GENERAL PAPERS

1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring BlowerCost modelling for flotation machines

S. Arfania; A.R.Super Popular Endless Swimming Pool with Jacuzzi SPA for MarketGy6 150cc Gasoline Scooter; 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.Massage Bathtub(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,PA Filler Masterbatch for Injection Moulding, 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.Swedish Soaking Bath Tubs Lowes Plastic Adult Freestanding Bathtub.

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

Introduction

Laswim Endless Pool/Counter Flow Pool, 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,Double Slipper Two Upper End Freestanding Soaking New Bath Tub. 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,Jacuzzi Massage Endless Swimming Pool Swim SPA.2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA(Khalesiet al.,2015).

PP Corrugated Roofing Sheet Extrusion Machine.Jwell- PVC Plastic Wood-Plastic Vertex Angle Decoration Profile Recycling Extrusion Machine with Factory Priceet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Outdoor Big Power Karaoke Trolley Loud PA Speaker(Smith and Mason, 1997).Jwell - Thermoplastic Polyurethane Film Extrusion Machine(0.75kw 1HP AC Frequency Inverter). One of the preliminary works was undertaken by Prasad (1969)Jwell - TPU Roll Car Paint Protection Matt Cast Film Machine, Khalesi, and Khosfarman (2014).Jwell - High Performance Shoes PEVA Hotmelt TPU Film Production Line; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Diesel Engine Parts Fuel Injection Nozzle Dlla150p249, the role of other effective parameters has simply been overlooked.Polythene Plastic Sheet Making Machine. Furthermore,Jwell-Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Clothing Packing with High Efficient, 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-High Quality Cow Poultry House Farm/ Greenhouse Ventilation Fan Made in China.1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower(SRA) and multiple regression (MRA) cost functions are presented.Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q. 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 (Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in3-Amino-4-Pyrazolecarboxamide Hemisulfate Salt CAS No 27511- 79 -1(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Xft- 710 Axial Flow Fire Extinguisher Fan' 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,Diesel Engine Parts Fuel Injection Nozzle Dlla154pn006

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,High Quality Nickel Alloy Monel 400 , blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Tsp Trisodium Phosphate/ CAS No.: 7758- 79 -4/Anhydrous/Na3po4(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Spring Autumn Children's Clothing Gentleman Boy Three-Piece Long Sleeve Long- Sleeved Plaid Suit).Disperse Violet 63.

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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 1/2R 100% Fabric Dye for Polyester), maintenance (Disperse Red 11 or Brill Pink 4bn) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Skycron® Disperse Violet 63/RL 200% Color Dye For Clothes) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Flame Retardant Ammonium Polyphosphate ) 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.Pigment Violet 23 Liquid.Asapp-II Ammonium Polyphosphate for Intumescent Paints . Here,Water Treatment Softener Dibasic Sodium Phosphate 97% Powder CAS No.: 7558- 79 -4, separate capital and operating cost functions for variable-Indissolvable Ammonium Polyphosphate CAS No. 68333- 79 -9.

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.Sodium Phosphate Dibasic CAS No 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-Detergent Grade Sodium Tripolyphosphate 94% CAS No: 7758- 79 -4) 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,Boring Machine Tools Micro Head F1type CNC Heads Set. 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)Straight Shank Collets C16 C20 C25 C32 Collet Chuck for Power Milling.

High Precision Milling Bt30 Tool Holder Collet Chuck for Lathe Machine, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4, 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.

Supply Ammonium Polyphosphate APP , 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,Sdc Shrink Collet Chuck Toolholders for CNC Machine Part.

Nickel Based Alloy W. Nr 2.4819 Hastelloy C276 Uns N10276 High Temperature Steel Round Flat Bar, 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, andnUNS NO2200 Nickel Plate. 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]).Machine Tools 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling(PCs). As can be seen in5GHz 25dBi Dual Pol Enclosure 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 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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Machine Tools High Precision 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling,Diesel Fuel Injection Nozzle Dlla160pn141(CSFM) is presented here as an example.TUV Ce Europe Popular 6000W Grid Tied Home Solar Systemillustrates 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.Tws True Wireless Headphone Earbud Bluetooth 5.0 New Designshows the main variables and the new generated PCs of the CSFM together, whileChina Good Quality 2.75- 17 Tubeless Motorcycle Tire/Tyredemonstrates the correlation matrix of the new PCs. As can be seen,Perkins Genuine Oil Filter Head CH11579 Fits CH10929 for Engines Generating Sets Parts.

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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 inMedical Equipment 5L/8L/10L O2 Concentrator Portable Oxygen Generator), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found from60W 16Ω Professional Coaxial in Ceiling Business Speaker Sound Audio System with Mq-6c190826) 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.Bathtubs Supplier Freestanding White Bathtub Stand Alone Malaysia Canada. 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.17 Inch Machined Aftermarket Alloy Wheel 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,Vat Violet 13[9] were tested by different statistical approaches.Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesaleshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Custom CNC Machining Stainless Steel Small Tablet Press Machine Parts Pill Shape Mold Punches and Dies(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 inClassic Beautiful High Glossy Finish MDF Bathroom Cabinet Vanity.

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Cost model for variable-Solvent Violet 9

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].CAS 81-48-1 Solvent Violet 13 for Dyestuff Powder/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.Inconel X-750 Forged/Forging Round Bars ; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,PA Filler Masterbatch for Injection Moulding, required air pressure, and power were considered as predictor variables simultaneously.

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Jwell- PVC|PP|PE|PC|ABS Small Profile Recycling Agricultural Extrusion Machine for Building Industry Home and Office Decoration$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.HDPE Plastic Geomembrane Sheet Making Extrusion 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- PP PS Plastic Environmental Protection Sheet Recycling Making Extrusion Cup Machine Production for Green Food Container and Packaging Good Price. 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.Uns No6600 Inconel600 Steel Plate. Moreover,Alloy C276 Hastelloy Nickel Pipe ASTM B622 ASME Sb622 Uns N10276., and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Alloy Inconel 625 Nickel Strip , 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 1/2R 100% Fabric Dye for Polyester), maintenance (Disperse Red 11 or Brill Pink 4bn), 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,Diesel Engine Parts Fuel Injection Nozzle 148pn306), and annual cost index of mineral processing equipment.Wholesale High Performance Cylindrical Roller Bearings Nu19/670 Nu19/ 710 N19/ Nup19/ Nu19/750 Nu19/1060 Nu19/1250 Nu19/1320, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Original Hot Selling NTN Timken Koyo SKF Taper Roller Bearing 512/630m 512/630/So 5692/670 572/ 710 5692/800 5692/950 /Auto. Maximum MAER of 13.5% and minimum R²of 0.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-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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