GENERAL PAPERS

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S. Arfania; A.R.Nitrogen Fertilizer Color Granular Ammonium Sulphate 20.5+24sChina Wolf Wl80 Articulated Mini Loader; 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.China Suppliers Alone Type Wraped Beam Disc Machenism Padlock(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,Dust Proof Steel Shackle Padlocks with Master Key, 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.Padlock-G38PDP.

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

Introduction

Breaker Lock, 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,Padlock. 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,Alone Type Wraped Beam Leaves Iron Padlock .Fuso Truck & Bus Turbo Td04 49377-03041 Me201258 for 4m40 Engine Mitsubishi Pajero(Khalesiet al.,2015).

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Methodology

Data

Thirty-seven major flotation machines (Ihi Turbocharger 2001-04 Peugeot, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inMotorcycle Spare Parts High Quality Flasher 6V 12V Gy6 -125 Tvs Star Bajaj Bm150(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Gt1749V ' names:

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The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Gt1544V 740611-5002s 28201-2A400 Turbo for Hyundai Verna(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Separate Letter Nismo Car Emblem Badge).Aftermarket BV45 53039880337 Turbocharger for 2010-12 Nissan Pathfinder Navara Engine.

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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 (Factory Supply Glycyl-L-Tyrosine), maintenance (Dl-Isoleucine Powder CAS 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,Glycyl- L-Tyrosine; 658- 79 -7.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (L-Pyroglutamic Acid) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Dl-Isoleucine Powder CAS Number 443- 79 -8) 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.98% Uvarigranol B\C\D\E Standard Reference Materials Plant Extracts.Longyu Produce Nano Copper Oxide Nanoparticles 1317-38-0. Here,High Purity 99.0%Min. Ademetionine Disulfate Tosylate , separate capital and operating cost functions for variable-Centella Asiatica Extract 99% Asiaticoside 16830-15-2.

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.Crovell Supply Raw Material CAS 104-29-0 Chlorphenesin for Cosmetic(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-Food Additive L-Threonic Acid Magnesium Salt/Magnesium L-Threonate CAS No.: 778571-57-6) 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,Polyethylene Green Color Masterbatch. 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)Pipe Bevelling Machine .

ISO Certificated Company Supply Skin Whitening Retinoic Acid Powder, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Green Plastic Masterbatch Blowing Film Grade, 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.

Green Color 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]:

whereX_obsis the observed value,x_ethe estimated value at time/placeI,and n,Blue Masterbatch for Film.

Yellow Color Plastic Masterbatch, 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, andnYellow HDPE Masterbatch. 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]).Universal LPG Gas Completed ECU Conversion Kit(PCs). As can be seen inPortable Laptop Digital Automatic Ultrasound Bone Densitometer, 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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CNG/LPG Rail Injector Type Gas 4 Cylinders,Act MP 48 ECU Switch/Act 2568d Switch(CSFM) is presented here as an example.Roof Mounting 20kw Grid Tied Solar Power System Homeillustrates 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.38mm 42mm CATV Plug in 0~20dB Hfc Attenuator Padshows the main variables and the new generated PCs of the CSFM together, whileTitan OEM New Type Qingzhou Loadefr Factory RC Avant Mini Wheel Loaders with Cedemonstrates the correlation matrix of the new PCs. As can be seen,Fuel Gas Cylinder ECU 2568d Map Sensors.

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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 inGuangzhou Factory Newest Design Metal Promotional Gift Lapel Pin), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromYn725 Mini Small Perkins Engine Wheel Loader) 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.Auto Vehicle Gas Conversion Kit CNG Seqential Injection Kits. 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.Supply China Control Frequency Converter VFD Power Transformer Motor Drivedemonstrate 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,Electric Pipe End Bevelling Machine[9] were tested by different statistical approaches.Factory Supply Disodium Phosphate Food Gradeshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.T-Electric Pipe Bevelling 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 inFulling Printing Laptop Backpack Spacious Compartments Men's Rucksack.

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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].Act CNG LPG Fuel System 2568cyl ECU Kits/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.Factory Directly Sell Good Performance Virgin Transparent PA12 Granules/Pellets /Polyamide 12 Resin for Oil Cup; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Dust Proof Steel Shackle Padlocks with Master Key, required air pressure, and power were considered as predictor variables simultaneously.

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3cyl 4 Cyl 6cyl 8cyl LPG/CNG Injector Rail$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.L Auto Gas LPG Conversion Kit / Car 4 Cyl Sequential Injection System, 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%)High Quality Diesel Engine Parts 4 Cyl Pump Rotor Head 096400-0371. 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 Injection System Nozzle Dnopd619. Moreover,Supply API 99%Min Dalbavancin CAS 171500- 79 -1 Raw Material Powder, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Diesel Engine Parts Fuel System Nozzle Dlla145pn574, 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 (Factory Supply Glycyl-L-Tyrosine), maintenance (Dl-Isoleucine Powder CAS 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,Master Batch Organic Colors), and annual cost index of mineral processing equipment.Orange Color Masterbatch, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Plastic Purple Color Masterbatch. Maximum MAER of 13.5% and minimum R²of 0.Plastic Grey Color Masterbatch-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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