728 IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 10, NO. 3, JULY 2013
used to select submodels. However, the size of the ensemble
numbers must be given manually. Recently, Wang et al. pro-
posed an evolutionary algorithm-based selective ensemble al-
gorithm with size control [40]. It shows the optimal ranges for
number of ensemble submodels is 2
8, which is an important
conclusion.
Surveys of the selective ensemble m odeling approach show
how to apply this modeling m etho d, in practice, problem is one
of the future directions [41], [42]. Thus, how to use selective
ensemble modeling technology for estimating ML parameters is
a valuable practice problem. It is very necessary and significant.
D. Motivation
Constructing effective selective ensem ble M L param eters’
models, the following pro blem s have to be addressed.
The first problem is how to construct ensembles. In this paper,
aim at the high-dimensional problem of the frequency spec-
trum, only “manipulating th e input features” approach is fo-
cused. Thus, we used the feature subsets selection and extraction
method in our recently published journal paper, see [22].
The second pro blem is how to construct effective submodels.
Modeling the high-dim e nsio nal frequency spectrum, the “curse
dimensionality” p rob lem has to be o verco me. Feature extraction
method based on kernel principal component analysis and fea-
ture selection method based on genetic algorith m- par tial least
squares have their disadvantage. The extracted features only
relate to most of the change of the frequency spectrum. The
selected features have to drop out some original features with
some criteria. KPLS can construct effective model using ex-
tracted latent features relative to i npu t and output data simul-
taneously, which is used to model ML parameters.
The third problem is how to select and weight submodels.
In this paper, we give a new perspective for the selective en-
semble mo deling approach. Now, we have known, three basic
steps for the selective ensemble: the selection of ensemble or-
ganization, the selection of ensemble submodels, and the combi-
nation methods of submodels [43]. When the ensemble organ-
ization and the com bination methods have been selected, the
problem of the selectiv e ensemble modeling can be looked at as
an optimal problem of select submodels. Minim um mean square
error-based AWF algorithm is always used to obtain the op-
timal observation value in a multisensor system. The branch and
bound (BB) algorithm is always used for finding optimal solu-
tions of various optimization problems. Large candidate subsets
are discarded by using upper and lower e stimated bounds of the
quantity being optimized [44]. It has been used widely in the fea-
ture selection problems [45]. When the nu mb ers of the features
exceeds 30, the computing consumption has to b e considered.
However, for our ML parameters modeling problem, number
of submodels based on feature subsets are limited. Therefore,
combining with the weightin g algorithm, BB algor ithm can be
used to obtain the optimal subm od els.
Motivated by the above discussions, a selective ensemb le
approach for modeling ML is proposed in this paper. First, the
shell v ibration and acoustical spectra are calculated. Then, the
frequency spectrum clustering algorithm is used to partitio n
the spectrum automatically to obtain the spectral segments; the
MI-based feature selection algorithm is used to select feature
subsets of the local peaks and frequency subbands. The candi-
date feature subsets include spectral segments, features of local
peaks, frequency subbands, origin fu ll spectru m and mill motor
current signal. Finall y, th e KPLS algorithm is u sed to construct
the nonlinear ML parameters models with each feature subset;
the BB and AWF algorithms are used to select submodels and
calculate the weighting coefficients.
This paper is divided into the following sections. Section II
describes the mill load of the grinding p ro cess. Section III
presents the strategy o f selective ensemble multisensor in-
formation approach. Section IV presents the realization of
the proposed approach in detail. Section V presents the ex-
perimental results and discussion. Section VI presents the
conclusions.
II. M
ILL LOAD (ML) DESCRIPTION OF THE GRINDING PROCESS
A. Description of Mill Load a nd Mill Load Parameters
Mill load (ML) is one of the key parameters and affected by
lots of factors. ML can be estimated by using parameters inside
of the ball mill, such as material to ball volume ratio (MBVR),
pulp density (PD) and charge volume ratio (CVR) [11]. The
mapping among the ML status, ML and ML parameters can be
represented as
(1)
where
represents the status of ML, which usually is divided
into low-load, normal load, and ove rload status;
and
are unknown functions; , and represent ball, water
and material load, respectively, in kg;
, and rep-
resent MBVR, PD, and CVR, respectively.
Combining with the mill volume, the density of the material,
ball and water, and the interstice rate of the balls, we can ob-
tained the mineral, b all and water load inside the mill based on
the MBVR, PD, and CVR w ith the followin g equations:
(2)
(3)
(4)
where
, ,and are the density of the ball, mineral and
water in
, respectively; is th e interstice rate of the balls,
whichis0.38and
is the i nner volume of the mill in .
Remark: Equations (2)–(4) are just a theoretical com pu tin g
based on the definition of ML parameters. The revision of these
equations need more research based on the mechanical analysis
and experiments.
B. Grinding Process Description
The fundam ental objective o f a grinding circuit (GC) is to
liberate valuable minerals in such a way that the su bsequen t
separation process can be operated at its maximum economic