CN105512690A - Ball mill material level measurement method based on supervised isometric feature mapping and support vector regression - Google Patents

Abstract

The invention relates to a detection method for detecting the material level of a tumbling ball mill and particularly provides a tumbling ball mill material level measurement method based on supervised isometric feature mapping and support vector regression. The method comprises the steps of acquiring the bearing vibration signal of the ball mill, conducting the time-frequency transformation on the vibration signal, conducting the nonlinear dimensionality reduction and the feature extraction on the power spectrum of the vibration within an effective frequency band through the supervised isometric feature mapping process, and establishing a regression model between the dimensionality reduction property and the material level through the support vector regression process. According to the technical scheme of the invention, the material level of the ball mill can be accurately and reliably measured. Meanwhile, the discrimination degree between material levels can be enhanced. Therefore, the method has a relatively high engineering application value.

Description

Based on the level of material for ball mill measuring method of supervising Isometric Maps and support vector regression

Technical field

The present invention relates to the detection method of ball mill level, specifically a kind of ball mill level detection method based on supervising Isometric Maps and support vector regression.

Background technology

Tumbling ball mill is a kind of for the major equipment in the fields such as electric power, mine, metallurgy, chemical industry and building materials, and its function, for raw material grinding mill is made powder, belongs to a kind of high energy consumption, inefficient equipment.According to research, bowl mill has the raw-material potentiality of saving steel of the energy-saving potential of more than 10% and more than 9%.By the material level of Measurement accuracy tumbling ball mill, and control effectively, will the excavation of these potentiality be conducive to.Because tumbling ball mill works in closed rotation status, lack the equipment of its inner material level of direct-detection, the phenomenons such as full mill, empty mill and stifled mill often occur, causes production efficiency to reduce, and affect product quality and equipment life.Therefore reliably detect level of material for ball mill, make it operate in optimum condition, significant to the stability and economy improving system.

At present, the detection method of ball mill level mainly contain pressure differential method, power method, shake sound method and vibratory drilling method.Differential pressure method utilizes the differential pressure of bowl mill gateway to characterize level of material for ball mill, its advantage is that site operation personnel is experienced to the method, shortcoming is because bowl mill gateway differential pressure is not only relevant with the retaining amount of bowl mill, also relevant to steel ball loading capacity and ventilation etc., in the use of reality, precision is lower.When power method runs by detecting, the change of current of electric reflects retaining amount indirectly, its advantage is that intuitive is strong, be not subject to surrounding environment influence, testing result is more accurate, shortcoming is that ball mill power is mainly by the impact of steel ball load, unloaded very little with full load changed power, and non-monotonic, sensitivity is low.To shake sound method, also known as electric ear method, Noise Method, the noise utilizing steel ball and collide between liner plate and steel ball is to characterize material level, belong to non-cpntact measurement, its advantage is that operating cost is low, structure is simple, shortcoming is the impact of the ground unrest being subject to the equipment such as adjacent mill noise signal, the machinery of itself and motor transmission mechanism, and during high charge level, sensitivity is lower.Vibratory drilling method utilizes the vibration signal of bowl mill to represent material level, its advantage low material level highly sensitive in being, sensor good seal, can adapt to work on the spot environment, and shortcoming is when high charge level, presses close to optimize district, and signal is very little with material level change, and sensitivity is lower.Visible vibratory drilling method is higher with sound method precision of shaking, but lower in the sensitivity at high charge level place.Current vibratory drilling method is widely used in industry spot, but its frequency spectrum exists higher-dimension, bulk redundancy, non-linear, therefore needs first to adopt the methods such as dimensionality reduction to process spectrum signature to rumble spectrum.

Summary of the invention

The present invention is directed to bowl mill vibration signal and there is non-linear, redundancy and the vibratory drilling method problem that sensitivity is lower when high charge level, provide a kind of level of material for ball mill measuring method based on supervision Isometric Maps and support vector regression.

The present invention adopts following technical scheme to realize, and based on the level of material for ball mill measuring method of supervising Isometric Maps and support vector regression, its model structure as shown in Figure 1, comprises off-line modeling stage and on-line measurement stage, and wherein the off-line modeling stage comprises the following steps:

Step one gathers material level Z={z ₁..., z _nunder bowl mill vibration signal S={s ₁..., s _n, wherein N is training sample number;

Step 2 asks for the power spectrum of vibration signal, and by [f ₁, f ₂] in power spectrum be divided into n _fpart, and average is asked for each several part, obtain oscillation power spectrum essential characteristic X={x ₁..., x _n, wherein f ₁, f ₂and n _fcan rule of thumb be determined by technician;

Step 3 supervision Isometric Maps (S-Isomap) is carried out Nonlinear Dimension Reduction to oscillation power spectrum essential characteristic X and extracts characteristic Y, and the Nonlinear Dimension Reduction process prescription based on supervision Isometric Maps is as follows.

1) to the training set data { (x that oscillation power spectrum essential characteristic X and material level true value Z forms ₁, z ₁) ..., (x _n, z _n) calculate distinctiveness ratio distance according to formula (1):

$D(x_i,x_j)=\{\begin{array}{cc}\sqrt{1-e^{\frac{-d^2(x_i,x_j)}{\mathrm{\β}}}}& z_i=z_j\\ \sqrt{e^{\frac{d^2(x_i,x_j)}{\mathrm{\β}}}}-\mathrm{\α}& z_i\≠z_j\end{array}---\left(1\right)$

Wherein d (x _i, x _j) represent Euclidean distance, α for regulate different material level point between distance, β is used for preventing d (x _i, x _j) larger time D (x _i, x _j) increase comparatively fast, be traditionally arranged to be the mean value of Euclidean distance between all-pair.

2) build neighbour and scheme G, if x _iand x _jdistinctiveness ratio distance D (x _i, x _j) be less than threshold value T, or x _ix _jk Neighbor Points, then judge that these two points are adjacent, namely in figure G, have limit to exist, and the length of side is D (x _i, x _j).

3) shortest path is calculated, for x according to Freud (Floyd) algorithm _iand x _jif there is limit to connect, its shortest path of initialization d _g(x _i, x _j)=D (x _i, x _j), otherwise establish d _g(x _i, x _j)=∞, to m=1 ..., N, calculates d _g(x _i, x _j)={ d _g(x _i, x _j), d _g(x _i, x _m)+d _g(x _m, x _j), obtain shortest path Distance matrix D like this _g={ d _g(x _i, x _j).

4) calculate d dimension to embed, multi-dimentional scale conversion (MDS) is applied to D _gin, calculate squared-distance matrix with centralization matrix H={ σ _ij-1/N}, makes τ (D _g)=-HSH/2, τ (D _g) maximum d eigenvalue λ ₁, λ ₂..., λ _dcharacteristic of correspondence vector u ₁, u ₂..., u _dthe matrix formed is U=[u ₁, u ₂..., u _d], then $Y=\{y_1,...,y_N\}=diag({\mathrm{\λ}}_1^{1/2},{\mathrm{\λ}}_2^{1/2},...,{\mathrm{\λ}}_d^{1/2})U^T$ For d ties up dimensionality reduction result.

The distinctiveness ratio distance that S-Isomap utilizes sample label to obtain between data point, substitute original Euclidean distance, thus relatively reduce inter-object distance, increase between class distance, again by adopting distinctiveness ratio distance to build neighbour figure, then in neighbour figure, obtaining with shortest path be similar to geodesic line distance, by setting up the Isometric Maps of the distance between the geodesic line distance of former data and dimensionality reduction data, completing Data Dimensionality Reduction.

Step 4: the Nonlinear Mapping of the supervision Isometric Maps of learning procedure three, training radial basis (RBF) neural network, it is made to approach supervision Isometric Maps, RBF neural input layer data are training set oscillation power spectrum essential characteristic X, output layer data are characteristic Y, oscillation power is composed essential characteristic X and input RBF neural, obtain mappings characteristics Y'={y' ₁..., y' _n.

S-Isomap is to the map information of on-line measurement data deficiency from higher dimensional space to lower dimensional space, therefore adopt suitable method to learn this Nonlinear Mapping in the off-line modeling stage, for carrying out dimensionality reduction to on-line measurement data, the present invention adopts RBF neural to learn this mapping.

Step 5: set up support vector regression (SVR) model between mappings characteristics Y' and material level Z, adopt SVR set up RBF neural gained characteristic Y ' and material level Z between nonlinear model.

RBF neural map gained characteristic Y ' SVR the training set { (y' that forms with material level Z ₁, z ₁) ..., (y' _n, z _n) obtain w and b by following optimization problem,

$\underset{w,b,\mathrm{\ξ},{\mathrm{\ξ}}^{*}}{min}\frac{1}{2}{w}^{T}w+C\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\ξ}}_i+C\underset{i=1}{\overset{N}{\Σ}}{{\mathrm{\ξ}}_i}^{*}$

s.t.w ^Tφ(y' _i)+b-z _i≤ε+ξ _i(2)

$z_i-w^T\mathrm{\φ}\left({y^{\′}}_i\right)+b\≤\mathrm{\ϵ}+{{\mathrm{\ξ}}_i}^{*}$

${\mathrm{\ξ}}_i,{{\mathrm{\ξ}}_i}^{*}\≥0,i=1,...,N$

Here ε is insensitive loss function, and C is penalty coefficient, ξ _i, for slack variable.

Utilize Lagrangian function and the principle of duality, obtain the dual problem of formula (2)

$\underset{\mathrm{\α},{\mathrm{\α}}^{*}}{min}\frac{1}{2}{(\mathrm{\α}-{\mathrm{\α}}^{*})}^{T}Q(\mathrm{\α}-{\mathrm{\α}}^{*})+\mathrm{\ϵ}\underset{i=1}{\overset{N}{\Σ}}({\mathrm{\α}}_i+{\mathrm{\α}}_i^{*})+\underset{i=1}{\overset{N}{\Σ}}{z}_i({\mathrm{\α}}_i-{\mathrm{\α}}_i^{*})$

s.t.e ^T(α-α ^*)＝0,(3)

$0\≤{\mathrm{\α}}_i,{\mathrm{\α}}_i^{*}\≤C,i=1,...,N$

Q in formula (3) _ij=K (y' _i, y' _j) ≡ Φ (y' _i) ^tΦ (y' _j), K (y' _i, y' _j) be kernel function, the present invention gets Radial basis kernel function,

K(y' _i,y' _j)＝exp(-||y' _i-y' _j|| ²/σ ²)(4)

Wherein i, j=1 ..., N, σ are nuclear parameter.

Thus support vector regression pattern function is

$f\left(y\right)=\underset{i=1}{\overset{N}{\Σ}}(-{\mathrm{\α}}_i+{\mathrm{\α}}_i^{*})K({y^{\′}}_i,y)+b---\left(5\right)$

The on-line measurement stage comprises the following steps:

Step one: gather the bowl mill vibration signal s under material level z;

Step 2: the power spectrum asking for vibration signal s, and by [f ₁, f ₂] in power spectrum be divided into n _fpart, and average is asked for each several part, obtain oscillation power spectrum essential characteristic x;

Step 3: utilize RBF neural mapping that oscillation power is composed essential characteristic x and be mapped as feature y';

Step 4: above-mentioned feature y' is inputted SVR and carries out material level prediction, obtain measured material level $\hat{z}=f\left(y^{\′}\right)=\underset{i=1}{\overset{N}{\Σ}}(-{\mathrm{\α}}_i+{\mathrm{\α}}_i^{*})K({y^{\′}}_i,y)+b.$

Accompanying drawing explanation

Fig. 1 is the soft-sensing model schematic diagram set up.

Fig. 2 is the curve map of the ratio of inter-object distance square between off-line training collection class.

Fig. 3 be on-line testing data class between the curve map of ratio of inter-object distance quadratic sum.

Fig. 4 is the bowl mill measurement result of on-line measurement data and the comparison diagram of actual value.

Embodiment

The present invention is for laboratory room small-sized bowl mill, and the cylindrical shell of this bowl mill is of a size of gather vibration signal to detect level of material for ball mill.

Based on the level of material for ball mill measuring method of supervising Isometric Maps and support vector regression, comprise off-line modeling stage and on-line measurement stage, the off-line modeling stage comprises the following steps:

Step one: gather material level Z={z ₁..., z _nunder training set bowl mill vibration signal S={s ₁..., s _n, in the present embodiment, N=300 is training sample number, and material level is 1L, 2L ..., 20L, each material level 15 samples.

Step 2: the power spectrum asking for vibration signal S, and by [f ₁, f ₂] in power spectrum be divided into n _fpart, and average is asked for each several part, obtain oscillation power spectrum essential characteristic X={x ₁..., x _n, in the present embodiment, rule of thumb, f1=600Hz, f2=6000Hz, n=180.

Step 3: to oscillation power spectrum essential characteristic X={x1 ..., xN} adopts S-Isomap to carry out dimensionality reduction, obtains extracting characteristic Y={ y ₁..., y _n, k=15, d=14, α=0.625 in the present embodiment.

Step 4: the Nonlinear Mapping adopting the S-Isomap of RBF neural learning procedure three, and oscillation power is composed essential characteristic X input RBF, obtain mappings characteristics Y'={y' ₁..., y' _n, Spread=1 in the present embodiment, maximum hidden node number Mn=80;

S-Isomap utilizes material level label relatively to reduce the data point spacing of same material level, increases the data point spacing of different material level, thus enhances the discrimination between material level.For inspection S-Isomap dimensionality reduction is on the impact of discrimination between classification, introduce the ratio Ratio of inter-object distance quadratic sum between class.

The definition ratio of inter-object distance quadratic sum (between the class) in sample U, for l the point of classification p, for v the point of classification r, between the class of classification p, the ratio of inter-object distance quadratic sum is

${\mathrm{Ratio}}_p=\frac{\underset{r\≠p}{\min }\left(\underset{v=1}{\overset{n_r}{\mathrm{\Σ}}}{\mathrm{dist}}^2\right(u_v^r-m_p))}{\underset{l=1}{\overset{n_p}{\mathrm{\Σ}}}{\mathrm{dist}}^2(u_l^p-m_p)}---\left(6\right)$

Wherein with get Euclidean distance, n _r, n _pfor the number of samples of classification r and p, m _pfor the center of classification p

$m_p=\frac{1}{n_p}\underset{l=1}{\overset{n_p}{\Σ}}{u}_l^p---\left(7\right)$

In the present embodiment, between off-line training collection class, the curve map of the ratio of inter-object distance square as shown in Figure 1.The Ratio of the dimensionality reduction gained feature of training set, all comparatively primitive character increases to some extent, and visible S-Isomap can increase the differentiation degree between the different material level of training set.

Step 5: set up support vector regression model between mappings characteristics Y' and material level, γ=4 in the present embodiment, penalty coefficient C=20, insensitive loss function ε=0.1.

The on-line measurement stage comprises the following steps:

Step one: gather the bowl mill vibration signal s under material level z;

Step 2: the power spectrum asking for vibration signal s, and by [f ₁, f ₂] in power spectrum be divided into n _fpart, and average is asked for each several part, obtain oscillation power spectrum essential characteristic x, f in the present embodiment ₁=600Hz, f ₂=6000Hz, n _f=180.

Step 3: utilize RBF that essential characteristic x is mapped as feature y'.

In the present embodiment, between the class of on-line testing data, the curve map of the ratio of inter-object distance square is as shown in Figure 2, on-line testing data totally 140, and material level is 1L, 2L ..., 20L, has 7 samples under each material level.The Ratio of the dimensionality reduction gained feature of on-line testing data, except indivedual material level, all comparatively primitive character increases to some extent, and visible S-Isomap can increase the differentiation degree between classification.

Step 4: above-mentioned feature y' is inputted support vector regression model and carries out material level prediction, obtain measured material level $\hat{z}=f\left(y^{\′}\right)=\underset{i=1}{\overset{N}{\Σ}}(-{\mathrm{\α}}_i+{\mathrm{\α}}_i^{*})K({y^{\′}}_i,y^{\′})+b.$

Step 5: adopt root-mean-square error (RMSE), maximum absolute error (MAXE) and mean absolute error (MAE) as model performance evaluation index, its definition is respectively:

$RMSE=\sqrt{\frac{1}{M}\underset{i=1}{\overset{M}{\Σ}}{({\hat{z}}_i-z_i)}^2}---\left(8\right)$

$MAXE=max\left(\right|{\hat{z}}_i-z_i\left|\right)---\left(9\right)$

$MAE=\frac{1}{M}\underset{i=1}{\overset{M}{\Σ}}|{\hat{z}}_i-z_i|---\left(10\right)$

In formula represent material level estimated value and the actual value of i-th sample respectively with zi, M is the number of samples of on-line testing collection.

Table 1 and the level of material for ball mill measurement result that fig. 3 gives on-line measurement data in the present embodiment, wherein LM represents low material level in 1 to 15L, H represents the high charge level of 16 to 20L, can find that the material level precision of prediction of this invention to bowl mill gamut is higher, can follow the tracks of material level curve preferably, during high charge level, measurement sensistivity significantly improves.

Table 1 level of material for ball mill measurement result

Advantage of the present invention: utilize S-Isomap to extract the nonlinear organization of vibration signal power spectrum, improve the discrimination between material level, then utilize SVR to set up regression model, improve the precision of prediction of the precision of prediction of model, particularly high charge level.And generally, bowl mill always runs on comparatively high charge level interval, therefore the method has larger using value in engineering reality, has greater significance to the safety and stability improving bowl mill.

Claims (1)

1., based on a level of material for ball mill measuring method of supervising Isometric Maps and support vector regression, it is characterized in that comprising off-line modeling stage and on-line measurement stage, wherein the off-line modeling stage comprises the following steps:

Step one: gather material level Z={z ₁..., z _nunder bowl mill vibration signal S={s ₁..., s _n, wherein N is training sample number;

Step 2: the power spectrum asking for vibration signal, and by [f ₁, f ₂] in power spectrum be divided into n _fpart, and average is asked for each several part, obtain oscillation power spectrum essential characteristic X={x ₁..., x _n;

Step 3: oscillation power spectrum essential characteristic X is carried out to Nonlinear Dimension Reduction and extracts characteristic Y={ y with supervision Isometric Maps ₁..., y _n;

Step 4: the supervision Isometric Maps of learning procedure three, Training RBF Neural Network, it is made to approach supervision Isometric Maps, radial base neural net input layer data are training set oscillation power spectrum essential characteristic X, output layer data are characteristic Y, and oscillation power is composed essential characteristic X input RBF, obtain mappings characteristics Y'={y ' ₁..., y' _n;

Step 5: set up support vector regression model between mappings characteristics Y' and material level Z, adopt SVR set up RBF map gained characteristic Y ' and material level Z between nonlinear model.

The on-line measurement stage comprises the following steps:

Step one: gather the bowl mill vibration signal s under material level z;

Step 2: the power spectrum asking for vibration signal s, and by [f ₁, f ₂] in power spectrum be divided into n _fpart, and average is asked for each several part, obtain oscillation power spectrum essential characteristic x;

Step 3: utilize RBF mapping that oscillation power is composed essential characteristic x and be mapped as feature y';

Step 4: above-mentioned feature y' is inputted support vector regression model and carries out material level prediction, obtain measured material level.