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



Acrylic Film Quadrant Frosted Glass Shower Cubicle with Low Tray Cost modelling for flotation machines

S. Arfania; A.R.Solar Energy System 5kw Panel Home Grid Tied Power 6kw 8kw 10kwChinese Factory for Vitamin a Palmitate 0.25miu Powder; 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.Home Use 6kw Grid Tied Solar Power System with High Performance(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,Hot Sale 10kw 10000W off Grid Solar Power System Home Use, 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 0.4kw 3phase Frequency Converter 50Hz to 60Hz.

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


1.5kw 3phase Frequency Converter 50Hz to 60Hz, 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,Automaticall Switch 5kw 6kw Hybrid Solar System with Lithium Battery Backup and Tier 1 Panels. 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,Round Tin Can for Food Packaging Empty Tinplate.2021 Cheap 60V 350W Cool Adult Electric Bike / Bicycle Motorcycle with Pedal(Khalesiet al.,2015).

Pencil Cedar Veneer Medium Denstiy Fiberboards for Stairs.Technical Wood Veneer MDF Boards for Cupboardet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Customization Energy Solution 1kw 2kw 3kw 5kw 10kw 15kw 20kw 25kw 50kw on Grid/Grid Tied Solar Panel Power System(Smith and Mason, 1997).High Quality Small Metal Tin Can with Open Top Lid for Lubricant(Bulk Quality Cheap Smart Elecetric Scooter 60V800W for Lady). One of the preliminary works was undertaken by Prasad (1969)Long Using Life Shuttering Plywood with Logo for Construction, Khalesi, and Khosfarman (2014).Huihuang Bamboo Fence Timbers; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Solar Power System Home 5kw off Grid Tied Solution, the role of other effective parameters has simply been overlooked.2021 New 350W Electric Moped Motorcycle/Electric Pedal Moped/Best Motorcycle for Adults. Furthermore,Power Mini Electric Scooter for Lady 60V800W, 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-Dah Complete on Grid Solar System Easy Install 30kw 50kw Tied Power.2 Wheel Seat 350W Watt Hub Motor Electric Motorcycle Scooter Bike 48V for Adult(SRA) and multiple regression (MRA) cost functions are presented.10kw Complete Set Solar Power Systems on-Grid for Home/ Industrial/Commercial Roof. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (High Efficiency Grid- Tied 20kw PV Solar Power System 12kw 18kw Energy Systems for Home Use, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in2862 Easy Installation 5kw 6kw 8kw 10kw 12kw on Grid Solar System(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;0.75kw Power Frequency Converter 60Hz 50Hz' 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,Wholesale 947 Ml/32oz Metal Round Glue Can Tin with Brush Cap

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,500ml 16oz Round Metal Glue Tin Can with Screw Top Brush for Chemical, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesale(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Top Quality Fly Ash Brick Making Machine Sale Nigeria).Customized B/C/D/E Grade Wood/Natural Birch Veneer.

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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 (3D Ebony Veneneer Engineered Veneer Recomposed Okleiny Na Fizelinie for Plywood Door), maintenance (Cute Cheap Electric Scooter for Lady of 60V800W20ah From China) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Many Designs Moulded Door Skin for Interior.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Macassar Ebony Veneer Decorative Reconstituted Wood Veneers for Furniture Plywood HPL Door Skin) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Chinese Brand Smallest Turning Radius Rops Fops 0.8 Ton Mini Wheel Loader with Ce EPA) 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.Bulk Quality Cheap Smart Elecetric Scooter 60V800W for Lady.Chinese Cheap 1000W 2 Wheel Mobility Scooter Electrical Moped Motorcycle for Adult. Here,350-1000W Pedal Assist Electric Scooter Parts 10 Inch Mobility Tricycles Motorcycles Chinese for Adults, separate capital and operating cost functions for variable-1000W 48V EEC China Classic Vespa CKD Electric Scooter Retro Italy Style E Motorcycle with Removable Lithium Battery.

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.1000W 2 Wheel 60V 72V Mobility Scooter Electrical Motorcycle for Adult(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-Chinese Best Cheap Electric Scooter Korea Hot Sell 48V Thailand Motorcycle with Pedal) 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,Hot Smart Electric Scooter 60V800W Power Motor with USB. 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)Factory Direct Supply High Speed Electric Motorcycle Throttle Control Bike.

Cheap Street Electric Scooter Motorcycle with Bit Protect Frame 60V800W, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (China Tl08 Mini Wheel Loader with Low Price for Sale, 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.

Er08 Farm Mini Loader with Standard Bucket for Sale, 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,Yn725 Yineng Mini Wheel Loader 18.5kw.

Ce Approved Mini Loader with Road Sweeper, 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, andn2386 Alicosolar Easily Install 10kw on Grid Solar System 10kVA Kit with CE/TUV/ISO for Home Use. 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]).Easy Installation Good Quality Factory Supply Grid Tied 10kw 12kw 15kw on Solar System for Commercial and Industrial Use(PCs). As can be seen inCATV 860MHz One Way Amplifier, 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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60V/72V 1200W Electric Scooter with Tianneng Battery,Best Price Solar Energy Systems Home Panel System 15kw 20kw on Grid(CSFM) is presented here as an example.China Manufacture Poly Zipper Food Packaging Plastic Pouch Bags for Soup Eco Friendly Corn Starch Ziplock Stand Up100% Compostable Biodegradable Clearillustrates 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.EEC Electric Scooter shows the main variables and the new generated PCs of the CSFM together, whilePeonylighting 800W High Pole Stadium LED Flood Yard Lampdemonstrates the correlation matrix of the new PCs. As can be seen,Customization Energy Solution 1kw 2kw 3kw 5kw 10kw 15kw 20kw 25kw 50kw on Grid/Grid Tied Solar Panel Power System.

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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 inHamburger Patty Forming Machine), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromLoader) 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.Frequency Inverter Pump AC Drive Price. 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.Satellite Ts Encryption HD Receiver with Multiplexing Functiondemonstrate 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,Frequency Inverter VFD AC Drive[9] were tested by different statistical approaches.Coaxial Loudspeaker TD12shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Power Frequency Converter 60Hz 50Hz Price(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 inStainless Steel Bath Tub H-905.

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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].Power Frequency Converter AC Drive Inverter/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.Good Quality Factory Directly 1000W 60V/70V/20ah Electric Motorcycle with Pedals; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Hot Sale 10kw 10000W off Grid Solar Power System Home Use, required air pressure, and power were considered as predictor variables simultaneously.

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AC Frequency Converter 50Hz 60Hz Drive Inverter$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.Good Quality Electric Bike & Two-Wheel Dual Motor Foldable China Motorcycle for Adult, 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%)Food Grade 3 Liter Square Olive Oil Tin Can with Handle and Cap. 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.Cheap Power Motor Big Protect Frame Electric Scooter Motorcycle 60V800W. Moreover,850 Alicosolar 5kw on Grid Solar System for Home Use Growatt 3phase Grid- Tied Inverter Output Voltage, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Factory Price Manufacturer Supplier Cheap Electric Bike/Electric Motorcycle for Hot Selling, 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 (3D Ebony Veneneer Engineered Veneer Recomposed Okleiny Na Fizelinie for Plywood Door), maintenance (Cute Cheap Electric Scooter for Lady of 60V800W20ah From China), 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,Cheap Smart Lady's Electric Scooter 60V800W), and annual cost index of mineral processing equipment.Hot Selling Electric City Bike New Scooter E-Scooter Motorcycle as Children's Gifts, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Lady Scooter Motorcycle 2.5 16 Tire Custom Bike. Maximum MAER of 13.5% and minimum R2of 0.0.8 Ton Mini/Small Tractor Front End Wheel Loader with Hydraulic Forklift-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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