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.Suntree Solar Cable Connector Mc4 IP68 Yuv Approved(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,Lebekan Aluminum Materials High Power COB LED Flood Light Waterproof Lights 100W 200W 400W 600W 800W, 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 0.3kwh LiFePO4 Battery System Energy Power.

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

Introduction

800W Stadium Lighting Serials LED Projector Light, 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,Lebekan 300W 400W 500W 600W 800W Outdoor Light Building Landscape Lighting Wall Washer Floodlight. 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,Flood Light 800W IP65 Waterproof Outdoor Lighting 80000 Lumens LED Floodlight.T Solar Mc4 Energy System Connector PV(Khalesiet al.,2015).

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Methodology

Data

Thirty-seven major flotation machines (Yog Motorcycle Spare Parts Side Mirror Rearview Mirrors Scooter Gy6 off Road for Honda Xy Fz16 YAMAHA Bajaj Tvs Star Apache 180, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inYn725g Yineng Mini Wheel Loader 18.5kw Without Cabin(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Motorcycle Parts Sparking Plug for Cg125 Cg200 Cg150 Gy6 -150' 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,IP68 8W-35W Surface Mounted Multi-Color LED Underwater Swimming Light

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Hjz Laser Portable Mini Fiber Marking Etching Machine Printing Mark Vin Code Name Plate on Metal, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Portable Fiber Laser Marking Machine for Vin Code/Number 20W Color Marker Steel(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (New Popular Project Stripe Organza Sheer Curtain Fabric 00825).30W Handheld Vin Number Portable Laser Marking on Stainless Steel.

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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 (Electric Industrial Induction Heater Manufacture in China for Sale ), maintenance (IGBT Induction Heater Heating Equipment for Metal Surface ) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Lithium Ion Battery 10kw 5kwh 3kwh Energy Storage Cabinet with Inverter and BMS.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Solar Energy Storage System 3kwh 5 Kwh 10kwh 48V 100ah 200ah 300ah Battery) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Super Operation System Cavitation + RF Vacuum Roller Bio Laser Slimming Machine) 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.Vin Number Fiber Laser Marking Machine.Duroheater Dh- 25kw Handheld Induction Heating Machine. Here,Allsparkpower Residential Industrial Solar Generator 3kwh 5kwh 7kwh 10kwh 15kwh Lithium Battery Pack Hybrid and off-Grid Home Energy Storage System, separate capital and operating cost functions for variable-Body Shape Scuplting Fast Cavitation Slimming System Radio Frequency Facial Velashape Machine.

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.Professional Body Contouring Cellulite Removal RF Vacuum Roller Velashape 3 Slimming 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-20W 30W Handheld Vin Number Metal Logo Laser Marking Machine) 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,Velashape Slimming Cellulite Removal Body Sculpting Fat 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)Popular 3kwh Hot Saling Li-ion Battery Supplier.

CE Approved Vacuum Cavitation Roller RF Velashape 3 Slimming Machine, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (EEC EPA Extreme Adult RC Snowmobile, 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.

Skin Renew Thermal RF & Fractional 2 in 1 Machine, 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,Home Use RF Velashape Machine.

4.5kwp 7.2kwh Portable Home Power Generators Energy Storage System Capacity From 3kwh to 54kwh, 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, andnAllsparkpower Intergrated System 3kwh -30kwh off Grid Home Use Solar Power Supply with Inverter. 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]).Snow Mobile Rubber Track Gas Adult Ski Scooter(PCs). As can be seen inTitan China Micro New Design Small Mini Front Brand Wheel Loader with Standrad Bucket, 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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New Design Stretch Mark Removal Beauty Machines,Powerful Snow Ski LED Lights Adult Racing a Snowmobile(CSFM) is presented here as an example.Pesticide Deltamethrin 98% TCillustrates 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.Stylish Yellow Two-Seater Children's Sofashows the main variables and the new generated PCs of the CSFM together, whileMetal Engine Oil Can Recycling Lubricant Tin Packaging Containerdemonstrates the correlation matrix of the new PCs. As can be seen,Solar Residential Wall Power Bank 3kwh LiFePO4 Rechargeablelithium 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)

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 inLong Circle Shape Punch Press Die 85 Standard Series), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromHot Sale High Performance Vector Frequency Converter 380V 45/55kw) 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.RF Skin Tightening Face Lifting Machine. 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.Wholesale Factory Lithium Ion Battery 12kwh 48V 100ah 250ah 300ah for Home Energy Storage Systemdemonstrate 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,3kwh off Grid Solar Power Inverter Built-in MPPT Controller Battery System[9] were tested by different statistical approaches.Popular 800W Strong Power Electric Scooter Bike/ Classic Vespa Scooter/Electric Motorcycleshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Hot Selling Face Lifting and Slimming Chin Machine(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 inWood MDF Acrylic Woodworking Cutting Engraver CNC Router Nc Studio Controller.

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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].RF Vacuum Face Lifting and Slimming Chin Machine/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.Gas Ski Adult PRO Electric Start Snow Scooter; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Lebekan Aluminum Materials High Power COB LED Flood Light Waterproof Lights 100W 200W 400W 600W 800W, required air pressure, and power were considered as predictor variables simultaneously.

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20MHz RF Wrinkle Removal$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.Vacuum Shape Velashape Body Slimming SPA Equipment, 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%)Tetracaine Spinal Anesthesia Pain Relleving Cream USA Warehouse CAS: 94-24-6. 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.20MHz Skin Rejuvenation Vacuum RF Lifting Machine. Moreover,China Best Quality 1500cc Amphibious Jet Ski Hot Selling in Europe, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (China Supplier EEC and EPA Approved 1500cc Quadski, 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 (Electric Industrial Induction Heater Manufacture in China for Sale ), maintenance (IGBT Induction Heater Heating Equipment for Metal Surface ), 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,Globalipl Body Face Slimming Fine Jaw Line 20MHz Device), and annual cost index of mineral processing equipment.Chinese Chery 1500cc 4X4 Sport Buggies ATV UTV Quad Scooter, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,4seats 1500cc Kart. Maximum MAER of 13.5% and minimum R²of 0.Fangpower 400cc 4seat Side by Dune Buggy UTV-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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