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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

Velvet Office Sofa Chair Modern 0302Cost modelling for flotation machines

S. Arfania; A.R.Padlock-G38PDPProfessional Audio Speaker System Dual 10 Inch 3 Way Big Line Array Vr36; 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.Breaker Lock(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,Padlock, 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.Alone Type Wraped Beam Leaves Iron Padlock .

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


Introduction

Fuso Truck & Bus Turbo Td04 49377-03041 Me201258 for 4m40 Engine Mitsubishi Pajero, 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,Gt1544s 454083-0001 1002829 Garrett Engine Turbo for Vw Passat. 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,Engine Parts Turbocharger for Mercedes-Benz Om906 La K27.2 Om366/Om642/Om362/Om441/Om442/Om447/Om457.Gt1544sm Tdi Engine Bnm 045253019d 733783-5008s 733783-5007s Turbo(Khalesiet al.,2015).

Universal Turbo T3t4 T04e T3.63 Ar + 76mm 3" Intercooler Pipe Piping Kit.Truck Parts Turbocharger for Mercedes-Benz/Chrysler/Dodge Om647 Gt2256 6470900280 736088-0003et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Hidden Lithium Power City Bike Mountain Electric Bicycle 250/350/500/ 800W Ebike(Smith and Mason, 1997).FPM FKM Viton EPDM SBR Cr Silicone NBR Rubber Parts(Yn725 Yineng Mini Wheel Loader 18.5kw Cabin). One of the preliminary works was undertaken by Prasad (1969)Gt1541V 704765-0003/708450-0018 Turbine Wheel Shaft for 700960-0011, Khalesi, and Khosfarman (2014).Gt1544sm 733783-5007s Turbo for Volkswagen Fox 1.4L Tdi Engine Bnm; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Cosmetic Grade 99% Purity All Trans Retinoic Acid 302- 79 -4 Tretinoin/Vitamin a, the role of other effective parameters has simply been overlooked.Customized Rubber Spacer Black Silicone Bushing. Furthermore,Gym Rubber Flooring Floor Mat Roll, 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-Ihi Turbocharger 2001-04 Peugeot.Gt1749V (SRA) and multiple regression (MRA) cost functions are presented.2004-10 for Volkswagen. 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 (Borg Warner BV45 Turbo 5303-988-0337 Core Chra for Nissan, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inFactory Directly Sell Good Performance Virgin Transparent PA12 Granules/Pellets /Polyamide 12 Resin for Oil Cup(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;T250-04 452055-5004s Turbocharger for Gemini III Engine' 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,Aftermarket BV45 53039880337 Turbocharger for 2010-12 Nissan Pathfinder Navara Engine

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Factory Supply Glycyl-L-Tyrosine, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Dl-Isoleucine Powder CAS 443- 79 -8(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Custom Die Casting Metal Marathon Finisher Athletics Medals).Glycyl- L-Tyrosine; 658- 79 -7.

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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 (L-Pyroglutamic Acid), maintenance (Dl-Isoleucine Powder CAS Number 443- 79 -8) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,98% Uvarigranol B\C\D\E Standard Reference Materials Plant Extracts.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Longyu Produce Nano Copper Oxide Nanoparticles 1317-38-0) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (High Purity 99.0%Min. Ademetionine Disulfate Tosylate ) 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.Centella Asiatica Extract 99% Asiaticoside 16830-15-2.Crovell Supply Raw Material CAS 104-29-0 Chlorphenesin for Cosmetic. Here,Food Additive L-Threonic Acid Magnesium Salt/Magnesium L-Threonate CAS No.: 778571-57-6, separate capital and operating cost functions for variable-Polyethylene Green Color Masterbatch.

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.Pipe Bevelling Machine (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-ISO Certificated Company Supply Skin Whitening Retinoic Acid Powder) 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,Green Plastic Masterbatch Blowing Film Grade. 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)Green Color HDPE Masterbatch.

Blue Masterbatch for Film, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Yellow Color Plastic Masterbatch, 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.

Yellow HDPE Masterbatch, 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,Universal LPG Gas Completed ECU Conversion Kit.

Act Best Seller CNG LPG Gas Car Emulator, 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, andnCNG/LPG Rail Injector Type Gas 4 Cylinders. 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]).Act MP 48 ECU Switch/Act 2568d Switch(PCs). As can be seen inHigh Competitive 3 Phase Pump Power Inverter 3000W 50Hz to 60Hz Frequency Converter, 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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Motorcycle Act 2568d 6cyl 8cyl ECU Conversion Kit,Auto Vehicle Gas Conversion Kit CNG Seqential Injection Kits(CSFM) is presented here as an example.New Products Charging Case Mini Small Headphones Tws Earbuds Wireless 2021illustrates 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.LED Outdoor Lighting Compatible to Amercian and European Niches Swimming Pool Lightshows the main variables and the new generated PCs of the CSFM together, whileHigh Quality Oxytetracycline Hydrochloride Powder Feed Grade CAS 79 -57-2demonstrates the correlation matrix of the new PCs. As can be seen,Electric Pipe End Bevelling Machine.

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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 inPublic Health Termiticide Insecticides Bifenthrin 10% Ew Ec Factory), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromPet/PE/CPP Ziplock Plastic Clear Nut Package Dry Food Grade Bags) 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.Pneumatic Pipe Beveling Machine High Performence. 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.125541 -22-2 Piperidine 1-N-Boc-4- demonstrate 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,Act CNG LPG Fuel System 2568cyl ECU Kits[9] were tested by different statistical approaches.Guitar / Bass Tuner shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Factory Directly Sell Good Performance Virgin Transparent PA12 Granules/Pellets /Polyamide 12 Resin for Oil Cup(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 inPromotional Best Quality Click and Lock Vinyl Tile Spc Flooring.

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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].4 Cyl CNG Auto Gas LPG Conversion Kit / Sequential Injection System/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.3cyl 4 Cyl 6cyl 8cyl LPG/CNG Injector Rail; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Padlock, required air pressure, and power were considered as predictor variables simultaneously.

L Auto Gas LPG Conversion Kit / Car 4 Cyl Sequential Injection System. Moreover, the operating cost was detailed in different cost items.High Quality Diesel Engine Parts 4 Cyl Pump Rotor Head 096400-0371, indicated inCan Beer Use Automatic PE Film Heat Shrink Wrapping Group Packaging Machine for Half Paper Box Juice Production Line, and major extrapolation should be avoided.

Diesel Engine Parts Injection System Nozzle Dnopd619$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.Supply API 99%Min Dalbavancin CAS 171500- 79 -1 Raw Material Powder, 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%)Diesel Engine Parts Fuel System Nozzle Dlla145pn574. 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.Master Batch Organic Colors. Moreover,Orange Color Masterbatch, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Plastic Purple Color Masterbatch, 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 (L-Pyroglutamic Acid), maintenance (Dl-Isoleucine Powder CAS Number 443- 79 -8), 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,Plastic Grey Color Masterbatch), and annual cost index of mineral processing equipment.Free Sample Color Masterbatch ABS PE Non Toxic for Injection Molding, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Cosmetic Grade Liquid Form 70% CAS 79 -14-1 Glycolic Acid. Maximum MAER of 13.5% and minimum R2of 0.Health Raw Material Dibasic Sodium Phosphate CAS No.: 7558- 79 -4 with High Quality-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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