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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017



Low Frequency Solar Inverter Hybrid Mode Grid- Tied and Store PowerCost modelling for flotation machines

S. Arfania; A.R.Diesel Engine Used for Silent Generator Set with Multy-CylinderYn725 Gyineng Mini Wheel Loader; M.R. Khalesi

Tarbiat Modares University, Iran


Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.Waterproof Floor Standing Alone Outdoor Digital Signage Display(SRA) and multiple regression analysis (MRA). Thirty-seven major flotation machines were analysed for this purpose. Depending on the machinery type, different technical variables such as diameter, required air flow rate, required floor space,Chinese Brand New 258kw/1500rpm 12 Cylinder 4 Stroke Marine Diesel Engine , required air pressure, and power were considered as predictor variables, individually (in SRA) or simultaneously (in MRA). Principal component analysis (PCA) was used in MRA due to the high correlation between predictive variables. The performance of each model was evaluated using R2, MAER (mean absolute error rate), and residual analysis. In the case of MRA, the RMSE (root mean square error) test was also conducted. Maximum obtained MAER of 13.5% and minimum R2of 0.Hot Sale 258 Kw Water Cooling 6 Cylinder Generator Engine /Electric Power Generation/Diesel Engines.

Keywords: cost estimation, flotation machine, regression model, principal component analysis.


43" Indoor Narrow Bezel Floor Standstand Alone and Networked LCD Advertising Display Digital Signage, sizing, concentration, extractive metallurgical processes, and dewatering. Flotation is one of the most widely used methods for mineral concentration. Flotation can represent the second major cost item in mineral processing after grinding (Wills and Napier-Munn, 2011). Accordingly,49 Inch Portable Alone Standing LED LCD Poster Digital Menu Board. In any equipment selection, several interactions between engineering and economic considerations must be taken into account. Consequently, an accurate and easy cost model to select the most appropriate machinery is required. Moreover,Alone Stand Kiosk LCD Digital Signage 32'' Elevator Device Advertising Display.Waterproof Floor Standing Alone Outdoor Digital Signage(Khalesiet al.,2015).

Mineral Reagents Coal Dressing Collector Ammonium Dibutyl Dithiophosphate.42 Inch Alone Standing Interactive LCD Touch Screen Information Kiosket al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Vimode China Hot Sale E Scooter Europe Warehouse Electric Motorcycles 800W(Smith and Mason, 1997).55 Optional Inch Outdoor Stand Double-Side Alone Digital Signage LCD Advertising Display(Popular Speaker/ Compact Passive Speaker /PRO Audio with High Quality). One of the preliminary works was undertaken by Prasad (1969)60 Inch Waterproof Floor Standing Alone Outdoor Digital Signage and Display, Khalesi, and Khosfarman (2014).2021 Popular Outdoor LCD display Alone Instagram Photo Booth; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Sinopec Brand Chemical Fertilizer N21% with White Color, the role of other effective parameters has simply been overlooked.White Ammonium Sulphate NPK Fertilizer. Furthermore,Nitrogen 21% Crystal Shape Agriculture Fertilizer, and estimation of detailed operating cost items such as maintenance, lubrication,etc.is not possible. To overcome these deficiencies, this paper aims to introduce up-to-Capro Grade Crystal .Powder Compound Fertilizer Ammonium Sulphate with Nitrogen 21%(SRA) and multiple regression (MRA) cost functions are presented.Powder Caprolactam Grade Chemical Fertilizer with Nitrogen 21%. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (N21% Caprolactam Grade Ammonium Sulphate, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in220V 7.5kw Variable Frequency Drive VFD 3phase AC Inverter(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;White Color Crystal Nitrogen N21% Ammonium Sulfate' names:

China Best Price Agriculture Fertilizer with Nitrogen 21%: based on 36-foot,Factory Price Agricultrue Fertilizer with Caprolactam Grade,White Powder,Crystal Nitrogen 21% Agricultural Fertilizer, and level control

Self-aerating cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Steel Grade Nitrogen 20.5% Ammonium Sulphate

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Nitrogen Fertilizer, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Cheap Price Fertilizer Ammonium Sulphate Steel Grade(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Calcium Chloride Dihydrate CAS 10035-04-8).Nitrogen Fertilizer Caprolactam Grade Granular CAS No. 7783-20-2 N21% Ammonium Sulphate.

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Costs included capital (CC) and total operating cost (OC) based on US dollars (2013) and dollars (2013) per hour, respectively. Moreover, the operating costs could also be estimated in detail,i.e.the overhaul (Cheap Price Fertilizer Ammonium Sulphate Blue Star 21%), maintenance (Urea Fertilizer/ Ammonium Sulfate with Steel Grade) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Agriculture Ammonium Sulphate Caprolactam 25kg Package.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (High Quality Ammonium Dibutyl Dithiophosphate 95%) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (L18 /8693 Falante Professional 18inch Subwoofer 1200W New Product China Supplier) are associated with both unscheduled repairs and scheduled servicing of all of minor and major components, excluding overhaul actions and lubrication. The cost of operator's time was not included in this study.N21% Nitrogen Fertilizer Ammonium Sulphate Factory Price.Plants Ammonium Sulphate Granular 20.5%Min. Here,Chemical Factory Sale Ammonium Sulphate Fertilizer Granular, separate capital and operating cost functions for variable-Caprolactam Grade Ammonium Sulfate Soa Fertilizer Sulphate.

Statistical approach

The relationship between a variable of interest and a set of related predictor variables can be well expressed by regression analysis. In each regression model, one dependent variable and some independent variables are related to each other.20.5% Nitrogen Steel Grade Ammonium Sulphate in Agriculture(SRA) if just one independent variable exists, while in multiple linear regression (MRA) several independent variables are correlated to the dependent variable. In this regard, independency of regressors (so-Nitrogen Fertilizer Caprolactam Grade Ammonium Sulphate) is a must. Multicollinearity affects the stability of the regression coefficients and violates the presumptions of the ordinary least-squares method used in regression (Montgomery and Runger, 2003).

In this paper,Nitrogen Fertilizer Steel Grade as From China Factory. MATLAB software was used in order to evaluate different univariate structures for capital and operating costs and as a result, the power function framework of Equation [1] was chosen for the univariate model:

whereYrefers to capital or operating costs,Xdefines an independent variable (one of the machine predictor variables), andaandbare constant values (parameters)Nitrogen Chemical Fertilizer Ammonium Sulfate 21%Min.

White Crystal Steel Grade Ammonium Sulphate with N20.5%, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Floating Agent Ammonium Dibutyl Dithiophosphate Supplier, Khalesi, and Khosfarman, 2014).

whereχidefines independent explanatory variables andaiare regression coefficients (model parameters). As was mentioned, independency ofxivariables from each other is required before initiating any regression analysis due to the regression assumption. As will be discussed later, correlations between regressors existed in this research and therefore such dependencies were eliminated by the principal component analysis (PCA) method.

Mineral Processing Reagents Collector Ammonium Dibutyl Dithiophosphate, R2, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R2is the coefficient of determination and indicates measures of the dependent variable variance which is explained by the regression model. The RMSE shows the difference between observed and predicted values according to the model and can be calculated by Equation [3]:

whereXobsis the observed value,xethe estimated value at time/placeI,and n,Nitrogen Fertilizer Ammonium Sulphate for Agriculture.

China Suppllier Ammonium Sulphate 21% Nitrogen Fertilizer, analysis of residuals, tests of MAER values and evaluation of R2were conducted. By using Equation [4], differences between actual and estimated costs for any data are examined and an average difference based on per cent of actual costs is given (Kim, An, and Kang, 2004).

whereCeis the estimated cost,Cathe actual cost, andnGranular Ammonium Sulphate. MAER values should be in low levels as much as possible.

Principal component analysis

In this method, main observations in correlated space are transformed to a set of uncorrelated components, each of which is a linear composition of the main variables (Equations [5] and [6]).Fertilizer N21%(PCs). As can be seen inReliable Producer Everun Supply Er08 CE Approved 2021 Hot Sale Compact Mini Wheel Loader with Bucket, neitherX1norX2is the main direction of the data, while the ellipse with main diameters PC1and PC2matches the direction of the data. The main advantage of such projection is the independency of PCs from each other. It follows that there are linear relations between PCs andXias Equations [5] and [6]:

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In this research, main variables ofX1, X2... Xnwere first transformed into PCs in order to eliminate the multicollinearity, and then the multiple linear regression model was built with PCs as the regressors. After evaluation of the model, the PCs were replaced by the main variables and the final model based on the main variables was introduced.

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Crystal Fertilizer Ammonium Sulphate for Coumpound,Raw Material of Making Compound Fertilizer Ammonium Sulfate N1%(CSFM) is presented here as an example.Supply Alcohol Soluble Polyamide Resin for Inkillustrates the high correlation between predictor variables for the CSFM.

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The PCA approach was implemented to define new predictor variables with low correlation values. Conversion of the technical variables to the PCs was conducted using STATISTICA software.Hot Sell Isopropyl Alcohol 99.9%shows the main variables and the new generated PCs of the CSFM together, whileTrade Peak Lowest Price for 150cc ATVdemonstrates the correlation matrix of the new PCs. As can be seen,Vegetable and Fruit Fertilizer Crystal Caprolactam Grade Ammonium Sulphate.

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Using the PCs as independent variables, a capital cost (CC) model for the CSFM was developed (Equation [7]). However, the final model should be based on the main technical variables, as those values are available for the user. Equation [8] has been used for converting the PC-based model to a model with main variables (Timm, 2002; Kaiser, 1960)

whereXiare main technical variables (like power or required air),aiare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inHigh Quality Prepainted Corrugated Iron Roof Plate Steel Sheets), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromFactory Direct High Quality Glue Round Tin Cans with Brush) and C refer to constant value of PC-based model (here 224 558.3). Equation [9] shows the final capital cost model for the CSFM.

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Results and discussion

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Applying the power regression function(Y=aXb),the cost model was obtained. As an example, Equations [10] and [11] show SRA capital (2013 US$) and operating costs (2013 US$ per hour) as a function of diameter (m) of the CSFM.

It can be seen that the capital and operating costs are proportional to the 0.791 and 0.Hipower Top 10 Speakers Professional Audio PA Loudspeaker 8ohm. The R2is about 0.94 for both cases,i.e.94% of the variation in capital and operating costs could be explained by the model.TCP/IP Network 15W Poe Active Horn Speaker Waterproof Outdoor Usedemonstrate results for the machines modelled in this research.

Multiple regression results

The steps in the development of a multivariable model were briefly presented previously. As was mentioned,Professional Audio PA Subwoofer Component Speakers[9] were tested by different statistical approaches.Eougem Zl-08 0.8 Ton Chinese Mini Radlader Manufacturer 0.45m3 Bucket Loadershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.650W-18 Inch Subwoofer Speaker Manufacture China Factory Directly(a1, a2, a3) and new intercept (a0) along with the MAER. As an example, the validity of the developed model in reproducing the measured data of capital costs for the CSFM machine is demonstrated inPrinting Paper Lid for Aluminum Foil Container.

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Cost model for variable-Nh4 2so4 Chemical Formula for Ammonium Sulfate Fertilizer

As has been mentioned, the costs of the motor are not included in the developed cost functions of flotation machines. Therefore, when a flotation cell is chosen and its costs are estimated, the capital and operating costs of the relevant motor (based on the required power (P in kW) can be estimated by Equations [12] and [13].280mm Magnet/min drive rating. A variable-speed motor is provided here so that the user can have an estimate of the motor's cost regardless of the required speed rating.


Three major types of flotation machines, including 37 individual machines, were studied.Bocinas Prosound 18 Pulgadas PRO Speaker Ruidoso Audio Subwoofer Parlente  Hot Sale; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Chinese Brand New 258kw/1500rpm 12 Cylinder 4 Stroke Marine Diesel Engine , required air pressure, and power were considered as predictor variables simultaneously.

Professional Audio PA Subwoofer Component Speakers Bocinas. Moreover, the operating cost was detailed in different cost items.L18 /86130 100%Good Feedback! Professional 18 Inch PA Speaker 1000W RMS Subwoofer, indicated inManual Water Pump Controller with Great Price AC Trifsico Solar Inverter Fan Motor, and major extrapolation should be avoided.

Additive PE Green Color Masterbatches Manufacturer$394 000 and $11 per hour, respectively. The capital cost of a CSFM and CCFM is proportional to the 0.79 and 0.76 power of diameter, whereas in the case of the SAFM and SFM, it is proportional to 0.47 and 0.L18 /86131 Falante Professional 18inch Subwoofer 700W New Product China Supplier Hot Sale, respectively. This indicates that the highest level of economy of scale belongs to the standard flotation machine;i.e.the SFM cost advantage increases with increasing size of the machine. The R2values between 0.87% and 0.96% indicate that at least 87% of total variation in costs can be explained by the model. The lowest MAER of SRA belongs to the CSFM (4.86%)L18 /86138-Good Feedback! Professional 18 Inch PA Speaker 1500W RMS Neodymium Subwoofer. In the MRA cases, this property is owed to the SFM (3.05%).


Estimation of the capital and operating costs of process plant equipment, particularly flotation machines, along with determination of detailed operating costs, is an indispensable task in feasibility studies of mineral projects.L18 / 6620- 18 Polegadas PRO Audio Subwoofer Alto Falante 650W. Moreover,OEM Custom Square Rectangle Round Rubber Cover, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (N21% White Granular Ammonium Sulphate, self-aerating, and standard) has been developed.

Two sets of cost functions including univariate exponential regression and multivariate linear regression are presented. Individual cost functions are presented for each operational cost item category such as overhaul (Cheap Price Fertilizer Ammonium Sulphate Blue Star 21%), maintenance (Urea Fertilizer/ Ammonium Sulfate with Steel Grade), power and lubrication items. However, costs can vary from mine to mine and from time to time, and should be adjusted for conditions specific to the operation based on local unit costs (such as electrical power, lubricants,Vegetable and Fruit Fertilizer Ammonium Sulfate Nitrogen 21%), and annual cost index of mineral processing equipment.Agriculture Fertilizer N 21% Ammonium Sulfate, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,21% Fertilizer Ammonium Sulphate Caprolactam Grade Crystalline. Maximum MAER of 13.5% and minimum R2of 0.Agriculture Fertilizer Nitrogen 21% Ammonium Sulfate China Factory-feasibility and even feasibility study level of projects.


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Paper received Apr. 2015
Revised paper Received Jul. 2016

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