As an important indicator of flotation performance, froth texture is believed to be related to operational condition in sulphur flotation process. A novel fault detection method based on froth texture unit distribution (TUD) is proposed to recognize the fault condition of sulphur flotation in real time. The froth texture unit number is calculated based on texture spectrum, and the probability density function (PDF) of froth texture unit number is defined as texture unit distribution, which can describe the actual textual feature more accurately than the grey level dependence matrix approach. As the type of the froth TUD is unknown, a nonparametric kernel estimation method based on the fixed kernel basis is proposed, which can overcome the difficulty when comparing different TUDs under various conditions is impossible using the traditional varying kernel basis. Through transforming nonparametric description into dynamic kernel weight vectors, a principle component analysis (PCA) model is established to reduce the dimensionality of the vectors. Then a threshold criterion determined by the

Sulphur flotation is a complex physical process influenced by multiple operational variables such as inlet air flow, pulp level, and it is naturally hydrophobic to attach to the air bubbles. The objective of sulphur flotation is to separate valuable sulphur minerals from useless materials or other minerals so as to gain the upgraded sulphur minerals [

It is shown that the froth texture is a good indicator to the performance of the flotation cells [

To relate the flotation operation condition with flotation performance, Jampana et al. revealed that the increase in pulp level causes concentrate grade to decrease [

The froth texture characterizes the roughness of the froth surface, which indicates the mineral contents of froth. When the pulp level is too high with slurry overflow, froth texture is smooth; in this case, the middle value takes a large portion of the texture unit number in the whole image, which results in a high peak in the texture unit distribution curve. On the other hand, when the pulp level becomes too low, the froth cannot overflow, such that the mineral contents in the froth accumulate to a high level. Therefore, the texture becomes coarse and the middle value takes a small portion of the texture unit number in the whole image, resulting in a low peak in the texture unit distribution curve. By transforming the texture unit distribution into the weight vector using the fixed kernel estimator, a weight PCA model can be established to handle the variation in the texture unit distribution. The sulphur froth image contains a great deal of noise because of the acid fog in the sulphur flotation.

The main advantages of the proposed method in this paper are that (i) the texture unit distribution can describe the froth texture feature more completely, by considering eight directions of grey level variation information, compared to the GLCM method. (ii) The mathematical model of texture unit distribution is unknown, as it is nonnormal and multipeaky, so nonparametric estimation method is more suitable to approximate it. The fixed kernel basis can compare the different flotation performance reflected by the weight coefficients of texture unit distribution, compared with the traditional varying kernel basis. (iii) The new statistic

This work aims to explore the froth texture by using kernel density estimation technique to approximate the surface froth TUD and its application on sulphur flotation process performance recognition. A nonparametric kernel estimator by the fixed kernel basis is designed to approximate texture unit distribution, such that the output TUD is formulated in terms of dynamic weights, on which a principle component analysis (PCA) model is established. Then an effective performance recognition criterion is determined using the proposed

Experimental setup consists of RGB camera with resolution of ^{2} are captured online at the rate of 15 frames/s. Meanwhile, the corresponding process operational and performance data are collected on industrial scale.

Froth images collected from industry field display that various froth texture feature leads to the different performance. The existing texture description method such as texture spectrum, spatial and neighboring grey-level cooccurrence matrix are derived from this fact. Froth image observed is a type of gradient images. Nevertheless, simple second-order statistical variables in the GLCM approach are difficult to accurately describe the froth texture, the texture unit (TU) oriented texture spectrum scheme proposed by [

As each element of TU has one of three possible values, the combination of all eight elements results in

In addition, the eight elements may be ordered differently. If the eight elements are ordered clockwise as shown in Figure

Eight clockwise, successive ordering ways of the eight elements of the texture unit. The first element

Figure

Example of transforming a neighborhood to a texture unit with the texture unit number.

TUD is defined as the occurrence frequency for every texture unit number, and it exhibits probability density function (PDF) distribution of froth texture unit number. The online acquired sulphur froth image in cleaner cell in normal condition is shown in Figure

The online acquired sulphur froth images in cleaner cell.

Surface froth texture unit distribution.

The surface sulphur froth TUD is nonnormal. Unlike traditional method applying singular feature such as mean or variance with the assumption that the distribution is normal, probability density distribution is suggested to accurately describe statistical feature of froth texture. The fact that the mathematical model of TUD is unknown makes nonparametric estimation method fitting to depict the unknown continuous process of froth flotation.

Consider a probability density function

Density estimation accomplishes the fitting of

Supposing there is a dynamic stochastic system with input

Denote

Since

However, the traditional kernel estimation cannot compare the various froth TUDs under different flotation conditions with the varying kernel basis. Therefore, the fixed kernel basis is proposed to describe the TUDs in various froth images, such that the TUD curves can be transformed into dynamic kernel weight vectors, based on which the fault condition can be detected in sulphur flotation. Meanwhile, the computational complexity is also reduced using the designed fixed kernel basis.

Adjusting to the range of froth texture unit number, a number of kernel bases are selected to depict the TUD in Figure

Normal kernel estimation and the weight coefficients.

Figure

Normal kernel based method to approximate the actual texture unit density estimation for Figure

A fault performance is defined as the departure from an acceptable range of an observed output or operating variable. Timeous detection of fault can determine whether the abnormal condition occurs [

PCA is a multivariate statistical technique used in MSPC and FDI perspectives [

The output TUD for sulphur flotation froth can be transformed to dynamic kernel weight vectors

Consider the weight matrix

Columns of matrix

Operating in (

The residual matrix

Finally the original data space can be calculated as

It is very important to choose the number of principal components

Having established a PCA model based on historical data collected when only common cause variation are present, multivariate control charts based on Hotelling’s

The sulphur flotation process is considered normal for a given significance level

New events can be detected by calculating the SPE or

The upper limit of this statistic can be computed as the next form:

When an unusual event occurs and it produces a change in the covariance structure of the model, it will be detected by a high value of

According to the formulae (

Through using the output TUD weight based PCA model, a criterion can be designed to detect the fault. The new statistical variable

To evaluate the proposed weight PCA model based fault detection approach, a series of industrial experiments are carried out in a Chinese sulphur froth flotation plant. In the test runs, froth image videos are captured through the previously introduced monitoring system in the last cleaner flotation cell. Subsequently, the froth videos are processed by the developed image analysis software which is capable of extracting froth features such as TUD online. Figure

Industrial froth images captured in a continuous time: (a) normal froth image, (b) fault A froth image, and (c) fault B froth image.

In practical sulphur flotation process experiments, the air flow rate and feed-in conditions are kept at a steady state so as to stabilize the production process. The adjustment of pulp level (or froth depth) becomes the major manipulating parameter, which directly determines flotation performance. As an indication of flotation performance, the froth texture feature is one of determinants of mineral separation efficiency. Bubbles with relative complex texture generally carry more valuable mineral particles, whose corresponding pulp level value is to be maintained to an acceptable bounded range. When one of the dominant operating variable pulp level is fluctuated, in this case the regulation of slurry underflow, froth surface visual features such as froth texture and color spectral information are reacting to the change of pulp level value. An increase in pulp level was considered, such that its simultaneous effect on froth texture unit distribution can be identified. As is shown in Figure

As for texture unit number calculation, normal kernel with following basis functions is selected according to formula (

By applying the kernel estimation on the TUDs of froth images in Figure

The 3D mesh plot of the output TUD. By applying the kernel estimation proposed in formula (

The weight PCA model applied in this case is established as

According to the formula (

The

Attempts have been made in calculating false alarm rate on a testing database. The testing data consist of 243 offline froth videos captured from the sulphur flotation industry during August of 2011. The fault detection is accomplished by a threshold criterion calculated from formula (

The detection performance of the testing database.

Samples with correct detection | Samples with incorrect detection | Accuracy rate (%) | |
---|---|---|---|

Normal status | 134 | 6 | 95.71 |

Fault A status | 48 | 5 | 90.57 |

Fault B status | 46 | 4 | 92 |

| |||

Total | 228 | 15 | 93.83 |

In this paper the description of texture unit number probability density distribution and its relationship to pulp level operational status are investigated. Unlike traditional discussion of froth texture feature focusing mostly on second-order statistics based on GLCM including angular second moment, entropy, moment of inertia, and moments of deficit and relevance, a nonparametric estimation method is proposed to describe the TUD more accurately based on the fixed normal kernel basis, and the fault performance is detected through the proposed

This work was financially supported by Key Program of Natural Science Foundation of China under Grant no. 61134006, National Science and Technology Pillar Program of China under Grant no. 2012BAF03B05, and National Science Fund for Distinguished Young Scholars of China under Grant no. 61025015.