GENERAL PAPERS

LoaderCost modelling for flotation machines

S. Arfania; A.R.1 Liter Metal Square Tin Can with Screw Lid for Oil Paint ChemicalLine Array System with Parts for PRO Audio Speaker ; 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.Wholesale 947 Ml/32oz Metal Round Glue Can Tin with Brush Cap(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,500ml 16oz Round Metal Glue Tin Can with Screw Top Brush for Chemical, 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.Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesale.

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

Introduction

Customized B/C/D/E Grade Wood/Natural Birch Veneer, 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,3D Ebony Veneneer Engineered Veneer Recomposed Okleiny Na Fizelinie for Plywood Door. 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,Cute Cheap Electric Scooter for Lady of 60V800W20ah From China.Many Designs Moulded Door Skin for Interior(Khalesiet al.,2015).

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Methodology

Data

Thirty-seven major flotation machines (China Tl08 Mini Wheel Loader with Low Price for Sale, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inCoaxial Loudspeaker TD12(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Er08 Farm Mini Loader with Standard Bucket for Sale' 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,Mars Solar 5kw on Grid Home Power System 5000W 5kVA 5000 Watts Energy Systems 10kw Tied

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,60V/72V 1200W Electric Scooter with Tianneng Battery, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Best Price Solar Energy Systems Home Panel System 15kw 20kw on Grid(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (30ml Gorgeous OEM Nail Extended Gel Kit Acrylic Poly Builder LED UV for DIY).Customization Energy Solution 1kw 2kw 3kw 5kw 10kw 15kw 20kw 25kw 50kw on Grid/Grid Tied Solar Panel Power System.

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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 (Metal Cans 0.925 Liter Tin Barrel for Packaging Container), maintenance (Frequency Inverter Pump AC Drive Price) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Frequency Inverter VFD AC Drive.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Power Frequency Converter 60Hz 50Hz Price) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Frequency Converter for Water Pump) 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.Power Frequency Converter AC Drive Inverter.Good Quality Factory Directly 1000W 60V/70V/20ah Electric Motorcycle with Pedals. Here,0.5L Tin Can with Dry Cover, separate capital and operating cost functions for variable-Food Grade Container 1 Liter Square Olive Oil Latest Design Metal Tin Cans.

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.AC Frequency Converter 50Hz 60Hz Drive Inverter(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-Good Quality Electric Bike & Two-Wheel Dual Motor Foldable China Motorcycle for Adult) 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,Food Grade 3 Liter Square Olive Oil Tin Can with Handle and Cap. 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)Cheap Power Motor Big Protect Frame Electric Scooter Motorcycle 60V800W.

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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.

Cheap Smart Lady's Electric Scooter 60V800W, 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,Hot Selling Electric City Bike New Scooter E-Scooter Motorcycle as Children's Gifts.

Lady Scooter Motorcycle 2.5 16 Tire Custom Bike, 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, andn0.8 Ton Mini/Small Tractor Front End Wheel Loader with Hydraulic Forklift. 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]).Yn725 Yineng Mini Wheel Loader 18.5kw(PCs). As can be seen in600W- 800W 48V/60V Lead-Acid Battery Electric Scooter, 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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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.5GHz 23dBi Dual Polarized Panel Antenna shows the main variables and the new generated PCs of the CSFM together, while8mm Thickness 316ss IP68 RGB DC12V 18W External Control Mode LED Swimming Pool Lightdemonstrates the correlation matrix of the new PCs. As can be seen,High Color Fastness Grey Oak Gris Platinum Engineered Veneer Chapa Precompuestas Fineline with Ayous Base.

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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 in2021 Fashion Portable Best Selling New Style Cosmetic Bag PVC), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromChina Supplier EEC and EPA Approved 1500cc Quadski) 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.Cheap Electric Scooter 500W Pedal Bicycle 25km/H for Export. 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.Alloy Ldx 2101 Uns S32101 Stainless Steel Platedemonstrate 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,Big 4000W 70V Electric Scooter[9] were tested by different statistical approaches.Tx6s H616 32GB ROM Recorder Android 4GB RAM Stick Set Top 2021 SIM Card Ott WiFi Andriod Smart TV Boxshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.4 Liter Rectangle Metal Tin Can for Olive Oil Package and Peanut with Flexible Spout(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 inChinese Product Sales High-Quality Drawing and Stamping Die with Long Service.

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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].Glue Tin Can with Plastic Lid / Square Metal Paint Sizes/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.Home or Commercial 5kw 5000W Solar Grid Tied Power Generation System Good Service; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,500ml 16oz Round Metal Glue Tin Can with Screw Top Brush for Chemical, required air pressure, and power were considered as predictor variables simultaneously.

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Pinergy Grid Tied Solar Panel System 6kw Energy 110V Single Phase$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.off Grid 5kw 10kw Solar Power 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%)Pinergy 9kw on- Grid Tied Solar Power System for Home or Industrial Roof. 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.2013 Popular Electric Motorcycle 90km with Pedal CE . Moreover,Chinese Zl08f Wheel Loader 0.8ton Mini with Quick Hitch for Sale, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Wolf Loader Wl80 Radlader Without Cabin, 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 (Metal Cans 0.925 Liter Tin Barrel for Packaging Container), maintenance (Frequency Inverter Pump AC Drive Price), 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,Yn725g Approved Hot Sale Mini Wheel Loader Yn725), and annual cost index of mineral processing equipment.Er08 New CE Approved Small Shovel Loader, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Everun Brand New Generation CE Approved Er408 0.8ton Mini Front End Wheel Loader. Maximum MAER of 13.5% and minimum R²of 0.Hot Sale Mini Wheel Loader Yn725g-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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