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.Seal Kits Hyundai R210-7 Boom Cyl Arm Bucketcyl Oil(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,Chinese Manufacture Jcb332/Y6195 Universal Cylinder Seal Kit, 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.Seal Kits Komatsu PC200-5/6 Boom Cyl Kit.

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

Introduction

Industrial Grade SHMP , 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,Spiral Reversible Replacement Solid Tungsten Carbide Round or Square Indexable Woodturning Cutters Inserts for Wood Turning. 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,E320L/B/C/D Boom Arm Bucket Cyl Seal Kit Excavator Oil Kits.Toothbrush Material Pellets Raw Granules Anti-Static Yellow Antistatic Masterbatch Customized Home Appliance(Khalesiet al.,2015).

K10 K20 P30 Tungsten Carbide Plate Strips for Cutting.Komastu PC60-6 Arm Cyl Oil Seal Kitet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Solar Pump Frequency Inverter MPPT Fuction 0.75kw(Smith and Mason, 1997).Cat320b/C/D Arm Cyl Seal Kit Excavator Oil Kits(Motorcycle Muffler Assy/Exaust Pipe for Scooter Parts Gy6 50/125/150). One of the preliminary works was undertaken by Prasad (1969)Pigment Violet 1 Toner for Ink, Khalesi, and Khosfarman (2014).Solvent Violet 59 ; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Solvent Violet 13 for Plastic Application, the role of other effective parameters has simply been overlooked.Solvent Violet 11. Furthermore,Solvent Violet G 49 for Plastic, 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-Manufacturer ASTM 316L Uns S32205 Duplex Stainless Steel Tubes.Solvent Violet 10b 9(SRA) and multiple regression (MRA) cost functions are presented.Duplex Stainless Steel Sheet Super 2507. 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 (ASTM A789 S32750 Uns Super Duplex Stainless Steel Pipe, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in1500W Frequency Converter Inverter VFD 3phase 380V Best Enclosure 50Hz to 60Hz(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Uns S32750 2507 S32760 F55 1.4501 Super Duplex Stainless Steel Bar' 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,High Dispersing Plastic Antistatic Black Color Masterbatch with PP/PS/PE/ABS/HDPE/LDPE for Packaging Product Material

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Wireless Earbuds Headphones with Bluetooth 5.0 Earphones True Stereo Tws Charging Case for Sports Drive or Work, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Bluetooth 5.0 Headset Mini Tws True Wireless Earbuds Stereo Bass in-Ear Earphone(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (ICTI Factory 11.5 Inch Beauty Fashion Doll Plastic Dolls Toy Africa).Mini Wireless Stereo Tws 5.0 Music Earphone L18.

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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 (Plastic Material PP Antistatic White Masterbatches with Anti Static Requirement Customized PP/PS/ABS/PE/LDPE/HDPE), maintenance (Plastic Products Raw Material Light Green Color Antistatic Masterbatch Customized for Film Package) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Jwell Plastic PVC Foamed Frame Profile Extrusion Machine.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Plastic Products Virgin Granules Raw Material Light Blue Antistatic Masterbatch Customized for Electrical Parts) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia) 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.PP/PC Sheet Extrusion Machine.Water Treatment Disodium Phosphate . Here,Food Grade Addictive Disodium Phosphate DSP, separate capital and operating cost functions for variable-Disodium Phosphate Anhydrous CAS No 7558- 79 -4.

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.Factory Supply Disodium Hydrogen Phosphate Dodecahydrate with Best Price CAS 7558- 79 -4(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-K05/K10/ K20 /K30/K40 Tungsten Carbide Flat) 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,Changhong Film Stack Flexo Printing Machine. 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)Xft- 710 Axial Flow Fire Smoke Fan.

Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Disperse Violet 26 Dyes, Khalesi, and Khosfarman, 2014).

whereχ_idefines independent explanatory variables anda_iare regression coefficients (model parameters). As was mentioned, independency ofx_ivariables 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.

Skyzon® Cationic Violet 3R/Cationic Dyes/Cloth Dye, 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]:

whereX_obsis the observed value,x_ethe estimated value at time/placeI,and n,Disperse Dyestuff Violet S3rl 200% C. I. 63.

Pigment Violet 1 or Fast Rose Toner/Fast Lake, 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).

whereC_eis the estimated cost,C_athe actual cost, andnDisperse Dyestuff Violet 200% P-CF for Textile. 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]).Disperse Red/Blue/Orange/ Violet /Black(PCs). As can be seen inWolf Loader Wl80 Zl08 Radlader Mini Wheel, 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 andX_ias Equations [5] and [6]:

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In this research, main variables ofX₁, X₂... X_nwere 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 Cost Qualified Effect Antistatic Plastic Blue Color Masterbatches for Electronic Components,Plastic Products Pellets Raw Granulesanti-Static Material Yellow Antistatic Masterbatch Customized Home Appliance(CSFM) is presented here as an example.Inverter Cabinet VFD Frequency AC Drive 55kwillustrates 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.Fractional RF & Thermal Machine shows the main variables and the new generated PCs of the CSFM together, whileRaw Material Anti Epilepsy Topiramate Powder with Best Pricedemonstrates the correlation matrix of the new PCs. As can be seen,Super Popular Endless Swimming Pool with Jacuzzi SPA for Market.

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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)

whereX_iare main technical variables (like power or required air),a_iare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inOutdoor Comfortable Crew Neck Pullover Sweatshirts), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromBl-Xgz Electric Motorcycle) 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.PA Filler Masterbatch for Injection Moulding. 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.Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertiademonstrate 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,Swedish Soaking Bath Tubs Lowes Plastic Adult Freestanding Bathtub[9] were tested by different statistical approaches.PA12 Resin Suppliers Glass Fiberpolyamide 12 Nylon Granulesshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Laswim Endless Pool/Counter Flow Pool(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 inPractical Rental P7.62 Full Color LED Advertising Display Screen.

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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].Jacuzzi Massage Endless Swimming Pool Swim SPA/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.2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Chinese Manufacture Jcb332/Y6195 Universal Cylinder Seal Kit, required air pressure, and power were considered as predictor variables simultaneously.

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Jwell - Thermoplastic Polyurethane Film Extrusion Machine$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.Jwell - TPU Roll Car Paint Protection Matt Cast Film Machine, 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%)Jwell - High Performance Shoes PEVA Hotmelt TPU Film Production Line. 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.Diesel Engine Parts Fuel Injection Nozzle Dlla150p249. Moreover,Polythene Plastic Sheet Making Machine, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Jwell-Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Clothing Packing with High Efficient, 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 (Plastic Material PP Antistatic White Masterbatches with Anti Static Requirement Customized PP/PS/ABS/PE/LDPE/HDPE), maintenance (Plastic Products Raw Material Light Green Color Antistatic Masterbatch Customized for Film Package), 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,High Quality Cow Poultry House Farm/ Greenhouse Ventilation Fan Made in China), and annual cost index of mineral processing equipment.1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q. Maximum MAER of 13.5% and minimum R²of 0.Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189-feasibility and even feasibility study level of projects.

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Mular, A.L. 1982.Skycron® Disperse Violet 1/2R 100% Fabric Dye for Polyester.Disperse Red 11 or Brill Pink 4bn.94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4, Montreal. 265 pp.         [0.75kw 1HP AC Frequency Inverter]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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