CybMod user manual - Personal WWW Pages
Contents
1. g g 3 Di prediction surface on a 2 D plot Two input variables have to be selected from the list boxes at the top of the diaologue The model prediction is calculated for the full range of the x axis variable and at set centre points for the stacked variable When more than two inputs are present an extra list at the bottom of the dialogue allows the stored values for the other inputs to be specified set centre points only 66 CybMod User Manual Chapter 4 Surface Plot 3D Surface Plot The 3 D surface plot presents similar information to the stacked plot and works in the same way 3D Surface Plot Fama E Feen E Feo BERN The 3 D surface can be rotated by clicking and dragging on the plot with the left mouse button The Controller Menu The controller menu is used to specify model based fuzzy controllers for CybFIMC and is described in that programs documention 67 CybMod User Manual Chapter 4 The Logfiles Menu Data and Model logs Logfile C sdata 2nord dlg created 16 7 98 11 43 Logfiles are created for both models and data The logfiles are automatically updated when something significant happens You can add your 68 CybMod User Manual Chapter 4 entries to the log file by typing into the edit box and pressing the Add entry button Log files are saved whenever the model or data files is saved A model log has a file extension of ml2. CybMod User Manual A fuzzy modelling program for process control PROCESS CYBERNETICS LIMITED Table of Contents Introduction uiros eS ee wae 1 System Requirements P PP 2 Installing CybMod 0005 2 How CybMod works 3 Why FUZZY ccc and came Saw mmt 3 FUZZY Sels csi ker dA eo tora 6 Fuzzy relational models rS 11 Relational model identification 14 Dynamic Modelling 15 BUY od seier iura rp t asma cn 18 Loading the data 2 19 Examining the data 20 Naming the fields 21 Cross correlation 055 22 Building the model 24 Identifying the model Sagas prance aaa a Sayeed S32 27 Testing the model 29 Refining the model 31 What next is LE EG uA 35 Program Reference 37 General program behaviour 37 File Menu reward nd d Era RES 38 New System 2 2 220 eee 39 LoadaModel 39 Save a Model 39 Save a Model AS 39 Load Data s sien ve ok Ste ost 40 Save Data As 05 40 EXIT ome ce tham NEU a 41 Data renun 41 Data file Summary E ase E A E E E EE E 41 Edit Field Names 43 Outliers Removal 43 Filter Data o REESE 45 Cross Correlate Data aap le Sock Melee Ae vase 2s M
3. There are two versions of this dialogue The first shown above is used when the Use data sequentially option is selected In this case identification is carried out by moving through the data from the start sample sequentially to the end sample The start sample and the end sample can be adjusted if you wish to use only part of the data 54 CybMod User Manual Chapter 4 set for identification perhaps to keep the rest for testing The maximum number of samples available for identification will be less than the number of samples in the data if lags are present in the model structure The identification parameters allows you to control the identification algorithm If the Clear Model First box is checked then the existing model will be erased prior to the identification If you are identifying a model from multiple data sets then you would need to make sure that this box is unchecked on processing the second and subsequent data sets The Forgetting Factor value allows the forgetting factor on the recursive least squares algorithm to be adjusted If this is moved to a value less than one then more recent information will be given more weight in the identification process This is only useful if you believe that the process is non stationary Unless you have a very good reason to change it then leave it at one Pressing OK will start the identification process This can take quite a long time with big data
4. Glasgow Scotland UK Tel 0141 548 2835 Email b postlethwaite strath ac uk 79 CybMod User Manual
5. they often come up with different sometimes conflicting sets of rules about the process behaviour and the best way to control it As a result applications of fuzzy control based around rule based systems all have to go through a period of difficult and expensive knowledge engineering where expert interviewers obtain rule sets from operators and then after several iterations refine them to a complete and consistent set of rules Another disadvantage with the rule based approach for control system design is that the rules the operators give are often very conservative A human operator is unable to devote all their attention consistently to a single control problem throughout an entire shift This means that they make control actions which don t move the process particularly quickly and so give them time to focus their attention elsewhere 11 CybMod User Manual Chapter 2 An alternative to the rule based modelling approach is fuzzy relational modelling The idea behind a relational model is that relationships exist to some extent among all the AND combinations of the inputs e g HIGH flow AND MED concentration and the output fuzzy reference sets These relationships are fuzzy relationships and are held in a relational array as values between zero and one zero representing no relationship and one a very strong relationship The modelling problem now becomes the assignment of appropriate values to the entries in the re
6. Bio Reference set centres Edit Reference Set Centre 7 10960 27301 530E0 Position of Set Centre 273 01 EXE Xie o Grade of Membership e en A fe To change the reference set postions double click the appropriate reference set group in the set frame This will bring up a dialogue which lists the individual set centres and also gives a graphical representation of the sets To change a set centre position then double click the appropriate entry and edit the value in the dialogue box 73 CybMod User Manual Chapter 5 Other Services from Process Cybernetics We hope that you find CybMod a useful and easy to use piece of software All our software is written in house and we are continually developing our products We are very interested in receiving your feedback on our products If you have any comments to make or suggestions for improvements to our products then please get in touch with us at the address given at the end of this chapter The rest of this chapter outlines some of the other products and services available from Process Cybernetics 74 CybMod User Manual Chapter 5 Other products CybOnLine On line fuzzy modelling CybOnLine provides an easy way of intergrating models developed in CybMod with a wide range of third party SCADA systems These models could be used for inferring the values of difficult to measure variables from other measurements or could be used to prov
7. Chapter 4 The manual editing dialogue works by taking two dimensional slices through the relational array The variables to be used for the x and y axes are selected from the two list boxes and the slice appears in the big box on the righthand side of the dialogue The values highlighted with a yellow background along the top of the box are the centre points of the reference sets for the x variable The yellow highlighted values down the lefthand edge are the reference set centres for the y variable The values in the edit boxes in the centre of the box are the relational array entries and can be changed simply by typing in a new value In cases where the model has more than two inputs there will be more than one possible 2 D slice To access the individual slices a list box appears at the bottom of the display when three or more inputs are present Clicking on an input in this list brings up a popup menu showing the set centres for that variable Clicking on one of these brings up the appropriate 2 D slice Once again manual editing in not something to undertake lightly There are usually better ways of dealing with model or data problems 53 CybMod User Manual Chapter 4 Identify a sub model w Identify a Sub Model FG Identification Data Lom ii Use data drawn randomly Start Sample fi End Sample 493 Identification Parameters v Clear Model First Forgetting factor fi
8. User Manual Chapter 3 giving you a chance to look at how the data is distributed Have a look at the data fields Field_0 is just the sample number and will produce a rather strange looking histogram Field_1 is the fuel flowrate deviation and the histogram shows an approximately Gaussian distribution Field_2 is the off gas concentration and the histogram shows a distribution which is slightly skewed towards higher gas concentrations Naming the fields It s easy to get confused when referring to the fields of data as Field O Field_1 etc and so it s worthwhile giving them meaningful names early in the model building process From the Data menu select the Edit Field Names item Edit Field Names x Fieia 0 OK Cancel The list box in this dialogue gives you access to all the field 21 CybMod User Manual Chapter 3 names stored internally by CybMod To change a name simply select a field from the list box and then edit it using the keyboard To edit another just repeat the process Change Field 0 to Sample No Field 1 to Fuel and Field_2 to Conc Press OK to tell CybMod to save the changes Cross correlation Cross correlation is a statistical technique which is sometimes useful in detecting dynamic relationships between variables It works by calculating the correlation coefficient between two variables at a range of different lags To run a cross correl
9. introduced into the input variables to represent 16 CybMod User Manual Chapter 2 process deadtime This deadtime will either be real and or will be included to approximate higher order process dynamics as a first order dead time model A typical fuzzy relational dynamic model for a process will therefore look like this Y R Y k amp d U k amp l amp 7 U k amp ld amp where Y possibility vector of the output U possibility vector of process input i k current sample T dead time on input i 17 CybMod User Manual Chapter 3 Chapter 3 Loading the data Start CybMod by selecting CybMOd from the Windows start menu From CybMod s File menu select the Load Data item This will bring up a standard Windows file dialogue Select the file boxjen dat from the c CybMod directory CybMod s Window display will change to show the model building dialogue Tutorial The best way to learn how to do something is to File Data todel Analysis Contoller LogFiles Help do it This chapter introduces you to the use of the CybMod program by going through the stages involved in building a model of a simple x CybMod Fuzzy Model Builder This card lets you specify some of the parameters for creating your new dynamic process You should read the manual sub model Once you have completed the card press Create anda card for your alongside your computer and follow the exercise ie D will appear Y ou
10. membership functions can take many forms but the most common and that used in CybMod is the triangular membership function Figure 2 1 shows a group of four typical triangular membership functions defined over a variable s range Three values can completely define each membership function the variable s value at the leftmost edge of the function where the grade of membership GM is zero the set centre where the GM is one and the rightmost edge of the set where the GM is again zero If we define a group of reference sets to be fully overlapping then the rightmost edge of a set is at the same value as the centre point of the immediately following set and as the leftmost edge of the set after that Just setting the centre points of each set in the series can completely define a group of overlapping triangular reference sets All set definitions in CybMod are fully overlapping triangular sets because of the simplicity of definition and because they possess very useful computational properties 7 CybMod User Manual Chapter 2 The two end sets of the group in fig 2 1 illustrate other features of triangular fuzzy sets The left most set has a left value equal to its centre value and is called a closed end set Variable values outside a closed end set to the left in this case have zero membership in any of the sets This can be useful in situations where an error needs to be flagged if a variable value falls outside a certain
11. o an external influence which cause both to move To prevent this from happening a de trending filter is applied to both sets of data The order of this filter can be adjusted by editing the Filter Order box The filter order shouldn t be changed unless you have a good reason for doing it Pressing the XCorr button will carry out the cross correlation calculation This will take a few seconds and the time required will increase with the size of the data set the maximum lag and the filter order When the calculation is complete the results will be displayed in the graph on right of the dialogue 48 CybMod User Manual Chapter 4 The x axis of the graph shows the relative lag of the input to the output Positive values of lag represent causal relationships between the input and the output Negative values represent causal relationships between the output and the input feedback relationships The y axis of the graph shows the value of the correlation coefficient Positive values indicate a positive gain between the input and output and negative values a negative gain Two yellow and two green dotted lines run horizontally across the graph These are the 95 yellow and 99 green confidence limits on the correlation coefficient based on a t test The solid line on the graph represents the results of the cross correlation The strongest peak positive or negative on the positive side of the x axis can give a rea
12. of the dialogue enclosed in the frame allows more detailed information to be obtained about each field within the data If you select a data field in the list box then CybMod will calculate the maximum minimum and mean values of the data and its standard deviation Clicking the Histogram button will generate a histogram showing the distribution of the values of the data in the currently selected field 42 CybMod User Manual Chapter 4 Edit Field Names IX Edit Field Names When a new data file is loaded the fields are automatically named Field O Field 1 etc It is much less confusing if the data fields are given meaningful names and this dialogue allows you to do this Simply select the field you would like to rename from the list of available fields and type the new name in the edit box Continue to select and edit as many names as you require and press OK to finish The Cancel button will close the dialogue without saving the edited field names Outliers Removal Sometimes process data will contain values which are unreasonably large or small The most common reason for these outliers are spikes from analytical instruments with gas analysers 43 CybMod User Manual Chapter 4 being particularly prone to this problem These i Outliers removal Field_2 Copy Graph Datafield 65 r Acceptable Data Range 60 Maxium 6 356 01 Miniumum 4 336401 Try it Ai Nu
13. range Usually however an open end set such as the rightmost of the group is much more useful An open set has a boundary which extends to infinity which means Grade of Membership 0 200 Concentration kg cubic m Figure 2 1 Triangular reference sets that all variable values on the open side of the set centre belong to the set with a GM of one All 8 CybMod User Manual Chapter 2 end sets in CybMod are open sets A group of fuzzy sets defined over a variable s range are usually called the reference sets for the variable because they establish a frame of reference for the computer to understand rules about the system We can give reference sets linguistic labels Z ero S mall M edium and L arge in figure 2 1 This is useful when working with rule based models but is unnecessary and cumbersome when working with the relational models described later in the chapter Going back to the example described earlier in the chapter we could define a set of reference sets for the process temperature as shown in figure 2 2 Using these fuzzy reference sets for the process temperature now produces a controller with a much more sensible control action At temperatures below 50 C the temperature completely belongs to the LOW set and belongs to the HIGH set with a zero GM This means that the rule associated with low temperature will fire at full strength and the steam pressure will be set to its LOW value As the t
14. sets lots of model inputs and lots of reference sets if you are finding it too long then the process can be stopped by pressing the Cancel button The other form of the identification dialogue appears when the Use data drawn randomly option is selected 55 CybMod User Manual Chapter 4 m Identify a Sub Model F3 hen this op tion is chosen identification will be carried out with a portion of the data drawn at random from the whole set of data This is useful where only part of the data is to be used for identification but where the data is non uniform with one operating state at the start of the data and another at the end Building a model sequentially would result in a very good model of the data at the start and no model at all of the end condition 56 CybMod User Manual Chapter 4 The dialogue allows the percentage of data to be used for identification and the random number seed to be specified Choosing the same random number seed will always result in the same sequence of data being drawn from the data set Test a sub model Free mj Cre crea 1 79E 01 This dialogue allows a prediction test to be run on a sub model using the currently loaded data set The range of data to be used for the test can be set by editing the start and end sample values 57 CybMod User Manual Chapter 4 The Steps ahead list controls the way the prediction is carried out Remembe
15. this Sub Model For this example however we want to build a dynamic model so leave the lagged output as it is At the bottom of the display the centre points of the reference sets for the model variables are listed These sets are automatically created by spacing them equally between the minimum and maximum values present in the data set for the variable in question Usually you should at least change the end set positions to the minimum and maximum values you would ever expect to see in the real world To change the set positions double click on the reference set centre points This brings up a set editing dialogue To change the position of a particular centre point double 25 CybMod User Manual Chapter 3 click on the value in the reference set centres I Edit reference sets Model Variable Conc k 1 Done Reference set centres 4 56E 01 6 056401 X Edit Reference Set Centre x Position of Set Centre 40 0 OK Cancel c Grade of Membership om on 0 0 42 44 46 48 50 52 54 56 58 60 62 64 frame and then edit the value in the edit box that pops up For this example change the two set centres to 40 and 65 Click the Done button to close the Edit reference sets dialogue We are now ready to add another input to the model Click the Add a new Input button on the main window dialogue Select Fuel from the list box in the dialogue that appears Set the lag
16. a This is useful if the data covers several different Identify a Sub Model x Identification Data Use data sequentially Use data drawn randomly of data to be used 75 Random number seed 1234 m Identification Parameters v Clear Model First Forgetting factor E operat ing regim es For DK Cancel this 28 CybMod User Manual Chapter 3 example choose random presentation by selecting the Use data drawn randomly option The 96 of data to be used is the number of presentations of data to the identification algorithm expressed as a percentage of the total number of samples in the data e g if a file consists of 500 samples a value of 150 will present 750 examples to the identification algorithm The random number seed is used to initialise the random number generator Leave both as they are and press the OK button to start the identification process A progress bar will appear and after a few seconds the dialogue will disappear identification is now complete Testing the model To test the model select the Test a sub model item from the Model menu The dialogue allows you to set the range of samples to be included in the test The Steps ahead list allows you to specify how far ahead you want the model to predict SIngle step ahead 29 CybMod User Manual Chapter 3 i Test a sub model E3 Start Sample E End Sample 236 S
17. ach variable This coincides with other investigations which have been carried out on this data set and which have concluded that the process is nearly linear in the range which the data covers What next Process modelling is an art Although CybMod provides a useful range of tools it will take experience to know when it is best to use them and how best to interpret the information which comes from them 35 CybMod User Manual Chapter 3 A good understanding of the process to modelled is very important for effective modelling Use your own process data and practise building models Are the models sensible Are the lags reasonable Does the prediction surface slope in the right direction The more you use CybMod the better you ll get 36 CybMod User Manual Chapter 4 Program Reference This chapter describes the functions available in CybMod in detail We recommend that you get familiar with the program using the tutorial first and then use this chapter to fill in you knowledge General program behaviour The information you will see in CybMod displays is colour coded according to what you can do with it Yellow background information only Blue background can be double clicked to bring up additional 37 CybMod User Manual Chapter 4 dialogues White background data can be typed in directly from the keyboard Most of the 2 D graphic displays can be zoomed to look at data in finer detail T
18. ation analysis select Cross Correlate Data from the Data menu Two list boxes are displayed on the dialogue box which appears Input variable and Output variable Select Fuel as the input variable and Conc as the output variable and then press the XCorr button to carry out the cross correlation After a few seconds a graph will appear on the right of the dialogue This graph shows the results of the cross correlation analysis The x 22 CybMod User Manual Chapter 3 x Cross Correlation Copy Graph Input variable 0 2 Fuel m Lag in samples between input and output Output variable E Conc x Maximum Lag 20 Filter Order fio 20 Correlation 04 Corr Done 06 axis is the relative lag between the input and the output The y axis is the correlation coefficient High absolute values of the correlation coefficient at positive lags indicate a causal relationship between the input and the output and high values at negative lags indicate a causal relationship between the output and the input due to feedback in the process In this example a high negative correlation occurs at a lag of five samples to zoom in on the graph left click and drag select the area you want magnify and right click to restore the graph This gives us an idea of the lag that we might want to apply to the input in the dynamic model we shall be building 23 CybMod User Manual Chapter 3 Cross
19. correlation suffers from a number of limitations In cases where an output is affected by several inputs and these inputs change in a non random manner the cross correlation results can be impossible to interpret Also with high order processes the best lag on the input can be over estimated Building the model If you haven t already done so close the cross correlation dialogue On the main Window you ll see a list box which lets you select the output for your new model From this list box select Conc Below this is another list box which allows you to select the default number of reference sets to be applied to each input in the new model For now just leave this at 2 To create the model press the Create button A new card will be created containing your initial model structure The current model structure is shown as a fuzzy relational equation By default a lagged value of the output is used as a model input creating the basis of a first order dynamic model If you want to create a steady state model just double click the lagged output and change it to the input you want remember to set the lag to zero 24 CybMod User Manual Chapter 3 CybMod Fuzzy Model Builder File Data Model Analysis Contoller LogFiles Help New SModel m Model Structure Cone k A o Conc k 1 Add a new Input r Reference Sets i 4 56E 01 5 05E 01 Default number of sets for 2 new inputs Delete
20. eam pressures The definition will be highly dependant on the 4 CybMod User Manual Chapter 2 application A high temperature in a water bath will be much different from a high temperature in a catalytic convertor Here we might say that all temperatures less than 50 C were LOW and all temperatures greater than 80 C were HIGH For the steam pressure we might say a LOW pressure is 0 5 barg and a HIGH pressure is 5 barg What happens if we use the rules and set definitions to control the process When we start the process the temperature is below 50 C and so is classified by the computer as LOW This means that the computer applies a HIGH steam pressure of 5 bar and the process heats up As the process temperature crosses the 50 C boundary the computer has a problem it has no rule to tell it what to do A temperature of 51 C or any other temperature between 50 C and 80 C belongs to neither the HIGH nor the LOW temperature sets If we had foreseen this problem we might have added code to tell the computer not to change anything when the temperature doesn t belong to either temperature set Then as the temperature crosses the 50 C boundary the controller will maintain the steam pressure at the high value and the temperature will continue to increase As the temperature crosses the 80 C boundary another unpleasant thing happens At 79 9 C the 5 CybMod User Manual Chapter 2 computer will maintain a HIGH stea
21. ed this is set at zero and the test has already been performed Pressing the Test button scans the F array and counts the values which are less than or equal to your minimum acceptable level The count is given as a percentage completeness 70 means the model is 70 complete i e 30 of the entries are equal to or below the minimum level The box below lists the indices of the F array entries which have failed the test For example an entry in the box of 1 3 means that the input combination of input 1 set 1 and input2 set 3 has a frequency value lower than your acceptable level There are a variety of ways of dealing with an incomplete model The most obvious is to gather more data in the incomplete regions but this is often difficult as there are usually practical reasons for the data being missing in the first place Another way is to alter the set definitions By shifting set boundaries or eliminating sets altogether most incompleteness problems can be solved but perhaps at the cost of overal model performance The last method is to go into the 65 CybMod User Manual Chapter 4 model and manaully edit the suspect entries This is a last resort Surface plots Stacked plot The stacked surface plot presents the sub models Stack Plots Field_Ofk 3 E Field_1 k 1 1 08E 00 Field 1 k 1 1 28E 01 Field 1 k 1 m Field 1 k 1 1 338400 I 04 03 02
22. eee Ree 2 47 The Model Menu 0005 50 Model Summary 51 Manual Edit 52 Identify a sub model RCM TCR REC ics an at 54 Testa sub model 57 Save test results 59 Prediction Plot 59 Residuals Plot 00 59 The Analysis Menu 62 Do a Quick prediction DEP 62 Model Completeness MEER 63 Surface plots Stacked plot 66 Surface Plot 3D Surface Plot 67 The Controller Menu n ERT OEE 67 The Logfiles Menu 68 The Help Menu lesse 69 The Main Window Dialogue 70 Other Services from Process Cybernetics Other products 00005 75 CybOnLine On line fuzzy modelling 75 CybFIMC Model based fuzzy control dio dite 8 tho auld ale dese dac Pate ad a 76 Services from Process Cybernetics 77 TAINO seee a RE Gon erent rw ies 77 Consultancy sees 77 Software services sth Md meh Ate U UE n ME 78 Contacting US zx ete RA RNAs 79 Introduction Welcome to CybMod Vs 3 0 CybMod is a powerful package for producing non linear process models using state of the art fuzzy relational techniques Models generated by CybMod can be easily loaded into CybOnLine and CybFIMC to provide fuzzy modelling and control functionality to your current Microsoft Windows based SCADA system The process of building a model starts with in
23. emperature moves above 50 C the GM in the LOW set starts to fall below one and the GM in the HIGH set starts to increase above zero This causes the rule 9 CybMod User Manual Chapter 2 GM 50 80 Temperature deg C Figure 2 2 Reference sets for the temperature controller associated with LOW temperatures to fire less strongly and that associated with HIGH temperature to fire more strongly After defuzzification this results in a steam pressure which gradually increases from a LOW value up to a HIGH value in the region of temperatures between 50 C and 80 C That is really all that there is to fuzzy modelling In this simple example the same controller could be produced more easily with a simple linear function but in practical systems more inputs are used and more reference sets are used for each variable leading to non linear relationships between the inputs to the model and the output Fuzzy models can represent any non linear function to any required degree of accuracy and 10 CybMod User Manual Chapter 2 this makes them a very powerful general purpose tool for process modelling and control applications Fuzzy relational models The idea of obtaining qualitative process models from knowledgeable operators is attractive in theory but difficult to do in practice Operators often find it difficult to express all the knowledge they have in a coherent set of rules When different operators are interviewed
24. ersations with the SCADA package If you intend to run multiple on line modellers then you need to make sure that the models they use are allocated different system names 51 CybMod User Manual Chapter 4 The General Remarks is just text that is saved along with the model You can use it to add reminders to yourself about the model Manual Edit a Manual Edit of the Fuzzy Model x Select the variables which will form 5 00E 00 1 33E 01 2 17E 01 the axes of the editing display 1 40E 01 Jgooe o0 jo00E 00 f0 00E 00 un Field 5ik3 A pon fox fo ooe 00 none 00 Y axis Field 611 j 473 01 foo oos n00c 00 Since there are more than two input 7 0 006 00 o 00e 00 0 00E 00 variables in your model there are several R values associated with each x y combination of the variables above By default the the R values for the lowest values of all the other variables are used but you can modify this by selecting the appropriate input from the list below RCI 350 2 56E 00 Make Edit Cancel 4 79F 400 6 89E 00 SER aj Manual editing allows you to go right into the relational array and change the values stored there Since changing relational array entries is likely to have wide ranging effects it is something that should only be attempted with extreme care It is however sometimes useful in situations where data is missing or suspect 52 CybMod User Manual
25. ets defined on this variable have increased in number Double click the reference set definitions for the Fuel variable in the Reference Sets frame to bring up the set centre editing dialogue Change the values of the sets centres to 3 0 1 0 1 3 0 and exit the editing dialogue Now identify the model again still using random presentation and default parameters Test the model as a free running predictor The value of the mean squared error should have dropped to 0 874 Although it looks as though we now have a better model we have to be careful The number of entries in the relational array have increased from four 2 x 2 to eight 2 x 4 and so that it is not surprising that the model error has reduced The 34 CybMod User Manual Chapter 3 AIC which balances model performance against model complexity has also reduced indicating that the change we have made could be worthwhile If you look at the residuals plot for the fuel however you ll find that the largest are still clustered near zero and so we haven t solved that problem The largest residuals actually come from the end of the data set where from earlier we think that the process has changed in some way The fuel flowrate in this region coincidently has values close to zero and it is this and not non linearity which is producing the cluster of residuals near zero fuel values It is probably best in this case to use only two reference sets on e
26. filter to the data field The only way to restore the original data will be to reload it into CybMod The Done button simply closes the dialogue Filtering is something that has to be done with caution Applying a filter can remove noise but it removes some useful data too Also you need to remember that if you have applied a filter to build a model in CybMod you must make sure that the same filter is applied to SCADA data prior to it being passed to CybOnLine or CybFIMC loaded with that model Cross Correlate Data Cross correlation is a tool to help in spotting relationships in dynamic data It essentially involves calculating the correlation coefficient between an input and an output data series with different values of lag between the data Cross correlation can be carried out in CybMod through the Cross Correlation dialogue The input and output data are selected from the list boxes itis possible to select the same data for each and carry out an auto correlation The maximum lag over which the correlation will be evaluated can be adjusted by changing the number in the maximum lag box 47 CybMod User Manual Chapter 4 Sometimes false correlations can be detected when both the input and output are subjected to Cross Correlation x Copy Graph Input variable 0 6 u Dutput variable 04 Maximum Lag 20 Filter Order fio orrelation 20 20 Lag in samples m een input and output
27. fying fuzzy relational models The method used in CybMod direct least squares is one of the best and is described below It isn t necessary to know how this identification algorithm works to use CybMod and the details are included for information only A fuzzy relational model is usually represented 13 CybMod User Manual Chapter 2 by YR X X 9 X n where Y Possibility vector of the output Possibility vector of the i input Fuzzy relational array Fuzzy compositional operator omx A Possibility Vector is a vector made up of the grades of membership of a particular variable value in each of the reference sets used to describe that variable The fuzzy compositional operator is the method used to combine the inputs and relationships to form a prediction there are several different ways of doing this If a particular form of fuzzy composition is used summated product and a property of fully overlapping reference sets invoked then the relational model equation can be expressed as y R kron X X 9 X where y Scalar non fuzzy value of the output R Reordered fuzzy relational array kron Kronecker tensor product just an ordered multiplication of the input possibility vectors 14 CybMod User Manual Chapter 2 This form of the relational equation is linear in the parameters R and can be identified using normal linear least squares techniques CybMod uses a recursive least squares ident
28. g and a data log has an extension of dlg Model logs are saved as ASCII file and are for your information only they do not affect the operation of CybMod The Help Menu Provides access to CybMod help Context sensitve help is also available by pressing the F1 function key Tooltips are also available on many controls Simply leave the mouse cursor over a dialogue item you are unsure about and a tooltip should appear 69 CybMod User Manual Chapter 4 The Main Window Dialogue ti CybMod Fuzzy Model Builder Model Analysis Contaller Feo 2 g e The main window dialogue is where the construction of a models structure takes place and is presented as a series of cards A model is a collection of up to nine individual sub models and each has their own card on the dialogue You can use the sub models to create and save different input structures for modelling the same input or you can use them to collect a group of different output models which are based on the same data set The first card on the dialogue allows you to create a new submodel Simply select the desired output 70 CybMod User Manual Chapter 4 variable and default number of reference sets from the lists and then press the Create button A CybMod Fuzzy Model Builder A new card will be created for the sub model The frame at the top of the card shows the current sub model structure as a fuzzy relational equa
29. gue If a model or another datafile is currently loaded then CybMod will check that the field count is consistent with the new data if it isn t then loading will be aborted and an error will be flagged Loading new data will erase the previous data set Data files for CybMod have to be standard ASCII text The data is arranged with the fields in comma space or tab delimited columns and the records samples in rows Non numeric information in a data file will cause an error on loading Save Data As Allows you to save the datafile under a different name and also saves the data log The data is saved with the default extension dat and the log file with the extension dlg This is only useful if you modify the data within 40 CybMod User Manual Chapter 4 CybMod either by filtering it or by removing outliers Exit Exits the program prompting you to save any modified models and or data Data menu Data file Summary Edit Field Names Remove Qutliers Filter Data Cross Correlate Data The data menu provides you with some tools to exam modify and process i o data files Data file Summary Shows a dialogue containing summary information about the currently loaded data The dialogue lists the model file name the number of samples of data and the number of fields in each sample 41 CybMod User Manual Chapter 4 Data Summary Information x C data D ata dat The lower part
30. ide what if support for process operators CybOnLine is a Dynamic Data Exchange DDE server It runs as a seperate task alongside your existing DDE capable SCADA system and communicates via DDE links These links are easy to set up usually just by setting an appropriate i o address Each CybOnline module can handle up to nine sub models the maximum which can be defined in CybMod and multiple copies of CybOnLine can be run simultaneously providing as many on line models as you require 75 CybMod User Manual Chapter 5 CybFIMC Model based fuzzy control CybFIMC adds fuzzy model based control capability to your existing Windows based SCADA system It takes a model generated in CybMod and incorporates it into a Fuzzy Internal Model Control FIMC scheme This provides full non linear feedback control with dead time compensation and feedforward action on any included disturbances CybFIMC like CybOnLine is a DDE server making it really easy to link to exisiting SCADA installations CybFIMC is a MISO Multi input Single output controller it controls a single output variable which can be subjected to several inputs Multiples copies of CybFIMC can be run simultaneously providing as many loops as you require 76 CybMod User Manual Chapter 5 Services from Process Cybernetics Training Process Cybernetics offers ocassional courses on various aspects of fuzzy modelling and control The courses include a m
31. ification algorithm which allows multiple i o data sets to be easily processed Dynamic Modelling Most models used directly for control are dynamic that is they model not only how big changes are but also how quickly they take place A fuzzy relational model is not inherently dynamic but is simply a static mapping between combinations of inputs and the corresponding output However a relational model can be formed to represent a discrete time sampled dynamic system Consider the following first order dynamic process dy S p fy u 9 u where y process output u i process input f some function a backward difference discrete time 15 CybMod User Manual Chapter 2 approximation of this process can be formed as NORSGERO f OXK84 u K81 8 u K amp 1 where k current sample number At sampling interval and after rearrangement y K PORSI u KS 8 u KEL where f is a modified form of the function f This can easily be expressed as a fuzzy relational model v Y R Y k amp 1 U k amp 1 X7 U kEA Higher order dynamic models can be created simply by adding additional lagged outputs and perhaps inputs on the right hand side of the relational equation In practical situations it usually isn t a good idea to go beyond first order model dynamics because of the problems in obtaining complete and representative data In most practical situations additional lags will be
32. ixture of both theory and practise If you would like to be kept informed of upcomming courses then tick the boxes on your registration card or contact us directly at the address given at the end of this chapter Consultancy Process Cybernetics can provide consultancy to help support your modelling and control projects The level of our consultancy involvement can range from telephone support to full project management We shall provide a fixed price quotation for any work we undertake If you are interested in our consultancy services then contact us at the address given at the end of the chapter TI CybMod User Manual Chapter 5 Software services All our software is written in house and as a result we are able to offer a bespoke tailoring service to make our software suit your particular requirements This could involve changing the look of the software changing the way it operates or integrating it with other applications If you have an application in mind that requires special software then contact us at the address at the end of the chapter We will discuss your requirements and provide you with a fixed price quotation for the work 78 CybMod User Manual Chapter 5 Contacting us Process Cybernetics no longer exists as a company but you can still contact Dr Bruce Postlethwaite Dept of Chemical and Process Engineering University of Strathclyde James Weir Building 75 Montrose St
33. l the first predictions can t be made and are instead replaced with the actual value of the output Prediction Plot This produces a graph comparing the predicted and actual outputs from the process The menu item isn t available until a test has been run on the current sub model Residuals Plot Generates a plot of the model residuals the difference between the predicted and actual outputs against either the sample number or each of the data fields Simply select the variable you want to plot the 59 CybMod User Manual Chapter 4 Model residuals plot Sy residuals against from the list By examining the residuals plot you can get an indication that your model is missing some important variables The residuals should be evenly distributed on either side of the x axis if they are not you may have a problem The residuals plot has to be used with caution in dynamic systems since there may be a lag in the effect of variables on the output It is useful however for giving a quick check on the suitability of a sub model 60 CybMod User Manual Chapter 4 XCorr Residuals Cross Correlation of Residuals TIONN _ 20 io E This dialogue allows you to cross correlate the model residuals against each of the fields of data A high value of the correlation coefficient indicates a significant contribution to the model error If it occurs for fields or lags that are not currently incl
34. l of data because it doesn t look right can lead to seriously flawed models Most data will not require outlier removal Filter Data Process i o data gathered for model identification should ideally already be properly filtered using analogue and digital filters In some cases however particularly in initial modelling investigations only unfiltered or poorly filtered data is available CybMod includes a simple first order filtering algorithm to deal with this 45 CybMod User Manual Chapter 4 Data filter x Copy Graph Data field name ps Sample time o PM Filtertime n SLE constant Try it Do it Done 100 200 300 400 500 Sample Number The filter parameters are specified through the filter dialogue The data field to be filtered is first selected from the list box This will trigger the production of a graph of the data in the right hand side of the dialogue The two edit boxes on the left of the dialogue allows the sample time at which the data was gathered to be set and a filter time constant to be specified The Try i button lets you try the filter on the data without actually changing the data stored in CybMod The graph will show the effect of the filter parameters you have chosen Increasing the value of the filter time constant will increase the amount of filtering which takes place 46 CybMod User Manual Chapter 4 The Do it button actually applies the
35. lational array Translating rules obtained from knowledge engineering into a relational array format is possible but it is much more common and useful to obtain the relational array directly from measured process input output i o data through an identification algorithm Obtaining the model directly from process i o data has two important advantages over the rule based knowledge engineering approach a Process i o data is easily available in most process plants Although obtaining a good representative set of i o data can be difficult sometimes it is still much less time consuming than generating a complete and consistent rule base 12 CybMod User Manual Chapter 2 b The model which is obtained will be a representation of the process i o relationships present in the identification supplied It will not represent the operator s opinion of and prejudices about the process behaviour Including such a model in a model based control scheme will allow much tighter control than that which could be achieved from the knowledge engineering approach Although a relational model doesn t usually incorporate human operators knowledge directly it does use the same qualitative structure that humans use to deal with real world complexity This provides computer based systems with a very powerful way of dealing with complex process behaviour Relational model identification There are a wide range of different ways of identi
36. m pressure but at 80 C the HIGH temperature rule will activate and steam pressure will suddenly switch to its LOW value The controller will then maintain the LOW value until the temperature drops to 50 C and then the steam pressure will suddenly switch to HIGH resulting in a temperature which oscillates between roughly 50 C and 80 C The problem with our system is that we haven t defined properly what a human means by the terms HIGH and LOW or BIG or SMALL or any of the other adjectives which are used in everyday life Humans don t make crisp boundaries to the sets they use to describe the world In our process example the operator would probably regard 70 C as quite a HIGH temperature not as HIGH as 80 C perhaps but still sufficient to require some attention These leads to the idea of Fuzzy Sets Fuzzy Sets A fuzzy set is a set where the elements can belong to the set with a variable degree of membership By convention this degree or grade of membership is a number which varies between zero and one with zero showing that the element doesn t belong to the set one that it belongs completely to the set and intermediate grades showing intermediate membership In 6 CybMod User Manual Chapter 2 process control problems where we are usually dealing with continuous variables rather than discrete elements the grade of membership of a variable to a fuzzy set is expressed as a continuous membership function These
37. mber of 0 Outliers 40 0 100 200 300 Sample Number Cancel values need to be removed prior to model identification to prevent them from skewing the results 55 50 45 The outliers removal dialogue provides access to CybMod s routine for removing outliers Select the field to be processed from the Datafield list A plot of the data will appear on the graph on the right hand side of the dialogue Two dotted green lines also appear on the plot showing the maximum and minimum acceptable values of the data This is initially set to 5 outside of the maximum and minimum values in the data set You can change the maximum and minimum 44 CybMod User Manual Chapter 4 acceptable data values to anything you wish by editing the boxes in the frame in the lefthand side of the dialogue Pressing the Try it button plots the new limits on the graph highlights the outliers with red crosses and provides a count of the outliers at the bottom of the dialogue At this stage the data is unchanged Pressing the Apply It button will apply CybMod s outlier removal CybMod does this by simply replacing outliers with a value interpolated from the nearest valid data Once this is done the data set loaded in CybMod has been changed irrevocably if you want to return to the old data then you must reload it Outlier removal should be used with caution It is necessary to remove genuinely spurious data but remova
38. n modelling non linear systems is obtaining a set of identification i o data which completely covers the required operating range CybMod includes a mechanism for keeping track of what data has been seen in a frequency or F array The F array stores the sum of the values of the input tensor products associated with particular combination of inputs The value stored in the F array is therefore a measure of how often and how strongly a particular combination of inputs 63 CybMod User Manual Chapter 4 Model Completeness F3 F array Statistics Minimum Value 4 03E 00 Maximum Value 5 05E 02 Average Value 1 11E 02 Completeness Level E amaso i i is 66 66666 Done 1 3 3 1 3 3 has been seen by the identification algorithm A zero value in the F array means that the input combination has never been seen and that the model shouldn t be used to predict in this region A low value means that the input combination has been seen only weakly and infrequently and that model performance in this region may be unreliable The completeness dialogue provides you with a way to examine the F array At the top of the 64 CybMod User Manual Chapter 4 dialogue a number of summary statistics are presenent giving the maximum minimum and mean values of the entries in the F array Underneath the statistics is an edit box which allows you to set a minimum level for the value of F when the form is load
39. nst the Fuel the dialogue works just like data cross correlation except that only the input needs to be set Your results should look like this Xs Cross Correlation of Residuals Copy Graph Cross correlate 027 residuals against P which input Lag in samples pei deen noit nd output Fuel E 2 4 1 20 Maximum Lag feo Fiter Order fig 7 ilter On i 10 8 0 27 0 37 Notic e that 9x 5 we 31 CybMod User Manual Chapter 3 are getting a strong correlation of the residuals with the Fuel at a lag of 4 samples This lag was not used in the original model and could be worth evaluating more carefully Close the cross correlation dialogue by pressing the Done button On the main window dialogue for model 1 double click on the Fuel k 5 term in the model structure display This will bring up an edit dialogue x Edit a Model Variable Ea Variable Name Lag in samples 4 Number of Sets 2 Usable as FIMC manipulation V OK Cancel Delete Change the lag on the Fuel variable from 5 to 4 and press the OK button to complete the edit Identify the model again using random presentation and the default identification parameters Run a model test with a free running predictor You should find that the mean squared error has dropped to 0 948 indicating a significant increase 32 CybMod User Manual Chapter 3 in model performance also reflected in the AIC dr
40. nventional mathematical approaches Although they might not easily create a mathematical model the operators who control the process obviously have a good understanding of it they must already have some sort of process model in their heads The model the operators will have of their 3 CybMod User Manual Chapter 2 process will not be one which can be formed from differential equations but will instead be made up of a set of rules which describe how the process will behave under different conditions e g If the inlet concentration is low then the reactor temperature will fall quickly If the operator s model was rule based and if they could express these rules then at first glance it would appear to be simple to convert the rule based model into a form which a computer could process all computer languages include if lt condition gt then lt action gt type statements However this isn t very easy to do using conventional mathematics To understand why imagine we had obtained two rules which described how an operator controlled a temperature in a process If T is HIGH then set the steam pressure LOW if T is LOW then set the steam pressure HIGH Putting these rules into a computer program is easy provided we can explain to the computer what LOW and HIGH temperatures and steam pressures mean We need to define what we mean by these terms by creating sets of LOW and HIGH temperatures and LOW and HIGH st
41. o zoom in left click and drag select the area of interest and then release the mouse button Click the right mouse button to reset the display back to the original size File Menu i CybMod Fuzzy Model Builder File i Model Analysis Contoller LogFiles Help New System Load a model Save a model twm Process CYBERNETICS Load Data EE CybMod V3 0 Exit A fuzzy modelling tool 1997 1998 Process Cybernefics 38 CybMod User Manual Chapter 4 New System Selecting this menu item will clear CybMod of all currently loaded model and data and reset the program for a new problem If you haven t saved your model or modified data you ll be given the option to do so Load a Model Loads a previously saved model If the number of data fields used to develop the loading model is different from the number of fields in any currently loaded data then loading will be stopped and an error announced Save a Model Saves the currently loaded model all submodels will be saved along with tagname definitions model summary information and the model log The model is saved with the default extension pcg and the log file with the extension mlg Save a Model As Allows you to save previously loaded model 39 CybMod User Manual Chapter 4 under a different name Load Data Loads a process i o data file Doing this when CybMod is empty will cause the main window to change to the model creation dialo
42. opping to 0 027 The maximum error however hasn t been reduced by much it still has a value of 3 83 Have a look at the prediction plot Model Prediction plot You should see that the model tracks the real process output closely for most of the range but loses accuracy in the last thirty or so samples itlooks as though the process has changed in some way in this region and more experimental investigation would be needed to find out what was happening The model we are using at the moment has only two reference sets defined for each variable and as a result is almost linear Highly non linear processes need more reference sets defined on one or more of the inputs depending where the non linearity is Look at the residuals plot for the fuel input X4 Model residuals plot Lopy Graph Select the variable for plotting against the residuals from the list low Cancel 33 CybMod User Manual Chapter 3 The largest values of the residuals seem to be clustered close to the 0 value which could indicate the presence of a non linearity in this region We need to add some more reference sets to the Fuel variable in this region to check this Close the residuals plot and double click the Fuel k 4 field in the model structure on the main window dialogue In the variable edit dialogue which appears change the number of reference sets to 4 Press the OK button to make the edit and note that the reference s
43. put output data gathered from the system to be modelled CybMod includes tools which let you examine this data filter it and remove outliers CybMod also includes cross correlation tools to help you generate appropriate structures for your models Once you have chosen a model structure building the model simply involves some pointing and clicking with the mouse CybMod includes a variety of tools that you can then use to verify the quality of the identified model 1 CybMod User Manual Chapter 1 We have developed CybMod from leading edge research in fuzzy modelling and control in the process industries Process engineers have designed the package with the process industries in mind We are continually developing our products and would be delighted to receive your feedback System Requirements Pentium PC running Microsoft WIndows 95 98 or NT Installing CybMod Insert the diskette number 1 into the floppy disc drive Choose the Run command from the Start menu and in the Run window type a setup exe and then press enter Follow the on screen instructions to complete the installation 2 CybMod User Manual Chapter 2 How CybMod works Although it isn t necessary to know anything about fuzzy modelling to use CybMod some knowledge will help you get the most out of the package Why fuzzy Imagine a unit in a process plant The behaviour of the process is complex and is difficult to model using co
44. r that a dynamic fuzzy model is generally of the form y k f K amp L Vosome inputs if the current value of y y k is predicted using the value of y k 1 from the i o data single step prediction then good prediction results are really easy to acheive In fact a pretty good single step predictor is just y k k amp d Although this gives good single step prediction results it is pretty useless for control and on line modelling purposes This means that single step prediction performance is not a particularly good measure of a model Multi step prediction where the model has to predict several steps ahead using its previous predictions as a base for the next is a much better test The most stringent test is a free running prediction where the model is only told the first value of the output and has to generate the rest of its predictions based on its own previous outputs The Test button starts a test and the Cancel button closes the dialogue When a test is complete a frame will appear at the bottom of the 58 CybMod User Manual Chapter 4 dialogue giving summary test statistics Save test results Selecting this menu item after a model test will bring up a dialogue allowing you to specify a filename and location for saving the test results The results are saved with the original data occupying the first fields and the model prediction placed in the last field Where lags are present in mode
45. sonable first estimate for the dead time between the input and the output Cross correlation works best for processes which are dominated by one big capacity a single big time constant In these cases a clear peak will be Observed and this can be used with some confidence to form a model structure When process involved multiple capacities with similar time constants then the results are less useful The best that can be hoped for in these cases is a rough idea of the most appropriate lag that can be 49 CybMod User Manual Chapter 4 refined by trial and error during model building Cross correlation results can also be difficult to interpret when an output is subject to several non random inputs The Model Menu The model menu is only activat ed when a sub model is selected from the main window model building dialogue Most of the functions on the model menu apart from the Model Summary act only on the currently selected sub model 50 CybMod User Manual Chapter 4 Model Summary The model summary simply provides information about the model you are working on The summary applies to and is the same for all the sub models Model Details ProCyb Test System C tmp data dat 28 07 98 19 32 34 This is just a demonstration of the way that the Model Details dialogue can be You can enter a suitable system name the system name is used by CybOnLine as the topic name for DDE conv
46. teps ahead Test Cancel prediction where the current value of the real output is used isn t too much ofa challenge Multi step ahead prediction where predictions are based on one or more previous predictions is a much better way of assessing model quality The most difficult test is the free running predictor where the model is only supplied with the initial value of the output and all subsequent predictions are based on previous model outputs Select Free from the list to run the model as a free running predictor Press the Test button After a few seconds summary results of the test will appear at the bottom of the dialogue Note that the mean squared error is 2 04 the maximum error is 4 57 and the AIC Akaike Information Criterion a measure of accuracy vs complexity is 0 742 Press the Cancel button to close the test dialogue 30 CybMod User Manual Chapter 3 Refining the model Model building is an iterative process where different models are built compared against each other and refined CybMod includes several tools to help you with this process One useful thing to do is to look at the model residuals the differences between the predicted and actual outputs CybMod lets you plot the residuals against all the data fields Model Residuals plot and also lets you cross correlate the residuals Model XCorr Residuals against the data fields For now cross correlate the residuals agai
47. tion A lagged value of the output is automatically inserted as an input but if you want to create a steady state model perhaps for an on line estimator for use in CybOnLine then simply double click the lagged input and change it to the desired input To add another input to the model click the Add a new input button This will bring up a dialogue allowing you to select the input from the list of 71 CybMod User Manual Chapter 4 Edit a Model Variable EJ Variable Name Field_1 m Lag in samples 4 Number of Sets 2 Usable as FIMC manipulation v OK Cancel Delete data fields the lag to be applied to the input and the number of reference sets to be used to describe the input The check box at the bottom indicates whether the variable is usable as a manipulation in a model for CybFIMC Checking an unchecked box will simply re order the model to make the variable the last model input see CybFIMC documentation for more details A similar dialogue appears if one of the existing inputs are double clicked allowing them to be edited In the frame at the bottom of the main window dialogue is a list of the reference set centre points for the currently defined inputs The reference set values are initialised by linearly spacing them from the minimum to the maximum value of the appropriate input 72 CybMod User Manual Chapter 4 Edit reference sets x Model Variable Field 1 k 1
48. uded in the sub model then it probably means that the model s prediction performance could be improved by including the data field as an input Remember that a high correlation does not necessarily imply that adding that variable will reduce the prediction error by a worthwhile amount 61 CybMod User Manual Chapter 4 The Analysis Menu Do a Quick prediction Th Model Completeness e analysis me Surf lot nu provides you LEES scis with some tool s to analyse the characteristics of the model rather than just its predictive performance Do a Quick prediction Immediate Model Calc FG Model Inputs Variable Name Value GEERT 2 27e 01 Calculated output value Go N one Done This dialogue 62 CybMod User Manual Chapter 4 can be used to obtain predicted output values for any desired set of inputs It s useful for checking particular points on the sub models prediction surface To carry out a quick prediction you first need to specify the values of the inputs Select an input from the Variable Name list and you will see its currently stored value appear in the edit box to the right By default all inputs are set to their lowest values You can edit the stored value of the input by typing directly into the box Once you ve set up your input list press the Go button and the model prediction will appear Press Done to exit the dialogue Model Completeness One of the problems i
49. value to 5 the value obtained from cross correlation leave the number of reference sets 26 CybMod User Manual Chapter 3 at 2 and press the OK button A new input Fuel k 5 will be added to the model structure display Change the values of the reference set centres for this variable to 3 and 3 Identifying the model Now that we have set the model structure we need to identify the relational array entries To do this select the Identify a sub model item from the Model menu Make sure that the Model 1 tab is selected on the main window display all the modelling menus refer to the currently selected sub model CybMod provides two ways of presenting the data to the identification algorithm The first is sequentially where the data is presented in sequence from the first sample to be used to the last The second is randomly where a fraction of the total number of examples are chosen at random from the data the same example can be chosen several time so that 7596 on the dialogue doesn t mean that three quarters of the data will be used 27 CybMod User Manual Chapter 3 If you intend to use all the data for identification or you want to identify only on a fixed portion of the data then sequential presentation is best If you intend to use only part of the data for identification but the whole set for testing then random presentation is best since samples will be chosen across the whole range of dat
50. will then be able to continue with a detailed edit of the through Select the output variable for your new model Fielo 7 A set of sample data boxjen dat is included with HY etd MURS 2 t allocated to new model variables by defaul CybMod and can be found in the c CybMod This can be changed later 2 directory This data is the famous Box Jenkins TRE laboratory furnace data and consists of three fields of data the sample number the fuel flowrate deviation and the off gas concentration The object is to build a dynamic model of the off gas concentration 18 CybMod User Manual 19 CybMod User Manual Chapter 3 Examining the data Before we start to build a model we need to look at the data that we have just loaded From the Data menu select the Data file summary item A window will appear which gives a summary of the information contained in the data file X Data Summary Information Data file name C CybMod B oxjen dat Number of samples 296 Number of fields 3 m Field Information Maximum value 296 Minimum value 1 Histogram Mean value 148 5 Standard deviation 85 59206 Close From the summary we can see that the data file consists of 296 samples of data each containing three data fields Information about the individual data fields can be obtained by selecting the field name from the Field Information list box The Histogram button plots a histogram of the data 20 CybMod
Download Pdf Manuals
Related Search