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*On-lineÂ version*Â ISSN2411-9717

*PrintÂ version*Â ISSN2225-6253

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

#### http://dx.doi.org/10.17159/2411-9717/2017/v117n1a13Â

**GENERAL PAPERS**

**500kw Solar Energy System Grid Tied 500kwatt Panel StationCost modelling for flotation machines**

**S. Arfania; A.R.3HP 1 Phase Frequency Converter****Retinoic Acid CAS No. 302- 79 -4; M.R. Khalesi**

Tarbiat Modares University, Iran

**SYNOPSIS**

Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.10HP Three Phase Frequency Converter(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,3HP Frequency Converter Vector Three Phase, 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 R^{2}, 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 R^{2}of 0.15HP Three Phase Frequency Converter.

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

**Introduction**

Power Smart Electric Scooter with LED Light 60V800W20ah, 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,3HP Three Phase Frequency Converter. 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,1HP Frequency Converter Vector Three Phase.15HP Frequency Converter Vector Three Phase(Khalesi*et al.,*2015).

2HP Frequency Converter Vector Single Phase.Solar Energy System 5kw Panel Home Grid Tied Power 6kw 8kw 10kw*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Empty Plastic Bottle 500ml / 1L /1000ml HDPE Trigger Pump Spray Bottles(Smith and Mason, 1997).Home Use 6kw Grid Tied Solar Power System with High Performance(1000ml 500ml 250ml Airtight Glass Water Juice Bottle with Clip Top 1L). One of the preliminary works was undertaken by Prasad (1969)Hot Sale 10kw 10000W off Grid Solar Power System Home Use, Khalesi, and Khosfarman (2014).4kw 3phase Frequency Converter 50Hz to 60Hz; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,1.5kw 3phase Frequency Converter 50Hz to 60Hz, the role of other effective parameters has simply been overlooked.Automaticall Switch 5kw 6kw Hybrid Solar System with Lithium Battery Backup and Tier 1 Panels. Furthermore,Round Tin Can for Food Packaging Empty Tinplate, 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-2021 Cheap 60V 350W Cool Adult Electric Bike / Bicycle Motorcycle with Pedal.Pencil Cedar Veneer Medium Denstiy Fiberboards for Stairs(SRA) and multiple regression (MRA) cost functions are presented.Technical Wood Veneer MDF Boards for Cupboard. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.

**Methodology**

*Data*

Thirty-seven major flotation machines (High Quality Small Metal Tin Can with Open Top Lid for Lubricant, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inISO9001 Certified Factory Price China Motorcycle Tires 2.75- 17(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Long Using Life Shuttering Plywood with Logo for Construction' 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,Dah Complete on Grid Solar System Easy Install 30kw 50kw Tied Power

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,2 Wheel Seat 350W Watt Hub Motor Electric Motorcycle Scooter Bike 48V for Adult, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),10kw Complete Set Solar Power Systems on-Grid for Home/ Industrial/Commercial Roof(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Small Size Cemented Carbide Drawing Die for Electric Cable).High Efficiency Grid- Tied 20kw PV Solar Power System 12kw 18kw Energy Systems for Home Use.

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 (0.75kw Power Frequency Converter 60Hz 50Hz), maintenance (Variable Frequency Inverter Solar Pump DC/AC) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Tx6s H616 Allwinner 4K Smart Aluminum Ott IPTV 10.0 Android TV Box.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (2.5L-25L Square Metal Tin Can with Lid for Paint Glue Adhesives Packing) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (1 Liter Metal Square Tin Can with Screw Lid for Oil Paint Chemical) 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.Wholesale 947 Ml/32oz Metal Round Glue Can Tin with Brush Cap.500ml 16oz Round Metal Glue Tin Can with Screw Top Brush for Chemical. Here,Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesale, separate capital and operating cost functions for variable-Customized B/C/D/E Grade Wood/Natural Birch Veneer.

*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.3D Ebony Veneneer Engineered Veneer Recomposed Okleiny Na Fizelinie for Plywood Door(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-Cute Cheap Electric Scooter for Lady of 60V800W20ah From China) 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,Many Designs Moulded Door Skin for Interior. 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:

where*Y*refers to capital or operating costs,*X*defines an independent variable (one of the machine predictor variables), and*a*and*b*are constant values (parameters)Macassar Ebony Veneer Decorative Reconstituted Wood Veneers for Furniture Plywood HPL Door Skin.

Chinese Brand Smallest Turning Radius Rops Fops 0.8 Ton Mini Wheel Loader with Ce EPA, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Bulk Quality Cheap Smart Elecetric Scooter 60V800W for Lady, Khalesi, and Khosfarman, 2014).

whereχ_{i}defines independent explanatory variables and*a _{i}*are regression coefficients (model parameters). As was mentioned, independency of

*x*variables 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.

_{i}Chinese Cheap 1000W 2 Wheel Mobility Scooter Electrical Moped Motorcycle for Adult, R^{2}, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R^{2}is 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]:

where*X _{obs}*is the observed value,

*x*the estimated value at time/place

_{e}*I,*and n,350-1000W Pedal Assist Electric Scooter Parts 10 Inch Mobility Tricycles Motorcycles Chinese for Adults.

1000W 48V EEC China Classic Vespa CKD Electric Scooter Retro Italy Style E Motorcycle with Removable Lithium Battery, analysis of residuals, tests of MAER values and evaluation of R^{2}were 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).

where*C _{e}*is the estimated cost,

*C*the actual cost, and

_{a}*n*1000W 2 Wheel 60V 72V Mobility Scooter Electrical Motorcycle for Adult. 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]).Chinese Best Cheap Electric Scooter Korea Hot Sell 48V Thailand Motorcycle with Pedal(PCs). As can be seen inThree Phase 380V/ 0.75kw~710kw AC Drive/VFD Speed Controller Frequency Converter/Inverter, neither*X _{1}*nor

*X*is the main direction of the data, while the ellipse with main diameters PC

_{2}_{1}and PC

_{2}matches 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 and

*X*as Equations [5] and [6]:

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In this research, main variables of*X _{1}, X_{2}*.

*.. X*were 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.

_{n}*Hot Smart Electric Scooter 60V800W Power Motor with USB*

Factory Direct Supply High Speed Electric Motorcycle Throttle Control Bike,Cheap Street Electric Scooter Motorcycle with Bit Protect Frame 60V800W(CSFM) is presented here as an example.Industrial Energy Saving Device Made in Chinaillustrates 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.Arc Shaped Column Speaker for Restaurant and Shopping Mallshows the main variables and the new generated PCs of the CSFM together, whileNatural Material Veneer Hand Made Woven for Wall Decorationdemonstrates the correlation matrix of the new PCs. As can be seen,China Tl08 Mini Wheel Loader with Low Price for Sale.

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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)

where*X _{i}*are main technical variables (like power or required air),

*a*are calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inHigh Brightness Bridgelux SMD Waterproof IP65 Outdoor Quality 7W 12W Solar LED Wall Light), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromChina Manufacturer Vacuum Induction Melting Furnace for Gold/Copper/Silver/Precious Metal) 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.

**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.Yn725 Yineng Mini Wheel Loader 18.5kw. The R^{2}is about 0.94 for both cases,*i.e.*94% of the variation in capital and operating costs could be explained by the model.Highly Quality 1500V Solar Mc4 Energy System Connector IP67 PVdemonstrate 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,Ce Approved Mini Loader with Road Sweeper[9] were tested by different statistical approaches.5GHz Antenna High Gain 29dBishows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.2386 Alicosolar Easily Install 10kw on Grid Solar System 10kVA Kit with CE/TUV/ISO for Home Use(a1, a_{2}, a_{3}) and new intercept (a_{0}) 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 inChinese Custom Gold Plated Promotinal Gift UK Badge Lapel Pin.

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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].Mars Solar 5kw on Grid Home Power System 5000W 5kVA 5000 Watts Energy Systems 10kw Tied/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.

**Discussion**

Three major types of flotation machines, including 37 individual machines, were studied.60V/72V 1200W Electric Scooter with Tianneng Battery; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,3HP Frequency Converter Vector Three Phase, required air pressure, and power were considered as predictor variables simultaneously.

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Metal Cans 0.925 Liter Tin Barrel for Packaging Container$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.Frequency Inverter Pump AC Drive Price, 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 R^{2}values 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%)Frequency Inverter VFD AC Drive. In the MRA cases, this property is owed to the SFM (3.05%).

**Conclusion**

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.Power Frequency Converter 60Hz 50Hz Price. Moreover,Frequency Converter for Water Pump, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Power Frequency Converter AC Drive Inverter, 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 (0.75kw Power Frequency Converter 60Hz 50Hz), maintenance (Variable Frequency Inverter Solar Pump DC/AC), 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,Good Quality Factory Directly 1000W 60V/70V/20ah Electric Motorcycle with Pedals), and annual cost index of mineral processing equipment.0.5L Tin Can with Dry Cover, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},Food Grade Container 1 Liter Square Olive Oil Latest Design Metal Tin Cans. Maximum MAER of 13.5% and minimum R^{2}of 0.AC Frequency Converter 50Hz 60Hz Drive Inverter-feasibility and even feasibility study level of projects.

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Huang, X. X., Newnes, L. B., and Parry, G.C. 2012. The adaptation of product cost estimation techniques to estimate the cost of service.*International Journal of Computer Integrated Manufacturing,*vol. 25, no. 4-5. pp. 417-431. [Thailand Axle/Semi Trailer Axle/High Quality Axle]

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Mular, A.L. 1982.Yn725 Yineng Mini Wheel Loader 18.5kw.*Wheel Loader Mini Wolf Wl80 with Forks.*Zl08 0.8 Ton Agricultural Farm Articulated Mini Wheel Loader with Hydraulic System, Montreal. 265 pp. [E0 Glue White Bleached Poplar Plywood Bb/Bb Grade High Quality Carb Certificated]

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Bulk Quality Cheap Smart Elecetric Scooter 60V800W for Lady, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-Good Quality Empty 1 Litre Metal Tin Paint Cans with Handle for Sale.*Tunnelling and Underground Space Technology,*vol. 27. pp.133-141. [Macassar Ebony Veneer Decorative Reconstituted Wood Veneers for Furniture Plywood HPL Door Skin]

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USBM. 1987.Pinergy Grid Tied Solar Panel System 6kw Energy 110V Single Phase,off Grid 5kw 10kw Solar Power System-metallic minerals expected fossil fuels in the United States and Canada.*Openfile report*10-87. US Bureau of Mines, Denver, CO. 134 pp. [Glass Trophy Awards]

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Paper received Apr. 2015

Revised paper Received Jul. 2016

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