CN101776531B - Soft sensing method for load parameter of ball mill - Google Patents

Abstract

A soft measurement method for ball mill load parameters, the method uses the vibration signal of the mill cylinder, vibroacoustic signal and current signal obtained by the hardware support platform to compare the internal parameters of the mill (material-to-ball ratio, pulp concentration, filling rate) that represent the mill load ) for soft measurement. The method includes the following steps: collecting the vibration, vibro-acoustic and current data of the mill cylinder and filtering in time domain, performing time-frequency conversion on the vibration and vibro-acoustic data, performing frequency division in the frequency domain on the vibration and vibro-acoustic data based on kernel principal elements The nonlinear feature extraction of the analysis, the nonlinear feature extraction is performed on the time domain current data, the feature selection is performed on the fused nonlinear feature data, and the soft sensor model based on the least squares-support vector machine is established. The soft measurement method of the invention has high sensitivity and accurate measurement results, has good practical value and popularization prospect, and helps to realize stable control, optimal control and energy saving and consumption reduction of the grinding production process.

Description

A kind of ball mill load parameter flexible measurement method

Technical field:

The invention belongs to the automatic technology fields of measurement, a kind of wet ball mill load parameter that particularly relates to the time in grinding production process is the flexible measurement method of the inner material ball ratio of bowl mill, pulp density, pack completeness.

Background technology:

Ball tube mill is widely used in the grinding operation of industries such as metallic ore and nonmetal ore-dressing factory, building materials, fire resistive material, cement, coal, chemical industry, electric power and metallurgy.The power consumption of grinding operation accounts for 3～4% of whole world gross generation, accounts for 30%～70%, 15%, 60%～70% of industrial process energy consumption separately respectively in industries such as ore dressing, electric power, cement, and the consumption of milling medium and liner plate reaches 0.4-3.0kg/t.According to experimental study, bowl mill has energy-saving potential and the 9% above raw-material potentiality of saving steel more than 10% at least.Because bowl mill has comprehensive complex characteristics such as non-linear, large dead time, strong coupling, random disturbance are big, rotary barrel internal operating environment complexity, grinding machine running status and inner parameter thereof are difficult to effectively measure, phenomenons such as empty mill, full mill, stifled mill often take place in the production, directly have influence on quality, output and the technical economical index of product.

At present, in the actual production generally be by the operator by the indirect methods such as sound (being commonly called as electric ear), vibration or power of shaking, by rule of thumb the ball mill load state is carried out artificial judgment and processing.For overcoming manually-operated subjectivity and randomness, in conjunction with domain-specialist knowledge, rule-based reasoning and statistical Process Control, the intelligent sphere mill load condition detection method of multiple signal has appearred merging.But the research at the ball mill load parameter that can reflect ball mill load (material ball ratio, pulp density, pack completeness) is less, and the input of institute's established model mostly is bear vibration, time domain or the frequency domain energy sum of the signals such as sound, bearing pressure, power that shake.Abroad at the bear vibration of bowl mill, the research of the sound that shakes, the mode that adopts the spectrum averaging segmentation to sue for peace is extracted the feature of Spectral variation, but the bowl mill inner parameter of its detection only limits to pulp density.

Summary of the invention:

Determine it mainly is the long-term work experience that relies on the site operation personnel at existing ball mill load, be difficult to measure the inner parameter that characterizes ball mill load, and existing detection method is difficult to fully extract the non-linear of signal, cause in the industrial process being the security of assurance equipment, bowl mill often operates in the underload state, influence bowl mill treatment capacity and product quality, can't produce the problem that obtains maximum economic benefits targetedly according to the market demand, but the invention provides a kind of ball mill load soft-sensing method based on the fusion of multi-source data feature of measure field ball mill load parameter.By adopting core pivot element analysis (KPCA) to carry out the nonlinear characteristic extraction respectively to ball mill barrel vibration and basic, normal, high three frequency ranges of acoustical signal in frequency domain of shaking, and the nonlinear characteristic of fusion time domain current signal, carry out feature selecting in conjunction with least square-support vector machine (LSSVM) method, to reach the purpose of accurate detection ball mill load parameter.

Flexible measurement method of the present invention is made up of bowl mill hardware support platform and soft Survey Software, and hardware platform provides the flexible measurement method desired data, and soft Survey Software is responsible for implementing flexible measurement method proposed by the invention.Soft Survey Software namely can be installed on the supervisory control comuter of distributed computer control system, also can run on independently on the computing machine.This method obtains real-time ball mill barrel vibration, the data of shake sound, current signal by carrying out communication with hardware support platform, detects ball mill load parameter (material ball ratio, pulp density, pack completeness).

It is as follows to the present invention includes step: as illustrated in fig. 1 and 2

Step 1: the vibration of collection bowl mill, shake sound and current data

Gather following signal by hardware support platform: the vibration acceleration signal X of ball mill barrel _VThe acoustical signal X that shakes of below, ball mill grinding zone _AThe current signal X of bowl mill driving motor _I

Above signal is carried out signal to be handled, with the input as soft-sensing model of the nonlinear characteristic extracting and select, On-line Estimation ball mill load inner parameter is material ball ratio, pulp density, pack completeness, ball mill load parameter flexible measurement method is formed sample according to following structure, and collects sample data.The sample expression formula is { x _k, y _k, wherein, x _kSignal---the vibration signal X of ball mill barrel that namely gathers for the input of sample _V, the acoustical signal of shaking X _A, current signal X _I, the output y of sample _kBe leading variable to be estimated---ball mill load parameter: material ball ratio y ₁, pulp density y ₂, pack completeness y ₃Recording mechanism such as the table 1 of sample, the time is the time that sample obtains.

Table 1 sample data structure

Consider that sample data should be representative, and coverage should comprise the high pulp density in the ball mill grinding process, low pulp density than money as much as possible; High pack completeness, low pack completeness; Operating modes such as high material ball ratio, low material ball ratio.Sample is divided into two groups, and one group of training that is used for the model error minimum comes preference pattern parameter (comprising model training sample and error training sample), and another group is used for verification of model.

Step 2: the bowl mill vibration of gathering, shake sound and current data are carried out filtering

Adopt finite impulse response filter respectively bandpass filtering and low-pass filtering to be carried out in vibration and the acoustical signal of shaking.The wave filter formula is formula as follows:

$y\left(m\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}h\left(n\right)x(m-n)---\left(1\right)$

In the formula, h (n)---the coefficient of wave filter;

The length of N---wave filter;

Y (m)---the output that wave filter is ordered at m;

X (m-n)---(m-n) individual input of wave filter;

N---sampling instant n=0,1 ... N-1;

M---current sampling instant;

Adopt the mean filter method that current signal is carried out filtering, formula is formula as follows:

$y\left(m\right)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{x}_n---\left(2\right)$

In the formula, y (m)---the output of wave filter, the i.e. arithmetic mean of N sampling;

x _n---the n time sampled value;

N---sampling number;

Step 3: the time-frequency conversion is carried out in filtered vibration and the data of shaking

Comprising a large amount of useful informations relevant with process of lapping in the steady periodic vibration that produces in the bowl mill mechanical lapping process and the acoustical signal of shaking.But in the time domain, this information is but covered by random noise signal " white noise ".Ball mill barrel vibration and the acoustical signal of shaking can be decomposed into the sinusoidal signal of stack in frequency domain, and the amplitude of the sinusoidal signal of these different frequency ranges is comprising directly and the operation state information of bowl mill.For guaranteeing that the nothing of power spectrum is estimated partially, adopt improved average period figure method to ask the ball mill barrel vibration of bowl mill rotation complete cycle and the power spectrum density (PSD) of the acoustical signal of shaking, by following formula:

$\tilde{P}\left(k\right)=\frac{1}{R}\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{P}^r\left(k\right),r=1,\·\·\·,R---\left(3\right)$

$P^r\left(k\right)=\frac{1}{N}{\left|X_N\left(k\right)\right|}^2---\left(4\right)$

In the formula,

---the general power spectrum;

P ^r(k)---the power spectrum of r section;

The hop count of R---segmentation;

N---the number of data points of X Serial No.;

K---for the frequency of trying to achieve is counted.

Step 4: frequency spectrum data and time domain current data to vibration and the acoustical signal of shaking are carried out the nonlinear characteristic extraction

4.1 the frequency spectrum data data of vibration and the acoustical signal of shaking are carried out nonlinear characteristic to be extracted

Analyze the feature of bowl mill frequency-region signal under the different operating modes of bowl mill, signal extension was to Mid Frequency when the time-frequency domain signal that dallies as can be known mainly concentrated on low-frequency range, dry grinding; And its Mid Frequency feature is obvious during wet-milling, and the concentration in bowl mill is lower, and there is tangible high band in pack completeness when higher; Then the high band feature is obvious during water mill.Therefore, the wet ball mill frequency-region signal can be divided into low-frequency range, Mid Frequency and high band, it is corresponding the natural frequency section of bowl mill, main frequency of impact section, less important frequency of impact section respectively.The ball mill barrel vibration signal remembered respectively in the data of basic, normal, high frequency be X _{V_LF_org}, X _{V_MF_org}, X _{V_HF_org}The acoustical signal of shaking is remembered respectively in the nonlinear characteristic of basic, normal, high frequency and is X _{A_LF_org}, X _{A_MF_org}, X _{A_HF_org}, there is the problem of higher-dimension and collinearity in these frequency spectrum datas, adopt core pivot element analysis (KPCA) respectively to X _{V_LF_org}, X _{V_MF_org}, X _{V_HF_org}, X _{A_LF_org}, X _{A_MF_org}, X _{A_HF_org}Carrying out dimensionality reduction and nonlinear characteristic extracts.

Nonlinear characteristic leaching process based on core pivot element analysis is described below:

The basic thought of core principle component analysis is to pass through a nonlinear transformation Φ earlier input data X (X ∈ R ^N) be mapped on the high-dimensional feature space F F={ Φ (X): X ∈ R ^N, carry out classical linear principal component analysis (PCA) at feature space F then, in order to realize the linear classification that the input space can't realize.Sample vector after supposing to shine upon is by centralization, and namely satisfying its average is 0, can be expressed as $\underset{k=1}{\overset{M}{\mathrm{\Σ}}}\mathrm{\Φ}\left(X_k\right)=0,$ Then mapping back covariance matrix of sample set on the F space may be defined as

$C=\frac{1}{M}\underset{k=1}{\overset{M}{\mathrm{\Σ}}}\mathrm{\Φ}\left(X_k\right)\mathrm{\Φ}{\left(X_k\right)}^T---\left(5\right)$

With this matrix characteristic of correspondence value equation be

λv＝Cv (6)

According to reproducing kernel (theory of reproducing kernel) theory, because in feature space F, corresponding proper vector v one is positioned by { Φ (X for arbitrary eigenvalue ≠ 0 ₁) ..., Φ (X _M) in the space of opening.Consider that the institute's directed quantity among the feature space F all can be by Φ (X _i) linear combination, so have:

$v=\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_k\mathrm{\Φ}\left(X_k\right)---\left(7\right)$

M * M rank nuclear matrix K is defined as:

K _i，j＝K(X _i，X _j)＝Φ(X _i) ^TΦ(X _j) (8)

In the formula: i, j all represent which concrete sample;

After formula (5), formula (7), formula (8) substitution formula (6), can get the following eigenwert equation of all representing with kernel function

$\mathrm{K\α}=\mathrm{M\λ\α}=\widehat{\mathrm{\λ}}\mathrm{\α}---\left(9\right)$

The problem that so just will find the solution formula (6) proper vector v converts the problem of the proper vector α of the formula of finding the solution (9) eigenwert equation to.If the solution of this eigenwert equation is descending be: λ ₁〉=λ ₁〉=... 〉=λ _M〉=0, the characteristic of correspondence vector is α ₁, α ₂..., α _M, be v corresponding to the eigenvector of formula (6) ₁, v ₂..., v _M, and hypothesis λ _MBe last nonzero eigenvalue, then advise a condition from the quadrature of eigenvector

$v_g^T{v}_r={\mathrm{\δ}}_{g,r},\∀g,r=\mathrm{1,2},\·\·\·,M---\left(10\right)$

Expression is to all g, r=1, and 2 ..., M has $v_g^T{v}_r=1$

Just can derive about proper vector α _kQuadrature advise a condition, namely

$\widehat{\mathrm{\λ}}{\mathrm{\α}}_g^T{\mathrm{\α}}_r={\mathrm{\δ}}_{g,r},\∀g,r=\mathrm{1,2},\·\·\·,M---\left(11\right)$

And then just can be drawn the unique solution { α of proper vector by formula (9) and conditional (11) _k, k=1,2 ... M};

So to arbitrary sample X of the input space, can try to achieve h the major component t of its Φ (X) in higher dimensional space F by following formula _h, namely it is at h major component eigenvector v _hProjection on the direction:

$t_h=(v^h\·\mathrm{\Φ}\left(X\right))=\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_k^{\left(h\right)}(\mathrm{\Φ}\left(X_k\right)\·\mathrm{\Φ}\left(X\right))=\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_k^{\left(h\right)}K(X_k,X),k=1,\·\·\·M---\left(12\right)$

In the formula: t _h---h pivot;

α _k---the proper vector of covariance matrix;

The eigenwert of λ---covariance matrix;

Φ---non-linear transform function;

The number of M---sample data;

v ^h---in the higher dimensional space, the eigenvector of h main composition;

K---M * M rank nuclear matrix;

The number of h---pivot.

Suppose the sample vector centralization of high-dimensional feature space before, so need handle carrying out centralization by the nuclear matrix after the original data space mapping by following formula:

$\tilde{K}=K-I_{M}K-{\mathrm{KI}}_M+I_M{\mathrm{KI}}_M---\left(13\right)$

In the formula:

---the nuclear matrix after centralization is handled;

I _M---coefficient is the unit matrix of 1/M;

Nuclear matrix before K---centralization is handled.

Thereby, to vibration and shake acoustical signal totally six frequency ranges extract nonlinear characteristics and all extract by following formula:

$t_h=(v^h\·\mathrm{\Φ}\left(X\right))=\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_k^{\left(h\right)}\tilde{K}(X_k,X)---\left(14\right)$

With the Spectral variation X of ball mill barrel vibration signal at basic, normal, high frequency _{V_LF_org}, X _{V_MF_org}, X _{V_HF_org}The nonlinear characteristic of extracting is remembered respectively and is X _{V_LF}, X _{V_MF}, X _{V_HF}The bowl mill Spectral variation X of acoustical signal at basic, normal, high frequency that shake _{A_LF_org}, X _{A_MF_org}, X _{A_HF_org}The nonlinear characteristic of extracting is remembered respectively and is X _{A_LF}, X _{A_MF}, X _{A_HF}, its value is represented with following formula respectively:

$X_{V\_\mathrm{LF}}=[t_{V\_\mathrm{LF}\_1},t_{V\_\mathrm{LF}\_2},\·\·\·,t_{V\_\mathrm{LF}\_h_{{\mathrm{VLF}}_{\max }}}];$

$X_{V\_\mathrm{MF}}=[t_{V\_\mathrm{LF}\_1},t_{V\_\mathrm{MF}\_2},\·\·\·,t_{V\_\mathrm{MF}\_h_{{\mathrm{VMF}}_{\max }}}];$

$X_{V\_\mathrm{HF}}=[t_{V\_\mathrm{HF}\_1},t_{V\_\mathrm{HF}\_2},\·\·\·,t_{V\_\mathrm{HF}\_h_{{\mathrm{VHF}}_{\max }}}];$

$X_{A\_\mathrm{LF}}=[t_{A\_\mathrm{LF}\_1},t_{A\_\mathrm{LF}\_2},\·\·\·,t_{A\_\mathrm{LF}\_h_{{\mathrm{ALF}}_{\max }}}];---\left(15\right)$

$X_{A\_\mathrm{MF}}=[t_{A\_\mathrm{MF}\_1},t_{A\_\mathrm{MF}\_2},\·\·\·,t_{A\_\mathrm{MF}\_h_{{\mathrm{AMF}}_{\max }}}];$

$X_{A\_\mathrm{HF}}=[t_{A\_\mathrm{HF}\_1},t_{A\_\mathrm{HF}\_2},\·\·\·,t_{A\_\mathrm{HF}\_h_{{\mathrm{AHF}}_{\max }}}];$

In the formula,

---represent the maximum pivot number that each frequency range is extracted.The following formula of the employing of its value:

$h_{{\mathrm{MNF}}_{\max }}={\arg }_{h_M}\min \{{\mathrm{CPV}}_{\mathrm{hM}}\≥99\%\};$

In the formula, CPV _HM---before expression vibration or the acoustical signal of shaking

The variance accumulation sum of individual pivot;

M=[V, A]---expression vibration (V) and the acoustical signal of shaking (A);

N=[L, M, H]---this do not represent frequency-region signal low (L), in (M), high (H) frequency range;

To the new samples data, press following formula produced nucleus matrix:

$K_{i^{\′},j^{\′}}^{\mathrm{test}}=K(X_{i^{\′}}^{\mathrm{test}},X_{j^{\′}}),i^{\′},j^{\′}=1,\·\·\·,L$

In the formula, X ^Test---expression new samples data;

K ^Test---the nuclear matrix of expression new samples data;

L---the sample size that is the new samples data is line number.

I _N' be a matrix that coefficient is 1/L L * M, L is the line number of new data.

New samples data core matrix carries out centralization by following formula:

${\tilde{K}}_{i,j}^{\mathrm{test}}=K^{\mathrm{test}}-I_M^{\′}K-K^{\mathrm{test}}{I}_M+I_M^{\′}{\mathrm{KI}}_M---\left(17\right)$

In the formula,

---the new samples nuclear matrix after the centralization;

I _M'---coefficient is the matrix of 1/L L * M;

4.2 current data is carried out nonlinear characteristic to be extracted

Many theoretical researches and application in practice show, have tangible nonlinear relationship between current signal and ball mill load.Adopt with step 4.1 in identical method be nonlinear characteristic in the KPCA extraction time domain bowl mill current signal.Nonlinear characteristic note after the extraction is X _I, its value can be represented by the formula:

$X_I=[t_{I\_1},t_{I\_2},\·\·\·,t_{I\_h_{I\max }}]---\left(18\right)$

In the formula, t---pivot, i.e. nonlinear characteristic of Ti Quing; h _Imax---expression is carried out maximum pivot number after nonlinear characteristic is extracted at the time domain current signal.Its value adopts following formula to determine:

$h_{I\max }={\arg }_{h_I}\min \{{\mathrm{CPV}}_{h_I}\≥99\%\}.---\left(19\right)$

In the formula, ---h before the expression current signal _ImaxThe variance accumulation sum of individual pivot.

Step 5: the fused data after vibration, the sound that shakes, the extraction of electric current nonlinear characteristic is carried out feature selecting

Pivot analysis (PCA) when being applied to nonlinear system, though less pivot represents unessential variance, may comprise important system information based on linear dependence and Gaussian statistics hypothesis.Though core pivot element analysis (KPCA) method is to determine pivot in high-dimensional feature space, have good non-linear approximation capability and feature extraction ability, but its essence remains the characteristic information of describing in the response variable X data space, and the size of the characteristic information among the X might not be relevant with predictive variable Y.Therefore, need rationally to determine the pivot number of KPCA.Simultaneously, the mill load parameter that this paper will predict, the different frequency range in the vibration of material ball ratio, pulp density and pack completeness and grinding machine, the acoustical signal of shaking is relevant, need be the pivot number of different forecast model selection varying number.The choose reasonable of model input variable can also improve the precision of prediction of mill load parameter model, prevents from fitting.The present invention with every class in the nonlinear characteristic input variable the set of optimization variables number (the pivot number of KPCA) be called the characteristic parameter collection, and be expressed as: ${\mathrm{FP}}_{\mathrm{sel}}=\left\{(h_{{\mathrm{VLF}}_{\mathrm{sel}}},h_{{\mathrm{VMF}}_{\mathrm{sel}}},h_{{\mathrm{VLF}}_{\mathrm{sel}}})(h_{{\mathrm{ALF}}_{\mathrm{sel}}},h_{{\mathrm{AMF}}_{\mathrm{sel}}},h_{{\mathrm{ALF}}_{\mathrm{sel}}})\left(h_{I_{\mathrm{sel}}}\right)\right\}.$ In conjunction with least square-supporting vector machine model, the definite of the characteristic parameter collection of material ball ratio, pulp density and pack completeness soft-sensing model all adopts following characteristic parameter to optimize model:

$s.t.\left\{\begin{array}{c}1\≤h_{{\mathrm{VLF}}_{\mathrm{sel}}}\≤h_{{\mathrm{VLF}}_{\max }}\\ 1\≤h_{{\mathrm{VMF}}_{\mathrm{sel}}}\≤h_{{\mathrm{VMF}}_{\max }}\\ 1\≤h_{{\mathrm{VHF}}_{\mathrm{sel}}}\≤h_{{\mathrm{VHF}}_{\max }}\\ 1\≤h_{{\mathrm{ALF}}_{\mathrm{sel}}}\≤h_{{\mathrm{ALF}}_{\max }}\\ 1\≤h_{{\mathrm{AMF}}_{\mathrm{sel}}}\≤h_{{\mathrm{AMF}}_{\max }}\\ 1\≤h_{{\mathrm{AHF}}_{\mathrm{sel}}}\≤h_{{\mathrm{AHF}}_{\max }}\\ 1\≤h_{I_{\mathrm{sel}}}\≤h_{I_{\max }}\end{array}\right.---\left(20\right)$

In the formula, RMSE _Val---the minimum of least square-supporting vector machine model is estimated error;

$h_{{\mathrm{MNF}}_{\max }}={\arg }_{h_{\mathrm{MN}}}\min \{{\mathrm{CPV}}_{\mathrm{hMN}}\≥99\%\}$ ---the low middle height of acoustical signal in frequency domain vibrates and shakes

Three frequency ranges are carried out the maximum pivot number that can select after KPCA dimensionality reduction and the feature extraction;

CPV _HMN---before expression vibration or the acoustical signal of shaking

The variance accumulation sum of individual pivot;

M=[V, A]---expression vibration (V) and the acoustical signal of shaking (A);

N=[L, M, H]---this do not represent frequency-region signal low (L), in (M), high (H) frequency range;

$h_{I\max }={\arg }_{h_I}\min \{{\mathrm{CPV}}_{h_I}\≥99\%\}$ ---be that the time domain current signal carries out the maximum pivot number after the KPCA nonlinear characteristic is extracted, generally get 1;

The line number of n---input variable is sample number;

Y---the true value of mill load parameter;

---the estimated value of mill load parameter is the calculated value of model.

According to the following steps material ball ratio model, concentration model, pack completeness model are carried out feature selecting, its selection course at first is to adopt whole characteristic variables to obtain the parameter of model as the input of least square-supporting vector machine model, and next carries out the selection of characteristic parameter.Its flow process as shown in Figure 3.Specific as follows:

(5.1) beginning: carry out initialization operation, by following formula assemblage characteristic variable and be designated as X _All, as the input variable of least square-supporting vector machine model: X _All=[X _{V_LF}, X _{V_MF}, X _{V_HF}, X _{A_LF}, X _{A_MF}, X _{A_HF}, X _I], the characteristic parameter collection of this moment ${\mathrm{FP}}_{\mathrm{sel}\_\mathrm{all}}=\left\{(h_{{\mathrm{VLF}}_{\max }},h_{{\mathrm{VMF}}_{\max }},h_{{\mathrm{VLF}}_{\max }})(h_{{\mathrm{ALF}}_{\max }},h_{{\mathrm{AMF}}_{\max }},h_{{\mathrm{ALF}}_{\max }})\left(h_{I_{\max }}\right)\right\};$

(5.2) whole sample datas are carried out standardization: the data that sample data are standardized as 0 average, 1 variance;

(5.3) setting range of Select Error punishment parameter and nuclear parameter: determine the error penalty of model training use and the interval range of kernel function are convenient to select the best model parameter according to experience;

(5.4) adjust error punishment parameter and nuclear parameter: from the lower limit of the scope setting of each autoregressive parameter, step-length of each parameter circulation as the parameter after adjusting, is used for setting up corresponding model and this group parameter being carried out error assessment at every turn;

(5.5) set up to select whole feature X _AllModel for the model input variable: the fundamental purpose of setting up this model is the initial option model parameter: error punishment parameter and nuclear parameter;

Based on the model of least square-support vector machine to set up process prescription as follows:

Be [x (k), y (k)] for given training set, k ∈ [1, M], wherein x (k) ∈ R ^d, y (k) ∈ R, d is the number of auxiliary variable, the basic idea about modeling of support vector machine be at first by Nonlinear Mapping Φ (X) with input vector from former space R ^dBe mapped to a high-dimensional feature space F, in this high-dimensional feature space, adopt structural risk minimization structure optimal decision function, and the kernel function of utilizing former space replaces the dot-product operation of high-dimensional feature space to avoid complex calculation, thereby the nonlinear function estimation problem is converted into the linear function problem of high-dimensional feature space, and the optimal decision function of its structure has following form:

f(x)＝W ^TΦ(x)+b (21)

In the formula, W---weight vector;

B---amount of bias;

Φ (x)---low-dimensional is to the Nonlinear Mapping of higher dimensional space;

The purpose of finding the solution is utilized structural risk minimization exactly, seeks parameter W ^TAnd b, make for the outer input x of sample have | y _k-(W ^TΦ (x _k)-b|≤ε seeks W ^TBe equivalent to b and find the solution following optimization problem;

$\min J=\frac{1}{2}{W}^{T}W+c\·R_{\mathrm{emp}}$

Wherein, the complexity of W control model; J is the performance index that need optimization; C＞0th, the error penalty, the smoothness of representative function and permissible error are greater than trading off between the numerical value of ε; R _EmpBe empiric risk, i.e. ε insensitive loss function, it is defined as:

$R_{\mathrm{emp}}\left(\mathrm{\θ}\right)=\frac{1}{M}\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{|y_k-(W^T\mathrm{\Φ}\left(x_k\right)+b)|}_{\mathrm{\ϵ}},k=1,\·\·\·,M;---\left(22\right)$

In the formula, M---sample size;

By defining different loss functions, just can construct different support vector machine, least square method supporting vector machine is exactly the quadratic term ξ that has selected error _k ²Loss function is ξ in the replacement standard support vector machine optimization aim _kNamely allow wrong slack variable of dividing, thereby the optimization problem of least square method supporting vector machine is:

$\underset{W\·b}{\min }{J}_p=\frac{1}{2}{W}^{T}W+\frac{1}{2}c\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{{\mathrm{\ξ}}_k}^2---\left(23\right)$

s.t：y _k＝W ^TΦ(x _k)+b+ξ _k

J in the formula _pBe the performance index that new needs are optimized, find the solution above-mentioned optimization problem with Lagrangian method, the definition Lagrangian function is as follows:

$L(W,b,\mathrm{\ξ},\mathrm{\α})=\frac{1}{2}{W}^{T}W+\frac{1}{2}c\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{{\mathrm{\ξ}}_k}^2-\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_k\left[(y_k-(W^T\mathrm{\Φ}\left(x_k\right)+b+{\mathrm{\ξ}}_k)\right]---\left(24\right)$

According to optimal conditions

$\frac{\∂L}{\∂W}=0,$ $\frac{\∂L}{\∂b}=0,$ $\frac{\∂L}{\∂\mathrm{\ξ}}=0,$ $\frac{\∂L}{\∂\mathrm{\α}}=0,$

Can get $W-\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_k\mathrm{\Φ}\left(x_k\right)=0,$ $\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_k=0,$ α _k＝cξ _k，W ^TΦ(x _k)+b+ξ _k-y _k＝0， (25)

Definition kernel function k (x, x _k)=(Φ (x) Φ (x _k)) replacing Nonlinear Mapping, the optimization problem that can find the solution according to following formula is converted into finds the solution linear equation:

$\left[\begin{array}{cccc}0& 1& \·\·\·& 1\\ 1& k(x_1,x_1)+\frac{1}{c}& \·\·\·& k(x_1,x_M)\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ 1& k(x_M,x_1)& \·\·\·& k(x_M,x_M)+\frac{1}{c}\end{array}\right]\·\left[\begin{array}{c}b\\ {\mathrm{\α}}_1\\ \·\\ \·\\ \·\\ {\mathrm{\α}}_M\end{array}\right]=\left[\begin{array}{c}1\\ y_1\\ \·\\ \·\\ \·\\ y_M\end{array}\right]---\left(26\right)$

Determine coefficient b and α=[α by following formula ₁..., α _M], can get soft-sensing model at last and be

$f\left(x\right)=\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\α}}_{k}k(x,x_k)+b,k=1,\·\·\·,M---\left(27\right)$

Wherein kernel function is that satisfied silent plucked instrument is any symmetric function of Mercer condition, and this method adopts radially basic kernel function to replace Nonlinear Mapping, sets up soft-sensing model, and this kernel function form is:

$k(x_k,x_l)=\exp (-\frac{{\left|\right|x_k-x_l\left|\right|}^2}{2{\mathrm{\δ}}^2}),k,l=1,\·\·\·,M$ In the formula: δ---nuclear parameter;

(5.6) read error assessment training sample data: read in one group of sample data preparing to be used for error assessment;

(5.7) recording error evaluation result and parameter: get error training sample data collection, the definition error function is:

$e=\sqrt{\frac{1}{L}\underset{k=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="L\; e\; k"\; filenames="HSA00000029006900051.png,HSA00000029006900052.png"\; state="\{\{state\}\}">L</figure-callout>}}{\mathrm{\&Sigma;}}}{e_k}^{}{{}_{}}^2}=\sqrt{\frac{1}{L}\underset{k=1}{\overset{L}{\mathrm{\&Sigma;}}}{(y_k-(\underset{k=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{k}k(x,x_k)+b))}^2},k=1,\&CenterDot;\&CenterDot;\&CenterDot;,L---\left(28\right)$

In the formula, the sample size of L---error assessment training sample is line number;

Final error assessment function is:

E(c，δ)＝min(e)；

In the formula, c---be error punishment parameter;

Utilize soft-sensing model to obtain the error assessment index between given parameter region, and the record corresponding parameters;

(5.8) whether the parameter adjustment reach upper limit: definition l is for adjusting step-length, and c is error punishment parameter, c _UpBe the upper limit of punishment parameter area, δ is nuclear parameter, δ _UpThe upper limit for the nuclear parameter scope.If c+l 〉=c _UpAnd δ+l 〉=δ _UpSatisfy simultaneously, illustrate that then the error assessment work of all parameter combinations is finished, otherwise, the work of repeating step (5.4)～step (5.8);

(5.9) recording error is estimated best model parameter: with the error assessment index of record in the step (5.7), seek minimal value wherein, the selection corresponding parameters is model parameter, and this model parameter will be used as the LSSVM model parameter in the following steps;

(5.10) read in training sample after the standardization again: read in the standardized training sample of step (5.2) characteristic variable again;

(5.11) whether the feature number of Xuan Zeing reaches setting value: to input matrix X _AllDimension judge how dimension is less than setting value, think that then the calculated amount of feature selecting is less, adopt trellis algorithm to carry out feature selecting, forward step (5.24) to; Otherwise the employing genetic algorithm forwards step (5.12) to, accelerates search speed;

(5.12) characteristic variable coding: adopt the feature selecting based on genetic algorithm, directly adopt binary coding that characteristic variable is encoded, chromosomal length is made as the number of characteristic variable;

(5.13) initialization of population: random initializtion population;

(5.14) the characteristic variable coding is deciphered: the binary coding of characteristic variable is decoded as actual characteristic variable, obtains the characteristic parameter collection FP of this moment _{Sel_GA_ini}

(5.15) set up the LSSVM model: the method for (5.5) is set up the LSSVM model set by step, adopts model parameter and the characteristic parameter collection of step (5.9) storage;

(5.16) read error assessment training sample data;

(5.17) calculate ideal adaptation degree value: the root-mean-square error in the employing LSSVM calibration model is as the fitness function of population individuality;

(5.18) recording feature parameter set: the best characteristic parameter collection of record fitness is FP _{Sel_GA_opt}

(5.19) reach the setting reproductive order of generation? judge whether GA reaches the reproductive order of generation of setting, if reach, change step (5.30); Otherwise, change step (5.20);

(5.20) population is copied: the size according to ideal adaptation degree value sorts to individuality, selects optimized individual, and the more weak individuality of fitness is replaced in randomly ordered back;

(5.21) population is intersected: the single-point intersection is carried out in the male parent of assortative mating and point of crossing at random;

(5.22) population variation: adopt basic mutation operator to carry out mutation operation;

(5.23) population upgrades: the initialization population of adopting the population replacement step (5.13) after upgrading to produce, and change step (5.14);

(5.24) read a stack features parameter: read the stack features parameter F P in the grid _{Sel_grid_ini}

(5.25) LSSVM calibration model: the method for (5.5) is set up the LSSVM model set by step, adopts the model parameter of step (5.9) storage and the characteristic parameter that step (5.24) is selected;

(5.26) read the error assessment training sample;

(5.27) the characteristic parameter collection FP of record root-mean-square error minimum _{Sel_grid_opt}

Does (5.29) the total-grid search finish? judging whether trellis algorithm finishes, is then to change step (5.30); Otherwise, change step (5.20), the characteristic parameter collection step (5.24) behind the storage optimization;

(5.30) the characteristic parameter collection behind the storage optimization: select the FP by the genetic algorithm selection _{Sel_GA_opt}Or the FP of trellis algorithm selection _{Sel_GA_opt}The characteristic parameter collection, and be rewritten as FP _Sel

(5.31) finish: the optimal characteristics of finishing the LSSVM model is selected;

Material ball ratio, pulp density and pack completeness model are carried out said process respectively, obtain preferred feature parameter set FP separately _{Sel_mbr}, FP _{Sel_den}, FP _{Sel_bmwr}Can unify to be expressed as FP _SelI, see following formula for details:

${\mathrm{FP}}_{\mathrm{sel}}i=\left\{(h_{{\mathrm{VLF}}_{\mathrm{sel}}i},h_{{\mathrm{VMF}}_{\mathrm{sel}}i},h_{{\mathrm{VLF}}_{\mathrm{sel}}i})(h_{{\mathrm{ALF}}_{\mathrm{sel}}i},h_{{\mathrm{AMF}}_{\mathrm{sel}}i},h_{{\mathrm{ALF}}_{\mathrm{sel}}i})\left(h_{I_{\mathrm{sel}}i}\right)\right\}---\left(29\right)$

In the formula, i=1, the feature selecting parameter of 2,3 difference corresponding material ball ratio, pulp density and pack completenesss.

Step 6: load parameter material ball ratio, pulp density, the pack completeness of determining bowl mill

The flow process of setting up of ball mill load parametric prediction model is seen accompanying drawing 4, and its detailed step is as follows.

(6.1) beginning: the characteristic parameter collection FP that adopts three ball mill load parameters _{Sel_i}Obtain the input variable of material ball ratio, pulp density and pack completeness model, the unified X that is expressed as _i, see following formula for details:

$X_i=[X_{V\_{\mathrm{LF}}_{\mathrm{sel}}i},X_{V\_{\mathrm{MF}}_{\mathrm{sel}}i},X_{V\_{\mathrm{HF}}_{\mathrm{sel}}i},X_{A\_{\mathrm{LF}}_{\mathrm{sel}}i},X_{A\_{\mathrm{MF}}_{\mathrm{sel}}i},X_{A\_{\mathrm{HF}}_{\mathrm{sel}}i},X_{I_{\mathrm{sel}}i}]$

$X_{V\_{\mathrm{LF}}_{\mathrm{sel}}i}=[t_{V\_\mathrm{LF}\_1},\&CenterDot;\&CenterDot;\&CenterDot;,t_{V\_\mathrm{LF}\_h_{{\mathrm{VLF}}_{\mathrm{sel}}i}}]$

$X_{V\_{\mathrm{MF}}_{\mathrm{sel}}i}=[t_{V\_\mathrm{MF}\_1},\&CenterDot;\&CenterDot;\&CenterDot;,t_{V\_\mathrm{MF}\_h_{{\mathrm{VMF}}_{\mathrm{sel}}i}}]$

$X_{V\_{\mathrm{HF}}_{\mathrm{sel}}i}=[t_{V\_\mathrm{HF}\_1},\&CenterDot;\&CenterDot;\&CenterDot;,t_{V\_\mathrm{HF}\_h_{{\mathrm{VHF}}_{\mathrm{sel}}i}}]$

$X_{A\_{\mathrm{LF}}_{\mathrm{sel}}i}=[t_{A\_\mathrm{LF}\_1},\&CenterDot;\&CenterDot;\&CenterDot;,t_{A\_\mathrm{LF}\_h_{{\mathrm{ALF}}_{\mathrm{sel}}i}}]---\left(30\right)$

$X_{A\_{\mathrm{MF}}_{\mathrm{sel}}i}=[t_{A\_\mathrm{MF}\_1},\&CenterDot;\&CenterDot;\&CenterDot;,t_{A\_\mathrm{MF}\_h_{{\mathrm{AMF}}_{\mathrm{sel}}i}}]$

$X_{A\_{\mathrm{HF}}_{\mathrm{sel}}i}=[t_{A\_\mathrm{HF}\_1},\&CenterDot;\&CenterDot;\&CenterDot;,t_{A\_\mathrm{HF}\_h_{{\mathrm{AHF}}_{\mathrm{sel}}i}}]$

$X_{I_{\mathrm{sel}}i}=[t_{I\_1},\&CenterDot;\&CenterDot;\&CenterDot;,t_{I\_h_{I_{\mathrm{sel}}i}}]$

(6.2) setting range of Select Error punishment parameter and nuclear parameter: the same step of method (5.3);

(6.3) adjust error punishment parameter and nuclear parameter: the same step of method (5.4);

(6.4) set up the model of ball mill load parameter: the same step of method (5.5), the material ball ratio of foundation, pulp density and pack completeness model are as follows:

$y_i=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{ki}}{k}_i(x_i,x_{\mathrm{ki}})+b_i,k=1,\&CenterDot;\&CenterDot;\&CenterDot;,M---\left(31\right)$

In the formula, i=1,2,3 difference corresponding material ball ratio, pulp density and pack completenesss;

(6.5) read error assessment training sample data: the same step of method (5.6);

(6.6) recording error evaluation result and parameter: the same step of method (5.7);

(6.7) the parameter adjustment reach upper limit whether: the same step of method (5.8);

(6.8) recording error is estimated best model parameter: the same step of method (5.9);

(6.9) determine model: according to the model parameter of selecting in the step (6.8), determine the model training result, determine soft-sensing model;

(6.10) read in the checking sample data: read in one group of sample data preparing to be used for modelling verification;

(6.11) modelling verification: adopt the definite model of step (6.9) according to the root-mean-square error in the step (5.7);

Does (6.12) model satisfy precision? precision meets the demands, and then changes the foundation that step (6.14) finishes model, adopts the model of setting up that material ball ratio, pulp density, pack completeness are carried out soft measurement; Otherwise, change step (6.13);

(6.13) collect the structure sample data again: the checking precision can not satisfy the needs of soft measurement, and needing increases test number (TN), re-constructs training sample, forwards step 2 to;

(6.14) finish.

Advantage of the present invention: utilize department of computer science the to unify ball mill barrel vibration that measuring instrument provides, shake sound and current signal, realized the soft measurement of ball mill load parameter (material ball ratio, pulp density, pack completeness).The present invention is highly sensitive by measurement, the ball mill barrel vibration signal of strong interference immunity, has increased sensitivity and the precision of prediction of model.Simultaneously, basic, normal, high three frequency ranges to cylindrical shell vibration and the acoustical signal of shaking that the present invention proposes are carried out the method that nonlinear characteristic is extracted respectively, combine the mechanism of production of grinding ball milling mechanism and vibration and the acoustical signal of shaking of bowl mill, fully extracted the ball mill load parameter information in the signal, the temporal signatures that has overcome vibration and the acoustical signal of shaking is difficult to extract, frequency domain variable superelevation is tieed up and the deficiency of common feature frequency range summation method.And, the feature selection approach that the present invention proposes, solve nonlinear characteristic quantity (pivot number) is difficult to rationally to determine and the input variable dimension of least square-supporting vector machine model too much causes training speed simultaneously slowly and the problem of over-fitting, improved robustness and the estimated performance of model.This method helps to realize optimal control and the stable operation of grinding process, reduces power consumption and the steel consumption of bowl mill, and treatment capacity when improving the platform of bowl mill has improved economic benefit of enterprises.

Description of drawings:

The structural drawing of a kind of ball mill load parameter of Fig. 1 the present invention flexible measurement method;

Total program flow diagram of a kind of ball mill load parameter of Fig. 2 the present invention flexible measurement method;

The nonlinear characteristic of a kind of ball mill load parameter of Fig. 3 the present invention flexible measurement method is selected process flow diagram;

The modeling process process flow diagram of a kind of ball mill load parameter of Fig. 4 the present invention flexible measurement method;

The vibration signal frequency domain figure of a kind of ball mill load parameter of Fig. 5 (a) the present invention flexible measurement method;

The acoustical signal frequency domain figure that shakes of a kind of ball mill load parameter of Fig. 5 (b) the present invention flexible measurement method.

Embodiment:

Be example with small grinder system in the laboratory.The cylindrical shell of this bowl mill is of a size of Φ 460mm * 460mm, and inwall is equipped with manganese, and mineral quantity and steel ball amount in the bowl mill can be shut down, be changed to the bowl mill intermediate openings at any time.The maximum weight of steel ball that this bowl mill is adorned is 80kg, and the mineral treatment capacity is 10kg/h.Drum's speed of rotation is 53 rev/mins.Use Φ 30mm, Φ 20mm and three kinds of manganese steel steel balls of Φ 15mm in the experimentation.The ore of handling in the experiment is the copper mine stone through fragmentation, and particle size is less than 6mm.

As illustrated in fig. 1 and 2, a kind of ball mill load parameter flexible measurement method comprises the steps: based on the KPCA-LSSVM method

Step 1: data acquisition

Press the experimental design scheme is added certain mass in bowl mill steel ball, ore and water, after treating evenly to mix, start bowl mill, the record process of lapping vibration, shake sound and current signal, after reaching the acquisition time of setting, stop bowl mill and clean the collection of preparing next sample.

Step 2: time-domain filtering

It is the bandpass filter of 100～12000Hz that the cylindrical shell vibration signal adopts frequency range; The acoustical signal of shaking then adopts the low-pass filter of 4000Hz; Current signal then adopts averaging method filtering.The data under gathering the wet-milling condition, also gathered bowl mill idle running, sky is pounded, the data under water mill and the dry grinding state.

Step 3: vibrate and the conversion of the time-frequency of the acoustical signal of shaking:

Adopt improved figure method average period (Welch) try to achieve bowl mill rotation weekly vibration and the power spectrum density (PSD) of the acoustical signal of shaking, the average of getting whole cycles is end product.A certain sample vibrates and shakes acoustical signal shown in Fig. 5 (a) and Fig. 5 (b).

Step 4: frequency spectrum data and time domain current data to vibration and the acoustical signal of shaking are carried out the nonlinear characteristic extraction:

4.1 the frequency spectrum data data of vibration and the acoustical signal of shaking are carried out nonlinear characteristic to be extracted:

Frequency-region signal feature when analyzing bowl mill idle running, dry grinding, water mill and wet-milling, the low frequency section that can get the ball mill barrel vibration signal is that 100～1800Hz, Mid Frequency are 1800～4000Hz, high band is 4000～11000Hz.100～1800,1800～4000,4000～7,500 three frequency ranges adopt the KPCA with RBF nuclear to do nonlinear characteristic and extract to three frequency ranges of training sample, and its result is as shown in table 2.Its first pivot is respectively 87.42%, 96.89% and 98.92% at the variance contribution ratio of basic, normal, high frequency range.

Table 2 cylindrical shell vibration signal different frequency range carries out the result that KPCA analyzes

The bowl mill acoustical signal of shaking can be divided into 1～800,800～2500,2500～4,000 three frequency ranges.The KPCA that three frequency ranges of training sample are examined with RBF does the nonlinear characteristic extraction, and its result is as shown in table 3.Its first pivot is respectively 46.72%, 42.31% and 65.5% at the variance contribution ratio of basic, normal, high frequency range, and the sensitivity of the acoustical signal of as seen shaking is lower than the cylindrical shell vibration signal.

The table 3 acoustical signal different frequency range that shakes carries out the result that KPCA analyzes

4.2 current data is carried out nonlinear characteristic to be extracted;

Current signal is carried out after nonlinear characteristic extracts, and the variance contribution ratio of its first pivot reaches 97.5%.Set up model with pack completeness with the signal after extracting, increased by one times, nonlinear existence between having shown before sending out first the ratio of precision extraction.

Step 5: the data splitting to vibration, shake sound, electric current nonlinear characteristic carries out feature selecting;

Combination model input variable preference pattern, the characteristic parameter of ball mill load parameter material ball ratio, pulp density, pack completeness model is respectively mbr_FP _{Sel_opt}={ (4,2,1) (3,1,1) (1) }, density_FP _{Sel_opt}={ (4,2,1) (1,1,6) (1) }, bmwr_FP _{Sel_opt}={ (4,2,1) (2,1,6) (1) }.

Step 6: determine ball mill load ginseng material ball ratio, pulp density, pack completeness

Characteristic parameter by the model selected input of last step, set up material ball ratio, pulp density, pack completeness pin least square-support vector machine soft-sensing model respectively, error punishment parameter and nuclear parameter are elected (28510.7,15), (19700 as, 447), (30000,83).Under this parameter, the parameter alpha of three models and the value of b are respectively:

The material ball ratio model:

α＝[-0.811?0.631?-1.71?-1.29?-11.8?6.49?-3.04?3.14?-2.68?0.0436?1.82?3.875.39]；b＝0.966；

The pulp density model:

α＝[0.514?-0.685?2.94?-41.2?0.517?18.7?2.81?-11.1?40.3?16.8?2.63?-54.89?23.8-0.719]；b＝0.686。

The pack completeness model:

α＝[0.693?-6.99?25.3?3.11?-11.4?-0.516?1.55?-26.8?-10.1?-3.66?36.2?-10.43.25]；b＝0.289。

Adopt root-mean-square error as the statistics of model accuracy, its calculating is undertaken by following formula:

$\mathrm{RMSE}=\sqrt{\frac{1}{N}\underset{k=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="N\; e\; k"\; filenames="HSA00000029006900051.png,HSA00000029006900052.png"\; state="\{\{state\}\}">N</figure-callout>}}{\mathrm{\&Sigma;}}}{e_k}^{}{{}_{}}^2}=\sqrt{\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{({\hat{y}}_k-y_k)}^2}$

Statistics sees Table 4.This table has provided the characteristic parameter collection of modeling and simultaneously based on PCA-LSSVM and select the modeling result of whole pivots.

The ball mill load parameter soft sensor modeling result of the different modeling methods of table 4

This example is based on the soft measurement of ball mill load parameter of laboratory bowl mill system, and the variation range of its material ball ratio, pulp density and pack completeness is greater than the industry spot bowl mill, but its measuring accuracy is still higher.Therefore, the present invention namely based on the ball mill load parameter flexible measurement method that the multi-source data feature merges can effectively extract vibration, shake and current signal in nonlinear characteristic and characteristic parameter carried out effective choice.The present invention can estimate ball mill load parameter (material ball ratio, pulp density and pack completeness) in real time according to the cylindrical shell vibration signal that produces in the bowl mill operational process, the acoustical signal of shaking and current signal, the pca method that precision is more general on average doubles, its root-mean-square error is respectively 0.0889,0.1006 and 0.09553.Therefore, the present invention is ball mill load parameter (material ball ratio, a pulp density and pack completeness) measurement means with fine practical value and promotion prospect.

Claims (1)

1. a ball mill load parameter flexible measurement method is characterized in that: comprise that step is as follows

Step 1: the vibration of collection ball mill barrel, shake sound and current data;

Gather following signal by hardware support platform: the vibration acceleration signal X of ball mill barrel _VThe acoustical signal X that shakes of below, ball mill grinding zone _AThe current signal X of bowl mill driving motor _I

Step 2: the bowl mill vibration of gathering, shake sound and current data are carried out filtering;

Adopt finite impulse response filter respectively bandpass filtering and low-pass filtering to be carried out in vibration and the acoustical signal of shaking, the wave filter formula is formula as follows:

$y_1\left(m\right)=\underset{n_1=0}{\overset{N_1-1}{\mathrm{\&Sigma;}}}h\left(n_1\right)x(m-n_1)$

In the formula, h (n ₁)---the coefficient of wave filter;

N ₁---the length of wave filter;

y ₁(m)---the output that wave filter is ordered at m;

X (m-n ₁)---(m-n of wave filter ₁) individual input;

n ₁---sampling instant n ₁=0,1 ... N ₁-1;

M---current sampling instant;

Adopt the mean filter method that current signal is carried out filtering, formula is formula as follows:

$y_2\left(m\right)=\frac{1}{N^2}\underset{n_2=0}{\overset{N_2-1}{\mathrm{\&Sigma;}}}{x}_{n_2}$

In the formula, y ₂(m)---the output of wave filter, i.e. N ₂The arithmetic mean of inferior sampling;

---n ₂Inferior sampled value;

N ₂---sampling number;

Step 3: the time-frequency conversion is carried out in filtered vibration and the data of shaking;

Adopt improved average period figure method to ask the ball mill barrel vibration of bowl mill rotation complete cycle and the power spectrum density of the acoustical signal of shaking; Press following formula:

$\tilde{P}\left(k\right)=\frac{1}{R}\underset{r=1}{\overset{R}{\mathrm{\&Sigma;}}}{P}^r\left(k\right)r=1,...,R$

$P^r\left(k\right)=\frac{1}{N_3}{\left|X_{N_3}\left(k\right)\right|}^2$

In the formula,

---the general power spectrum;

P ^r(k)---the power spectrum of r section;

The hop count of R---segmentation;

N ₃---the number of data points of X Serial No.;

K---for the frequency of trying to achieve is counted;

Step 4: frequency spectrum data and time domain current data to vibration and the acoustical signal of shaking are carried out the nonlinear characteristic extraction;

4.1 the frequency spectrum data to vibration and the acoustical signal of shaking carries out the nonlinear characteristic extraction;

The wet ball mill frequency-region signal is divided into low-frequency range, Mid Frequency and high band, it is corresponding the natural frequency section of bowl mill, main frequency of impact section, less important frequency of impact section respectively, the ball mill barrel vibration signal is remembered respectively in the data of basic, normal, high frequency be X _{V_LF_org}, X _{V_MF_org}, X _{V_HF_org}The acoustical signal of shaking is remembered respectively in the nonlinear characteristic of basic, normal, high frequency and is X _{A_LF_org}, X _{A_MF_org}, X _{A_HF_org}, there is the problem of higher-dimension and collinearity in these frequency spectrum datas, adopt core pivot element analysis respectively to X _{V_LF_org}, X _{V_MF_org}, X _{V_HF_org}, X _{A_LF_org}, X _{A_MF_org}, X _{A_HF_org}Carrying out dimensionality reduction and nonlinear characteristic extracts;

To vibration and shake acoustical signal totally six frequency ranges extract nonlinear characteristics and all extract by following formula:

$t_h=(v^h\&CenterDot;\mathrm{\&Phi;}\left(X\right))=\underset{k=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_k^{\left(h\right)}\tilde{K}(X_k,X)$

In the formula: k represents k sample, scope from 1 to M ₁t _h---h pivot; α _k---the proper vector of covariance matrix; Φ---non-linear transform function; Φ (X) expression input sample data X is in the Nonlinear Mapping of high-dimensional feature space; v ^h---in the higher dimensional space, the eigenvector of h main composition; K---M ₁* M ₁The rank nuclear matrix; The number of h---pivot;

---the nuclear matrix after centralization is handled;

With the Spectral variation X of ball mill barrel vibration signal at basic, normal, high frequency _{V_LF_org}, X _{V_MF_org}, X _{V_HF_org}The nonlinear characteristic of extracting is remembered respectively and is X _{V_LF}, X _{V_MF}, X _{V_HF}The bowl mill Spectral variation X of acoustical signal at basic, normal, high frequency that shake _{A_LF_org}, X _{A_MF_org}, X _{A_HF_org}The nonlinear characteristic of extracting is remembered respectively and is X _{A_LF}, X _{A_MF}, X _{A_HF}, its value is represented with following formula respectively:

$X_{V\_\mathrm{LF}}=[t_{V\_\mathrm{LF}\_1},t_{V\_\mathrm{LF}\_2},...,t_{V\_\mathrm{LF}\_h_{\mathrm{VL}{F}_{\max }}}]$ ;

$X_{V\_\mathrm{MF}}=[t_{V\_\mathrm{MF}\_1},t_{V\_\mathrm{MF}\_2},...,t_{V\_\mathrm{MF}\_h_{\mathrm{VM}{F}_{\max }}}]$ ；

$X_{V\_\mathrm{HF}}=[t_{V\_\mathrm{HF}\_1},t_{V\_\mathrm{HF}\_2},...,t_{V\_\mathrm{HF}\_h_{\mathrm{VH}{F}_{\max }}}]$ ；

$X_{A\_\mathrm{LF}}=[t_{A\_\mathrm{LF}\_1},t_{A\_\mathrm{LF}\_2},...,t_{A\_\mathrm{LF}\_h_{\mathrm{AL}{F}_{\max }}}]$ ；

$X_{A\_\mathrm{MF}}=[t_{A\_\mathrm{MF}\_1},t_{A\_\mathrm{MF}\_2},...,t_{A\_\mathrm{MF}\_h_{\mathrm{AM}{F}_{\max }}}]$ ；

$X_{A\_\mathrm{HF}}=[t_{A\_\mathrm{HF}\_1},t_{A\_\mathrm{HF}\_2},...,t_{A\_\mathrm{HF}\_h_{\mathrm{AH}{F}_{\max }}}]$ ；

In the formula, ---vibrate and acoustical signal low in frequency domain of shaking in a Senior Three frequency range carry out the maximum pivot number that can select after KPCA dimensionality reduction and the feature extraction;

---before expression vibration or the acoustical signal of shaking

The variance accumulation sum of individual pivot;

M ₂=[V, A]---expression vibration (V) and the acoustical signal of shaking (A);

N ₄=[L, M, H]---represent respectively frequency-region signal low (L), in (M), high (H) frequency range.

4.2 current data is carried out nonlinear characteristic to be extracted;

Adopt with step 4.1 in identical method be that core pivot element analysis extracts the nonlinear characteristic in the time domain bowl mill current signal, the nonlinear characteristic after the extraction is remembered and is X _I, its value can be represented by the formula:

$X_I=[t_{I\_1},t_{I\_2},...,t_{I\_h_{I\max }}]$

In the formula, t---pivot, i.e. nonlinear characteristic of Ti Quing; h _Imax---be that the time domain current signal carries out the maximum pivot number after the KPCA nonlinear characteristic is extracted, its value adopts following formula to determine:

$h_{I\max }={\arg }_{h_I}\min \{{\mathrm{CPV}}_{h_I}\&GreaterEqual;99\%\}$ ；

In the formula,

---before the expression current signal

The variance accumulation sum of individual pivot;

Step 5: the fused data after vibration, the sound that shakes, the extraction of electric current nonlinear characteristic is carried out feature selecting;

Be that the set of the pivot number of KPCA is called the characteristic parameter collection with the optimization variables number of every class in the nonlinear characteristic input variable, and unified being expressed as: ${\mathrm{FP}}_{\mathrm{sel}}=\left\{(h_{{\mathrm{VLF}}_{\mathrm{sel}}},h_{{\mathrm{VMF}}_{\mathrm{sel}}},h_{{\mathrm{VLF}}_{\mathrm{sel}}})(h_{{\mathrm{ALF}}_{\mathrm{sel}}},h_{\mathrm{AM}{F}_{\mathrm{sel}}},h_{{\mathrm{ALF}}_{\mathrm{sel}}})\left(h_{I_{\mathrm{sel}}}\right)\right\}$ , adopt the setting range of LSSVM Model Selection error punishment parameter and nuclear parameter, obtain the characteristic parameter collection behind the storage optimization, determine material ball ratio preferred feature parameter set, pulp density preferred feature parameter set and pack completeness preferred feature parameter set at last,

The following characteristic parameter of definite employing of characteristic parameter collection is optimized model:

In the formula, RMAE _Val---the minimum of least square-supporting vector machine model is estimated error;

---vibrate and acoustical signal low in frequency domain of shaking in a Senior Three frequency range carry out the maximum pivot number that can select after KPCA dimensionality reduction and the feature extraction;

---before expression vibration or the acoustical signal of shaking

The variance accumulation sum of individual pivot;

M ₂=[V, A]---expression vibration (V) and the acoustical signal of shaking (A);

N ₄=[L, M, H]---represent respectively frequency-region signal low (L), in (M), high (H) frequency range;

---be that the time domain current signal carries out the maximum pivot number after the KPCA nonlinear characteristic is extracted, generally get 1;

n ₃---the line number of input variable is sample number;

Y---the true value of mill load parameter;

---the estimated value of mill load parameter is the calculated value of model;

Step 6: load parameter material ball ratio, pulp density, the pack completeness of determining bowl mill;

Input variable x by material ball ratio, pulp density and pack completeness model _i, adopt the LSSVM model, definite material ball ratio, pulp density and pack completeness:

$Y_i=\underset{k=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{\mathrm{ki}}{k}_i(x_i,x_{\mathrm{ki}})+b_{i}k=1,...,M_1$ , i=1,2,3 difference corresponding material ball ratio, pulp density and pack completenesss, α _Ki, b _iCoefficient for model;

Obtain load parameter material ball ratio, pulp density and the pack completeness of bowl mill.

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