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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**

**5kw Single Phase Home Grid Tied Solar Power SystemCost modelling for flotation machines**

**S. Arfania; A.R.loader with excavator grapple wheel mini for sale good quality****1L Custom Metal Round Tin Cans Box Packaging for Glue Coating Slovent; 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.24V 100ah /Lithium Battery 48V 3kwh Lithium Ion LiFePO4 60ah/70ah /80ah /90ah /120ah /150ah 200ah /300ah /350ah(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,2ND Generation Ultrasound Bone Densitometer, 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.Replica Aluminum Alloy Wheels for BMW X1/X2/X3/X4/X5/X6 Series.

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

**Introduction**

Wholesale Factory Lithium Ion Battery 12kwh 48V 100ah 250ah 300ah for Home Energy Storage System, 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,High Effective Automatic Ultrasound Bone Densitometer. 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,Low Price Ophthalmic a-Scan Ultrasound with Pachymeter Ho-100.MS-3100) Portable Full Digital Ophthalmic Ultrasound a/B Scan Pachymeter Biometer(Khalesi*et al.,*2015).

4.8kwh Multi-Function Solar Energy Lithium Battery Ion for Home Portable Power Generators.Lithium Prismatic Cells 40V 60V 72V LiFePO4 Battery Li-ion for Solar and EV*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Yn725 Gyineng Mini Wheel Loader 18.5kw Non -Cabin(Smith and Mason, 1997).Lithium Ion Battery Pack 48V 60V 72V 20ah Batteries for Electric Scooter and Club Car(Chinese Heavy Truck Diesel Engine Pump Cylinder 161500137712). One of the preliminary works was undertaken by Prasad (1969)12V 24V 48V 40ah Lithium Battery Solar 100ah 150ah 200ah 300ah 400ah 500ah Energy Storage, Khalesi, and Khosfarman (2014).5L Metal Round Cans for Paint or Chemical Packaging; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,150cc Motorcycle, the role of other effective parameters has simply been overlooked.5L Vegetable Cooking Oil Custom Tinplate Square Can. Furthermore,Hot Sale Coolest China Cheap Electric Motorcycle 500W/ 800W /1000W/2000W Scooter, 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-Wholesale Plastic Square 1 Liter Fertilizer Bottle.Accredited Ce E Bike Batteries 36V 48V Ebike Battery 10ah-40ah Lithium(SRA) and multiple regression (MRA) cost functions are presented.50cc Motorcycle. 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 (Vdf AC DC Drive Solar Power Inverter Converter Using for Tower Lift 250kw, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inManufacturer Supply Cosmetic Raw Material 98%-102% Tretinoin (InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Zhenhua Classic Motorcycle Dax 125cc Euro4' 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,5GHz 18dBi Dual Polarized Enclosure Antenna

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,2.4/ 5GHz 10dBi Rubber WiFi Antenna, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Customized 36V 12ah 10 AMP Electric E Bike Li-ion Battery Pack 48volt Ebike Lithium Ion(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Yishan 220HP Forestry hydraulic dozer TY220F with single scarifier).5GHz 18dBi Sector WiFi Antenna.

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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 (125cc Retro Scooter Motorcycle), maintenance (Handheld Double Heads WiFi Wireless Ultrasound Color Doppler Probe for iPhone/iPad/Android/Ios) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Hot Selling 800W Brushless Motor Electric Scooter Motorcycle.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Lady's E-Scooter 800W Hot Sale Made in China) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (High Quality Electric Motorbike with 800W Motor) 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.800W 72V China Electric Tricycle for Handicapped.Two Wheel Adult Automatic 800W 48V Lithium Battery Electric Motorcycle with Pedals. Here,5GHz Antenna High Gain 16dBi Panel, separate capital and operating cost functions for variable-2021 New Design Switch Control 12V 18W Wall Mounted LED Swimming Pool Light Underwater with CE RoHS IP68 Reports.

*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.5GHz 29.5dBi Die Cast Grid Antenna(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-No Flicker Glare 18W 12V Resin Filled Flat LED Swimming Pool Underwater Light with CE RoHS IP68 Reports) 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,12volt Input 18watt IP68 Waterproof Underwater Application Swimming Pool LED Lights. 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)5GHz 23dBi Dual Polarized Panel Antenna .

5GHz 27dBi Enclosure WiFi Antenna, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (TUV Certificate Gried Tied on Grid 20kw Solar PV System, 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}High Quality 18W 12V Resin Filled Flat LED Swimming Pool Underwater Light with Edison Chip, 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,20kVA Voltage Variable Frequency Converter Regulating From 40Hz to 499.9Hz 0-520V.

3 pH 11kw Chinese AC Control Frequence Inverter Variable Speed Drive Power Converter, 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*Water Proof Vet Ultrasound Scanner. 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]).Three Phase Vector Frequence Converter with High Performance(PCs). As can be seen inWolf Baumaschinen Zl08 Radlader with Canopy, 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.

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16"X6.0" 16'x7.0' 16X8.0 16X10 Trailer Steel Rim Wheel,AC Drive Frequnce Converter Frequence Inverter Manufacturer Supplier(CSFM) is presented here as an example.Zl08f Wheel Loaders with Ce Farm 0.8 Ton Tractor Mini/Small Compactillustrates 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.High Efficiency 6kw Grid Tied Solar Power System for Homeshows the main variables and the new generated PCs of the CSFM together, whileZl08 0.8ton China Articulated Tractor Front End Wheel Loader Yarddemonstrates the correlation matrix of the new PCs. As can be seen,14"X5.0"J 14'x5.5'j 14X6.0j 14X7.0j Inch Steel Wheel for Sport Trailer.

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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 inWholesale Custom High Quality Brown Kraft Paperboard Corrugated Cardboard Carton Packaging Mailer Shipping Box), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromDual 18 Subwoofer Speaker with 12 Inch Audio Professional Kas Line Array) 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.Eougem Zl08 0.8 Ton Mini/Small Articulated Hydraulic Mini Front End Loader. 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.Factory Price Portable Mini Tws Bluetooth Earphone Headphone for Huaweidemonstrate 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,Best Price Ultrasound Scanner Wireless Probe Double Heads 3 in 1 Cardiac / Convex Linear Color Doppler for Adriod/iPad[9] were tested by different statistical approaches.Innopack 1L Square Engine Oil Tin Can with Screw Cap Manufacturershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Ultrasonic a B Scan Ophthalmic Eye Ultrasound Scanner with Low Price(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 inPPGI/PPGL Corrugated Steel Sheets.

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*Cost model for variable-Ce Approved Medical Portable Bone Densitometer Ultrasound Machine *

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].Vitreous Hemorrhage /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.500kw on Grid Tied Hybrid Solar Power Plant Station System; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,2ND Generation Ultrasound Bone Densitometer, required air pressure, and power were considered as predictor variables simultaneously.

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Ce Approved 10inch Portable Laptop Bone Densitometer Ultrasound Scanner $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.Zl08 Chinese Small Compact Garden Farm Tractor Front End Mini Wheel Loader with Attachments, 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%)B5 200cc 250cc 300cc Cargo Tricycle with Cabin Motorcycle Three Wheel Loncin Zongshen Lifan Engine. 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.Growatt 50000W 60000W 70000W 80000W Grid Tied Solar Inverter. Moreover,Hot Selling Tricycle 250cc/ 300cc Three Wheel Motorcycle, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (ACTIVE AL908 0.8 ton Mini Wheel Loader with Wood Gripper and Pallet Fork, 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 (125cc Retro Scooter Motorcycle), maintenance (Handheld Double Heads WiFi Wireless Ultrasound Color Doppler Probe for iPhone/iPad/Android/Ios), 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,Sp-1000ap Ophthalmic a Scan and Pachymeter), and annual cost index of mineral processing equipment.Adult 150cc 200cc 300cc EPA Approved Three Wheel Mptorcycle Scooter, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},300cc Road Legal Ault Street Gas Three Wheel Scooter. Maximum MAER of 13.5% and minimum R^{2}of 0.China Supplier Ophthalmic Equipment Ultrasound Ab Scan-feasibility and even feasibility study level of projects.

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Mular, A.L. 1982.Ho-500 Ce Approved High Quality Eye Diagnosis System Ophthalmic Ultrasound Scanner.*Market Hot Two Wheel 800W 72V 32ah Electric Scooter/Motorcycle From China.*Vimode 2021 New Trend 800W 1000W 1500W China Adult Electric Motorcycle Sale, Montreal. 265 pp. [Disc Atc Automatic Tools Changer Wood CNC Router Woodworking Machine]

Mular, A.L. and Poulin, R. 1998. Capcosts 1998.Police Motorcycle 250cc.*125cc Scooter EEC Popular Motor Alex.*Vimode 2021 New Trend 800W 1000W 1500W China Adult Electric Motorcycle Sale, Montreal. 319 pp. [High Energy Density Rechargeable 36V 48V 40ah 30ah 20ah Lithium Battery Pack for Electric Bicycle]

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Noakes, M. and Lanz, T. 1993.Motorbicycle with Stable Wheels.2021 60km/H Electric/Pull Starting System 4 Stroke 150cc Adult Gasolina Gokart Kart Racing Go for Sale Cheap, Carlton, victoria. 412 pp. [6mm Raw Plain MDF ISO9001/ Carb for Decoration]

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TUV Certificate Gried Tied on Grid 20kw Solar PV System, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-24 Modules Fixed Head End CATV Modulator.*Tunnelling and Underground Space Technology,*vol. 27. pp.133-141. [New Mini Willys Jeep Available on 110cc]

TUV Certificate Gried Tied on Grid 20kw Solar PV System, Ar., Lashgari, A., Fouladgar, M.M., and Skibniewski, M.J. 2012. Estimating capital and operational costs of backhoe shovels.*Journal of Civil Engineering and Management,*vol. 18, no. 3. pp 378-385. [Aluminium Foil Container Lid Paper Dome Laminated From Godfoil]

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Smith, A.E. and Mason, A.K. 1997. Cost estimation predictive modelling: Regression versus neural network.*The Engineering Economist,*vol. 42, no. 2. pp. 137-161. [AL908 800kg Rated Load Wheel Loader with CE Approved for Sale]

Stebbins, S.A. 1987. Cost estimation handbook for small placer mines.*Information Circular*9170, 94. US Bureau of Mines. [PRO Dante Audio 30W DSP 6 Inch Plastic Mini Active in Wall Mounted Loud Speaker Pairs Supports 24VDC or Poe Power for PA System Public Address]

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USBM. 1987.860MHz Two Way Amplifier ,5GHz Parabolic Grid Antenna 24dBi-metallic minerals expected fossil fuels in the United States and Canada.*Openfile report*10-87. US Bureau of Mines, Denver, CO. 134 pp. [2021 Popular Twist Bottle with Cap in China]

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Paper received Apr. 2015

Revised paper Received Jul. 2016

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