable set Z is known, called I (X ⊥ Y | Z) given that the X condition is independent of Y;
expressing the causal relationship strength between nodes of the causal graph by mutual information, two discrete random variables X and Y have a joint probability function p (X, Y) and an edge probability function p (X), p (Y), and then the average mutual information I (X, Y) is defined as:
Figure BDA0001698443940000041
also, the conditional mutual information I (X, Y | Z) is defined as:
Figure BDA0001698443940000042
when the causal graph structure learning algorithm is used, firstly, connection exists among all nodes, and whether causal association exists between nodes X and Y is judged by adopting conditional mutual information;
in the usual case, a threshold of positive real numbers is set, when I (X, Y | Z) ≦ indicating that the X condition is independent of Y given the Z condition, i.e. there is no causal relationship between X and Y, thus removing the connection between X and Y;
and (4) after n (n-1)/2 CI tests, the complete potential graph is finally trimmed into a sparse ideal potential cause-effect graph.
Preferably, the causal graph structure learning algorithm is implemented by the following steps:
step a: initializing a full potential graph of a causal graph
Establishing a complete connection graph according to given specific problems and process data, namely, assuming that a dependency relationship exists between any two variables, and representing causal correlation between the variables by using a connection edge to form a complete potential graph PDCD;
step b: fusing expert knowledge
According to expert experience and priori knowledge, node variables definitely without causal relationship in the complete potential graph of the causal graph are determined, and undirected edges among the nodes are deleted to obtain a relatively sparse potential graph of the causal graph;
step c: potential map pruning
C, performing CI testing on the potential graph obtained in the step b, if the CI testing is a true value, namely I (X, Y | Z) is less than or equal to the true value, deleting the undirected edges between the corresponding two node variables, and otherwise, keeping the undirected edges until the CI testing among all the variables is finished, so as to obtain an ideal potential cause-effect graph DDCD;
step d: converting undirected graph into causal graph
And determining the causal relationship among the variables according to the actual process mechanism and expert knowledge, and converting the optimal undirected latent graph into a causal graph with directed edges.
Preferably, step a further includes DCD parameter learning, and the DCD parameter learning includes the following steps:
step 1: basic event probability acquisition
Basic event variables which cannot be directly measured exist in the hydrometallurgical leaching process, so that the basic event probability is directly given out according to process technological mechanisms and experiences by experts and field personnel, and the basic event probability is acquired by integrating knowledge and experiences of all the experts to obtain the basic event probability of the cause-effect diagram;
meanwhile, measured basic event variables also exist in the hydrometallurgical leaching process, and the probability value of the basic event can be acquired by analyzing process data;
probabilities of states of elementary event variables, e.g.
Figure BDA0001698443940000051
Is a variable BiIn all possible states of
Figure BDA0001698443940000052
Assuming that N is collectediHistorical data of strip samples, among them
Figure BDA0001698443940000053
One sample is in variable BiThe kth state of (1), i.e. variable BiThe k-th state of (1) occurs, then
Figure BDA0001698443940000054
Step 2: connection event probability acquisition
Probability value of connection event
Figure BDA0001698443940000055
Represents the variable ViKthiA state
Figure BDA0001698443940000056
Result in a variable VjKthjA state
Figure BDA0001698443940000057
Similarly to the step 1, the probability value can be directly given by experts and field personnel according to process mechanism and experience on one hand, and can be obtained by process data analysis on the other hand;
assuming that enough V is collectediAnd VjData of (1), wherein
Figure BDA0001698443940000058
The number of data samples occurring is
Figure BDA0001698443940000059
Figure BDA00016984439400000510
And
Figure BDA00016984439400000511
the number of simultaneous data samples is
Figure BDA00016984439400000512
Then there is
Figure BDA00016984439400000513
Preferably, the accurate connection event probability value is obtained by a parameter estimation method on the basis of obtaining the connection probability, and the method specifically includes the following steps:
step a: prior distribution of joint strength parameters
For any given result node Y, it is set to have m states Yj(j ═ 1,2, L, m), n cause nodes Xk(k＝1,2,L n)，XkHas mkIn one state, the ith (i ═ 1,2, L, m) of the kth causal nodek) The connection event between the j-th state of the individual state and the result node Y is
Figure BDA0001698443940000061
Figure BDA0001698443940000062
Probability value of (i.e. connection strength)
Figure BDA0001698443940000063
θij＝(θij1,θij2,L,θijn)，j＝1,2,L,m；
In the causal graph, all the basic events and the connection events are independent of each other, and it can be demonstrated that when the example data is complete, the parameter θijThe posterior distribution of the parameters is mutually independent, so that the posterior distribution of each parameter can be independently calculated, and the posterior distribution can be used for parameter estimation respectively;
in practical application, the parameter thetaijThe prior distribution of (a) can be given by a domain expert, and if not, a Dirichlet distribution with conjugation can be selected as the prior distribution, i.e. the prior distribution
Figure BDA0001698443940000064
Wherein λk∈(0,1](k is 1,2, Λ, n) represents the degree of correlation between the causal node and the causal node, i.e. the probability that any state of the causal node will cause the causal node to occur is equal, and the probability is equal to λkAnd is independent of the node state,
Figure BDA0001698443940000065
a normalization constant called a result node;
step b: posterior distribution of joint strength parameters
Due to the fact that
P(θij|D)＝P(D|θij)P(θij)
While at the parameter thetaijWhen known, the data samples obey a polynomial distribution, i.e.
Figure BDA0001698443940000066
Wherein N isijkSatisfaction in representing instance dataset D
Figure BDA0001698443940000067
And Y isiThe number of example samples (c) is obtained by combining the above two formulas when the reason is that when the ith state of the kth node is the ith state and the result node is the jth state
Figure BDA0001698443940000068
Step c: probability value of connection event
From the foregoing, θ can be knownijIs also a dirichlet distribution, so that the connection strength parameter can be represented by the mathematical expectation of the posterior distribution, i.e.
Figure BDA0001698443940000071
Thus, if the correlation between each cause node and the result node is λkIt is known that the connection strength parameter θ can be determined from the above formula using the known example data set DijkIs estimated.
Preferably, step B includes DCD online process fault diagnosis
When in online fault diagnosis, whether the variable enters an abnormal state is judged by monitoring the process variable in real time, if the abnormal state of the variable occurs, a fault reasoning mechanism is entered to diagnose the occurrence reason of the current fault, and the specific steps of the process are as follows:
step 1) obtaining a causal graph model structure and parameters through a causal graph structure learning algorithm and a parameter learning algorithm, and completing establishment of a fault diagnosis model in the causal graph leaching process;
step 2) monitoring process variables in real time, judging whether the variables are abnormal or not by comparing whether the variables exceed a normal range or not, and taking the variables as an evidence E if the variables are abnormal;
step 3) substituting the evidence E and related causal graph parameters into the causal graph reasoning calculation process to obtain the final cut set expression CS of the node events-f and disjoint cut-set expression DCSs-f, calculating each according to Bayes' theoremPosterior probability of possible failure cause P (A/B):
Figure BDA0001698443940000072
and 4) comparing the posterior probabilities of all fault reasons, and determining the fault reason with the maximum posterior probability.
(III) advantageous effects
The invention has the beneficial effects that:
1) acquiring a causal graph knowledge base and a causal graph reasoning model by using expert knowledge and process data, and providing guarantee for acquiring accurate and reliable fault diagnosis results;
2) the method for determining the causal graph only by means of empirical knowledge is replaced by a DCD structure learning algorithm, the difficulty of knowledge provided by experts is reduced, errors are reduced, and the accuracy of fault diagnosis is improved, so that the fault diagnosis technology is more suitable for fault diagnosis in the hydrometallurgy leaching process;
3) and combining expert experience knowledge with the process data, and analyzing to obtain a primary probability value. And then a DCD parameter estimation algorithm is utilized to obtain a more accurate probability value of the connection event. In the process, the technology reduces the subjectivity of the expert knowledge, effectively fuses the expert knowledge and the data, and ensures the accuracy of obtaining the probability value.
4) The real-time fault diagnosis result is provided, so that the working personnel can put forward and implement a solution to the current production fault in time, the loss of the production benefit and the economic benefit of an enterprise is reduced, and the potential safety hazard is reduced.
Drawings
FIG. 1 is a process flow diagram of a hydrometallurgical leaching process according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating the effect of oxygen concentration and cyanide ion concentration on the gold dissolution rate according to an embodiment of the present invention;
FIG. 3 is a graphical illustration of the effect of NaCN concentration on leaching rate provided by an embodiment of the present invention;
FIG. 4 is a non-oriented potential diagram of a cause and effect diagram of a leaching process provided by an embodiment of the present invention;
FIG. 5 is a cause and effect diagram of a leaching process provided by an embodiment of the present invention;
FIG. 6 is an illustration of a related cause and effect diagram provided in accordance with an embodiment of the present invention;
FIG. 7 is a schematic diagram illustrating the DCD fault diagnosis procedure provided in the embodiment of the present invention;
FIG. 8 is a diagram illustrating conditional probabilities under abnormal pH conditions in accordance with an embodiment of the present invention;
FIG. 9 is a graph illustrating the real-time diagnosis result of abnormal pH according to an embodiment of the present invention;
FIG. 10 is a schematic diagram of conditional probability under abnormal cyanide ion concentration conditions according to an embodiment of the present invention;
FIG. 11 is a graph of the real-time diagnosis result of abnormal cyanide ion concentration according to an embodiment of the present invention;
FIG. 12 is a schematic diagram of the conditional probability of abnormal air flow and oxygen concentration conditions provided by an embodiment of the present invention;
fig. 13 is a graph showing the results of real-time diagnosis of abnormal air flow and oxygen concentration according to the embodiment of the present invention.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
The embodiment provides a fault diagnosis method for a hydrometallurgical leaching process based on a DCD (Dynamic cause and effect Diagram), which comprises the following steps of:
step A: establishing a DCD knowledge base model of a diagnosis object, specifically, establishing a dynamic causal graph knowledge base by extracting expert knowledge and information in process data as prior information, wherein the dynamic causal graph knowledge base comprises selection and definition of basic event variables and intermediate event variables, connection and establishment of causal relations among the variables, and setting of various parameters required by the variables;
and B: and monitoring whether the process is abnormal or not in real time through real-time running data acquired in the actual process, starting an inference process to carry out inference calculation and analysis if the monitored variable is in an abnormal state, and obtaining an inference result according to a quantitative probability numerical value.
(1) Leaching process DCD event determination
The causality graph model comprises the structure and parameters of the causality graph, and before the structure is built and the parameters are determined, the event variables involved in the hydrometallurgical leaching process are firstly determined. In determining the DCD event of a leaching process, the present invention follows the following principles: and taking the process state variable as a cause and effect graph node event, and taking the abnormity or the fault as a cause and effect graph basic event. Therefore, the basic events and node events of the cause and effect graph need to be determined through analyzing the faults and reasons thereof which are common in the process.
After analyzing the abnormal conditions of the main variables of the leaching process and the main fault causes thereof, the principle followed by the invention determines the 9 monitoring variables and 10 fault cause variables of the leaching process as the node events and the basic events of the leaching process cause-and-effect diagram, as shown in table 1.
Figure BDA0001698443940000091
Figure BDA0001698443940000101
Table 1 event definition table
(2) DCD structure learning
The method utilizes a structure learning method based on mutual information to determine the causal relationship among all variables so as to establish a causal graph model. The traditional causal graph is established by mainly relying on expert and field personnel experience knowledge to obtain the causal relationship among the variables, for a complex industrial process such as a hydrometallurgical process, the process variables are more and the causal relationship among the variables is very complex, the causal relationship among the variables of the causal graph is determined only by the experience knowledge and has larger uncertainty, and further the result of the causal graph fault diagnosis is deviated, so the invention provides a causal graph structure learning algorithm to reduce the error.
1) Basic principle of algorithm
The basic idea of the causal graph structure learning algorithm is that based on expert experience and given sample data, through Conditional Independence (CI) tests, edge deletion operations are conducted on complete potential graphs of the causal graph to obtain an optimal causal graph undirected potential graph, and finally the direction of directed edges among variables is determined according to causal relationships among the variables to obtain a final causal graph. The conditional independence between any two node variables X and Y given a set of node variables can be judged by marginal probability and conditional probability in a probability table that can be directly calculated from a given set of data. Two definitions are given here:
definition 1: the causal graph model, which consists of undirected edges between any two nodes of the causal graph, is called a complete latent graph (PDCD) of the causal graph.
Definition 2 if there is a relationship between the variable X, Y and the variable set Z, P (X | Z) ═ P (X | Y, Z), i.e. the state and probability of the variable Y do not affect the state of the variable X given the variable set Z is known, called I (X ⊥ Y | Z) given that the X condition is independent of Y.
Mutual information is used herein to express the causal relationship strength between causal graph nodes. According to the information theory, two discrete random variables X and Y have joint probability functions p (X, Y) and edge probability functions p (X), p (Y), and their average mutual information I (X, Y) is defined as:
Figure BDA0001698443940000111
also, the conditional mutual information I (X, Y | Z) is defined as:
Figure BDA0001698443940000112
when the causal graph structure learning algorithm is used, connection exists among all nodes, and whether causal association exists between the nodes X and Y is judged by adopting conditional mutual information. In general, a threshold of small positive real numbers is set, when I (X, Y | Z) ≦ indicating that the X condition is independent of Y given the Z condition, i.e., there is no causal relationship between X and Y, thereby removing the connection between X and Y. At most, the complete potential graph is trimmed to a sparse ideal potential cause-effect graph (DDCD) through n (n-1)/2 CI tests.
2) Algorithm implementation step
a) Initializing a full potential graph of a causal graph
Establishing a complete connection graph according to given specific problems and process data, namely, assuming that a dependency relationship exists between any two variables, and representing causal correlation between the variables by using a connection edge to form a complete potential graph PDCD;
b) fusing expert knowledge
According to expert experience and priori knowledge, node variables definitely without causal relationship in the complete potential graph of the causal graph are determined, and undirected edges among the nodes are deleted to obtain a relatively sparse potential graph of the causal graph;
c) potential map pruning
Performing CI test on the potential graph obtained in the step b), if the CI test is a true value, namely I (X, Y | Z) is less than or equal to the true value, deleting the undirected edge between the corresponding two node variables, otherwise, keeping the undirected edge until the CI test between all the variables is finished, and obtaining an ideal potential cause-effect graph DDCD;
d) converting undirected graph into causal graph
And determining the causal relationship among the variables according to the actual process mechanism and expert knowledge, and converting the optimal undirected latent graph into a causal graph with directed edges.
3) Cause and effect diagram of leaching process
The node events and the basic events of the leaching process cause-and-effect graph are determined through the previous analysis, and the final leaching process cause-and-effect graph is determined by using a cause-and-effect graph structure learning algorithm.
All events are firstly formed into a complete potential cause-and-effect graph of the leaching process, and connecting edges between nodes without cause-and-effect in the complete potential graph are deleted according to the experience of experts and field personnel, and a undirected potential graph of a preliminary cause-and-effect graph is formed as shown in figure 4.
As can be seen from FIG. 4, there is also an uncertain relationship in the pruned complete latent graph, namely variable X5And B6、X6And X0、X8And X0Whether there is a direct causal graph relationship between them. So its cause and effect relationship is determined by performing CI tests. Calculated, the variable X is determined5And B6The causality exists between the two, namely the change of the liquid level of the sodium cyanide storage tank can influence the addition amount of the sodium cyanide; and variable X6、X8And X0There is no direct causal relationship between the flow rate of the slurry and the PH of the slurry, which does not directly affect the feed rate. The final optimal latent graph is obtained by pruning the complete latent graph of the causal graph, and the directional direction of the directed edge is determined by the process mechanism and expert knowledge, so that the latent graph is converted into the final causal graph as shown in fig. 5.
(3) DCD parameter learning
The present invention makes the determination of event probability values for measurable and non-measurable events, respectively. The probability value for the non-measurable event is mainly determined according to expert experience, the probability value for the measurable event is mainly determined by analyzing the process data, and on the basis, the probability value of the connection event is further refined by using a parameter estimation algorithm. Due to the numerous parameters of the hydrometallurgical process and the complex relation among the variables, the expert is difficult to directly give out more accurate model parameters, the model parameters are incomplete depending on single expert knowledge, and the most direct result is inaccurate diagnosis results. Therefore, the invention combines the expert experience and the process data more effectively, thereby obtaining more accurate parameters and establishing a more accurate fault diagnosis model.
1) Basic event probability acquisition
The probability of the failure of the fan, the probability of the damage of the air valve and the like in the hydrometallurgical leaching process cannot be directly measured, so the probability of the basic events is directly obtained according to the process mechanism and experience of experts and field personnel. The hydrometallurgical process system is huge, and different experts have differences in the areas where the hydrometallurgical process system is good at, so that the acquisition of the basic event probability needs to be integrated with knowledge and experience of all experts, and therefore, the reasonable basic event probability of the causal graph is given.
Meanwhile, basic event variables which can be measured, such as conditioning water flow and the like, also exist in the hydrometallurgical leaching process, and the probability value of the basic event can be obtained by analyzing process data. Probabilities of states of elementary event variables, e.g.
Figure BDA0001698443940000131
Represents the variable BiIn all possible states of
Figure BDA0001698443940000132
The probability value of (2). Suppose N is collectediHistorical data of strip samples, among them
Figure BDA0001698443940000133
One sample is in variable BiThe kth state of (1), i.e. variable BiThe k-th state of (1) occurs, then
Figure BDA0001698443940000134
2) Connection event probability acquisition
Probability value of connection event
Figure BDA0001698443940000135
Represents the variable ViKthiA state
Figure BDA0001698443940000136
Result in a variable VjKthjA state
Figure BDA0001698443940000137
Probability value of occurrence. The same principle is 1), on one hand, the method can be directly given by experts and field personnel according to process technological mechanisms and experiences, and on the other hand, the method can be obtained by process data analysis.
Assuming that enough V is collectediAnd VjData of (1), wherein
Figure BDA0001698443940000138
The number of data samples occurring is
Figure BDA0001698443940000139
Figure BDA00016984439400001310
And
Figure BDA00016984439400001311
the number of simultaneous data samples is
Figure BDA00016984439400001312
Then there is
Figure BDA00016984439400001313
In practical applications, experts usually give direct causal strength of each cause to the intermediate variable, rather than complex conditional probability tables in belief networks, and they are not even aware of the existence of other causes when considering the effect of a cause on the outcome, which is in line with the thinking of the experts. Meanwhile, the probability value of the causal graph connection event is obtained by combining a part of experts in related engineering fields according to experience knowledge and analyzing process data, but the probability value of the causal graph event obtained by not effectively fusing the expert knowledge and field data has errors. Then, the invention obtains more accurate causal graph parameters on the basis of the parameter estimation method.
a) Prior distribution of joint strength parameters
For any given result node Y, it is set to have m states Yj(j ═ 1,2, ^, m), n causal nodes Xk(k＝1,2,∧n)，XkHas mkIn this state, the ith (i ═ 1,2, ^, m) of the kth causal nodek) Connections between individual states and the jth state of the result node YReceive an event of
Figure BDA0001698443940000141
Figure BDA0001698443940000142
Probability value of (i.e. connection strength)
Figure BDA0001698443940000143
θij＝(θij1,θij2,∧,θijn) J is 1,2, Λ, m. In the causal graph, all the basic events and the connection events are independent of each other, and it can be demonstrated that when the example data is complete, the parameter θijThe posterior distribution of the parameters is mutually independent, so that the posterior distribution of each parameter can be independently calculated, and the posterior distribution can be used for parameter estimation respectively.
In practical application, the parameter thetaijThe prior distribution can be given by a domain expert, if the prior distribution can not be obtained, a conjugate Dirichlet distribution can be selected as the prior distribution[45]I.e. by
Figure BDA0001698443940000144
Wherein λk∈(0,1](k is 1,2, Λ, n) represents the degree of correlation between the causal node and the causal node, i.e. the probability that any state of the causal node will cause the causal node to occur is equal, and the probability is equal to λkRegardless of the node state.
Figure BDA0001698443940000145
Referred to as the normalization constant of the result node. In practical application, the correlation degree lambda between each reason node and the result nodekGenerally given by an expert.
Here, the correlation is described as a simple example. In the causal graph structure shown in FIG. 6, X1、X2For reason event node, Y is result event node, X1、X2There are two states and Y has three states. The correlation λ is required when the expert gives a probabilitykIs a constant (generally designated by λ)kTo 1) can be understood as:
Figure BDA0001698443940000146
Figure BDA0001698443940000147
for example:
Figure BDA0001698443940000148
λ1＝0.1+0.2+0.3＝0.6
Figure BDA0001698443940000149
λ1＝0.15+0.25+0.2＝0.6
Figure BDA00016984439400001410
λ1＝0.25+0.35+0.2＝0.8
Figure BDA0001698443940000151
λ1＝0.3+0.25+0.25＝0.8
b) posterior distribution of joint strength parameters
Due to the fact that
P(θij|D)＝P(D|θij)P(θij) (7)
While at the parameter thetaijWhen known, the data samples obey a polynomial distribution, i.e.
Figure BDA0001698443940000152
Wherein N isijkSatisfaction in representing instance dataset D
Figure BDA0001698443940000153
And Y isiThe number of example samples in (1), that is, the number of example samples in the case that the result node is in the jth state when the reason is the ith state of the kth node, can be obtained by combining the above two formulas:
Figure BDA0001698443940000154
c) probability value of connection event
From the foregoing, θ can be knownijIs also a Dirichlet (Dirichlet) distribution, so that the connection strength parameter can be represented by the mathematical expectation of the posterior distribution, i.e.
Figure BDA0001698443940000155
Thus, if the correlation between each cause node and the result node is λkIt is known (given by the expert in the field) to use the known example data set D to determine the connection strength parameter θ from the above formulaijkIs estimated.
(4) DCD online process fault diagnosis
When the online fault diagnosis is carried out, whether the variable enters an abnormal state or not is judged by monitoring the process variable in real time, and if the abnormal state of the variable occurs, a fault reasoning mechanism is entered to diagnose the occurrence reason of the current fault.
The steps for online fault diagnosis using DCD are shown in fig. 7:
1) acquiring a causal graph model structure and parameters through a causal graph structure learning algorithm and a parameter learning algorithm;
2) monitoring process variables in real time, judging whether the variables are abnormal or not by comparing whether the variables exceed a normal range or not, and taking the variables as an evidence E if the variables are abnormal;
3) substituting the evidence E and related causal graph parameters into the causal graph reasoning calculation process to obtain a final cut set expression CS of the node events-f and disjoint cut-set expression DCSs-f, calculating the possible faults according to Bayesian theoremA posterior probability of cause P (A/B);
Figure BDA0001698443940000161
4) comparing the posterior probability of each fault reason, and considering the one with the highest posterior probability as the fault reason.
The device comprises a hydrometallurgical leaching process fault diagnosis system, an upper computer, a P L C and a field sensing transmission part, wherein the field sensing transmission part comprises detection instruments for concentration, pressure, flow and the like, the detection instruments are installed on the field of the hydrometallurgical process, the detection instruments transmit acquired signals to the P L C through a Profibus-DP bus, the P L C transmits the acquired signals to the upper computer at regular time through Ethernet, and the upper computer transmits the received data to the hydrometallurgical leaching process fault diagnosis system for online process fault diagnosis.
The functions of each part of the device are as follows:
1) the field sensing and transmitting part: the concentration, pressure, flow and other detection instruments are composed of sensors and are responsible for collecting and transmitting process data;
2) p L C, for A/D conversion of the collected signal and transmitting the signal to the upper computer through Ethernet;
3) and the upper computer collects local P L C data, transmits the data to the hydrometallurgy leaching process fault diagnosis system, enters an inference mechanism and diagnoses the fault reason.
The fault diagnosis technology for the DCD-based hydrometallurgical leaching process comprises the following steps: (1) determining a DCD event in a leaching process, (2) learning a DCD structure, (3) learning DCD parameters, (4) diagnosing DCD online process faults and the like.
The DCD-based hydrometallurgical leaching process fault diagnosis method is mainly oriented to a leaching process, and a process detection system mainly comprises concentration detection, pressure detection, flow detection and the like. The embodiment also provides a specific application process of the method, which comprises the following steps:
the P L C controller adopts Simens 400 series CPU 414-2, has Profibus DP port connection distribution IO. and is equipped with an Ethernet communication module for P L C, and is used for an upper computer to access P L C data, and the P L C controller and the Ethernet communication module are arranged in a P L C cabinet in a central control room.
The pH value is detected on line by a BPHM-II acidimeter developed by Beijing mining and metallurgy research institute, the change of the pH value of the solution is converted into the change of a mV signal, a glass electrode pH measuring system blows the end part of a glass tube of a glass film sensitive to the pH into a bubble shape, the tube is filled with 3mol/l KC L buffer solution containing saturated AgCl, the pH value is 7, the potential difference existing on the two sides of the glass film and reflecting the pH value is led out by an Ag/AgCl conduction system, and then a mA collecting instrument converts the mA number into the pH value to be displayed.
The concentration of the ore pulp is measured on line by a BDSM type online concentration meter of Beijing mining and metallurgy research institute. The sensor sends a beam of ultrasonic pulse to a measured medium, the ultrasonic wave is attenuated due to scattering and absorption of suspended particles when passing through the suspended particles, the attenuation of the ultrasonic wave in the sludge or the solid suspended matters is related to the sludge concentration or the solid suspended matter concentration in the liquid, and the sludge or the solid suspended matter concentration can be calculated by measuring the attenuation value of the ultrasonic wave.
The pressure is detected on line by a DSIII pressure detector produced by SIEMENS company, the pressure of medium directly acts on a sensitive diaphragm, a Wheatstone bridge consisting of resistors distributed on the sensitive diaphragm realizes the conversion from the pressure to an electric signal by using piezoresistive effect, and a millivolt signal generated by a sensitive element is amplified into an industrial standard current signal by an electronic circuit.
The dissolved oxygen concentration was measured on-line by an inpro6870+ M400 type oxygen amount measuring sensor manufactured by mettleltoreq corporation. The oxygen measuring sensor consists of cathode, counter electrode with current and reference electrode without current, the electrode is immersed in electrolyte, the sensor is covered with diaphragm, the diaphragm separates the electrode and electrolyte from the measured liquid, only dissolved gas can permeate the diaphragm, so that the sensor is protected, the electrolyte can be prevented from escaping, and the pollution and poisoning caused by invasion of foreign matter can be prevented. The current signal is sent to the transducer, and the oxygen content is calculated by using the relationship curve between the oxygen content and the oxygen partial pressure and temperature stored in the transducer, and then converted into a standard signal to be output.
The upper computer selects an i7 associative computer and adopts a WINDOW XP operating system.
The P L C signaling software is programmed using C # 2008.
A detection instrument is installed on the site of the hydrometallurgy process, the detection instrument transmits collected signals to a P L C through Profibus-DP, the P L C transmits the collected signals to an upper computer through Ethernet at regular time, and the upper computer transmits the received data to a process fault diagnosis system for online fault diagnosis.
First step, determination of DCD event in leaching process: the event variables involved in the hydrometallurgical leaching process are first defined. In determining the DCD event of a leaching process, the present invention follows the following principles: and taking the process state variable as a cause and effect graph node event, and taking the abnormity or the fault as a cause and effect graph basic event. Therefore, the basic events and node events of the cause and effect graph need to be determined through analyzing the faults and reasons thereof which are common in the process.
Step two, DCD structure learning: based on expert experience and given sample data, the invention carries out edge deletion operation on a complete potential graph of the cause-effect graph through a Conditional Independence (CI) test to obtain an optimal cause-effect graph undirected potential graph, and finally determines the direction of directed edges between variables according to the cause-effect relationship between the variables to obtain a final cause-effect graph. The conditional independence between any two node variables X and Y given a set of node variables can be judged by marginal probability and conditional probability in a probability table that can be directly calculated from a given set of data.
Thirdly, learning DCD parameters: the parameters of the causal graph mainly comprise the prior probability values of the basic events and the connection events.
In the process of acquiring the probability value of the basic event, the probability value of the basic event which cannot be directly measured is directly given according to the process technology mechanism and experience of experts and field personnel. The hydrometallurgical process system is huge, different experts are good at in different fields, and the acquisition of the probability of the basic event needs to be integrated with knowledge and experience of all the experts. Meanwhile, for the probability value of the measurable basic event, the occurrence probability value can be obtained by analyzing the process data.
In the process of acquiring the probability value of the connection event, firstly, a primary probability value can be obtained by combining a part of knowledge and knowledge according to related engineering field experts through process data analysis, and then, a more accurate probability value of the connection event is obtained on the basis through a parameter estimation method.
Fourthly, diagnosing the fault of the DCD on-line process: when the online fault diagnosis is carried out, the process variables are monitored in real time, whether the process is abnormal or not is monitored in real time through real-time operation data acquired in the actual process, if the process variables are monitored to be in an abnormal state, the inference process is started to carry out inference calculation and analysis, and the inference result is obtained according to the quantitative probability numerical value.
The data used is 1000 groups of sample data collected from a certain cuprite cyanidation leaching simulation platform, and a probability table of basic events and connection events of a leaching process causal graph model is determined after the collected historical production data is analyzed and learned by using the causal graph parameter learning algorithm, as shown in tables 2 and 3.
Figure BDA0001698443940000191
TABLE 2 probability of elementary events of leaching process
Figure BDA0001698443940000192
TABLE 3(a) X3X6X8Probability of connection event
Figure BDA0001698443940000193
TABLE 3(b) X5X7Probability of connection event
Figure BDA0001698443940000194
TABLE 3(c) X1X4Probability of connection event
Figure BDA0001698443940000195
Figure BDA0001698443940000201
TABLE 3.3(d) X0X2Probability of connection event
The following is a diagnostic analysis of several common anomalies in the leaching process.
(1) PH anomaly diagnostic analysis
200 samples were taken and the pH X was monitored from the sampling time of the 100 th sample8Abnormally decreased, i.e. evidence E ═ X8. Firstly, the corresponding cut set expression CS is calculateds-f and DCSs-f are respectively as follows:
Figure BDA0001698443940000202
from the causality map of the leaching process established previously, the root cause variable which may cause pH abnormality is B7、B8、B9And B10According to the fault diagnosis step of the causal graph, the relevant variable parameters are substituted into the reasoning process to calculate the conditional probability of each basic event, and the result is shown in fig. 8.
Comparing the conditional probability values of FIG. 8, we can determine that the reason for the abnormally low PH value is B9I.e. the peristaltic pump adding the milk of lime fails. Actual condition analysis shows that the peristaltic pump cannot work normally, lime milk cannot be added according to a set value, the addition amount of the lime milk is reduced abnormally, and the pH value is reduced abnormally due to the fact that the addition amounts of other mixed liquid are unchanged. The real-time diagnosis of PH anomalies is shown in fig. 9, where the abscissa represents the sampling moment and the ordinate represents 10 common causes of failure in the leaching process. From the analysis of fig. 9, it can be seen that PH is monitored at the 101 st sampling timeIf the value is abnormal, the diagnostic process is started immediately, and the fault source is diagnosed as B9。
(2) Cyanide ion concentration anomaly diagnostic analysis
200 groups of samples are collected, and the concentration X of the cyanide ions is monitored from the sampling moment of the 120 th sample2Abnormally decreased, i.e. evidence E ═ X2. Firstly, the corresponding cut set expression CS is calculateds-f and DCSs-f are respectively as follows:
Figure BDA0001698443940000203
as can be seen from the cause and effect diagram of the leaching process, the root cause variable which can cause the abnormal concentration of cyanide ions is B4、B5、B6、B7And B8According to the causal graph fault diagnosis step, the condition probability of each basic event is calculated by substituting the related variable parameters into the reasoning process, and is shown in fig. 10.
Comparing the obtained conditional probability value with the obtained conditional probability value, the reason that the concentration of the cyanide ions is abnormally low can be judged to be B7I.e. the ore coming material is too large in the leaching process. The excessive coming stone directly causes the abnormal increase of the input flow of the ore pulp of the leaching tank, and inevitably causes the abnormal reduction of the concentration of cyanide ions in the ore pulp when the addition amount of NaCN is kept constant. The real-time diagnosis results are shown in fig. 11.
(3) Air flow and oxygen concentration anomaly diagnostic analysis
200 samples were taken and the air flow X was monitored from the sampling time of the 100 th sample4Abnormally decreases and the oxygen concentration X is monitored from the sampling time of the 120 th sample1Also starts to decrease abnormally, corresponding to E respectively1＝X4And E2＝X1X4The failure diagnosis is performed in the case of (1). Corresponding cut set expression CSs-f and DCSs-f are respectively as follows:
CSs-f
Figure BDA0001698443940000211
DCSs-f
Figure BDA0001698443940000212
as can be seen from the cause and effect diagram of the leaching process, the root cause node which can cause the abnormal oxygen flow has B1，B2And B3The root cause node causing the abnormal oxygen concentration is B1、B2、B3、B7And B8. Substituting probability values into evidence E1And E2The lower calculation conditional probability values are shown in fig. 12.
From evidence E1The conditional probability value can firstly judge that the root node causing the abnormal reduction of the air flow is B1Namely, the air flow introduced into the leaching tank is reduced due to the failure of the fan. Then, due to the abnormal reduction of the air flow, the abnormal reduction of the oxygen concentration is monitored, and the air flow and the ore pulp oxygen concentration are reduced simultaneously, namely when the evidence E shows that2＝X1X4Then, the reasoning calculation is performed again according to the evidence E2The conditional probability value under the condition is also diagnosed as B1And relative to the initial evidence E1The following diagnosis results are more accurate, and the real-time diagnosis result is shown in fig. 13.
The technical principles of the present invention have been described above in connection with specific embodiments, which are intended to explain the principles of the present invention and should not be construed as limiting the scope of the present invention in any way. Based on the explanations herein, those skilled in the art will be able to conceive of other embodiments of the present invention without inventive efforts, which shall fall within the scope of the present invention.

Claims (6)

1. A DCD-based hydrometallurgical leaching process fault diagnosis method is characterized by comprising the following steps: which comprises the following steps:
step A: establishing a DCD knowledge base model of a diagnosis object, wherein the model comprises selection and definition of basic event and intermediate event variables, connection and establishment of causal relationship among the variables, and setting of various parameters required by the variables;
in the step A, determining a DCD event in a leaching process, and determining event variables related to the hydrometallurgical leaching process; in the process of determining the DCD events in the leaching process, the process state variables are used as causal graph node events, the abnormal events or faults are used as basic events of the causal graph, and the basic events and the node events of the causal graph are determined by analyzing the faults and the reasons thereof which are common in the process; the process state variables comprise leaching rate, oxygen concentration, cyanide ion concentration, ore pulp concentration, air flow, sodium cyanide addition, ore pulp input flow, air pipeline pressure and pH value; the abnormality comprises sodium cyanide storage tank liquid level abnormality, ore incoming material abnormality and size mixing water flow abnormality; the faults comprise a fan fault, a ventilation pipeline fault, an air valve fault, a computer dosing machine fault, a metering pump fault, a peristaltic pump fault and a lime milk regulating valve fault;
and B: monitoring whether the process is abnormal or not in real time through real-time running data acquired in the actual process, if the process is monitored to be abnormal, starting an inference process to carry out inference calculation and analysis, and obtaining an inference result according to a quantitative probability numerical value;
in step B including DCD online process fault diagnosis,
when in online fault diagnosis, whether the variable enters an abnormal state is judged by monitoring the process variable in real time, if the abnormal state of the variable occurs, a fault reasoning mechanism is entered to diagnose the occurrence reason of the current fault, and the specific steps of the process are as follows:
step 1) obtaining a causal graph model structure and parameters through a causal graph structure learning algorithm and a parameter learning algorithm, and completing establishment of a fault diagnosis model in the causal graph leaching process;
step 2) monitoring process variables in real time, judging whether the variables are abnormal or not by comparing whether the variables exceed a normal range or not, and taking the variables as an evidence E if the variables are abnormal;
step 3) substituting the evidence E and related causal graph parameters into the causal graph reasoning calculation process to obtain the final cut set expression of the node eventFormula CSs-f and disjoint cut-set expression DCSsF, calculating the posterior probability P (A/B) of each possible fault cause according to Bayesian theorem:
Figure FDA0002470000410000021
step 4) comparing posterior probabilities of all fault reasons, wherein the fault reason with the highest posterior probability is considered as the fault reason; when the air flow and oxygen concentration abnormity diagnosis and analysis are carried out, the evidence E has two values, each value is replaced into the causal graph reasoning calculation process, and the diagnosis result is obtained after the calculation results are compared.
2. The DCD-based hydrometallurgical leaching process fault diagnosis method of claim 1, further comprising DCD structure learning in step A, after the node events and the basic events of the causal graph are determined, the causal relationship between the variables is determined, and the causal relationship between the variables is determined based on mutual information causal graph structure learning algorithm to establish the causal graph model.
3. The DCD-based hydrometallurgical leaching process fault diagnostic method of claim 2, wherein,
the causal graph structure learning algorithm comprises the following steps:
the basic idea of the causal graph structure learning algorithm is that based on expert experience and given sample data, through conditional independence test, edge deletion operation is conducted on a complete potential graph of the causal graph to obtain an optimal causal graph undirected potential graph, and then the direction of directed edges among variables is determined according to causal relationships among the variables to obtain a final causal graph;
the conditional independence between any two node variables X and Y given a set of node variables can be judged by marginal probability and conditional probability in a probability table that can be directly calculated from a given data set;
and gives two definitions as follows:
definition 1: a causal graph model consisting of undirected edges between any two nodes of the causal graph, called a complete potential graph of the causal graph;
definition 2 if there is a relationship between the variable X, Y and the variable set Z, P (X | Z) ═ P (X | Y, Z), i.e. the state and probability of the variable Y do not affect the state of the variable X under the condition that the variable set Z is known, called I (X ⊥ Y | Z) given that the X condition is independent of Y;
expressing the causal relationship strength between nodes of the causal graph by mutual information, two discrete random variables X and Y have a joint probability function p (X, Y) and an edge probability function p (X), p (Y), and then the average mutual information I (X, Y) is defined as:
Figure FDA0002470000410000031
also, the conditional mutual information I (X, Y | Z) is defined as:
Figure FDA0002470000410000032
when the causal graph structure learning algorithm is used, firstly, connection exists among all nodes, and whether causal association exists between nodes X and Y is judged by adopting conditional mutual information;
in the usual case, a threshold of positive real numbers is set, when I (X, Y | Z) ≦ indicating that the X condition is independent of Y given the Z condition, i.e. there is no causal relationship between X and Y, thus removing the connection between X and Y;
and (4) after n (n-1)/2 CI tests, the complete potential graph is finally trimmed into a sparse ideal potential cause-effect graph.
4. The DCD-based hydrometallurgical leaching process fault diagnostic method of claim 3, wherein,
the causal graph structure learning algorithm is realized by the following steps:
step a: initializing a full potential graph of a causal graph
Establishing a complete connection graph according to given specific problems and process data, namely, assuming that a dependency relationship exists between any two variables, and representing causal correlation between the variables by using a connection edge to form a complete potential graph PDCD;
step b: fusing expert knowledge
According to expert experience and priori knowledge, node variables definitely without causal relationship in the complete potential graph of the causal graph are determined, and undirected edges among the nodes are deleted to obtain a relatively sparse potential graph of the causal graph;
step c: potential map pruning
C, performing CI testing on the potential graph obtained in the step b, if the CI testing is a true value, namely I (X, Y | Z) is less than or equal to the true value, deleting the undirected edges between the corresponding two node variables, and otherwise, keeping the undirected edges until the CI testing among all the variables is finished, so as to obtain an ideal potential cause-effect graph DDCD;
step d: converting undirected graph into causal graph
And determining the causal relationship among the variables according to the actual process mechanism and expert knowledge, and converting the optimal undirected latent graph into a causal graph with directed edges.
5. The DCD-based hydrometallurgical leaching process fault diagnosis method of claim 4, further comprising DCD parameter learning in step A, the DCD parameter learning comprising the steps of:
step 1: basic event probability acquisition
Basic event variables which cannot be directly measured exist in the hydrometallurgical leaching process, so that the basic event probability is directly given out according to process technological mechanisms and experiences by experts and field personnel, and the basic event probability is acquired by integrating knowledge and experiences of all the experts to obtain the basic event probability of the cause-effect diagram;
meanwhile, measured basic event variables also exist in the hydrometallurgical leaching process, and the probability value of the basic event can be acquired by analyzing process data;
probabilities of states of elementary event variables, e.g.
Figure FDA0002470000410000041
Is a variable BiIn all possible states of
Figure FDA0002470000410000042
Assuming that N is collectediHistorical data of strip samples, among them
Figure FDA0002470000410000043
One sample is in variable BiThe kth state of (1), i.e. variable BiThe k-th state of (1) occurs, then
Figure FDA0002470000410000044
Step 2: connection event probability acquisition
Probability value of connection event
Figure FDA0002470000410000045
Represents the variable ViKthiA state
Figure FDA0002470000410000046
Result in a variable VjKthjA state
Figure FDA0002470000410000047
Similarly to the step 1, the probability value can be directly given by experts and field personnel according to process mechanism and experience on one hand, and can be obtained by process data analysis on the other hand;
assuming that enough V is collectediAnd VjData of (1), wherein
Figure FDA0002470000410000048
The number of data samples occurring is
Figure FDA0002470000410000049
Figure FDA00024700004100000410
And
Figure FDA00024700004100000411
the number of simultaneous data samples is
Figure FDA00024700004100000412
Then there is
Figure FDA00024700004100000413
6. The DCD-based hydrometallurgical leaching process fault diagnosis method of claim 5, wherein the accurate connection event probability value is obtained by a parameter estimation method on the basis of obtaining the connection probability, which comprises the following steps:
step a: prior distribution of joint strength parameters
For any given result node Y, it is set to have m states Yj(j ═ 1,2, L, m), n cause nodes Xk(k＝1,2,Ln)，XkHas mkIn one state, the ith (i ═ 1,2, L, m) of the kth causal nodek) The connection event between the j-th state of the individual state and the result node Y is
Figure FDA0002470000410000051
Probability value of (i.e. connection strength)
Figure FDA0002470000410000052
θij＝(θij1,θij2,L,θijn)，j＝1,2,L,m；
In the causal graph, all the basic events and the connection events are independent of each other, and it can be demonstrated that when the example data is complete, the parameter θijThe posterior distribution of the parameters are independent of each other, and the posterior distribution of the parameters can be calculated independently and can be used for calculatingEstimating line parameters;
in practical application, the parameter thetaijThe prior distribution of (a) can be given by a domain expert, and if not, a Dirichlet distribution with conjugation can be selected as the prior distribution, i.e. the prior distribution
Figure FDA0002470000410000053
Wherein λk∈(0,1](k is 1,2, Λ, n) represents the degree of correlation between the causal node and the causal node, i.e. the probability that any state of the causal node will cause the causal node to occur is equal, and the probability is equal to λkAnd is independent of the node state,
Figure FDA0002470000410000054
a normalization constant called a result node;
step b: posterior distribution of joint strength parameters
Due to the fact that
P(θij|D)＝P(D|θij)P(θij)
While at the parameter thetaijWhen known, the data samples obey a polynomial distribution, i.e.
Figure FDA0002470000410000055
Wherein N isijkSatisfaction in representing instance dataset D
Figure FDA0002470000410000056
And Y isiThe number of example samples (c) is obtained by combining the above two formulas when the reason is that when the ith state of the kth node is the ith state and the result node is the jth state
Figure FDA0002470000410000061
Step c: probability value of connection event
From the foregoing, θ can be knownijIs also a dirichlet distribution, so that the connection strength parameter can be represented by the mathematical expectation of the posterior distribution, i.e.
Figure FDA0002470000410000062
Thus, if the correlation between each cause node and the result node is λkIt is known that the connection strength parameter θ can be determined from the above formula using the known example data set DijkIs estimated.
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