Todor P. Petrov University of Minig and Geology “St. Ivan Rilsky” - Sofia

APPLICATION OF BAYESIAN BELIEVE NETWORKS FOR CONTINUOUS APPLICATION OF BAYESIAN BELIEVE NETWORKS FOR CONTINUOUS

RISK EVALUATION AND DECISION SUPPORT OF SAFETY RISK EVALUATION AND DECISION SUPPORT OF SAFETY

MANAGEMENT IN MININGMANAGEMENT IN MINING Todor P. PetrovTodor P. Petrov

University of Minig and Geology “St. Ivan Rilsky” - SofiaUniversity of Minig and Geology “St. Ivan Rilsky” - SofiaDepartment of Mine Safety and VentilationDepartment of Mine Safety and Ventilation

e-mail: [email protected]: [email protected]

Today the investigation and Today the investigation and registering of an accident requires:registering of an accident requires:

more than 60 fields of different data format more than 60 fields of different data format describing quantitative and qualitative describing quantitative and qualitative characteristics;characteristics;

more than 3000 massive of data for more than 3000 massive of data for description of approximately 50 accidents description of approximately 50 accidents annuallyannually

The psychology and cognitive The psychology and cognitive sciences are ascertain the fact that:sciences are ascertain the fact that: the human mind cannot effectively the human mind cannot effectively

manipulate a large amount of data manipulate a large amount of data streams and meet serious difficulties to streams and meet serious difficulties to make an inference when the possible make an inference when the possible decision have more than three alternativesdecision have more than three alternatives

the chance of bad decisions runs high, the the chance of bad decisions runs high, the frequency of wrong actions increasing and frequency of wrong actions increasing and the safety become pursuit rather than the safety become pursuit rather than achieved purpose. achieved purpose.

Practical decision makingPractical decision making

It is well known that taking into account It is well known that taking into account only quantificators of occupational safety only quantificators of occupational safety risk like coefficients and indexes of risk like coefficients and indexes of frequency and severity of the accidents frequency and severity of the accidents are not sufficient for characterization of are not sufficient for characterization of safety state.safety state.

Important features of safety Important features of safety managementmanagement

the probability and fuzzy uncertainty;the probability and fuzzy uncertainty; manipulating of multisource quantitative and qualitative data;manipulating of multisource quantitative and qualitative data; rendering the expert opinion.rendering the expert opinion.

The inherited “disease” of the The inherited “disease” of the typical approach for safety analisystypical approach for safety analisys Analyzing the safety risk by separately Analyzing the safety risk by separately

studying of isolated factors inevitably studying of isolated factors inevitably relates to loses of information about the relates to loses of information about the mutuality in the examined system; mutuality in the examined system;

In the terms of information such a disjoint In the terms of information such a disjoint is irreversible process is irreversible process

New synergetic approach should New synergetic approach should perceive for decision support in perceive for decision support in

occupational safetyoccupational safety

A model putting together the dangers, the A model putting together the dangers, the human factors and the control impacts human factors and the control impacts including their mutual influences is including their mutual influences is needed. needed.

MAR.NET projectMAR.NET project

Mine Accident Risk dot Net is an expert Mine Accident Risk dot Net is an expert system for decision support of mine safety system for decision support of mine safety management;management;

providing information fusion of different providing information fusion of different sources and types of evidence such as sources and types of evidence such as history databases, real time control history databases, real time control systems and expert opinions.systems and expert opinions.

CALCULATION OF RISK LEVELCALCULATION OF RISK LEVEL

Risk = Probability x SeverityRisk = Probability x Severity (1)(1)

80 10.3 R

The low threshold of occupational risk The low threshold of occupational risk can be calculated oncan be calculated on

In practice the accident without looses of In practice the accident without looses of working days are not registered.working days are not registered.

We can thing about Ro as a threshold of We can thing about Ro as a threshold of sensitivity of the safety monitoring systemsensitivity of the safety monitoring system

Calculation of RISK LEVELCalculation of RISK LEVEL

The purpose of risk level is to give one-value The purpose of risk level is to give one-value quantification of the current state of the safety quantification of the current state of the safety relative to the acceptable threshold taking into relative to the acceptable threshold taking into account the sensitivity of the risk measuring.account the sensitivity of the risk measuring.

)/log( 0RRL cR Where:Where: Rc – is the current risk;Rc – is the current risk;

Ro – is the low threshold of Ro – is the low threshold of occupational risk.occupational risk.

Properties of LProperties of LRR

LLRR is dimensionless; is dimensionless; LLRR is always positive; is always positive; If the current and the threshold risk are become If the current and the threshold risk are become

equal than the safety level is calculated to zero. equal than the safety level is calculated to zero. LLRR=0 means no risk upper the threshold limit is =0 means no risk upper the threshold limit is detected.detected.

Natural way of risk representation becauseNatural way of risk representation because the the human perceptions are determined exactly from human perceptions are determined exactly from logarithmic levels as stated in psychophysical logarithmic levels as stated in psychophysical law of Veber-Fehnerlaw of Veber-Fehner

DRAWING OF INFERENCES FOR DRAWING OF INFERENCES FOR OCCUPATIONAL RISK OCCUPATIONAL RISK

0

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0 1 2 3 4 5 6 7 8 9 10 11 12

Nu

mb

er o

f A

ccid

ents 1982

1990

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Fig. 1. Annually accident distribution

DRAWING OF INFERENCES FOR DRAWING OF INFERENCES FOR OCCUPATIONAL RISKOCCUPATIONAL RISK

012345678910111213

0 10 20 30 40 50 60 70 80

Monhts

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of A

ccid

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Fig. 2. Time row of accident frequencies


Reconstruction of phase spaceof the accident frequency per month in 3D

Fmonth, Fmonth-1, Fmonth-2


Time row and reconstructed phase space of 15 minutes beats of a human heart

Panchev S. Chaos Theory, Academic Publisher, Sofia 1996

Bayesian approach for statistical Bayesian approach for statistical inferenceinference

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(1) is a result known as law for complete probability;(1) is a result known as law for complete probability; (2) is a result known as Bayes Theorem and;(2) is a result known as Bayes Theorem and; (3) is a result known as chain rule, with significant (3) is a result known as chain rule, with significant

importance in Bayesian believe networks (BBN)importance in Bayesian believe networks (BBN)


MAR.NET project – Structure of the networkMAR.NET project – Structure of the network TMTM

Powered byPowered by Hugin Lite Hugin Lite


Initial probability table of the chance node “10. Job”

State Probability

A. Transport and load 0.2

B. Ordinary exploration 0.2

… 0.2

E. Other 0.2


Initial conditional probability table P(17.Body|18.Injury)

18.Injury A B … Z

17.Body

A.Head 0.25 0.25 0.25 0.25

B.Hands 0.25 0.25 0.25 0.25

C.Legs 0.25 0.25 0.25 0.25

D.Body 0.25 0.25 0.25 0.25

Total 1 1 1 1


Posterior probability distribution of node “10.Job” about all given states from A to E

Learning and adoption of MAR.NETLearning and adoption of MAR.NETLearning and adoption of MAR.NET

Learning and adoption of Learning and adoption of MAR.NETMAR.NET

Learning of MAR.NET from data casesLearning of MAR.NET from data cases

Node01 Node02 Node03 … Node21

A N/A Q … D

C I N/A … N/A

… … … … …

The machine learning method used in MAR.NET is known as EM-algorithm and it is commonly used in BBNfor graphical associated models with missing data.

Structure Learning of MAR.NETStructure Learning of MAR.NET

The algorithms for structure learning of The algorithms for structure learning of BBN are known as PC-algorithmsBBN are known as PC-algorithms

Structure Learning of MAR.NETStructure Learning of MAR.NET

As a result of the structure machine learning of As a result of the structure machine learning of MAR.NET with 122 data cases for registered accidents MAR.NET with 122 data cases for registered accidents in coal mine of Babino – Bobov dol, the conditional in coal mine of Babino – Bobov dol, the conditional dependency of the following variables was accepted in dependency of the following variables was accepted in LC=0.05:LC=0.05:

Occupation >> Time of occurrence of the Occupation >> Time of occurrence of the accident;accident;

Length of service >> Human factor;Length of service >> Human factor; Education Level >> Day after weekend;Education Level >> Day after weekend; Day after weekend >> Deviation from ordinary Day after weekend >> Deviation from ordinary

actions.actions.

Entering Expert Opinions in Entering Expert Opinions in MAR.NETMAR.NET

The algorithm for entering of expert The algorithm for entering of expert opinion used in MAR.NET allows control of opinion used in MAR.NET allows control of the actuality of learned experience. The the actuality of learned experience. The control of the actuality uses special data control of the actuality uses special data structures for reducing the impact of past structures for reducing the impact of past called fading tables. called fading tables.

Simulation of data cases Simulation of data cases

A way to test the safety system in lack A way to test the safety system in lack of data and uncertaintyof data and uncertainty

Three approaches for obtaining simulated Three approaches for obtaining simulated experience are easy applicable in MAR.NET model:experience are easy applicable in MAR.NET model:

generating of simulated data cases based on variations generating of simulated data cases based on variations of the current prior distribution;of the current prior distribution;

generating data cases with simulation model of the generating data cases with simulation model of the object using advanced tools as special languages;object using advanced tools as special languages;

to change structure of the net depending of new to change structure of the net depending of new knowledge, and to derive conclusions against the knowledge, and to derive conclusions against the direction of the edgesdirection of the edges

MAR.NET example MAR.NET example

Example is based on the real data for a Example is based on the real data for a Bulgarian coal mining company with Bulgarian coal mining company with underground mining, open pit mining and dress underground mining, open pit mining and dress factory.factory.

Structural changes in company are provided in Structural changes in company are provided in the future time. From the company structure will the future time. From the company structure will be ousting the underground mines and the repair be ousting the underground mines and the repair shops, but the steam power plant will be shops, but the steam power plant will be incorporated. incorporated.

MAR.NET exampleMAR.NET example

What we need to expect about the risk for What we need to expect about the risk for different groups of workers and the different groups of workers and the probabilities of environment causes?probabilities of environment causes?

Prior distributions

The knowledge about the object is extracted from data cases about registered accidents with learning algorithm

Posterior distributionPosterior distribution

Structural changes in the company are reflected in BBN node structure ;Structural changes in the company are reflected in BBN node structure ; After Bayesian propagation through the network the posterior distribution After Bayesian propagation through the network the posterior distribution

is computed.is computed.

Back propagation.Back propagation.Obtaining inference Obtaining inference

against the edges of MAR.NETagainst the edges of MAR.NET Let now to propagate the opinion that in Let now to propagate the opinion that in

future the fatalities will increase twice;future the fatalities will increase twice; It will change the Bayesian probability in It will change the Bayesian probability in

station F. Fatalities of node 3 from 0.08 to station F. Fatalities of node 3 from 0.08 to 0.16;0.16;

Let start the back-propagation of this new Let start the back-propagation of this new prior probability distribution;prior probability distribution;

The new posterior distribution is achieved.The new posterior distribution is achieved.

The new posterior distributionThe new posterior distributionis the answer of the question:is the answer of the question:

What we need to expect about the risk for What we need to expect about the risk for different groups of workers and the probabilities different groups of workers and the probabilities of environment causes?of environment causes?

Using of faulty, unassured machines and Using of faulty, unassured machines and facilities;facilities;

Using equipment inadequate of working Using equipment inadequate of working conditions.conditions.Will lead to increasing of risk of fatalities in the Will lead to increasing of risk of fatalities in the groups ofgroups of

Staff at the surface and; Open pit mine workers.

ConclusionsConclusions

MAR.NET project produced a decision support MAR.NET project produced a decision support method with a supporting tool for quantifying method with a supporting tool for quantifying safety in complex systems using Bayesian safety in complex systems using Bayesian Networks as a core technology. ;Networks as a core technology. ;

The system can be adopted for different The system can be adopted for different industries;industries;

The well learned MAR.NET models can be used The well learned MAR.NET models can be used for decision support of safety management, for decision support of safety management, education and training.education and training.

MAR.NET key benefitsMAR.NET key benefits

rationally combine different sources and types of rationally combine different sources and types of evidence in single model;evidence in single model;

identify weaknesses in the safety argument identify weaknesses in the safety argument such that it can be improved;such that it can be improved;

specify degrees of confidence associated with specify degrees of confidence associated with prediction;prediction;

provide a sound basis for rational discussion provide a sound basis for rational discussion and negotiation about the safety system and negotiation about the safety system development and deployment.development and deployment.

Thank YouThank You

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Todor P. Petrov University of Minig and Geology “St. Ivan Rilsky” - Sofia