Transcript APPLICATION OF BAYESIAN BELIEVE NETWORKS FOR …

APPLICATION OF BAYESIAN BELIEVE NETWORKS FOR CONTINUOUS
RISK EVALUATION AND DECISION SUPPORT OF SAFETY
MANAGEMENT IN MINING
Todor P. Petrov
University of Minig and Geology “St. Ivan Rilsky” - Sofia
Department of Mine Safety and Ventilation
e-mail: [email protected]
Today the investigation and
registering of an accident requires:
 more
than 60 fields of different data format
describing quantitative and qualitative
characteristics;
 more than 3000 massive of data for
description of approximately 50 accidents
annually
The psychology and cognitive
sciences are ascertain the fact that:
 the
human mind cannot effectively
manipulate a large amount of data
streams and meet serious difficulties to
make an inference when the possible
decision have more than three alternatives
 the chance of bad decisions runs high, the
frequency of wrong actions increasing and
the safety become pursuit rather than
achieved purpose.
Practical decision making
 It
is well known that taking into account
only quantificators of occupational safety
risk like coefficients and indexes of
frequency and severity of the accidents
are not sufficient for characterization of
safety state.
Important features of safety
management



the probability and fuzzy uncertainty;
manipulating of multisource quantitative and qualitative data;
rendering the expert opinion.
The inherited “disease” of the
typical approach for safety analisys
 Analyzing
the safety risk by separately
studying of isolated factors inevitably
relates to loses of information about the
mutuality in the examined system;
 In the terms of information such a disjoint
is irreversible process
New synergetic approach should
perceive for decision support in
occupational safety
 A model
putting together the dangers, the
human factors and the control impacts
including their mutual influences is
needed.
MAR.NET project
 Mine Accident
Risk dot Net is an expert
system for decision support of mine safety
management;
 providing information fusion of different
sources and types of evidence such as
history databases, real time control
systems and expert opinions.
CALCULATION OF RISK LEVEL
 Risk
= Probability x Severity
(1)
The low threshold of occupational risk
can be calculated on
8
R0  3.10


In practice the accident without looses of
working days are not registered.
We can thing about Ro as a threshold of
sensitivity of the safety monitoring system
Calculation of RISK LEVEL
LR  log(Rc / R0 )
Where:

Rc – is the current risk;
Ro – is the low threshold of
occupational risk.
The purpose of risk level is to give one-value
quantification of the current state of the safety
relative to the acceptable threshold taking into
account the sensitivity of the risk measuring.
Properties of LR



LR is dimensionless;
LR is always positive;
If the current and the threshold risk are become
equal than the safety level is calculated to zero.
LR=0 means no risk upper the threshold limit is
detected.
Natural way of risk representation because the
human perceptions are determined exactly from
logarithmic levels as stated in psychophysical
law of Veber-Fehner
DRAWING OF INFERENCES FOR
OCCUPATIONAL RISK
13
12
11
10
Number of Accidents
9
1982
1990
8
1992
1993
1994
1995
7
6
5
1996
1997
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Fig. 1. Annually accident distribution
10
11
12
Number of Accidents
DRAWING OF INFERENCES FOR
OCCUPATIONAL RISK
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
Monhts
Fig. 2. Time row of accident frequencies
70
80
DRAWING OF INFERENCES FOR
OCCUPATIONAL RISK
Reconstruction of phase space
of the accident frequency per month in 3D
Fmonth, Fmonth-1, Fmonth-2
DRAWING OF INFERENCES FOR
OCCUPATIONAL RISK
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
inference
(1) P( B)  P( B | A1 ) P( A1 )  P( B | A2 ) P( A2 )  ...
(2) P( Aj | B) 
P( B | A j ) P ( A j )
P( B | A1 ) P( A1 )  P( B | A2 ) P( A2 )  ...
(3) P( A1 , A2 ,..., An )  P( A1 | A2 , A3 ,..., An ) P( A2 | A3 , A4 ,...An )..
...P( An 1 | An ) P( An )

(1) is a result known as law for complete probability;
 (2) is a result known as Bayes Theorem and;
 (3) is a result known as chain rule, with significant
importance in Bayesian believe networks (BBN)
MAR.NET project
MAR.NET project – Structure of the network
TM
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MAR.NET project
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
MAR.NET project
Initial conditional probability table P(17.Body|18.Injury)
A
B
…
Z
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
1
1
1
1
18.Injury
17.Body
Total
MAR.NET project
Learning and adoption of MAR.NET
Posterior probability distribution of node
“10.Job” about all given states from A to E
Learning and adoption of
MAR.NET

Learning 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 BBN
for graphical associated models with missing data.
Structure Learning of MAR.NET
The algorithms for structure learning of
BBN are known as PC-algorithms
Structure Learning of MAR.NET
As a result of the structure machine learning of
MAR.NET with 122 data cases for registered accidents
in coal mine of Babino – Bobov dol, the conditional
dependency of the following variables was accepted in
LC=0.05:

Occupation >> Time of occurrence of the
accident;
 Length of service >> Human factor;
 Education Level >> Day after weekend;
 Day after weekend >> Deviation from ordinary
actions.
Entering Expert Opinions in
MAR.NET
The algorithm for entering of expert
opinion used in MAR.NET allows control of
the actuality of learned experience. The
control of the actuality uses special data
structures for reducing the impact of past
called fading tables.
Simulation of data cases
A way to test the safety system in lack
of data and uncertainty
Three approaches for obtaining simulated
experience are easy applicable in MAR.NET model:



generating of simulated data cases based on variations
of the current prior distribution;
generating data cases with simulation model of the
object using advanced tools as special languages;
to change structure of the net depending of new
knowledge, and to derive conclusions against the
direction of the edges
MAR.NET example

Example is based on the real data for a
Bulgarian coal mining company with
underground mining, open pit mining and dress
factory.
 Structural changes in company are provided in
the future time. From the company structure will
be ousting the underground mines and the
repair shops, but the steam power plant will be
incorporated.
MAR.NET example
 What
we need to expect about the risk for
different groups of workers and the
probabilities of environment causes?
Prior distributions
The knowledge about the object is extracted from data cases
about registered accidents with learning algorithm
Posterior distribution


Structural changes in the company are reflected in BBN node structure ;
After Bayesian propagation through the network the posterior distribution
is computed.
Back propagation.
Obtaining inference
against the edges of MAR.NET
 Let
now to propagate the opinion that in
future the fatalities will increase twice;
 It will change the Bayesian probability in
station F. Fatalities of node 3 from 0.08 to
0.16;
 Let start the back-propagation of this new
prior probability distribution;
 The new posterior distribution is achieved.
The new posterior distribution
is the answer of the question:




What we need to expect about the risk for
different groups of workers and the probabilities
of environment causes?
Using of faulty, unassured machines and
facilities;
Using equipment inadequate of working
conditions.
Will lead to increasing of risk of fatalities in the
groups of
Staff at the surface and;
Open pit mine workers.
Conclusions

MAR.NET project produced a decision support
method with a supporting tool for quantifying
safety in complex systems using Bayesian
Networks as a core technology. ;
 The system can be adopted for different
industries;
 The well learned MAR.NET models can be used
for decision support of safety management,
education and training.
MAR.NET key benefits

rationally combine different sources and types of
evidence in single model;
 identify weaknesses in the safety argument
such that it can be improved;
 specify degrees of confidence associated with
prediction;
 provide a sound basis for rational discussion
and negotiation about the safety system
development and deployment.
Thank You