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Application of glyph-based techniquesfor multivariate engineeringvisualizationVladimir Glazara, Gordana Marunica, Marko Percica & ZlatkoButkovicb

a Department of Mechanical Engineering Design, Faculty ofEngineering, University of Rijeka, Rijeka, Croatiab Graduate University Study Programme of MechanicalEngineering, Faculty of Engineering, University of Rijeka, Rijeka,CroatiaPublished online: 06 Jan 2015.

To cite this article: Vladimir Glazar, Gordana Marunic, Marko Percic & Zlatko Butkovic (2015):Application of glyph-based techniques for multivariate engineering visualization, EngineeringOptimization, DOI: 10.1080/0305215X.2014.994866

To link to this article: http://dx.doi.org/10.1080/0305215X.2014.994866

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Engineering Optimization, 2015http://dx.doi.org/10.1080/0305215X.2014.994866

RESEARCH ARTICLE

Application of glyph-based techniques for multivariateengineering visualization

Vladimir Glazara∗, Gordana Marunica, Marko Percica and Zlatko Butkovicb

aDepartment of Mechanical Engineering Design, Faculty of Engineering, University of Rijeka, Rijeka,Croatia; bGraduate University Study Programme of Mechanical Engineering, Faculty of Engineering,

University of Rijeka, Rijeka, Croatia

(Received 13 February 2014; accepted 28 October 2014)

This article presents a review of glyph-based techniques for engineering visualization as well as practi-cal application for the multivariate visualization process. Two glyph techniques, Chernoff faces and starglyphs, uncommonly used in engineering practice, are described, applied to the selected data set, runthrough the chosen optimization methods and user evaluated. As an example of how these techniquesfunction, a set of data for the optimization of a heat exchanger with a microchannel coil is adopted forvisualization. The results acquired by the chosen visualization techniques are related to the results of opti-mization carried out by the response surface method and compared with the results of user evaluation.Based on the data set from engineering research and practice, the advantages and disadvantages of thesetechniques for engineering visualization are identified and discussed.

Keywords: glyphs; Chernoff faces; star glyphs; heat transfer; optimization

1. Introduction

The term visualization has numerous meanings and definitions, which can cause a loss of focusand some confusion. According to the Oxford English Dictionary (2013), the verb visualizemeans ‘to form a mental image of something or to make (something) visible to the eye’. Moderndefinitions of visualization involve the tools or methods of data interpretation. Wright (2007)states that, ‘visualization as a human activity predates computing by hundreds of years, possiblythousands if we include cave paintings as examples of Man’s attempts to convey mental imageryto his fellows’. Earnshaw (1992) defined the term scientific visualization as follows: ‘Scientificvisualization is concerned with exploring data and information in such a way as to gain under-standing and insight into the data’. To achieve this goal, this interdisciplinary branch of scienceembraces the areas of computer graphics, user-interface methodology, image processing, systemdesign and signal processing (Aref, Charles, and Elvins 1994). This discipline was referred to bya report for the US National Scientific Foundation (McCormick, De Fanti, and Brown 1987).

Among a growing number of published articles with the keyword ‘visualization’ there can befound valuable review articles. Ropinski, Oeltze, and Preim (2011) conducted a survey of glyph-based visualization techniques. Although the focus of this investigation was on medical data, the

*Corresponding author. Email: vglazar@riteh.hr

© 2015 Taylor & Francis

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taxonomy of glyph properties, followed by guidelines to improve glyph-based visualization, canbe applied without reference to data type. Six proposed guidelines have been derived from thebest medical practice and they reflect the current state of the art. Edmunds et al. (2012) presentan up-to-date overview of the surface-based flow visualization that highlights the solved andunsolved problems in the visualization of three-dimensional (3D) flow. While two-dimensional(2D) flow obtains a lot of good solutions, the visualization of 3D flow is affected by issues suchas domain coverage, perception and speed of computation. A scene-graph based visualizationmethod that can verify time-varying continuous analysis simulation in a virtual reality environ-ment using the computer-aided engineering data of structural analysis in product developmentwas proposed by Song and Yang (2011). They used the visualization system for manipulationwith an OpenSG scene graph to translate and represent continuous simulation data consisting ofa sequence of time-step scenes and analysis data.

This article focuses on the practical application of glyph-based techniques in a multivari-ate engineering visualization process, which involves a number of independent mathematical orstatistical variables. Two glyph techniques that are uncommonly used in engineering practice,namely Chernoff faces and star glyphs, are assessed. Chernoff faces are simplified, cartoon-like faces that can be used to graphically display complex multivariate data (Chernoff 1973),while the star glyph is a multivariate graphing technique in which each variable is representedby a ray that extends out of a common origin, with equal angular distances between the rays(Chambers et al. 1983). Kindlmann (2004) reported the results and experience gained in theinvestigation of diffusion tensor glyph visualization. Diffusion tensor magnetic resonance imag-ing (DT-MRI) is a method used to non-invasively reveal abnormalities in the white matter fibrestructure and to provide models of brain connectivity. By carefully distributing glyphs throughoutthe field, using potential energy profiles shaped by the local tensor value, the underlying contin-uous features became more apparent. Kindlmann (2004) demonstrated the improved method ona DT-MRI scan. The same author proposed new glyphs and demonstrated them on the fieldsof diffusion tensors from the human brain (Kindlmann and Westin 2006). Likewise, Rusu etal. (2009) proposed enhanced star glyphs for multiple-source data analysis. Their techniquesincluded clustering, using the colour as identifiers and 3D graphing capabilities to present moredata that otherwise might not have been shown in a 2D environment. They applied these tech-niques to compare several air traffic trajectory predictors currently being analysed by the USFederal Aviation Administration.

The considered techniques are well known but scarcely applied to engineering. The dataused for visualization in this article were acquired from experimental and numerical analysisof heat transfer and fluid flow in compact heat exchangers. A detailed mathematical approachand detailed description of the experimental apparatus can be found in several articles (Glazar,Frankovic, and Trp 2014; Glazar, Trp, and Lenic 2012). The acquired investigation results havebeen partly related to the results of optimization carried out by the response surface method(Kanaris, Mouza, and Paras 2009).

2. Glyph-based visualization

According to a simple definition, a glyph is an individual mark on a written medium that con-tributes to the meaning of what is written. The word glyph comes from Greek glyphe, whichmeans to carve, and glyphein, to engrave. In science, a glyph is generally a graphical object thatrepresents data values at a point in space. An example of glyph application in engineering is amodel with arrows, where the arrow orientation represents the air flow and the length of the arrowits magnitude. As another example, to visualize complex molecular structures, chemists may use

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Engineering Optimization 3

coloured balls to represent individual atoms in the molecule and sticks of different length theconnections between the atoms. Glyphs are widely used in data visualization and are suitable fordisplaying all kind of multivariate data sets as they translate data using different attributes, suchas size, colour, position and shape.

2.1. Chernoff faces

Herman Chernoff, mathematician, physicist and statistician, who is currently a professor emeri-tus at Harvard, first used faces to represent points in n-dimensional space graphically (Chernoff1973). Later, his invention was appreciated by others and named after him as the technique ofChernoff faces.

Put simply, Chernoff faces are 2D glyphs that allow the display of multivariate data in the formof a human face. Some face parts, such as eyes, ears, mouth and nose, are the values of variablesaccording to their shape, size, position and orientation. The idea of using the face was developedso that people could easily recognize and notice small changes in the data visualized withoutdifficulty and confusion. Since some facial features can be easily distinguished from others, it isvery important that the variables are carefully selected. An example of a Chernoff face is shownin Figure 1.

This technique enables the presentation of several variables on a 2D surface. Different vari-ables can be attached to the selected facial properties, such as eye spacing, head eccentricity,eye size, nose size, mouth curvature, mouth width, mouth openness, nose width, pupil size, eyeeccentricity and eyebrow slope (Gonick and Smith 1993).

Among numerous applications of this method, a well-known one is the display of life qualityin certain parts of Los Angeles (Zhou and Spinelli 2004). The authors defined the faces in sucha way that the colour of the face was determined by the percentage of white population, the sizeof the eyes represented the urban stress level, the mouth gesture reflected the unemployment rate(smiling, serious or sad) and the head shape was determined by the affluence of people in thatpart of the city.

Although Chernoff faces are discussed and referenced on every information/data visualizationcourse, some argument about their usability can be found among scientific articles (Kosara 2007).According to Kosara et al. (2008),

criticism is a vital part of the practice of design, architecture, and art, and as such, is taught and practiced aroundthe world. As visualization is in many aspects similar to design and art, criticism isn’t a bad thing, it should beappreciated as a valuable tool for pointing out and learning from mistakes.

The motivation for using this approach in this article, and in general, is taken along with thestatement that humans are excellent at recognizing faces and noticing small changes in them(Song, Zhao, and Wang 2010).

Figure 1. Chernoff faces technique.

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Figure 2. (a) Main star glyph; (b) star glyph with spheres; and (c) clustered star glyph.

2.2. Star-based glyphs

The star glyph is a graphical multivariate technique in which each variable is shown as a ray.Each ray is associated with a common origin and the angle between the rays is the same. Thelength of ray is proportional to the value of a certain variable (Chambers et al. 1983).

The main star glyph, sometimes called a basic star glyph, has two dimensions: the categoricalvalue is represented by different spokes and the quantifiable value by their length. Figure 2(a)shows the main star glyph. With the addition of another attribute axis, data can be visualizedas shown in Figure 2(b), where the radius of each sphere represents a proportional value of anadditional attribute. More data can be added to the same star glyph by using differently colouredspheres. Star glyphs are very effective in the determination of unsuitable members of a group.However, problems occur when the data set becomes too large and the graph thus becomes toocluttered to be useful, as shown in Figure 2(c).

In this article, multiple star glyphs have been used, allowing the comparison of multivariateresults from several different geometries.

3. Background of data sets adopted for the visualization

All data used in this article were acquired from the experimental and numerical analysis of heattransfer and fluid flow in compact heat exchangers (Glazar 2011). The working media temper-atures, mass flow rates and pressure drops for two heat exchangers with a microchannel coilwere measured in an open-circuit wind tunnel. In accordance with the heat exchangers usedfor the experiments, numerical 3D models of adequate geometry were developed. Good agree-ment between the experimental and numerical results was attained. A short description of thebackground to the data follows.

3.1. Experimental set-up

Figure 3 is a schematic representation of the wind tunnel available at the Faculty of Engineering,University of Rijeka, Croatia, with the provision to supply high-pressure air to the test unit atambient temperatures.

The wind tunnel was used to measure the working media temperatures and mass flow ratesof two heat exchangers with a microchannel coil. Air and distilled water were used as workingfluids. The main components of the system were heat exchangers with a microchannel coil, water

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Engineering Optimization 5

Figure 3. Schematic representation of the wind tunnel test apparatus.

flow loops, air supply unit, instrumentation and data acquisition systems. The open-circuit windtunnel system was used to suck the air from the laboratory or from the open air over the airhandling unit, with the capability of preheating the air. The National Instruments SCXI dataacquisition, automation and control module system was used. A National Instruments DAQ-Card was used to connect the system to a personal computer (PC). All virtual instruments weredeveloped in LabView, which was installed on a PC.

During the experiments, the mass flow rate mw(kg · h−1) of the water was varied from 200 to2000 kg h−1 using the flow control valve and high-efficiency smart pump. The air velocity va (ms−1) in the ducts was varied from 1 to 6 m s−1 by adjusting the damper positions using a levermechanism. The temperature of water at the inlet and outlet Tw,in, Tw,out (K), the inlet and outlettemperatures of air Ta,in, Ta,out (K), and the pressure drop across the air and water sides �pa,�pw (Pa) were measured for different flow rates.

3.2. Heat exchanger with microchannel coil

The microchannel coil used in this article consists of 68 parallel flat tubes connected withwavy fins. Flat tubes were made of 18 rectangular channels, each with a hydraulic diameterof dh = 0.99 mm. The fin pitch value is Fp = 1.45 mm and the fin thickness Ft = 0.1 mm. Thetested heat exchanger with a microchannel coil is shown in Figure 4.

Figure 4. Front view of the microchannel coil used in the experiments.

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Figure 5. Schematic view of the computational domain.

3.3. Mathematical and numerical approach

The air/water model (Borrajo-Pealez, Ortega-Casanova, and Cejudo-Lopez 2010) was used.Owing to limitations of the computer resources, only the portion of the heat exchanger ableto describe the flows of air and water was taken into account. Two planes of symmetry wereassumed in the z-direction, perpendicular to the fin surface so that the flat tubes were dividedinto two identical parts. A schematic view of the computational domain is shown in Figure 5.

In Figure 5, the upstream and downstream regions have not been presented in proportionaldimensions. The computational domain consists of six volume groups: the air upstream region(1), the internal airspace (2), the air downstream region (3), fins (4), the water region (5) andthe two halves of flat tubes (6). The total length of the computational domain has been extendednine times from the actual internal airspace. The upstream region has been extended two-and-a-half times to ensure inlet uniformity and the downstream region has been extended six times toprevent flow recirculation.

The results acquired by the numerical model were compared in the same ranges of airand water temperature and velocities used in the experimental investigation. A good agree-ment between the results was obtained for more than 100 measurements and can be seen inGlazar (2011).

4. Prescribed data set

Compact heat exchanger geometry optimization was carried out for the doctoral thesis (Glazar2011). Multivariate optimization included three geometric parameters that have been shown toinfluence the hydrodynamic behaviour of the system. These geometric parameters are shown inFigure 6: the distance between flat tubes Pt, the fin pitch Fp and the number of small rectangularchannels nsc.

In addition, one operating condition expressed by the water inlet velocity vw,in (m s−1) wasincluded in the multivariate analysis and optimization, making a total of four independentvariables for this design.

5. Optimization method

For design problems that involve computation-intensive analysis or simulation processes,approximation models are usually introduced to reduce the computation time. Wang, Dong, and

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Figure 6. Schematic view of the tested heat exchanger with microchannel coil.

Aitchison (2001) presented the adaptive response surface method, which they tested successfully.A detailed description of the method was followed by a discussion on the advantages and limita-tions of the newly developed method. Response surface-based design optimization has been alsocommonly been used for optimizing large-scale design problems in the automotive industry (Shi,Yang, and Zhu 2013). The authors created and presented an efficient response surface strategy,which minimizes the number of computationally intensive simulations.

The applied response surface method includes the collection of techniques (i.e. design ofexperiments, regression analysis and analysis of variance) that allow the designer to extractas much information as possible from a limited number of test cases. A four-level full facto-rial design would require 81 design points, compared to the 27 design points required by theBox–Behnken method (Box and Behnken 1960; Kanaris, Mouza, and Paras 2009).

For the purposes of this article, a set of 15 design points of a heat exchanger with amicrochannel coil was filtered and prescribed (Table 1).

The previously experimentally validated numerical model was used to predict the heat transferrate Qhe (W) and pressure drops of air �pa and water �pw in this type of equipment (Table 2).

Several objective functions have been developed and employed as an optimization procedureusing the response surface method. The developed objective functions f 1–f 5 are subjected to theresults from the air and water pressure drops �pw and �pa, the heat transfer rate Qhe and the

Table 1. Set of prescribed design points.

x1 x2 x3 x4No. Pt (mm) Fp (mm) nsc (/) vw,in (m/s)

1 15 2 25 0.82 10 1.5 25 0.83 5 2 25 0.84 15 1.5 30 0.85 5 1.5 30 0.86 5 1 25 0.87 10 2 30 0.88 10 1 20 0.89 10 1.5 25 0.8

10 15 1 25 0.811 15 1.5 20 0.812 10 1.5 25 0.813 10 2 20 0.814 5 1.5 20 0.815 10 1 30 0.8

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Table 2. Numerically determined heat transfer rate and pressuredrops.

No. �pw (Pa) �pa(Pa) Qhe (W) mhe (kg)

1 241 6 1875 0.182 241 11 2524 0.253 241 11 2077 0.354 233 10 2590 0.235 233 17 2812 0.426 241 29 3391 0.427 233 7 2070 0.258 224 19 3391 0.279 241 11 2524 0.25

10 241 19 3359 0.2711 225 8 2336 0.1812 241 11 2577 0.2513 225 7 1846 0.2014 225 15 2486 0.3315 233 25 3466 0.34

mass of the heat exchanger mhe (kg). In functions f 2–f 5 parameter values are compared to theappropriated values acquired for the referent heat exchanger Qhe,ref, �pw,ref, �pa,ref and mhe,ref.The referent heat exchanger is defined by the prescribed design points for case no. 2, shown inTable 1.

Objective function f 1 combines the heat transfer rate and the weight of heat exchanger:

f1(x1, x2, x3, x4) = Qhe

mhe(1)

Objective function f 2 linearly combines the heat transfer rate with the pressure drop of air,using a weighting factor g1 = 0.9:

f2(x1, x2, x3, x4) = g1 · Qhe

Qhe,ref+ (1 − g1) · �pa,ref

�pa(2)

Objective function f 3 linearly combines the heat transfer rate with the pressure drop of water,using a weighting factor g2 = 0.7:

f3(x1, x2, x3, x4) = g2 · Qhe

Qhe,ref+ (1 − g2) · �pw,ref

�pw(3)

Objective function f 4 linearly combines the heat transfer rate and the mass of the heatexchanger, using a weighting factor g3 = 0.95:

f4(x1, x2, x3, x4) = g3 · Qhe

Qhe,ref+ (1 − g3) · mhe

mhe,ref(4)

Objective function f 5 linearly combines the pressure drop of air and pressure drop of water,using a weighting factor g4 = 0.5:

f5(x1, x2, x3, x4) = g4 · �pa,ref

�pa+ g4 · �pw,ref

�pw(5)

In all cases, the weighting factor accounts for the cost of energy in accordance with the rel-evant literature (Kundu, Barman, and Debnath 2008; Kundu and Das 2009.). Table 3 shows

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Table 3. Calculated values for the prescribed design pointsaccording to objective functions.

No. f 1 f 2 f 3 f 4 f 5

1 10,371 0.77 1.07 0.78 1.422 10,016 1.00 1.00 1.00 1.003 5,806 0.84 0.88 0.82 1.004 11,260 1.03 1.05 1.03 1.035 6,695 1.11 0.97 1.09 0.816 8,016 1.31 1.05 1.31 0.697 8,363 0.84 1.05 0.83 1.278 12,771 1.32 1.11 1.32 0.759 10,016 1.00 1.00 1.00 1.00

10 12,650 1.30 1.11 1.31 0.7911 12,905 0.94 1.06 0.95 1.1512 10,226 1.02 1.01 1.02 1.0013 9,430 0.77 0.98 0.76 1.2514 7,535 0.99 0.91 0.97 0.8315 10,270 1.34 1.09 1.34 0.70

all calculated values for the prescribed data according to the objective functions used in thevisualization process, as described in the next section.

6. Visualization results for the heat exchanger objective functions

6.1. Visualization by the Chernoff faces technique

The previously described data sets for visualization using Chernoff faces were employed. Theresults obtained for the five objective functions were associated with five different facial char-acteristics. For each of 15 prescribed data sets, one specific Chernoff face was constructed. Inthe early 1970s, the cost associated with drawing these faces was rather expensive. The imple-mentation of modern software packages that support this kind of visualization, such as Statistica,has made this technique more accessible. The program used for visualization in this article wasStatistica 64, version 10 (StatSoft 2010). This statistical and analytical software package includesdata analysis, data management, statistics, data mining and data visualization procedures. Figure7 shows the visualization results of the heat exchanger objective functions for the prescribeddesign points using Chernoff faces.

Chernoff faces carry each carefully selected variable. The first variable (objective function f 1)is displayed as the face width. The wider the face, the greater the heat transfer per weight and viceversa. It can be concluded that the values of prescribed data sets no. 8 and 10 are the highest,and the value of no. 3 is the lowest. To display the value of the second independent variable(objective function f 2), the vertical position of the ears is used (maximum at the top position).From Figure 7 it can be seen that the values of cases no. 6, 8, 10 and 15 have the highest verticalpositions, and the values of the no. 1 and 13 the lowest positions. To display the third variable(objective function f 3), the length of the nose is used. From this feature, it can be concluded thatcases no. 8 and 10 have the highest values, and cases no. 3 and 14 the lowest values. The fourthvariable (objective function f 4) is displayed as the length of the mouth. According to objectivefunction f 4, and Figure 7, it can be concluded that cases no. 6, 8, 10 and 15 have the highestvalues, and cases no. 1 and 13 the lowest values. The fifth variable (objective function f 5) isshown as the width of the nose: the wider the nose the greater the value, and the thinner the nosethe lower the value. From Figure 7, it can be concluded that cases no. 1 and 7 have the highestvalues and cases no. 6, 8, 10 and 15 the lowest values.

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Figure 7. Visualization of heat exchanger objective functions results using Chernoff faces.

6.2. Visualization by the star glyphs technique

The same data sets used for visualization by Chernoff faces were used for visualization by thestar glyph technique. The results are shown in Figure 8.

Different variables are displayed in Figure 8, with five rays starting from the same origin thatare arranged equidistantly in a circular pattern. The first independent variable (objective functionf 1) is set at 12:00 (as on a clock face) and the other variables are placed on the rays in a clockwisedirection (as shown on the legend at the bottom of the figure). The values of the variables areexpressed by the ray length, which is proportional to the value: a longer ray means a higher

Figure 8. Visualization of heat exchanger objective functions results using star glyphs.

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Engineering Optimization 11

value and vice versa. All values have been normalized to have the same length for the maximumobjective function value.

Star glyphs facilitate the detection of cases with multiple maximum values; in this investiga-tion these were cases no. 8 and 10, with four out of five possible objective function values at themaximum. However, as in case no. 3 in Figure 8, where the value of one ray compared to otherrays is much lower, perceptual recognition can become too difficult.

To examine and compare the convenience of the presented techniques for practical use,engineering students were tested on the visualization of the data set described previously.

6.3. Results of optimization(s)

Objective functions f 1–f 5 were described in Section 5. For each set of prescribed design points(Table 1), the heat transfer rate and pressure drops were numerically determined (Table 2) andused to calculate values according to all five objective functions (Table 3). When dealing withseveral responses, the optimum setting for each response can lead to conflicting results that haveto be checked and balanced. According to objective functions f 1–f 5, optimum values of param-eters x1–x3 were determined by the response surface method and are shown in Table 4. Theprocedure and details of the optimization method can be found in Glazar (2011).

Cases no. 8 and 10, described in Table 1, have the closest parameter values to the acquiredoptimal values of x1–x3 (Table 4). The water inlet velocity operating condition (x4) was includedin the optimization only to show hydrodynamic behaviour gains compared to the referent heatexchanger. These gains for the determined optimal values of geometric parameters were 10% inthe case of lower water inlet velocity, 30% in the middle range and 45% in the case of higherwater velocities.

Although the response surface method has been proven to be reliable and accurate, additionalverification of the acquired parameter optimal values was carried out. Of the objective functionsf 1–f 5, function f 2 was chosen to perform additional optimization by another method. A geneticalgorithm method was applied. The function f 2 linearly combines the heat transfer rate and thedecrease in air pressure drop, and accordingly has the determined final optimal values of thegeometric parameters that correspond to the maximal function values.

Genetic algorithms (Haupt and Haupt 1998) are a type of optimization algorithm used to findthe optimal solution, or solutions, to a given computational problem that maximizes or minimizesa particular function (Fung et al. 2014). These algorithms are far more powerful and efficientthan random search and exhaustive search algorithms, yet require no extra information about thegiven problem. This feature allows them to find solutions to problems that other optimizationmethods cannot handle because of a lack of continuity, derivatives, linearity or other features(Kanagaraj et al. 2013). The optimization results presented in this article with genetic algorithmswere obtained using the MatLab software package for practical solutions (MathWorks 2014).

Comparison of the results for optimal parameter values obtained previously by the responsesurface method and additionally by means of genetic algorithms indicated very good agreement.

Table 4. Optimal values of design parameters for the prescribeddata sets of objective function f 2.

Design parameter Optimal value

Distance between flat tubes (Pt) 12.5 mmFin pitch (Fp) 1 mmNumber of small rectangular channels (nsc) 24

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Table 5. Results for the best and worst combination of objective functions f 1–f 5 obtainedby the used optimization method and from insights into students’ testing results.

Students’ testing results

Response Chernoff faces Star glyphsurface method technique technique

Best case(s) No. 8 Case no. 817.9% 10.7%

No. 10 Case no. 107.1% 21.4%

Worst case No. 3 Case no. 317.9% 92.9%

6.4. Relation between the results of visualization techniques and optimization

The significant influence of objective function f 2 (along with f 1) on the heat exchanger perfor-mance has been selected for presentation by Chernoff faces with facial features that are the mostnoticeable. According to head size/eccentricity and vertical ear position, faces no. 8 and 10 areeasiest to perceive, followed by faces no. 6 and 15.

Similar results were achieved using star glyphs, where star glyphs no. 8, 10 and 15, and partlyno. 6, can be distinguished most clearly from the others, simply by the length of all the rays.

Both glyph visualization techniques pointed to cases no. 8 and 10 from the prescribed datasets, which in the previous section were detected as the ones with parameter values closest tothe optimal values. To determine which of the presented techniques is preferred by the user, theywere tested by engineering students, as described below.

6.5. Evaluation of glyph techniques through testing by engineering students

Comparison of the optimization results obtained by the applied response surface method and theinsight based on the same data visualization through glyph techniques indicated a good match.In an attempt to additionally evaluate these glyph techniques, the objective functions presentedin Figures 7 and 8 were submitted to a group of 28 students. They all were undergraduate uni-versity students in the first year of mechanical and electrical engineering study at the Facultyof Engineering, University of Rijeka, Croatia. The participants had no experience in the relatedsubject, and the explanation about the test solving given at the beginning was intentionally shortand general. The participants were asked to indicate the cases that give the best and worst overallcombinations of parameters, i.e. objective functions. The results of student testing are presentedin Table 5, along with the cases determined as the best and worst by the optimization methodsused in this study.

The percentage of the indicated cases obtained by testing that corresponds to optimizationmethod indicates that the star glyph technique gives better insight into the data for engineeringstudents in comparison with the Chernoff faces technique. Therefore, the star glyph techniquecan be considered as a simple and quick tool, which could be of even more interest to trainedpersonnel.

7. Conclusion

In this article, visualization using Chernoff faces and star glyph techniques has been describedand performed. Data sets from the experimental and numerical investigation of a heat exchanger

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Engineering Optimization 13

with a microchannel coil have been the subjects of visualization. Analysis of the results indicatedthe following.

It can be concluded that visualization using Chernoff faces is a good method when the goal isto determine which cases are similar, or which variables have comparable values. It is rather diffi-cult to determine just one face which has the minimum or maximum of the included independentvariables.

Regarding the visualization technique using star glyphs, it is easier to spot differences betweenthe values of certain variables with the length of rays. Difficulties in perceptual recognition mayoccur when the value of one variable, i.e. the ray length, is much lower than the value of othervariables. This method of visualization is good for spotting similar elements in the examinedcases, and quickly identifying variables with similar values.

The main finding from the evaluation of related glyph techniques based on the engineeringstudents’ testing is that the star glyph technique is a simple visualization tool for the presentationof multivariate data sets. The intention for the future work is to use a wider set of prescribeddesign points and to perform user evaluation of glyph techniques based on a population withconsiderable knowledge in the related engineering field.

The visualization of the adopted data sets, accomplished by multivariate analysis of two glyphtechniques, points to the cases that the optimization found to be optimal and furthermore canindicate possible optimal cases. However, the decision to apply glyph techniques for engineeringvisualization as a simple and low time-consuming method relies on careful thought about itsadequacy related to the demands of a certain visualization task.

Funding

This research was performed as part of the scientific projects Research and Development of Renewable Energy Compo-nents and Systems, and Design and Optimization of Power Transmissions, both supported by the Ministry of Science,Education and Sports of the Republic of Croatia.

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