Neural Networks for Cost Estimation of Shelland Tube Heat Exchangers

Orlando Duran ∗Nibaldo Rodriguez †Luiz Airton Consalter ‡

Abstract—The objective of this paper is to developand test a model of cost estimating for the shell andtube heat exchangers in the early design phase via theapplication of artificial neural networks (ANN). AnANN model can help the designers to make decisionsat the early phases of the design process. With anANN model, it is possible to obtain a fairly accurateprediction, even when enough and adequate informa-tion is not available in the early stages of the designprocess. This model proved that neural networks arecapable of reducing uncertainties related to the costestimation of a shell and tube heat exchangers.

Keywords: Cost Estimation, Heat Exchangers, Neural

Networks, Shell and Tube.

1 Introduction

Cost estimation is a key factor during the developmentphases of manufactured products. Early approximationsof cost as a function of a set of general characteristics helpdesigners in decisions such as selecting materials, produc-tion processes and mainly morphological characteristicsof the product. Studies have shown that the greatest po-tential for cost reduction is at the early design phases,where as much as 80% of the cost of a product is de-cided. As the design phase itself accounts for a relativelysmall percentage of the total development cost, devotinga greater effort to design to cost is a reasonable and nec-essary step towards optimizing product costs. Making awrong decision at this stage is extremely costly furtherdown the development process. Product modificationsand process alterations are more expensive the later theyoccur in the development cycle. Thus, cost estimatorsneed to approximate the true cost of producing a prod-uct. In addition, since cost estimating is the start of thecost management process and influences the ’go/no-go’decisions concerning a new product development, ideally,these go decisions regarding new product development orproduct design changes must be based on quantitativeanalysis instead of guesswork. Rush et all. [2] examineboth traditional and more recent developments in cost es-

∗orlando.duran@ucv.cl. Pontificia Universidad Catolica de Val-paraiso, Chile.

†nibaldo.rodriguez@ucv.cl, Pontificia Universidad Catolica deValparaiso, Chile.

‡lac@upf.br FEAR, Univesidade de Passo Fundo, Passo Fundo,RS , Brasil.

timating techniques in order to highlight their advantagesand limitations. The analysis includes parametric esti-mating, feature based costing, artificial intelligence, andcost management techniques. Niazi et all. [4] provide adetailed review of the state of the art in product cost es-timation covering various techniques and methodologiesdeveloped over the years. The overall work is categorizedinto qualitative and quantitative techniques. The qual-itative techniques are further subdivided into intuitiveand analogical techniques, and the quantitative ones intoparametric and analytical techniques. Curran et all. [5]provide a comprehensive literature review in engineeringcost modeling as applied to aerospace. Three main quan-titative approaches can be identified for cost estimationpurposes:

Analogy-based techniques: these techniques are based onthe definition and analysis of the degree of similarity be-tween the new product and another one, which has beenalready produced by the firm.

The parametric method: the cost is expressed as an ana-lytical function of a set of variables that consist or repre-sent some features of the product which are supposed toinfluence mainly the final cost of the product. These func-tions are called Cost Estimation Relationships (CERs)and are built using statistical methodologies.

Analytical Models: in this case the estimation is basedon the detailed analysis of the manufacturing process andof the features of the product. The estimated cost of theproduct is calculated in a very analytical way, as the sumof its elementary components, constituted by the value ofthe resources used in each step of the production process(raw materials, components, labor, equipment, etc.). Dueto this, the engineering approach can be used only whenall the characteristics of the production process and of theproduct are well defined. Therefore, the application ofthis approach is limited to situation where a great amountof input data is available.

Through a review in the cost estimation literature it canbe observed that an incipient number of cases that useartificial intelligence (AI) techniques have been reported.These techniques constitute the last generation of toolsfor manufactured product cost estimation. The basic con-cept behind the application of AI in cost estimating is to

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol IIIMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3 IMECS 2008

imitate the behavior of a human expert in determiningthe main variables that rule (and in what extend theydo) the final cost of a manufactured product. Thus far,the most used AI technique in cost estimation is the CaseBased Reasoning. This technique is similar, in essence, tothe analogy based technique. AI techniques allow model,store and reuse information and to capture the relativeknowledge about products yet produced for adapting it tonew situations i.e. new products under development. [1]proposed Case-Based Estimator (CBE). CBE is a smallmodel, consisting of five input features, one output and asmall case base. According to the authors, an experimentwas performed to assess the ability of two retrieval mech-anisms (one a simple mathematical formula, the otheran adaptation of the ID3 decision tree generating algo-rithm) to measure similarity. The simple formula wasfound to be more preferable, both in terms of consistencyand development effort. Another case based system forthe cost estimation is presented in [6]. They proposed anintelligent system for predicting of total cost of stampingtools. The work is limited to tools for manufacture ofsheet metal products by stamping. On the basis of tar-get and source cases, the system prepares the predictionof costs. The results show that the quality of predictionsmade by the intelligent system is comparable to the qual-ity assured by the experienced expert. Artificial NeuralNetworks (ANN) has been the most explored AI basedtechnique in research on cost estimation. Neural net-works, as non-parametric approximators attempt to fitcurves through data without being provided a predeter-mined function with free parameters. Neural networksare therefore able to detect hidden functional relation-ships between product attributes and cost, i.e. relation-ships unknown to the cost engineer [7]. investigates thepotential of neural networks to support cost estimation atthe early stage of product development. The cost estima-tion performance is compared to conventional methods,i.e. linear and non-linear parametric regression. Neuralnetworks achieve lower deviations in their cost estima-tions. Cavalieri et all. [19] reported the compared resultsof the application of two different approaches-respectivelyparametric and artificial neural network techniques-forthe estimation of the unitary manufacturing costs of anew type of brake disks produced by an Italian manu-facturing firm. Kim and Han [8] proposed hybrid arti-ficial intelligence techniques to resolve these two prob-lems. Genetic algorithms are used to identify optimalor near-optimal cost drivers. In addition, artificial neu-ral networks are employed to allocate indirect costs withnonlinear behavior to the products. Empirical resultsshow that the proposed model outperforms the conven-tional model. Some applications of ANN not properly incost estimation but in cost drivers estimation in Activitybased Costing (ABC) are reported in the literature. Kimand Han [9] applied hybrid models of neural networksand genetic algorithms (GA) to cost estimation of res-idential buildings to predict preliminary cost estimates.

Kwan and Ahn [10] presented a learning algorithm basedestimation method for maintenance cost as life cycle costof product concepts.

Seo et all. [11] explores an approximate method for pro-viding the preliminary life cycle cost. Learning algo-rithms trained to use the known characteristics of ex-isting products allow the life cycle cost of new productsto be approximated quickly during the conceptual designphase without the overhead of defining new LCC mod-els. Artificial neural networks were trained to generalizeproduct attributes and life cycle cost data from preexist-ing LCC studies. Because of this approach, there is stillconsiderable uncertainty within the estimate, which canaffect the final result. One approach that arises is ap-plying fuzzy sets and fuzzy reasoning for modeling situa-tion using linguistic variables. With this approach calledfuzzy logic, it is possible to handle the uncertainty incost estimation problems that cannot be addressed bythe traditional techniques. This uncertainty is productof a sort of tolerance for imperfection of human when istransferring ideas or information as the emission of opin-ions. Shehab and Abdalah [12] proposed an intelligentknowledge-based system for product cost modeling. Thedeveloped system has the capability of selecting a mate-rial, as well as machining processes and parameters basedon a set of design and production parameters; and of es-timating the product cost throughout the entire productdevelopment cycle including assembly cost. The proposedsystem is applied without the need for detailed design in-formation, so that it can be used at an early design stage.Fuzzy logic-based knowledge representation is applied todeal with uncertainty in the knowledge of cost model togenerate reliable cost estimation. The system has beenvalidated through a case study. Other proposals includethe use of non traditional techniques for cost estimation.Koonce et all. [13] presents the design and implemen-tation of a customizable cost integration tool to supportdesign time optimization that considers cost as an objec-tive function or constraint. Giachetti and Arango [14]reported an activity-based printed circuit board (PCB)cost estimation model. The proposed model estimatesPCB cost based on the design parameters. The activitiesare defined so that the design decisions become the costdrivers and thus enable the cost estimation model to beutilized early in design process when sufficient time re-mains to make design changes. The cost model is usedto rapidly compare different PCB design alternatives andlets the designer assess the impact of their decisions onfinal cost and aid the designer in generating lower costalternatives. Zbayraka et all. [15] discussed the imple-mentation of the Activity Based Costing (ABC) approachalongside a mathematical and simulation model to esti-mate the manufacturing and product cost in an auto-mated manufacturing system. ABC was been used tomodel the manufacturing and product costs. An exten-sive analysis was been carried out to calculate the product

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol IIIMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3 IMECS 2008

costs under the two strategies. The comparison of thetwo strategies in terms of effects on the manufacturingand product costs are carried out to highlight the dif-ference between the two strategies. H’midaa et all. [16]introduces the new concept of Cost Entity and proposedtwo models, a Product Model and a Costgrammes Model.The cost estimating reasoning procedure, that takes intoaccount alternative process plans of a product, is modeledand solved by a constraint satisfaction problem (CSP). In[18] a framework for estimating the manufacturing costin terms of a feature-based approach is proposed. Thissystem tends to estimate the manufacturing cost of a de-sign according to the shapes and precision of its features.The approach integrates a feature-based CAD model anda database-storing product and process cost.

2 Heat Exchangers Design

Shell-and-tube heat exchangers are probably the mostcommon type of heat exchangers applicable for a widerange of operating temperatures and pressures. Theyhave larger ratios of heat transfer surface to volume thandouble-pipe heat exchangers, and they are easy to man-ufacture in a large variety of sizes and flow configura-tions. They can operate at high pressures, and theirconstruction facilitates disassembly for periodic mainte-nance and cleaning. Shell-and-tube heat exchangers findwidespread use in refrigeration, power generation, heat-ing and air conditioning, chemical processes, manufac-turing, and medical applications. A shell-and-tube heatexchanger is an extension of the double-pipe configura-tion. Instead of a single pipe within a larger pipe, a shell-and-tube heat exchanger consists of a bundle of pipes ortubes enclosed within a cylindrical shell. One fluid flowsthrough the tubes, and a second fluid flows within thespace between the tubes and the shell (Fig. 1).

The main purpose of a heat exchanger is to capture heatthat would otherwise be lost through waste gases or liq-uids and return that heat to some stage of the produc-tion process. Heat exchangers have been used in variousindustrial processes for more than 60 years. The mostcommonly used type of heat exchanger is the shell-and-tube heat exchanger, the optimal design of which is themain objective of this study. Various strategies are ap-plied for the optimal design of heat exchangers. The mainobjective in any heat exchanger design is the estimationof the minimum heat transfer area required for a givenheat duty, as it governs the overall cost of the heat ex-changer. However there is no concrete function that canbe expressed explicitly as a function of design variablesand in fact many numbers of discrete combinations of thedesign variables are possible.

Early cost estimate of a part is important information andforms a basis for preparing quotations, which are compet-itive from a market point of view. The cost of any highly

A Removable channeland cover 1.03

B Integral Cover 1.00C Integral with Tubesheet

removable cover 1.06N Channel Integral with

tubesheet and removable cover 1.05D Special High Pressure closures 1.60

Table 1: Correction factor for front or stationary headtypes.

L Fixed Tube SheetLike ”A” Stationary Head 0.83

M Fixed Tube SheetLike ”B” Stationary Head 0.80

N Fixed Tube SheetLike ”C” Stationary Head 0.85

P Outside Packed Floating Head 1.04S Floating Head with Backing Device 1.00T Pull-Through Floating Head 1.05U U-Tube Bundle 0.90

Table 2: Correction factor for rear head types.

engineered product is impacted significantly by decisionsmade at the design phases. While this influence decreasesthough all phases of the life cycle, the committed costsincrease. It is seen that a commonly adopted approachof variant cost estimation based only on geometric infor-mation of the component is not always accurate. Tra-ditional cost estimating methods for the different phasesof a project can be observed in the literature, including:traditional detailed breakdown cost estimation; simpli-fied breakdown cost estimation; cost estimation based oncost functions; activity based cost estimation; cost indexmethod; and expert systems. While traditional cost esti-mating makes use of blueprints and specifications, com-parative cost estimating assumes a linear relationship be-tween the final cost and the basic design variables of theproject. By the emergence of Artificial Intelligence (AI)tools (i.e., neural networks) possible multi- and non-linearrelationships can now be investigated.

Several authors have concluded that the area of the ex-changer bears a strong relation to the total cost and whileit considerably impacts the cost, therefore, the estimationof the cost of purchase is usually based on estimations ofthe heat transfer surface, and on earlier knowledge andexperience of exchanger manufacturing. In addition, theshell diameter and tube diameter also become importantfactors influencing directly the area of the exchangers un-der development. At the other hand, the pitch and con-figuration of the bundle are also clearly important fac-tors for the cost of the new heat exchanger. Finally,the heat exchanger type is identified as one of the mainkey parameters; Types of the exchanger are classified by

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol IIIMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3 IMECS 2008

Figure 1: Typical shell and tube heat exchanger withshell side fluid flow.

TEMA with a well-known nomenclature. Accordingly, ashell and tube exchanger is divided into three parts: thefront end, the shell, and the rear head. Please refer toreference [3] for more details on Shell and tube heat ex-changers. We use correction factors related to front orstationary head type (f) and rear head type (r) as factorsthat represent the heat exchanger type. Tables 1 and 2show the correction factors f and r respectively. Finallythe cost per area can be expressed as a function of tubepitch (Pi), f and r factors and shell and tube diameters(Dsi and do, respectively).

3 Methodology

The main hypothesis of this research is that by using neu-ral networks based techniques is possible to develop costsestimation models for shell and tube exchangers duringearly design stages in a make to order production sce-nario. Through experimentation using simulated datathese models will be used to provide answer to the fol-lowing research questions:

• Is possible estimate the product costs using soft com-puting methods?

• Incomplete information is an impediment to effectiveproduct costs estimations?

• A very small set of product characteristics can beused for cost estimation using soft computing basedmethods?

A case of shell and tube heat exchangers was simulatedusing data based on a cost function. In this simulation,it was pretended that a company wanted to estimate thecost of a new heat exchanger in its conceptual design

Design Parameter ParameterParameter Definition Rangex1: Pi Tube Pitch(in) 0.40-2.00x2: Dsi Shell diameter(mm) 10.0-150x3: do Tube diameter (mm) 0.60-2.00x4: r Rear head factor 0.80-1.50x5: f Stationary head factor 1.00-1.60

Table 3: Design parameters for the input layer of theANN tested

stage. The experiment presupposed that product costs ofall similar exchangers follow the same single cost function,so that costs are completely determined by the productattributes known at the time of cost estimation. Infor-mation about heat exchangers provided by different man-ufacturers and designers was used for construct plausiblecost function. This function was used to generate train-ing and test data. function. Situating the simulations atan early phase of development, only six attributes aboutthe product in question are available. Table 3 depictsthe attributes and their value ranges for all simulations.Training and testing data for all simulations were gener-ated with randomly chosen input values. Neural networkswere then applied to these data, and it was tested howwell they were able to fit the underlying cost function.

A set of configurations of neural networks for cost estima-tion during early design stages in a make to order produc-tion scenario were defined and tested. The performanceof the different configurations and training strategies usedin this research were compared and tested. In a number ofexperiments, neural networks were trained and applied toa set of case data. The accuracy of the cost estimation re-sults and other indicators of performance were explored.The experiments were made up according to the follow-ing strategy: training and test data for the experimentswere generated by the MonteCarlo method ascertainingthat they follow a given cost function. In this simulation,a hypothetical company wants to estimate the cost of anew heat exchanger during its conceptual design stage.The experiment presuppose that product costs follow thesame single cost function, so that product costs are com-pletely determined by the product attributes totally orpartially known at the time of cost estimation. Oncethe data be generated by the simulation experiment, al-ternatives of configuration of neural networks were thenapplied to these data, and tested how well they wereable to fit the underlying cost function. Therefore, sev-eral sensibility experiments were carried out for testingthe correlation degrees of the parameters included in themodels. The neural network modeling phase correspondsto a complex and dynamic process that requires the de-termination of the internal structure (i.e., the numberof hidden layers and neurons and the type of activationfunctions, plus the learning algorithm for training phase).Usually, the number of processing elements and hidden

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol IIIMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3 IMECS 2008

Test Training Set Testing Set Number ofNumber Size Size neurons/layer

1 200 100 4,4,12 100 100 10,20,13 50 100 10,20,14 200 100 10,20,15 200 100 10,10,16 200 100 10,17 100 100 4,4,18 100 200 10,10,19 100 100 10,1

10 50 100 4,4,111 50 100 10,10,112 50 100 10,1

Table 4: Alternative configurations of tested ANN.

Test CPENumber %

2 75,3811 69,63 68,49

12 67,877 64,158 57,91

10 57,789 48,911 20,454 20,456 5,325 5,31

Table 5: Results obtained in test runs

layers are determined by trials, since there is no rule todetermine it. Therefore, the neural network model weredetermined empirically, rather than theoretically derived.With regard to the specific neural architecture used, themultilayer perceptron (MLP) has been preferred, since itusually leads to the most satisfactory results. The properstructure has been selected after having tested more ANNconfigurations with different numbers of hidden layers,different numbers of neurons for each level, and differentinter-unit connection mechanisms as illustrated in table1.

The models performance is measured by using the costpercentage error (CPE) formula (Eq. (1)):

CPE =E(i)− T (i)

T (i)∗ 100% (1)

Where E(i) is the model output, T(i) is the target output.The results of the testing phase are reported in Table 5.

In addition, some comparison between actual costs ver-sus predicted costs were performed. Figure 2 shows the

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T

A

Best Linear Fit: A = (1.11) T + (−0.00689)

R = 0.97Data PointsBest Linear FitA = T

Figure 2: Comparison between test data and output dataas scatterplot.

scatterplot of actual versus predicted costs for experi-ment 5. It is seen that most of the points lie very closeto the line for strong prediction. For perfect prediction,all points should lie on this line. Hence, this chart pro-vides the linear equation of the regression line (in theform of Y=Ax+B) between predicted and actual values.In this equation the closer to 0 is the B factor and thecloser to 1 is the slope of the line (A factor), the bettercan be considered the estimation. The model number 5has been selected. The configuration of the neural net-work include an input layer of 5 neurons correspondingto the five input parameters and an output layer of oneneuron as the target (cost per exchange area). Two hid-den layers both with 10 neurons. The input parameters(design variables and predominant cost drivers) for theinput layer are presented in Table 1. The learning algo-rithm selected corresponds to Levenberg-Marquardt andthe transfer function is logsig. Figure 3 plots the com-parisons between simulated and real values of the testingset. Note that the determination coefficient R2 is equalto 0,94 and the correlation coefficient (R) is equal to 0,97.

4 Conclusions

A neural network based model has been developed forearly cost estimation of shell and tube heat exchangersby applying the principles of supervised learning of neu-ral networks. This model proved that neural networksare capable of reducing uncertainties related to the costestimation of a shell and tube heat exchangers. The useof cost estimation predictive models in the first stages ofthe highly product development process is of fundamen-tal importance to start of the cost management processand influences the ’go/ no go’ decisions. The anticipatedknowledge of cause-effect relationships between design so-lutions and the production costs is extremely useful bothfor internal manufacturing activities, and for purchasedparts. Through the Artificial Neural Networks approach

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol IIIMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3 IMECS 2008

0 20 40 60 80 1000

0.1

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Figure 3: Comparison between test data and output data.

the possibility of building a full-scale knowledge-basedmodel for predicting the total cost of heat exchangers isbroaden. This approach solves the complex non-linearmapping for predicting the total heat exchanger cost atany phase of the design process.

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[19] Cavalieri, S., Maccarrone, P., Pinto R., Parametricvs. neural network models for the estimation of pro-duction costs: A case study in the automotive indus-try Int. J. Production Economics 91 (2004) 165-177

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol IIIMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3 IMECS 2008