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On-line version ISSN2411-9717
Print version ISSN2225-6253
J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017
http://dx.doi.org/10.17159/2411-9717/2017/v117n1a13Â
GENERAL PAPERS
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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.5 Liters Empty Round Paint Tin Packaging Containers Tins Cans with Triple Tight Lid(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,Factory Supply Customization 10kw Grid Tied Solar System on for Home/Industry/Office 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.Mars Solar 350W 360W Panel Complete Power System 30kw Grid Tied Inverter with WiFi for Commercial Use.
Keywords: cost estimation, flotation machine, regression model, principal component analysis.
Introduction
High Quality 5000W Grid Tied Solar Power Generation System Competitive Price, 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,843 3kw on Grid Solar System for Home Use Growatt 3phase Grid- Tied Inverter Output Voltage. 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,Electric Motorcycle 1000W Motorbike 60V Fast Speed Moped 65km/H.Promotion Price High Speed Motorcycle Scooter 1000W 500W Electric Chopper Bike(Khalesiet al.,2015).
Yangtze 10kw Grid- Tied Solar System.Frequency Converter AC Drive 220V Inverter China Variable Speed Controlleret al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Mini Wheel Loader Small Dumper Hoflader Wolf Zl08(Smith and Mason, 1997).4 Liter Metal Tin Can F-Style with Lid and Plastic Handle for Oil(High Quality CAS No. 63428-84-2 Alcohol Soluble Polyamide PA Resin for Packaging Ink). One of the preliminary works was undertaken by Prasad (1969)Chemical Use 10L 20L Metal Tin Paint Bucket Pail with Flower Cover / Ring Lock Lid, Khalesi, and Khosfarman (2014).Innopack 16oz 0.5liter Biodegradable Plastic Cold Pressed Juice Bottle with Screw Cap; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,7.5 Liter Protein Powder Tubs Jars for Sports Food/HDPE Plastic Container, the role of other effective parameters has simply been overlooked.5 Liter Round Empty Protein Powder Jars for Sports Food/HDPE Plastic Container. Furthermore,Yn725g Hot Sale Mini Wheel Loader, 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-Articulated Loader Mini Compact Wheel with Shovel.Good Quality Empty Metal Tin Paint Glue Cans(SRA) and multiple regression (MRA) cost functions are presented.Everun 0.8ton Chinese Articulated Mini Wheel Loader. 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 (Yn725 Yineng Mini Wheel Loader 1t 0.5cbm Capacity, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inMaunfacturing Price Sealed Food Packaging Vacuum Bag(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;500ml Round Resealable Tin Can with Easy Open Screw Top Lid' 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,China E Bike Electric Bicycle 48V 20A Ebike Nakto Motorcycle
►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,60V 800 Watt 150kg Load Electric E Bike Motorcycle Moped 45 Km H for 2 Person Adults UK, blowers, and launders.
The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Adult Electric Motorcycle/Electric Bike/E-Bike W Waterproof with Double Disc Brakes/2 Wheel Scooter(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Colorful Mini Touch Player MP3 Necklace).China Single Phase Variable Frequency Inverter AC 220V.
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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 (Adult Electric Motorcycle/Scooter 60V20ah Lithium Battery China), maintenance (Hot Selling G31 GPU A95xf3 Air Control Remoto PARA IPTV Smart 2GB Ramg Ratis Saluran Android 9.0 Box TV) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,AC Drive Frequency Variable General Power Supply Solar Motor Pump.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.
The overhaul costs (Pipo X8 PRO Win 10 Android 5.1 Z8350 Support Bluetooth 4.0 7 Inch Tablet PC) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (500kw Solar Energy System Grid Tied 500kwatt Panel Station) 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.Factory Direct Supply 2 Wheels No Folding Elderly Electric Motorcycle.Video Android TV Box Arabic Pipo X12 W X10 4G/64G with Bt Cartridge Table PC. Here,Factory Price 7000W Home Solar Power Generator System Grid Tied, separate capital and operating cost functions for variable-Planer Using VFD AC Drive Frequency Inverters 3pH 380V 11kw.
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.Everun Brand CE Approved Articulated 0.8 Ton Wheel Loader(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-Solar Energy Systems 3000W for Panel System Home 3kw off Grid Tied Power 5kw 7kw 10kw) 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,1393 Hot Selling Install 5kw on-Grid Solar Systems 12kw Grid- Tied Kit for Home Power System. 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 Wheel Loader.
Solar Energy System 5kw Panel Home Grid Tied Power, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Professional Electric Adult Motorcycle 70km/H Cheap Fast Coc Design, 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.
Yn725g 18.5kw No Cabin Yineng Mini Wheel Loader, 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,Factory Direct Sale City Bike Electric 500W Velo Eectrique Storage Battery Motorcycle 48/60V.
Haolin Lithium Battery 60V/20ah, 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, andnSuper Fashion Cheap Electric Scooter 60V 72V Long Range Powerful Motorcycle. 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]).Empty Gal Metal Round Tin Can 118ml 4oz Bundi PVC Pipe Glue Bottle with Brush(PCs). As can be seen inGMP Wholesales BMK White Powder Europe Free Shipping Pmk Glycidate CAS: 13605-48-6, 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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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.10kw Cheap Solar Panels Complete Grid Tied Systemshows the main variables and the new generated PCs of the CSFM together, whileChina Supplier 1demonstrates the correlation matrix of the new PCs. As can be seen,Good Quality Factory Directly Electric Portable Motorcycle with Lithium Removable Battery.
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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 inProtective Face Mask Surgical Medical Mask), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromIron Oxide Yellow for Pet Feeds) 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.Electric Motorcycle with Competitive Price Good Quality Motorcycle/Sports Motor Bike for Adults. 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.Food Grade L-Arginine with Best Pricedemonstrate 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,Solar Inverter Pump Inverters 5.5kw[9] were tested by different statistical approaches.6-Cylinder Diesel Engine with Four-Strke for Silent Generator Setshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.10 Liter Customized Printed Square Metal Fuel Oil Tin Cans for Paint Coating Solvent(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 in1-5W AC or DC Us Plug Switching Power Adaptor with Ce UL.
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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].9L Tight Head Tin Can with Tap for Oilve Oil Ink and 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.
Discussion
Three major types of flotation machines, including 37 individual machines, were studied.Pipo X9s Latest Dual Boot Mini PC 2GB 32GB Wins 10+Android 5.1 TV Box 4K Full HD; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Factory Supply Customization 10kw Grid Tied Solar System on for Home/Industry/Office Use, required air pressure, and power were considered as predictor variables simultaneously.
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DC/AC Frequency Inverter Solar Pump Power 400-600V Input 1.5kw$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.Frequnce Converter AC Drive 380V 11kw, 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%)Solar Inverter Pump 15kw. 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.China Manufacturer 5000W Grid Tied Home Solar Energy System Low Cost. Moreover,TUV Ce Europe Popular 6000W Grid Tied Home Solar System, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (High Quality X96 Max Android 9.0 Smart 4K Set Top Set-Top 4GB 64GB Firmware Ott TV Box, 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 (Adult Electric Motorcycle/Scooter 60V20ah Lithium Battery China), maintenance (Hot Selling G31 GPU A95xf3 Air Control Remoto PARA IPTV Smart 2GB Ramg Ratis Saluran Android 9.0 Box TV), 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,Yn725g Yineng Mini Front End Loader), and annual cost index of mineral processing equipment.China Everun Er408 Small Loader Compact with Pallet Forks, and over- extrapolation could result in misguiding estimates.
The MAER, RMSE, R2,Yn725g 18.5 Kw/2. Maximum MAER of 13.5% and minimum R2of 0.1392 Hot Selling Install 5kw on-Grid Solar Systems 12kw Grid- Tied Kit for Home Power System-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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