313
d. Seismicity:
These parameters intend to respond the following question: “How is the energy distributed
among the pillars?” They are defined as follows:
i. Relevant Nearby Seismic Events: The number of seismic events with a radiated seismic
energy higher than the 1 MJ in a radius of 70 m around the centroid of a determined
pillar.
ii. Density of Radiated Seismic Energy (S & P Components): An estimation of the radiated
seismic energy per squared distance unit based on the S and P seismic waves for each analyzed pillar. This estimation is done by using an “inverse-square of the distance” assignation, taking the hypocenters of each seismic event with a magnitude M w larger than zero
as the emitting source of seismic radiated energy, assuming these sources as central force
fields.
e. Operation:
These parameters intend to respond the following question: “What do we do during the mining process in terms of operation?” They are defined as follows:
i. Pre-conditioning Status: A variable that denotes the implementation of the hydraulic fracturing technique in the rockmass where a determined pillar is emplaced. It is expressed as
a binary value which is equal to 1 when the pillar is located in a hydro-fractured area, and
0 when it is not.
ii. Mass Flow Rate of Ore: The linear mass density of ore divided per height of extraction
column in a determined draw point (the latter known as height of draw), measured in
t/m. That being said, since this is a distinctive property of a draw point, it needs to be
assigned to the pillars in the same fashion as the seismic radiated energy, making this with
an inverse-square estimation for each one of them, using a search radius of 20 m around
the analyzed pillar.
5 MODELLING METHODOLOGY
5.1 Ensemble learning and tree-based gradient boosting technique
The methodology used for collapse vulnerability modelling was based on a Machine Learning (ML) ensemble learning algorithm. The concept of ML is understood as the science (and
art) of programming computers so they can learn from data.
Let us suppose we wish to ask a highly complex question to a random set composed by a
thousand people to posteriorly count and sort their answers forming an aggregated answer.
In many cases this kind of answer is even more reliable than a single answer given by an
expert. This is usually known as “wisdom of the crowd”. Similarly, if we aggregate the predictions or estimations of several bad or “weak” learners (information classificators or regressors), we will frequently find better results than we would have obtained with a single learner.
This kind of approach is known as an “ensemble” method.
The model was developed based on the “tree gradient boosting” ensemble structure, using
binary decision trees as the base weak learners. The empirical binary conceptualization of the
pillar state (as target value) was defined as shown as Eq. 3:
Y =
1
0
;
;
/
When the pillar is damaged c
/ ollapsed
When the pillar is undama age
a a d stable
/
⎧
⎨
⎧ ⎧
⎩
⎨ ⎨
(3)
Let Y be the output value of a function to be modelled, while X is the random vector
consisting of the sum of the information sets described in section 4, specified for each pillar
that is to be analyzed. Then, the problem we wish to model is represented by a joint probability distribution P(X,Y). If the training set is described as Λ = {
}
(
) =
i
n ,
}
) i 1 being (x i ,y i )
d. Seismicity:
These parameters intend to respond the following question: “How is the energy distributed
among the pillars?” They are defined as follows:
i. Relevant Nearby Seismic Events: The number of seismic events with a radiated seismic
energy higher than the 1 MJ in a radius of 70 m around the centroid of a determined
pillar.
ii. Density of Radiated Seismic Energy (S & P Components): An estimation of the radiated
seismic energy per squared distance unit based on the S and P seismic waves for each analyzed pillar. This estimation is done by using an “inverse-square of the distance” assignation, taking the hypocenters of each seismic event with a magnitude M w larger than zero
as the emitting source of seismic radiated energy, assuming these sources as central force
fields.
e. Operation:
These parameters intend to respond the following question: “What do we do during the mining process in terms of operation?” They are defined as follows:
i. Pre-conditioning Status: A variable that denotes the implementation of the hydraulic fracturing technique in the rockmass where a determined pillar is emplaced. It is expressed as
a binary value which is equal to 1 when the pillar is located in a hydro-fractured area, and
0 when it is not.
ii. Mass Flow Rate of Ore: The linear mass density of ore divided per height of extraction
column in a determined draw point (the latter known as height of draw), measured in
t/m. That being said, since this is a distinctive property of a draw point, it needs to be
assigned to the pillars in the same fashion as the seismic radiated energy, making this with
an inverse-square estimation for each one of them, using a search radius of 20 m around
the analyzed pillar.
5 MODELLING METHODOLOGY
5.1 Ensemble learning and tree-based gradient boosting technique
The methodology used for collapse vulnerability modelling was based on a Machine Learning (ML) ensemble learning algorithm. The concept of ML is understood as the science (and
art) of programming computers so they can learn from data.
Let us suppose we wish to ask a highly complex question to a random set composed by a
thousand people to posteriorly count and sort their answers forming an aggregated answer.
In many cases this kind of answer is even more reliable than a single answer given by an
expert. This is usually known as “wisdom of the crowd”. Similarly, if we aggregate the predictions or estimations of several bad or “weak” learners (information classificators or regressors), we will frequently find better results than we would have obtained with a single learner.
This kind of approach is known as an “ensemble” method.
The model was developed based on the “tree gradient boosting” ensemble structure, using
binary decision trees as the base weak learners. The empirical binary conceptualization of the
pillar state (as target value) was defined as shown as Eq. 3:
Y =
1
0
;
;
/
When the pillar is damaged c
/ ollapsed
When the pillar is undama age
a a d stable
/
⎧
⎨
⎧ ⎧
⎩
⎨ ⎨
(3)
Let Y be the output value of a function to be modelled, while X is the random vector
consisting of the sum of the information sets described in section 4, specified for each pillar
that is to be analyzed. Then, the problem we wish to model is represented by a joint probability distribution P(X,Y). If the training set is described as Λ = {
}
(
) =
i
n ,
}
) i 1 being (x i ,y i )