GENERAL PAPERS

Inverter Cabinet VFD FrequencyCost modelling for flotation machines

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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.Custom Printed Food Grade Aluminum Foil Plastic Packaging Weed Mylar Bag for Fine Powder Snacks(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,Foil Liquid Packaging Stand up Spout Pouch Food Bag, 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.Smell Proof Waterproof Weed Bag Plastic Food Packaging Child Resistant.

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

Introduction

Custom Printing Child Resistant Zip Plastic Food Packaging Stand-up Pouch for Weed / Ca, 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,Mylar Child Resistant Waterproof Plastic Bag with Zipper. 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,Plastic Pouch Custom Water Proof Weed Packaging Food Pack Stand up Bag.Mylar Custom Printed Plastic Weed Bag Stand up Pouch with Zipper(Khalesiet al.,2015).

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Methodology

Data

Thirty-seven major flotation machines (Speaker 2way Double 10inch Full Range High Power Neodymium Speakers Line Array , 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inPA Speaker with Single-Point Angles Regulator (InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;China 10 " DJ Indoor/Outdoor Audio Sound System Line Array Speakers ' 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,High Quality Chemical Product 4-

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Bluetooth Speaker Indoor Outdoor Party Sound 10 Inch Active Arrray System, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Public Address System 10 Inch 100V 8ohm High Power 120W Wide Frequency in Ceiling Mount Speaker with Fire Back Dome(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Yishan 180HP hydraulic dozer TY180 with 510/610mm track shoes).Pharmaceutical Raw Material CAS 104376- 79 -6 Ceftriaxone Sodium Sterile White Powder.

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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 (Dual 10inch Powerful Line Array Speaker Ds210), maintenance (Hot Sale Free Sample CAS 302- 79 -4 Retinoic Acid with Best Quality) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Dual 10 Inch Top and Double 15 Bass Portable Multi-Functional Line Array Speaker System.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Cheap Price PRO Sound Professional Audio 10 Inch Speakers 200W) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Vitamin a Acid/ Tretinoin CAS: 302- 79 -4 for Skin Disease with Fast Delivery) 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.Cold&Heat Seal Plastic Film Roll Chocolate Bar Food Cookies Packaging Bag Frosted Zipper Container Made Craft Drawstring Low MOQ Printing.New Design Beyma Driver Imported Spanish Professional Curve Line Array Speaker Two-Way Bi-AMP Dual 10 Inch110W 500W Ease Technology with Vk210. Here,10 Inch Coaxial Speaker Professional Driver 250wrms " Subwoofer, separate capital and operating cost functions for variable-Aicrowe L- .

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.Diase PRO Audio Dual 10inch Professional Line Array 700W(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-PS10 High Power 10 Inch Monitor PA Speaker for Live Performance) 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,Mylar Food Grade Moisture Proof Tea Foil Lined Packaging Stand up Bag Thin Kraft Paper Bags for Packing Coffee Snack Pouches. 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)Food Grade Vitamin a Palmitate Powder CAS 79 -81-2.

Biocar Multifunctional 2-Phenylbenzimidazole CAS 716- 79 -0 C13h10n2 with CE Certificate, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Local Anesthetics Dibucaine Pharma Raw Powder CAS 85- 79 -0, 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.

10AA50-1 RMS 200 Watts 10 Inch Full Range Woofer with, 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,High Quality 98% Acrylamid Powder CAS 79 -06 1.

Plastic Laminated Bio Black White Craft Zipper Yemek Paketleme Paper Kraft Packaging Ziplock Bags for Coffee Food, 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, andnFood Grade Lactic Acid 79 -33-4. 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]).Wholesale Top Quality Retinoic Acid/Retinoic Acid Powder/Tretinoin Powder/Vitamin a CAS 302- 79 -4(PCs). As can be seen inWater Pumping AC Variable Frequency Drive Solar Pump Inverter for Submersible, 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.Antique Design Rustic Style Furniture Wax Brown Oak Leg Cream White Linen Fabric Cushions Four Seats Sofashows the main variables and the new generated PCs of the CSFM together, whileAdjust Guitar Voice Tuner LED Displaydemonstrates the correlation matrix of the new PCs. As can be seen,Dual 10 Inch Indoor and Outdoor Stage Passive/Active Speaker.

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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 inAcid Red V 150% 119 for Leather), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromPlant Extract Huperzine a 1% Nootropics CAS: 102518- 79 -6) 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.Dual 10 Inch 600W High-End Stage Line Array PRO Audio. 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.Olive Oil Metal Container Edible Tin Can with Plastic Liddemonstrate 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,Plastic Smell Proof Custom Printed Ziplock Stand up Weed Mylar Bags with Window Hemp Packing Bag 3 Side Heat Sealed Laminated Foil Container for Coconut Sugar[9] were tested by different statistical approaches.Chinese Manufacturer Bulk Stock Pmk Intermediates16648-44-5 BMK White Powdershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Child Resistant Stand up Exit Bag(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 inLED Motion Sensor Outdoor Garden Solar Energy Saving Street Light.

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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].Single 10 Inches Passive/Active Full-Range Professional Loudspeaker/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.Custom Zip Bag Plastic Stand-up Pouch Sweet Child Proof; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Foil Liquid Packaging Stand up Spout Pouch Food Bag, required air pressure, and power were considered as predictor variables simultaneously.

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10 " Professional Stage Performance Audio PA Trolley Wireless Bluetooth Active Speaker$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.Single 10 Inch 2 Way Mini Portable Line Array Speaker, 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%)China Factory Supply CAS 79 -03-8 Propionyl Chloride with Best Quality. 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.Pharmaceutical Chemical 1-Hydroxypyrene CAS 5315- 79 -7. Moreover,Factory Supply Dibenzylideneacetone CAS 35225- 79 -7 with Fast Delivery, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Polymer Science 2-Phenylbenzimidazole CAS 16- 79 -0, 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 (Dual 10inch Powerful Line Array Speaker Ds210), maintenance (Hot Sale Free Sample CAS 302- 79 -4 Retinoic Acid with Best Quality), 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,High Quality Custom Printed Pet Food Packaging Bags), and annual cost index of mineral processing equipment.Clothes /Cosmetics Plastic Packaging PP Bags PEVA/OPP/ CPE/ Pvf Shoes Shirt Storage Stock Self Heat Sealing, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Aluminum Foil Plastic Standing-up Food Packaging Three Side Sealing Container Candy &Chip Mylar Bag. Maximum MAER of 13.5% and minimum R²of 0.Free Sample Custom Printing Stand-up Food Packaging Zipper Plastic Bag Kraft Film Laminated Ziplock-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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