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.Laswim Endless Pool/Counter Flow Pool(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,Double Slipper Two Upper End Freestanding Soaking New Bath Tub, 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.Jacuzzi Massage Endless Swimming Pool Swim SPA.

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

Introduction

2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA, 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,PP Corrugated Roofing Sheet Extrusion Machine. 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,Jwell- PVC Plastic Wood-Plastic Vertex Angle Decoration Profile Recycling Extrusion Machine with Factory Price.Jwell - Thermoplastic Polyurethane Film Extrusion Machine(Khalesiet al.,2015).

Jwell - TPU Roll Car Paint Protection Matt Cast Film Machine.Jwell - High Performance Shoes PEVA Hotmelt TPU Film Production Lineet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Fractional RF Vacuum Slimming Machine for Lose Weight(Smith and Mason, 1997).Diesel Engine Parts Fuel Injection Nozzle Dlla150p249(AC Drive Three Phase High Performance Vector Control Variable Frequency Converter VFD). One of the preliminary works was undertaken by Prasad (1969)Polythene Plastic Sheet Making Machine, Khalesi, and Khosfarman (2014).Jwell-Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Clothing Packing with High Efficient; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,High Quality Cow Poultry House Farm/ Greenhouse Ventilation Fan Made in China, the role of other effective parameters has simply been overlooked.1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower. Furthermore,Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q, 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-Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189.Xft- 710 Axial Flow Fire Extinguisher Fan(SRA) and multiple regression (MRA) cost functions are presented.Diesel Engine Parts Fuel Injection Nozzle Dlla155p274. 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 (Diesel Engine Parts Fuel Injection Nozzle Dlla153p049, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inVoomaster Brand Big Diamonds Tread Pattern Motorcycle Tyre 3.00- 17 (InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Diesel Engine Parts Fuel Injection Nozzle Dlla155p273' 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,Disperse Violet 63

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Skycron® Disperse Violet 1/2R 100% Fabric Dye for Polyester, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Disperse Red 11 or Brill Pink 4bn(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Fleece Fashion Girl Woman Women's Casual Long Sleeve Pullover Hoodies Crop Tops Sweatshirt Hoodie Top Sweatshirts).94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4.

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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 (Skycron® Disperse Violet 63/RL 200% Color Dye For Clothes), maintenance (Flame Retardant Ammonium Polyphosphate ) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Pigment Violet 23 Liquid.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Asapp-II Ammonium Polyphosphate for Intumescent Paints ) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Water Treatment Softener Dibasic Sodium Phosphate 97% Powder CAS No.: 7558- 79 -4) 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.Indissolvable Ammonium Polyphosphate CAS No. 68333- 79 -9.Sodium Phosphate Dibasic CAS No 7558- 79 -4. Here,Detergent Grade Sodium Tripolyphosphate 94% CAS No: 7758- 79 -4, separate capital and operating cost functions for variable-Boring Machine Tools Micro Head F1type CNC Heads Set.

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.Straight Shank Collets C16 C20 C25 C32 Collet Chuck for Power Milling(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-High Precision Milling Bt30 Tool Holder Collet Chuck for Lathe 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,94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4. 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)Supply Ammonium Polyphosphate APP .

Sdc Shrink Collet Chuck Toolholders for CNC Machine Part, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Nickel Based Alloy W. Nr 2.4819 Hastelloy C276 Uns N10276 High Temperature Steel Round Flat Bar, 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.

UNS NO2200 Nickel Plate, 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,Machine Tools 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling.

Diesel Engine Parts Fuel Injection Nozzle Dlla148p591, 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, andnMachine Tools High Precision 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling. 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]).Diesel Fuel Injection Nozzle Dlla160pn141(PCs). As can be seen inPA Filler Masterbatch for Injection Moulding, 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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Diesel Engine Parts Fuel System SD265 Nozzle,Bathtubs Supplier Freestanding White Bathtub Stand Alone Malaysia Canada(CSFM) is presented here as an example.Professional Dual 15" Multi-Purpose Speakerillustrates 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.Safe Delivery BMK Glycidate Pmk White Powder Eurore Warehouse CAS: 13605-48-6shows the main variables and the new generated PCs of the CSFM together, whileAlloy Inconel 625 Nickel Strip demonstrates the correlation matrix of the new PCs. As can be seen,Vat Violet 13.

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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 inR. S High Quality UV Soak off Builder Nail Art One Step Gel Primer Polish), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found from2021 Hot Sale Switch Control 12V 18W Nichless Flat Wall Mounted Resin Filled LED Swimming Pool Light with CE RoHS IP68 Reports) 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.Solvent Violet 9 . 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.E0 Glue1250*2500mm Wenge Engineer Veneer for Decorationdemonstrate 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,CAS 81-48-1 Solvent Violet 13 for Dyestuff Powder[9] were tested by different statistical approaches.Two Way 10 " Mini Portable PRO Audio Active Loudspeaker PS10shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Inconel X-750 Forged/Forging Round Bars (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 inCustom Crew Neck Patchwork Color Block Sweatshirts Mens.

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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].Laswim Swim SPA Endless Swimming Pool Whirlpool Bathtub/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.Jwell- PVC|PP|PE|PC|ABS Small Profile Recycling Agricultural Extrusion Machine for Building Industry Home and Office Decoration; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Double Slipper Two Upper End Freestanding Soaking New Bath Tub, required air pressure, and power were considered as predictor variables simultaneously.

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Uns No6600 Inconel600 Steel Plate$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.Alloy C276 Hastelloy Nickel Pipe ASTM B622 ASME Sb622 Uns N10276., 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%)Alloy Inconel 625 Nickel Strip . 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 148pn306. Moreover,Wholesale High Performance Cylindrical Roller Bearings Nu19/670 Nu19/ 710 N19/ Nup19/ Nu19/750 Nu19/1060 Nu19/1250 Nu19/1320, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Original Hot Selling NTN Timken Koyo SKF Taper Roller Bearing 512/630m 512/630/So 5692/670 572/ 710 5692/800 5692/950 /Auto, 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 (Skycron® Disperse Violet 63/RL 200% Color Dye For Clothes), maintenance (Flame Retardant Ammonium Polyphosphate ), 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,Perkins Engine Spare Parts Fan Belt Gasket - Cylinder Head Seal Cyl Cover 403D-11g 403A-11g1 403D-15g 403A-15g2 404D-22g 080109134 111147491 U11996410), and annual cost index of mineral processing equipment.Zys Rolling Mill Bearing Four Row Taper Roller Bearings 3810/ 710, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Virgin PA12 Resin GF20 GF30 Pellets. Maximum MAER of 13.5% and minimum R²of 0.PA410 Resin Q-Hgm24 10 -20% Glass Mineral Filled Heat Stabilized-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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