Analysis Of Thermal Transient Processes By Means Of Neural .
25Analysis of Thermal Transient Processes byMeans of Neural Network TechniqueRafał Rakoczy and Stanisław MasiukInstitute of Chemical Engineering and Environmental Protection Process,West Pomeranian University of Technologyal. Piastów 42, 71-065 SzczecinPoland1. IntroductionParticularly in the past decade, a very large effort has been expended in developingnumerical methods for solving complex multidimensional problems in area of engineeringprocesses. In the last few years the complex behaviour of biological, chemical and industrialsystems has been explained in terms of dynamic analysis and many techniques to obtainpredictions have been developed. The dynamic investigations of a various processes havefocused attention on the problem of the mathematical description. In principle, thisknowledge may be obtained by many computational modelling. As an easier alternative, theexperimental data may be used to find out a black-box model or an empirical correlationdefining the system behaviour. The limitation of this approach is that it requires assumptionof the functional form of the proposed correlation.The popular approach to analyse the unsteady and steady heat transfer problems isassociated with the availability of non-linear empirical modelling methodologies, such asneural networks, inspired by the biological network of neurons in the brain (Hussain, 1999;Ou & Achenie, 2005). Authors (Liau & Chen, 2006) proposed this methodology to modeloptimal concentrations of reactants for preparing sub-micron silica particles. Different setsof the reactant concentrations were selected within an operating range and were designed toevaluate the PSD data. The relationship between the reactant concentration and resultantPSD can be evaluated by means of the ANN modelling approach. The neural networkmodels can be successfully used to compute PSD of particles with different shapes in highlyconcentred suspensions from laser diffraction measurements (Nascimento et al., 1997;Guardani et al. 2002). The ANN pattern recognition (ANNPR) approach has also beenproposed for fed-batch cultivation processes of Escherichia coli (Duan et al., 2006). A noveldata mining macro-kinetic approach based on ANN was proposed to develop the macrokinetic model of oxidation of p-xylene to terephthalic acid in a industrial type of continuousstirred tank reactor (Yan, 2007). Authors (Liu & Kim, 2008) used the purely mathematic andmechanical model with ANN to model membrane filtration process. As a tool of modelling,neural network technique has been used by (Jones et al., 1999) to magnetic inverse problemof determining the anisotropy field distribution from experimental transverse susceptibilitydata. Approximation models such as artificial neural networks (ANNs) are powerful andreliable in predicting the complex conditions such as nonlinear and time-variant biologicalwww.intechopen.com
526Artificial Neural Networks - Applicationprocesses (Liu et al., 2008). Consequently, this approach has been used to predict hold-up inslurry pipelines (Lahiri & Ghanta, 2008), for mapping the structure of a liquid spray(Heinlein et al., 2007), for analysis of heat and mass transfer (Kahrs & Marquardt, 2007).The dynamic investigations of the unsteady heat transfer process has focused attention onthe problem of the mathematical description. In principle, this knowledge can be obtainedby many computational modelling. As an easier alternative, the experimental data may beused to find out a black-box model or an empirical correlation defining the systembehaviour. The limitation of this approach is that it requires assumption of the functionalform of the proposed correlation. The popular approach to analyse the unsteady and steadyheat transfer problems is associated with the availability of non-linear empirical modellingmethodologies, such as neural networks, inspired by the biological network of neurons inthe brain. The implementation of ANN technique in heat transfer science literature islimited. For the identification or analysis of heat transfer problems a neural networkapproach has been attempted by authors (Thibault & Grandjean, 1991; Christtofindes, 2001;Alotaibi et al., 2004; Zdaniuk, 2006; Ashforth-Frost et al.,1995 and Yilmaz & Atik,2007).In the relevant thermal scientific literature is most concerned with the performanceprediction and control of heat exchangers (Islamoglu, 2003; Diaz et al., 2001; Pacheco-Vegaet al. 2001).In the present work, an attempt has been made to use ANN to model the thermal transientprocess and the thermal behaviour of reciprocating mixer. We believe that this modellingapproach is considerably interesting than the more conventional empirical correlationapproach. This encouraged us to investigate the problem which is presented in this chapter.2. Experimental detailsThe investigations of the temperature transient processes were made using the experimentalset-up shown in Figure 1. The experimental investigations were performed using a verticalcylindrical vessel of 0.248 m in inside diameter and 0.678 m in height. The mixing wasvaried out with a single perforated plates agitators with the different degree of perforation(ratio of hole-to-solid area of plate) oriented horizontally were reciprocating in a verticaldirection. The agitator was always placed at half of the liquid height in the vessel and thediameter is equal to 0.241 m. An electric a.c. motor coupled through a variable gear andV-belt transmission turned a flywheel. A vertical oscillating shaft with a single plateperforated and a hardened steel ring through a sufficiently long crankshaft were articulatedeccentrically to the flywheel. This system were used to generate reciprocating movements ofagitator. The water was used as the mixed liquid as well as cooling medium. The flow ratesof municipal water continuously flowing through the mixer and jacket surrounding internaltubular vessel were established and controlled by means of flow meters. The temporalvariations of temperature as a transient thermal processes were measured by using themicroprocessor sensors. Therefore, these processes were obtained by means of the thermalresponse technique. This method is very flexible and may be applied to large scale systemsbut it required very sensitivity measuring sensors. The measured electronic signalsproportional to the temperature were passed through converter and system of temperaturesequential sampling to personal computer where the temperature transient processes maybe easily analytically recorded and formed the database including the characteristicquantities of this process. These processes were generated by the thermal disturbance of thecold water stream introducing on the free surface of the mixer vessel by means of centrallywww.intechopen.com
527Analysis of Thermal Transient Processes by Means of Neural Network Techniquemounted perforated distributor. This loading device was protected against prematurepenetration of cold bulk liquid in the mixer vessel9410115GwTw tw8Gj62GpGp1213317G j GpTk TkFig. 1. Experimental set-up: 1 - tubular vessel, 2 - perforated plate agitator, 3 - externaloverflow, 4 - generator of input temperature signal and hot liquid feeder,5 - hardened ring with inductive transducer, 6 – flow meters, 7 - temperature sensors,8 - distributor of cold liquid, 9 - electromechanical eccentric drive,10 - power cube, 11 - controller of motor speed, 12 - system of temperature sequentialsampling, 13 - personal computerThe thermal disturbance as the pulse temperature input signal was the volume of hot liquiddescribed by parameters Gw , Tw and tw . Before the experimental measurements the mixerbulk was mixed to constant field temperature inside the mixed and flowing water. This fieldwww.intechopen.com
528Artificial Neural Networks - Applicationwas controlled by the set of movable temperature sensors. Next the hot water was injected tothe stream of cold water and the temperature transient process was recorded simultaneously.The transient process was regarded as a complete when the temperature variation in thestream flowing out the mixer vessel did not change with time. Then the transient responsecurve is asymptotic to the time axis. As mentioned above, experimental studies of the thermaltransient processes were conducted in the reciprocating mixer and the databases included theoperational parameters, such as: perforation degree of the reciprocating plate agitator - ψ ,amplitude of reciprocating motion - Γ , frequency of reciprocating motion - ω , mass flow rateof water in mixer vessel - Gp , mass flow rate in cooling jacket - G j , mass of hot waterintroduced into the steam of the water flowing through the mixed vessel - Gw , time durationof the thermal impulse signal - tw , temperature of hot water - Tw and temperature of the mixedwater - Tk are collected in Table 1.parameterminimalvaluemaximalvalueψ m2 m 2 Γ [m]ω s 1 Gp kg s 1 G j kg s 1 Gw kg s 1 tw [s]Tw o C Tk o C 670.1528612092.910Table 1. The range of operational parametersSuch programming of the experimental investigations enables to explore many aspects ofthe unsteady heat transfer realised by using the mixed vessel equipped with thereciprocating agitator. The results of the experiments for the various set of the operationalparameters may be graphically presented as a dependence of the output temperatureresponse on the time duration of the temperature variation. Figure 2 illustrates the typicalexample of transient response curve. The response curves obtained for the differentcombination of the operational parameters were similar to the typical example of thermalresponse curve (see Figure 2).Fig. 2. Typical example of thermal-response curvewww.intechopen.com
Analysis of Thermal Transient Processes by Means of Neural Network Technique529TmaxTEMPERATUREThe influence of the operational parameters on the transient process may be assessed by theanalytically approximated of transient curves or characterized in the more simple way usingthe specially chosen characteristic quantities of these curves. As follows from thecomparison of these thermal transient process for the different sets of operationalparameters, it may be found that these thermal-response curves should be defined by meansof the five characteristic parameters such as: the time lag of thermal process - t0 , themaximal value of temperature - Tmax , the time of the achievement of maximal value oftemperature - tmax , the time duration of thermal process - t p and the quantity of areabetween the thermal response of transient process and the time axis - A .The typical example of thermal response curve with the marked characteristic quantities isgraphically presented in Figure 3.t0tmaxtpTIMEFig. 3. Typical example of thermal-response curve with the marked characteristic quantitiesThe series of the 3000 experimental values of the five characteristic quantities were obtainedfor the various sets of operational parameters. Recent approaches to building mathematicaldescription have been based on the statistical or numerical modelling of experimentaldatabase. In the case of the absence of accurate theoretical models, regression methods havebeen employed to find an approximate functional form that can best describe therelationship between the independent variables and the observed dependent parameters.Artificial neural networks (ANN) are an attempt to predict the effect of changing input dataon the dependent variables. Earlier experimental works have reported from the use of thevarious types of networks to analysis the number of engineering problems. The produceANN model estimates the five characteristic parameters with respect to the establish valuesof operational condition. The great advantage of the proposed methodology is that thecomplex mathematical relationship for the non-linear unsteady heat transfer processes isomitted. Consequently, the computational time required to solve the classical mathematicalmodels is significantly reduced and the description of the dynamic behaviour of thermaltransient process with various effects under constantly changing conditions is possible.www.intechopen.com
530Artificial Neural Networks - Application3. Results and discussion3.1 Predictions of operational characteristics value by using the ANN modelThe nature of obtained databases is permitted to analyse and describe the experimentalresults applying the statistical or numerical modelling. In the case of the absence of accuratetheoretical models, regression methods should be exploded to find an approximatefunctional form for description of the relationship between the independent variables andthe observed dependent quantities. Artificial neural networks have offered of the splendidattempt to predict the effect of changing input data on the dependent variables. The produceANN model estimates the power characteristics for the novel construction of static mixerwith respect to the establish values of operational parameters. The great advantage of theproposed methodology is that the computational time required to solve the classicalmathematical models is significantly reduced and the description of the operationalbehaviour of the static mixer under constantly changing conditions is possible.Traditionally, ANN has been used to model complex non-linear systems and appeared to bea good alternative to traditional empirical, phenomenological or statistical correlations. TheANN models are more powerful and can manipulate non-linear input-output relationshipsmore successfully than available literature conventional correlations.The critical step in building a robust ANN is to create an architecture, which should be assimple as possible and has a fast capacity for learning of the data set. The choice of the inputvariables is the key to insure complete description of the analysed systems, whereas theexperimental data set have a tremendous impact on the reliability and performance of theANN model. This type of model provides a non-linear mapping between input and outputvariables and is also useful in providing cross correlation among these variables. The ANNis a very useful tool in rapid predictions such as steady-state or transient process flow sheetsimulations, on-line process optimization and visualisation and parameter estimation.The experimental database are processed using ANN models. The neural network approachwas thus carried out by means of the Statistica Neural Network software. The multi layerperceptron (MLP) networks consist of three layers, namely the input layer, the hidden layerand the output layer. For practical application, the RBF network is structured so that it canapproximate the five characteristic quantities of thermal-transient curves (transientprocesses) and estimate the dynamic behaviour of temperature at unsteady heat transfer inthe reciprocating mixer. To achieve this, the input layer of the analysed network isformulated so that it contains the input parameters as follows:x ψ Γ ω Gp G j Gw t w Tw Tk T(1)The neural network output is the estimation of the five characteristic parameters of thethermal-transient processes, which are calculated as a weighted sum of the responses of thehidden layer nodes. Figure 4 presents the structure of the MLP network used to model thethermal-transient processes.It should be noticed that the training a MLP network is conducted by the minimal deviationbetween the predicted and the true values of the output variables over the set of theavailable experimental database. As follows from the realised analysis, the MLP modelconsisting of 11 nodes in the hidden layers. This number of nodes is caused by thewww.intechopen.com
Analysis of Thermal Transient Processes by Means of Neural Network Technique531Fig. 4. The MLP neural network architecture for the characteristic quantities of the thermaltransient processcomplexity of the analysed heat transfer problem and the non-linear relationship betweenthe input vector of the operational parameters and the approximated values of outputparameters. As follows from the analysis of the proposed ANN architecture model, thevalues of qualitative coefficients for the training, validating and testing sets are amount to0.991136, 0.987181 and 0.989819, respectively. Moreover, the operational parameters (inputparameters) may be reorganised from the most to the least important parameter for theproposed architecture of the MLP model as follows:x tw Gp ψ Tk Γ ω Tw Gw G j T(2)Figure 5 gives the generalization result, by plotting the power characteristics for the noveltype of static mixer calculated by using the ANN model as a function of the experimentalinvestigations.The first conclusion drawn from the inspection of these graphs is that the proposed neuralnetwork is predicted the analysed experimental data very well. Therefore, these resultssuggest that the characteristic parameters for the novel type of static mixer my besuccessfully approximated by means of the ANN methods.Moreover, the radial basic function (RBF) network was used to model the thermal-transientcurves. Figure 6 presents the values of time duration of thermal-transient process, t p ,obtained from the RBF model and the values measured from experiments. Almost all theresults lay in the limits of the 30% maximal error. As follows form the analysis of theobtained results, the MLP model is shown to be superior to the RBF network approach.www.intechopen.com
532Artificial Neural Networks - Applicationa)b)c)d)e)Fig. 5. The graphical comparison of values of characteristic quantities for results obtainedexperimentally and using ANN model: a) the time lag of thermal process - t0 ,b) the maximal value of temperature - Tmax , c) the time of the achievement of maximal valueof temperature - tmax d) the time duration of thermal process - t p and the e) quantity of areabetween the thermal response of transient process and the time axis - Awww.intechopen.com
Analysis of Thermal Transient Processes by Means of Neural Network Technique(tp)ANN [s]3000533Δ 30%200010000Δ 30%0100020003000(tp)exp [s]Fig. 6. The graphical comparison of the experimental and predicted values of the time lag ofthermal process ( t0 ) for the RBF network model3.2 Effects of operational parameters on characteristic quantities of thermal transientprocessThe practical utility of the results presented here is to illustrate the effects of operationalparameters on the characteristic quantities for the realized transient process in thereciprocating mixing system. In recognition this fact, the three-dimensional responsesurfaces were generated and used to study the liquid properties and operating conditionson characteristic quantities.Figure 7 illustrate the effect of the selected operational parameters on the time lag of thermaltransient process ( t0 ) . As it can be observed in Figure 7, this parameter dependssignificantly on the operational conditions.a)b)c)Fig. 7. The effect of selected operational parameters on the time lag of thermal transientprocess ( t0 )Figure 7a shows the effect of the parameter connected with the reciprocating mixer on onthe time lag of thermal transient process ( t0 ) as an attempt to simulate the effect ofchanging the perforation degree of the reciprocating plate agitator (ψ ) and the amplitude ofreciprocating motion ( Γ ) . It was found that, t0 values seem to decrease with increasing theamplitude of reciprocating motion of the tested mixer. Moreover, this figure shows that theobtained t0 values increase with increasing amplitude of reciprocating motion. In thisstudy, the effect of the temperature of hot water (impulse temperature - Tw ) appears to bewww.intechopen.com
534Artificial Neural Networks - Applicationstronger than the mixed water temperature (Tk ) leading to an increase of the time lag ofthermal transient process ( t0 ) , as can be seen in Fig.6b. In analy
In the relevant thermal scientific literature is most concerned with the performance prediction and control of heat exchangers (I slamoglu, 2003; Diaz et al ., 2001; Pacheco-Vega et al. 2001). In the present work, an attemp t has been made to use ANN to model the thermal transient process and the thermal behaviour of reciprocating mixer.
steady state response, that is (6.1) The transient response is present in the short period of time immediately after the system is turned on. If the system is asymptotically stable, the transient response disappears, which theoretically can be recorded as "! (6.2) However, if the system is unstable, the transient response will increase veryFile Size: 306KBPage Count: 29Explore furtherSteady State vs. Transient State in System Design and .resources.pcb.cadence.comTransient and Steady State Response in a Control System .www.electrical4u.comConcept of Transient State and Steady State - Electrical .electricalbaba.comChapter 5 Transient Analysis - CAUcau.ac.krTransient Response First and Second Order System .electricalacademia.comRecommended to you b
thermal models is presented for electronic parts. The thermal model of an electronic part is extracted from its detailed geometry configuration and material properties, so multiple thermal models can form a thermal network for complex steady-state and transient analyses of a system design. The extracted thermal model has the following .
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Transient Thermal Measurements and thermal equivalent circuit models Title_continued 2 Thermal equivalent circuit models 2.1 ntroduction The thermal behavior of semiconductor components can be described using various equivalent circuit models: Figure 6 Continued-fraction circuit, also known as Cauer model, T-model or ladder network
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