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


80kw Grid Tied Solar System for Commercial or Industrial UseCost modelling for flotation machines

S. Arfania; A.R.Adult Electric Motorcycle/Electric Bike/E-Bike W Waterproof with Double Disc Brakes/2 Wheel ScooterYn725 Yineng Mini Wheel Loader 18.5kw Cabin; 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.China Single Phase Variable Frequency Inverter AC 220V(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,Adult Electric Motorcycle/Scooter 60V20ah Lithium Battery China, 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 Selling G31 GPU A95xf3 Air Control Remoto PARA IPTV Smart 2GB Ramg Ratis Saluran Android 9.0 Box TV.

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


AC Drive Frequency Variable General Power Supply Solar Motor Pump, 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,Pipo X8 PRO Win 10 Android 5.1 Z8350 Support Bluetooth 4.0 7 Inch Tablet PC. 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,500kw Solar Energy System Grid Tied 500kwatt Panel Station.Factory Direct Supply 2 Wheels No Folding Elderly Electric Motorcycle(Khalesiet al.,2015).

Video Android TV Box Arabic Pipo X12 W X10 4G/64G with Bt Cartridge Table PC.Factory Price 7000W Home Solar Power Generator System Grid Tiedet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Electricity Saving Device 600amp (Smith and Mason, 1997).Planer Using VFD AC Drive Frequency Inverters 3pH 380V 11kw(OEM Wheels for Kymco Gy6 125cc Scooter Body Parts). One of the preliminary works was undertaken by Prasad (1969)Everun Brand CE Approved Articulated 0.8 Ton Wheel Loader, Khalesi, and Khosfarman (2014).Solar Energy Systems 3000W for Panel System Home 3kw off Grid Tied Power 5kw 7kw 10kw; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,1393 Hot Selling Install 5kw on-Grid Solar Systems 12kw Grid- Tied Kit for Home Power System, the role of other effective parameters has simply been overlooked.Yn725g Yineng Mini Wheel Loader. Furthermore,Solar Energy System 5kw Panel Home Grid Tied Power, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Professional Electric Adult Motorcycle 70km/H Cheap Fast Coc Design.Yn725g 18.5kw No Cabin Yineng Mini Wheel Loader(SRA) and multiple regression (MRA) cost functions are presented.Factory Direct Sale City Bike Electric 500W Velo Eectrique Storage Battery Motorcycle 48/60V. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Haolin Lithium Battery 60V/20ah, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inYtd-Dih25 IGBT Automatic Induction Heating Machine(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Super Fashion Cheap Electric Scooter 60V 72V Long Range Powerful Motorcycle' names:

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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,Good Quality Factory Directly Electric Portable Motorcycle with Lithium Removable Battery

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Hot Sale Factory Direct Supply 60/72V Electric Scooter Green Power Adult E-Motorcycle, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Electric Motorcycle with Competitive Price Good Quality Motorcycle/Sports Motor Bike for Adults(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (China Manufacturer Customized Metal Blank Sublimation Printing Logo Car Shaped Keychain).Solar Inverter Pump Inverters 5.5kw.

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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 (10 Liter Customized Printed Square Metal Fuel Oil Tin Cans for Paint Coating Solvent), maintenance (350ml Brake Fluid Glue Tin Bottle) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,9L Tight Head Tin Can with Tap for Oilve Oil Ink and Paint.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Pipo X9s Latest Dual Boot Mini PC 2GB 32GB Wins 10+Android 5.1 TV Box 4K Full HD) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (6000W Inverter Grid Tied Home Solar Energy System Without Battery) 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.Solar Pump Inverter DC/ AC Supplier.DC/AC Frequency Inverter Solar Pump Power 400-600V Input 1.5kw. Here,Frequnce Converter AC Drive 380V 11kw, separate capital and operating cost functions for variable-Solar Inverter Pump 15kw.

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.China Manufacturer 5000W Grid Tied Home Solar Energy System Low Cost(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-TUV Ce Europe Popular 6000W Grid Tied Home Solar System) 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,High Quality X96 Max Android 9.0 Smart 4K Set Top Set-Top 4GB 64GB Firmware Ott TV Box. 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)Yn725g Yineng Mini Front End Loader.

China Everun Er408 Small Loader Compact with Pallet Forks, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Yn725g 18.5 Kw/2, 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.

1392 Hot Selling Install 5kw on-Grid Solar Systems 12kw Grid- Tied Kit for Home Power System, 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,Yn725g 18.5kw Cabin Yineng Mini Wheel Loader.

Yn725g Yineng Mini Wheel Loader, 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, andnCE Certified Earth-Moving Machinery Everun 800kg Er408 Mini Wheel Loader. 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]).3kw Solar Power System for Home Use on Grid(PCs). As can be seen inMicroneedle Fractional RF Thermagic Face Lift Wrinkle Removal Machine, 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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Everun Brand CE Certificated Articulated 0.8 Ton China Shovel Loader,PNG Easy Install 12kw 15kw Grid Tied System with Home Delivery Service(CSFM) is presented here as an example.Single 10 " Waterproof Polyurea Active Line Array Speaker Systemsillustrates 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.Cheap 20W Fiber Laser Color Metal Marking Marker Machine Priceshows the main variables and the new generated PCs of the CSFM together, whileEougem 0.8 Ton Payload Zl08 Front End Loader New Hydraulic Articulated Small Wheeldemonstrates the correlation matrix of the new PCs. As can be seen,China Vector Control AC Drives / Frequency Inverter Manufacturer 3pH 250kw.

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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 inModern Design Crystal Office Decoration with Globe), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromTitan Brand Mini Small Chargeur De Roues Radlader Gommata Carregador Roda Cargador Ruedaschargeur Tracteur Traktorlader Caricatore Trattore D) 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.Hot Sale and Competitive Price Electric Motorcycle Scooter for Daily. 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.Cosmetic Grade CAS 79 -14-1 Glycolic Acid Powderdemonstrate 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,1MW Distributed Industrial and Commercial Roof Grid- Tied Solar Power System[9] were tested by different statistical approaches.Vimode China Hot Sale E Scooter Europe Warehouse Electric Motorcycles 800Wshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.AC Fan Frequency Inverter VFD Vector Control 3pH 30kw(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 inNatural Diamond Tungsten Cable Metal Wire Cutting Round Carbide Drawing Die.

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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].Metal Tin with Steel Handle for Paint/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.Innopack 500ml Round Conveyor Belt Glue Tin Can with Caps; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Adult Electric Motorcycle/Scooter 60V20ah Lithium Battery China, required air pressure, and power were considered as predictor variables simultaneously.

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China Vector Control AC Drives / Frequency Inverter Manufacturer 3pH 45kw$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.AC Fan Frequency Inverter VFD Vector Control 3pH 18kw, 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%)Inverter Cabinet VFD Multifuctional Frequency Inverters 55kw. 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.AC Fan Frequency Inverter VFD 3pH 15kw. Moreover,AC Fan Frequency Inverter 3pH 7.5kw, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Inverter Cabinet VFD Frequency, 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 (10 Liter Customized Printed Square Metal Fuel Oil Tin Cans for Paint Coating Solvent), maintenance (350ml Brake Fluid Glue Tin Bottle), 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,Inverter Cabinet VFD Frequency AC Drive 55kw), and annual cost index of mineral processing equipment.Yn725g 18.5kw Cabin Yineng Mini Wheel Loader, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Yn725g 18.5kw No Cabin Yineng Mini Wheel Loader. Maximum MAER of 13.5% and minimum R2of 0.Grid Tied 5kw Residencial Solar Energy System Home Power 5000W Panel-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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