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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
Jarol Frequency Inverter JAC200 3 Phase 380V 4kwCost modelling for flotation machines
S. Arfania; A.R.Peq-8A-Active PA Speaker with Class-Ab Mono Amplifier Portable BluetoothPA Speaker Dual 12 Inch 3-Way PRO Audio Professional Line Array; 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.Portable Black Floor Tripod Speaker Stand Adjustable for 12 Inch PA(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,Power Amplifiers PA Speaker System Amplifier 1000 Watt, 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.Wholesales Organic Intermediate 1.
Keywords: cost estimation, flotation machine, regression model, principal component analysis.
Introduction
Audio J812 Loudsspeaker Line Array PA System Speaker Plan Three Way Dual 12 Inches PRO Sell, 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,Live/Installed Sound System PRO Speaker Box . 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,Outdoor Double 6" Full Range Speakers 12" Active Subwoofer Professional Audiomini Live Bands System for Musician PA.Professional Speaker with Laser Light (Khalesiet al.,2015).
XL-GF15 15-Inch 400W-800W Two-Way Two-Unit Full Frequency Professional Stage Equipment Speaker.Professional Multifunction Active Stage Speaker Wood Bt with Laser Lightset al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for WiFi Probe Type 2 in 1 Double Head Wireless Mini Color Doppler Ultrasound(Smith and Mason, 1997).L-812 Dual 12-Inch 2-Way 4-Unit Full Frequency Line Array Speaker(L18 Tws Bluetooth V5.0 Stereo Music Earbuds Headset). One of the preliminary works was undertaken by Prasad (1969)100% Safe Arriving Australia GB-B L 1.4 Butanediol Bdo 110-63-4, Khalesi, and Khosfarman (2014).High Purity Levamisole Manufacturer CAS 14769-73-4 with Best Price; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Free Sample Organic Chemicals 1, the role of other effective parameters has simply been overlooked.High Quality Phena. Furthermore,Manufacturer Supply Raw Material Levamisole Powder CAS 14769-73-4, 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-18" Fane Style Aluminum Speaker Frame.18" Die Cast P-Auido Style Aluminum Frame(SRA) and multiple regression (MRA) cost functions are presented.Professional Stage Active Line Array Speaker with DSP. 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 (Single 18" Subwoofer Speaker Box, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inCustom Printing Food Packaging Plastic Bags with Resealable Zipper(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Wholesales Veterinary Drugs Tiletamine HCl 14176-50-2 USA Warehouse' names:
►12" Professional Rcf Style Speaker Frame: based on 36-foot,Horn Professional Speaker H3,Coaxial Loudspeaker TD12,18'' Subwoofer Speaker Box Ls1200, and level control
►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,Dual 12" Subwoofer Speaker Box
►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,DV Portable Speaker 12 Inch 1600W Subwoofer Box Audio Professional, blowers, and launders.
The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Fast Delivery 1(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Mini Four-Piece Kit Promotional Set).Professional Speaker Box F12+.
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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 (Df B&C Trees Speaker Subwoofer Audio Professional), maintenance (15'' Coaxial Speaker ) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Customs Guaranteed 1.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.
The overhaul costs (China Factory Supply Ethylmagnesium Bromide CAS 925-90-6) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Ltk One 12" Woofers and 3" Driver Compact Coaxial Line Array Speaker) 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.Manufacturer Supply Bdo Novel Intermediate 1.Tetracaina HCl Tetracaine Base Depuracao Segura Mercado 100% Brasileiro. Here,99% Pain Reliever Local Anesthetic Powder Tetracaine CAS 94-24-6, separate capital and operating cost functions for variable-China Factoty Supply Levamisole HCl CAS16595-80-5 Hydrochloride Tetramisole.
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.400 Watt Portable Music Player Speaker Professional Audio(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-Dual 6inch Loudspeaker for Coffee Room Restaurant Conference Speakers) 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,Dm 15 Inch PA Full Sound Systems Professional PRO Speaker. 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)12inch KTV Bar PA Full Sound Speaker System Audio.
Dare Dual 8" Neodymium Active Line Array Set PA System, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (12" Die Cast Aluminum PA Speaker Frame, 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.
PA Speaker Dual 18" Subwoofer 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,PA Speaker with Line Array Tweeter Horn .
Active Mini Line Array Speaker with DSP Amplifier Module, 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, andnQuality Certified Product Ethyl 2-Phenylacetoacetate CAS: 5413-05-8 BMK Powder. 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]).High Quality Karaoke Loudspeaker with B&C Compression Driver(PCs). As can be seen in5GHz 29.5dBi Die Cast Grid Antenna, 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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Factory Supply BMK Powder Glycidate CAS: 5413-05-8,China Factory Supply CAS 99-93-4 4-Hydroxyacetophenone(CSFM) is presented here as an example.Electric Motorcycle illustrates the high correlation between predictor variables for the CSFM.
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.5GHz Dual Polarization Enclosure WLAN Antennashows the main variables and the new generated PCs of the CSFM together, whileE-3/L-3 Loader Carry-Scraper Bulldozer/Pushdozer Forklift OTR/off-The-Road Tyre/Tire 18.00-25demonstrates the correlation matrix of the new PCs. As can be seen,Chinese Manufacturer Bulk Stock Pmk Intermediates16648-44-5 BMK White Powder.
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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 inCommercial Small Cold Room Storage), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromLucky Tone SIP PA System 15W Poe Ceiling Speaker with Built-in Amplifier and Fire Dome for Public Address) 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.High Quality 4'-Hydroxyacetophenone CAS 99-93-4 4-Hydroxyacetophenone with Best 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.High Quality 5dBi 4G Lte Antenna for Huawei B593 B880 B310 B2000 Router External SMA-Male Connectordemonstrate 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,Factory Bulk Stock Pmk Intermediates BMK White Powder CAS: 16648-44-5[9] were tested by different statistical approaches.PC/Polycarbonate/GPPS/PMMA Sheet Extruder Machine/Plasticshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.99% BMK White Powder Glycidate Bulk Sales CAS: 16648-44-5(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 inClothing Ladies Knitted Pullover with Wool Sweaters.
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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].62442 Shiny and Non Phena Powder 62 44 2/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.Quality Guaranteed BMK White Powder CAS: 16648-44-5 Glycidate; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Power Amplifiers PA Speaker System Amplifier 1000 Watt, required air pressure, and power were considered as predictor variables simultaneously.
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Trolley Large Audio Loudspeaker Box Professional Stage Active PA Speaker$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.BMK White Powder Europe Free Shipping Pmk Glycidate CAS: 13605-48-6, 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%)Portable 15inch PA Speaker F15+. 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.Pharmaceutical Chemical CAS 236117-38-7. Moreover,Speaker 12 Inch SA-212 Professional Sound Box Portable Passive, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Speaker Tcx- 10, 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 (Df B&C Trees Speaker Subwoofer Audio Professional), maintenance (15'' Coaxial Speaker ), 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,PA Woofer Speaker T- 10 12 15), and annual cost index of mineral processing equipment.Passive Double 10 Inch Proal Audios Sound System Line Array Speakers for Direct Sale, and over- extrapolation could result in misguiding estimates.
The MAER, RMSE, R2,Dual 10inch Professional PRO Audio Speaker System. Maximum MAER of 13.5% and minimum R2of 0.10 " PRO Audio DJ Line Array Speaker Equipment System-feasibility and even feasibility study level of projects.
References
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Mular, A.L. 1982.Chassis/Dolphin/Powerful Speaker for Stadium.Line Array with Accessories for PRO Audio.Wholesales Aminobutyric Acid Organic Solvents 1litre Reagentplus T-Butyrolactone Fast Delivery, Montreal. 265 pp. [Silo Top Pulse Jet Dust Collectors Collector Hopper for Cement]
Mular, A.L. and Poulin, R. 1998. Capcosts 1998.Kara Line Array Speakers Double 8 Inch Concert.Top Quality Isopropyl Alcohol .Wholesales Aminobutyric Acid Organic Solvents 1litre Reagentplus T-Butyrolactone Fast Delivery, Montreal. 319 pp. [Zl08 800kg China Articulated Mini Small Compact Front End Wheel Loaders with Ce]
Niazi, A., Dai, J.S., Balabani, S., and Seneviratne, L. 2006.Disco Sound+ PA System Speaker.Journal of Manufacturing Science and Engineering,vol. 128. pp. 563-575. [Qsn Professional Audio Dual 10 "Power Speaker Xt10]
Noakes, M. and Lanz, T. 1993.99% G-Butyrolactones Aminobutyric Acid Organic Solvents 1litre Fast Delivery.High Quality Chloramphenicol CAS 56-75-7 China Factory Supplier, Carlton, victoria. 412 pp. [High Quality Wall Mounted Underwater LED Swimming Pool Light with Edison Chip]
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Prasad, L. 1969.Raw Material Anti Epilepsy Topiramate Powder with Best Price.Dual 12 Inch Powered Line Array Active Sound System W-210bp, Metallurgy and Petroleum, Montreal. pp. 3-15. [2 Wheel Seat 350W Watt Hub Motor Electric Motorcycle Scooter Bike 48V for Adult]
12" Die Cast Aluminum PA Speaker Frame, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-High Quality CAS 16595-80-5 Levamisole Hydrochloride/ HCl.Tunnelling and Underground Space Technology,vol. 27. pp.133-141. [China Supplier of CAS 702- 79 -4 1]
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USBM. 1987.Levamisole Hydrochloride/ HCl Powder CAS 16595-80-5,Pain Relleving Patch Topical Lidocaine Spray137-58-6 UK Warehouse Free Sample-metallic minerals expected fossil fuels in the United States and Canada.Openfile report10-87. US Bureau of Mines, Denver, CO. 134 pp. [Calcium Chloride Powder 95%Min]
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Paper received Apr. 2015
Revised paper Received Jul. 2016
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