CN117436532B - Root cause analysis method for gaseous molecular pollutants in clean room - Google Patents
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Abstract
The invention relates to the technical field of root cause analysis of gaseous molecular pollutants, and discloses a root cause analysis method of the gaseous molecular pollutants in a clean room, wherein indoor gaseous molecular pollutant data are input into a root cause analysis model to obtain root cause analysis results; the root cause analysis model construction specifically comprises the following steps: data acquisition and pretreatment: determining a primary Bayesian analysis network based on expert knowledge and by a probability method; determining an optimal Bayesian analysis network based on an evolutionary algorithm; based on the optimal Bayesian analysis network, parameter estimation is carried out on the root cause analysis model by estimating the prior probability distribution of the root cause and the conditional probability distribution of the training characteristics. The root cause analysis model is not a network structure uniquely designated by an expert, but is a measurement of the probability of the association relationship between the root cause and the characteristics, and the optimal Bayesian analysis network is finally determined by combining an evolutionary algorithm, so that the root cause analysis model is obtained.
Description
Technical Field
The invention relates to the technical field of gaseous molecular pollutant root cause analysis, in particular to a clean room gaseous molecular pollutant root cause analysis method.
Background
The semiconductor manufacturing process is particularly critical to the cleanliness of the manufacturing environment, and thus the entire manufacturing process is performed in a tightly controlled clean room environment. Gaseous molecular contaminants (Airborne Molecular Contaminants, AMC) may originate from outside air or operators, and may also be generated by processes, by cleanroom material outgassing, or by equipment leaks. Gaseous molecular pollutants can cause oxidation and corrosion of the surface of a semiconductor crystal, so that the product yield is reduced, and the method is a key link of a production process.
For gaseous molecular pollutants in a clean room, traditional root cause analysis relies on the experience of an expert, the expert proposes possible investigation directions, and then staff gathers relevant data to verify the guess of the expert. However, the method is seriously dependent on expert experience, has poor timeliness, cannot quickly find out the reasons for exceeding the standard of gaseous molecular pollutants, and greatly influences the treatment efficiency.
Disclosure of Invention
In order to solve the technical problems, the invention provides a root cause analysis method for gaseous molecular pollutants in a clean room.
In order to solve the technical problems, the invention adopts the following technical scheme:
the root cause analysis method of the gaseous molecular pollutants in the clean room comprises the steps of inputting indoor gaseous molecular pollutant data into a root cause analysis model to obtain root cause analysis results; the root cause analysis model construction and training process specifically comprises the following steps:
step one, data acquisition and pretreatment:
collecting indoor gaseous molecular pollutant data of a clean room, and normalizing the indoor gaseous molecular pollutant data through means and variances;
step two: determining a first-generation Bayesian analysis network based on expert knowledge and by a probability method;
step three: determining an optimal Bayesian analysis network based on an evolutionary algorithm: generating offspring of the Bayesian analysis network through mixing scoring functions and individual selection, crossing and variation based on the first-generation Bayesian analysis network, and outputting an optimal Bayesian analysis network;
step four: based on an optimal Bayesian analysis network, estimating parameters of a root cause analysis model by estimating prior probability distribution of the root cause and conditional probability distribution of training characteristics; wherein the prior probability distribution of root causes is calculated by indoor gaseous molecular pollutant data.
Further, in the second step, when the first-generation bayesian analysis network is determined based on the knowledge of the expert and by a probability method, the bayesian analysis network includes: root cause node setFeature node setThe method comprises the steps of carrying out a first treatment on the surface of the The structure of a Bayesian analysis network is defined by a structure matrix>The composition is as follows:
;
for the number of types of root node +.>For the number of types of feature nodes +.>Representing a structural matrix->Elements of (a) and (b); />Representing an ith root cause node in the Bayesian analysis network; />Representing a j-th feature node in the Bayesian analysis network; if the root cause node in the Bayesian analysis network is +.>And feature node->Related +.>The method comprises the steps of carrying out a first treatment on the surface of the If the root cause node in the Bayesian analysis network is +.>And feature node->Irrelevant, I/O>;
Defining an uncertainty matrixRepresenting expert knowledge, < >>Uncertainty matrix->Each element of->Representing root cause node +.>And feature node->The size of the correlation; expert determines +.>If expert supports root node +.>And featuresNode->Related +.>Assigned a value greater than a set threshold, e.g., a value greater than 0.8, if the expert does not support the root cause nodeAnd feature node->Related +.>A value given to be smaller than a set threshold value, for example, a value smaller than 0.2;
a first generation bayesian analysis network is generated by the following random generation algorithm:
;
is a random variable subject to uniform distribution, +.>Representing matrix elements in a first-generation bayesian analysis network matrix.
Further, in the third step, based on the primary bayesian analysis network, generating the offspring of the bayesian analysis network through the mixed scoring function and the three evolutionary operations, and outputting the optimal bayesian analysis network, specifically including:
step three A, setting a first generation population: converting a structural matrix R of a primary Bayesian analysis network into a one-dimensional sequenceOne-dimensional sequenceThe genes representing each individual in the initial population, i.e., the genes of each individual in the primary population are the same, each individual representing a bayesian analysis network;
step three B, scoring the quality of each individual in the population through a mixed scoring function:
;
wherein,for the mass fraction of the individual, < > A->The Bayes-Dirichlet equivalent score is used for measuring the coincidence degree of the Bayes analysis network and the actual data; />As a penalty term for measuring Bayesian analysis network and uncertainty matrix>Is matched with the degree of the matching; />The coefficients representing the trade-off expert knowledge contributions,representing a decision tree calculation item;
step three, selecting individuals with mass fractions higher than a set value, carrying out mutation operation to generate new individuals, and forming a new population with the individuals with mass fractions higher than the set value; if the termination condition is met, performing a step III; if the termination condition is not met, performing the step III; when mutation operation is performed, ifThe value of (1) is changed from 0 to 1, then +.>And characteristic node->Adding a boundary between the two; if->The value of (1) is changed from 1 to 0, the root cause node is deleted +.>And characteristic node->A boundary between them.
And thirdly, selecting an optimal Bayesian analysis network by adopting a roulette selection method.
Further, in the fourth step, when parameter estimation is performed on the root cause analysis model:
;
is root cause node->Take the kth state and root in node +.>Conditional probability when the parent node of (1) takes the j-th joint distribution,/and (2)>Representing the condition that the limit is met->Representing a calculated conditional probability; conditional probability according to maximum likelihood ruleOptimal estimation of +.>The method comprises the following steps:
;
indicating compliance->Adopt the kth state and +.>The father node of the (j) th joint distribution condition is adopted; intermediate variable->Further obtaining a final root cause analysis model;
wherein the joint distribution represents a joint of a priori probability distribution and a conditional probability distribution.
Compared with the prior art, the invention has the beneficial technical effects that:
the structure of the traditional Bayesian analysis network is only constructed by expert knowledge, is often not an optimal solution, and cannot be dynamically adjusted along with the operation of the system, so that the analysis accuracy is in a continuous reduction trend. The root cause analysis model is not a network structure uniquely specified by an expert, but is used for converting expert knowledge into a measure for the probability of the association relationship between the root cause and the characteristics, and finally determining the optimal Bayesian analysis network by combining an evolutionary algorithm. The root cause analysis model of the gaseous molecular pollutants established by the invention can rapidly analyze the cause of exceeding the standard of the gaseous molecular pollutants in the clean room, the analysis accuracy reaches 92%, and the disposal efficiency is also improved to 90%.
Drawings
FIG. 1 is a flow chart of the construction of root cause analysis model in the present invention.
Detailed Description
A preferred embodiment of the present invention will be described in detail with reference to the accompanying drawings.
According to the root cause analysis method of the clean room gaseous molecular pollutants, indoor gaseous molecular pollutant data are input into a root cause analysis model to obtain root cause analysis results; as shown in fig. 1, the process of constructing and training the root cause analysis model specifically includes:
step one, data acquisition and pretreatment:
indoor gaseous molecular pollutant data of the clean room are collected, and the indoor gaseous molecular pollutant data are normalized through means and variances.
Step two: the first generation bayesian analysis network is determined based on expert knowledge and by means of probability.
The bayesian analysis network comprises: root cause node setFeature node setThe method comprises the steps of carrying out a first treatment on the surface of the The structure of a Bayesian analysis network is defined by a structure matrix>The composition is as follows:
;
for the number of types of root node +.>For the number of types of feature nodes +.>Representing a structural matrix->In a structural matrixIs 0 or 1; />Representing the ith root cause node in a Bayesian analysis network +.>;/>Representing a j-th feature node in the Bayesian analysis network; if root cause node in Bayesian analysis network +.>And feature node->Related, thenThe method comprises the steps of carrying out a first treatment on the surface of the If root cause node in Bayesian analysis network +.>And feature node->Irrelevant, I/O>。
The structure of the traditional Bayesian analysis network is determined according to expert knowledge, and the probability method provided by the invention can be used for fuzzily expressing the expert knowledge, so that the difficulty in structure construction is reduced, and the non-optimal influence of the network structure caused by subjective factors of the expert can be reduced.
Defining an uncertainty matrixRepresenting expert knowledge, < >>Each element in the uncertainty matrix +.>Representing root cause node +.>And feature node->The size of the correlation; expert determines +.>If expert supports root node +.>And feature node->Related +.>Is given a larger value if the expert does not support root cause node + ->And feature node->Related, thenIs given a smaller value.
A first generation bayesian analysis network is generated by the following random generation algorithm, and its distribution situation coincides with expert knowledge. The basic idea of the random generation algorithm is that ifThe larger the>The more likely it is 1; the method comprises the following steps:
;
is a random variable subject to uniform distribution, +.>Representing matrix elements in a first-generation bayesian analysis network matrix.
Step three: determining an optimal structure based on an evolutionary algorithm: starting from the first-generation Bayesian analysis network, generating Bayesian analysis network offspring based on the mixed scoring function and three evolutionary operations, and outputting the optimal Bayesian analysis network. The method specifically comprises the following steps:
step three A, setting a first generation population: conversion of a structural matrix R of a primary Bayesian analysis network into a one-dimensional sequenceOne-dimensional sequenceThe genes representing each individual in the initial population, i.e., each individual in the primary population, are identical, each individual representing a bayesian analysis network.
Step three B, scoring the quality of each individual in the population through a mixed scoring function:
;
wherein,for the mass fraction of the individual, < > A->The Bayesian-Dirichlet equivalent score is a commonly used method for evaluating the Bayesian network and is used for measuring the coincidence degree of the Bayesian analysis network and the actual data; />As a penalty term for measuring Bayesian analysis network and uncertainty matrix>To keep the coincidence degree with expert knowledge; />Coefficients representing trade-off expert knowledge contributions, +.>Representing the decision tree computation term.
Step three, selecting individuals with mass fractions higher than a set value, carrying out mutation operation to generate new individuals, and forming a new population with the individuals with mass fractions higher than the set value; if the termination condition is met, performing a step III; if the termination condition is not reached, step three B is performed.
And step three D, selecting and outputting an optimal Bayesian analysis network by adopting a roulette selection method.
Step four: based on an optimal Bayesian analysis network, estimating parameters of a root cause analysis model by estimating prior probability distribution of the root cause and conditional probability distribution of training characteristics, and specifically comprising:
;
is root cause node->Take the kth state and root in node +.>Conditional probability when the parent node of (1) takes the j-th joint distribution,/and (2)>Representing the condition that the limit is met->Representing a calculated conditional probability; conditional probability according to maximum likelihood ruleOptimal estimation of +.>The method comprises the following steps:
;
indicating compliance->Adopt the kth state and +.>The father node of the (j) th joint distribution condition is adopted; intermediate variable->;
And then obtaining a final root cause analysis model.
The prior probability distribution is calculated by indoor gaseous molecular pollutant data, and the calculation mode belongs to common knowledge in the field. The joint distribution represents a combination of the prior probability distribution and the conditional probability distribution. The state of the root node refers to the case of gaseous molecular contaminants in the room of the clean room, such as: above the upper limit of the normal interval, below the lower limit of the normal interval, and within the normal interval.
Based on the obtained root cause analysis model, when the pollutant exceeds the standard (the characteristic node is abnormal), the probability of possible root cause occurrence can be calculated according to the following formula, and the root cause with the maximum probability is taken as the real root cause.
;
Wherein the method comprises the steps ofRepresenting posterior probability; />Representing a priori probabilities; />Representing conditional probabilities; />Is the number of types of root cause nodes.
The clean room production management system can intelligently match the optimal disposal scheme according to the root cause in the knowledge base, and the proposal is given to corresponding staff by a work order mode to dispose of the gaseous molecular pollutants.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a single embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to specific embodiments, and that the embodiments may be combined appropriately to form other embodiments that will be understood by those skilled in the art.
Claims (1)
1. The root cause analysis method of the gaseous molecular pollutants in the clean room comprises the steps of inputting indoor gaseous molecular pollutant data into a root cause analysis model to obtain root cause analysis results; the construction process of the root cause analysis model specifically comprises the following steps:
step one, data acquisition and pretreatment:
collecting indoor gaseous molecular pollutant data of a clean room, and normalizing the indoor gaseous molecular pollutant data through means and variances;
step two: determining a first-generation Bayesian analysis network based on expert knowledge and by a probability method; the bayesian analysis network comprises: root cause node setThe method comprises the steps of carrying out a first treatment on the surface of the The structure of a Bayesian analysis network is defined by a structure matrix>The composition is as follows:
;
for the number of types of root node +.>For the number of types of feature nodes +.>Representing a structural matrix->Elements of (a) and (b); />Representing an ith root cause node in the Bayesian analysis network; />Representing a j-th feature node in the Bayesian analysis network; if the root cause node in the Bayesian analysis network is +.>And feature node->Related +.>The method comprises the steps of carrying out a first treatment on the surface of the If the root cause node in the Bayesian analysis network is +.>And feature node->Irrelevant, I/O>;
Defining an uncertainty matrixRepresenting expert knowledge, < >>Uncertainty matrix->Each element of->Representing root cause node +.>And feature node->The size of the correlation; expert determines +.>If expert supports root node +.>And characteristic nodeRelated +.>Is given a value greater than the set threshold, if the expert does not support the root node +.>And feature node->Related, thenA value smaller than a set threshold value;
a first generation bayesian analysis network is generated by the following random generation algorithm:
;
is a random variable subject to uniform distribution, +.>Representing matrix elements in a first-generation bayesian analysis network matrix;
step three: determining an optimal Bayesian analysis network based on an evolutionary algorithm: generating offspring of the Bayesian analysis network through mixing scoring functions and individual selection, crossing and variation based on the first-generation Bayesian analysis network, and outputting an optimal Bayesian analysis network; the method specifically comprises the following steps:
step three A, setting a first generation population: converting a structural matrix R of a primary Bayesian analysis network into a one-dimensional sequenceOne-dimensional sequence->Genes representing each individual in the initial population, each individual representing a bayesian analysis network;
step three B, scoring the quality of each individual in the population through a mixed scoring function:
;
wherein,for the mass fraction of the individual, < > A->The Bayes-Dirichlet equivalent score is used for measuring the coincidence degree of the Bayes analysis network and the actual data; />As a penalty term for measuring Bayesian analysis network and uncertainty matrix>Is matched with the degree of the matching; />Coefficients representing trade-off expert knowledge contributions, +.>Representing a decision tree calculation item;
step three, selecting individuals with mass fractions higher than a set value, carrying out mutation operation to generate new individuals, and forming a new population with the individuals with mass fractions higher than the set value; if the termination condition is met, performing a step III; if the termination condition is not met, performing the step III;
selecting an optimal Bayesian analysis network by adopting a roulette selection method;
step four: based on an optimal Bayesian analysis network, estimating parameters of a root cause analysis model by estimating prior probability distribution of root cause nodes and conditional probability distribution of feature nodes; the prior probability distribution of root cause nodes is calculated through indoor gaseous molecular pollutant data; the parameter estimation of the root cause analysis model specifically comprises the following steps:
;
is root cause node->Take the kth state and root in node +.>Conditional probability when the parent node of (1) takes the j-th joint distribution,/and (2)>Representing the condition that the limit is met->Representing a calculated conditional probability; conditional probability according to maximum likelihood rule>Optimal estimation of +.>The method comprises the following steps:
;
indicating compliance->Adopt the kth state and +.>The father node of the (j) th joint distribution condition is adopted; intermediate variable->The method comprises the steps of carrying out a first treatment on the surface of the Obtaining conditional probability->Obtaining a final root cause analysis model;
wherein the joint distribution represents a joint of a priori probability distribution and a conditional probability distribution.
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