Revision 01/07/2020


CTrend ©


Manual Content


Centrifugal gas compressors are critical equipment that can lead to a high cost of operation and maintenance if subjected to unnoticed performance degradation and unscheduled down time. Major causes for performance deterioration faults, some of which requiring major overhaul of the compressor, are as follows:

CTrend is software for monitoring and investigating performance degradation in centrifugal compressors. It uses digitalized versions of the performance maps provided by the manufacturers and field measurements to estimate the deviation between the actual degraded performance and the undegraded performance (pristine state) provided by the manufacturer performance maps.

Degraded operation can be due to: (1) machine state alteration (clean vs. degraded state) and/or (2) process conditions which are offset such as changes of gas composition, pressure, temperature, flow and operating speed vs. design.

When process conditions are off-design and, at the same time, machine performance is degraded, the benchmarking of compressor performance becomes an even more complex task.

On top of this, multi-section train arrangements add a further layer of complexity as prediction inaccuracies amplify when multiple sections are dependent thermodynamically. In all these situations, the use of CTrend is advocated (see upper right quadrant hereunder).

Thermodynamic Modeling

The tool allows modeling and calculation of the so called “performance signature” of a compressor based on the original machine performance map from which invariant parameters are extracted.

The calculations of the thermodynamic properties use accurate real gas equation of state (EOS) based on Helmholtz free energy framework (see accuracy comparison in Table 1).

Equation of State



Helmholtz (ISO 20765)

Very High














Ideal gas law



Table 1 – Comparison of Helmholtz free energy EOS to others

Real gas equation of state is also employed for the handling of flow measurement device (FMD) calculations per ISO-5167 (see Table 2).

FMD design type

FMD Location

  • Orifice (corner, flange, taps)

  • Suction

  • Venturi Nozzle (ASME, ISA)

  • Lo-loss tube, Dall tube

  • Discharge

Table 2 – Available FMD design

A summary of available technical features is provided in Table 3.

Deviation Monitoring

Monitoring of performance is achieved by comparison of measured data against performance signature of the compressor. To do so, analog inputs data are fetched from the machine control system.

Communication with machine control system is available via the current following protocols: Modbus TCP/IP, ASCII/RTU, and RTU/UDP over TCP/IP. There is ongoing work to add OPC communication capability to the tool.

The standard instrumentation set up consists of six analog inputs per process section as follows:

Gas composition is essential information and shall be obtained from an online analyzer or gas sample analysis.

The performance deviation for a monitored parameter X is noted DEVX (%) and is expressed as:

DEVX (%) = 100 * [ xpredicted - xactual (measured)    ]/ xpredicted

What is Measured by Key Performance Deviations

ETAP_DEV.: Given (P_in, T_in, Flow, Speed, Mixture %)|actual -> Predict Efficiency -> Compare to Actual Efficiency (Measurement-inferred)

WIF_DEV.: Given (P_in, T_in, Flow, Speed, Mixture %)|actual -> Predict WIF -> Compare to Actual WIF (Measurement-inferred)

Flow_DEV.: Given (P_in, T_in, Speed, Mixture %)|actual and P_out|predicted -> Predict Flow -> Compare to Actual Value (Measured)

PressureRatio_DEV.: Given (P_in, T_in, Flow, Speed, Mixture %)|actual -> Predict Discharge Pressure -> Compare to Actual Value (Measured)

T_Out_DEV.: Given (P_in, T_in, Flow, Speed, Mixture %)|actual -> Predict Discharge Temperature -> Compare to Actual Value (Measured


Machine Learning

Equation of State

Head Calculation

Extended Modeling

Iterated Parameter

  • Liner regression (STD)

  • ISO-20765 Part II (STD)

  • 3-point (STD)

  • Design case (STD)

  • Discharge pressure

  • Nonlinear regression

  • AGA8 / ISO-20765 Part I

  • Schultz (PTC10)

  • Design + off-design

  • Suction pressure

  • Artificial Neural Network


  • Average suction and discharge

  • Fan law

  • Fixed-speed machine

  • Speed

  • Flow

Table 4 – Summary of technical feature


CTrend trending tool is not intended for tracking transient or process variations of a fast nature (e.g., surge).

Instead, the tool builds a degradation profile of the machine as its performance deteriorates through time; this requires suitable time intervals to be set (this is done via T1 delay, see figure hereunder).

How to Set Up a New Project

Click on New Project icon then populate the new project information in the project description window. When finished, click ok.

Browse and select a folder to save the project file to.    Folder shall have user write/read access are granted. Make also sure that the project ID name chosen does not exist already in the target folder.

A new empty project is created.

Train Configuration

In the train groupbox, proceed as follows:

Process Data and Stage Configuration

Select the active process section in the relevant treeview as depicted (in this example only one section applies).

Click on Process Configuration Button

Fill in the data in the process mask as depicted. Click on the Save button when finished.

Configure the mechanical stage by specifying the impeller tip diameter for each impeller pertaining to the active process section.

Configuration of Operating Cases

Right-click on the process condition tree view area then click on Add Case.

Name the case as applicable then click OK.

Select the new condition by highlighting its relevant node then proceed by populating operating condition data in process mask.

Special Case: <Ref_OP>

Right-click in the process tree view area, then Click on ‘Create Reference OP’.

<Ref_OP> copies design case process data as an operating condition. This is required to generate performances and map for that condition.

Consequently, <Ref_OP> case is read only.

How to Build Performance Signature (Characterization)

Foreword Considerations

Selecting Map Variables

Two independent thermodynamic outputs (ordinates Ya & Yb) versus flow (abscissa X) shall be supplied in order to build a performance characterization. There are currently four optional combinations that can be selected to suit the OEM information available:




Option 1

Polytropic Head

Polytropic Efficiency

Actual Volume Flow

Option 2

Outlet Pressure

Outlet Temperature

Actual Volume Flow

Option 3

Polytropic Efficiency

Polytropic Head

Mass Flow

Option 4

Polytropic Head

Polytropic Efficiency

Mass Flow

Table 4 – Map variables combinations availabl


Units and Digit Precision

The tool adopts the following system of units and numeric format representation:

Pressure [MPa-a]

(Format #.#### or lesser precision)

Temperature [K]

(Format #.## or lesser precision)

Mass Flow [kg/h]

(Format #.)

Volume Flow [Am3/h]

(Format #.# or lesser precision)

Polytropic Head [kJ/kg]

(Format #.## or lesser precision)

Efficiency %    

(Format #.### or lesser precision)

Unit converter tool (spreadsheet) is available for conversion from units different than above. Refer to install folder: Help/unit_conversion_tool_NoEOS.xlsm

Data Input Structure of Supplied Scattered Data



Data Set General Structure

Provide the data, row by row per the following structure:

Group the data point by series of constant speed (i.e., group of data points which altogether form a speed line). 

Data Points at Constant Speed (Ascending or Descending Flow Pattern)

For each group at constant speed, provide the data points in rows whereby it is ensured that:

Flow values need to be either descending or ascending. Whichever pattern is selected (descending or ascending), preserve that same pattern consistently across the whole data set.

Data Points at Constant Speed (One-to-One Data Pairing)

The couple of output variables selected for map characterization (Ordinates Ya, Yb) shall be paired one-to-one to same set of flow data values (abscissa X).


Ya=Pressure, Yb=Temperature, X = Volume Flow

Ya1,Ya2,...Yan = Fa(X1,X2,...Xn)

Yb1,Yb2,...Ybn = Fb(X1,X2,...Xn)

Repetition / Duplicates

Do not repeat groups of identical speed (no duplicates).

Do not repeat flow data for a constant speed (no duplicates).

Table 5 – Data structure of supplied dat


Qualitative and Quantitative Aspects of Supplied Data

As a general rule, the wider the speed range, the wider the predictability window for treating new or off-design conditions. A sufficient number of speed lines and data points must be available in order to train the model and obtain generalization. Depending on the characterization method selected, this number can increase (e.g., artificial neural network method).

Moreover, certain methods are sensitive to outlier points, for example due to reading errors. It is also important that supplied data are denser in curve areas where steeper gradients occur.

The following guidance should be observed:

No. of Speed Lines

Three (3) speed curves are required as minimum.

No. of Data Point Per Speed Line

A minimum of 11 points is suggested. A higher no. of flow data points per speed line can be considered to catch steep changes of curvature.

Table 6 – Requirements on supplied dat

aSteps for Building Performance Characterization

Click on the button Performance Signature in the toolstrip menu below

In the displayed mask, select Map Variables as depicted below

Copy the tabular curves (located in install folder: Help/Example_Tutorial.csv) and paste the numeric data into grid view.

Scroll down on condition basis column to select all rows which are not empty at the left.

Select the relevant condition in process tree view area (for this example: design case)

Right click on the highlighted area of the grid view and click on Assign Condition Basis

Click on chart display

The performance curves will be displayed for both maps Pressure vs. Flow and Temperature vs. Flow, thereby allowing performing a sanity check.

Fill in the design speed value   

In the parameters tab, select Standard Method / Linear and leave all parameters as default.

Click on Save Parameters    

Click on Thermodesign Parameters button

Set the parameters as depicted below

When completed, click on Apply.

Click on Generate Signature ; if prompted (overwriting an existing characterization), confirm the message box.

Verification of the Characterization Results

Click on the button Thermo Design run for the process section

Confirm the prompted message.

The Console Output button becomes visible, click on it to review the summary calculation report

Ensure that the calculated thermodesign speed matches closely the design speed specified for the characterization.

Other Modeling Considerations

Fixed Speed Machine

If a set of varying operating conditions at compressor inlet (gas composition, temperature) is provided - even though the operating speed is constant - and performance curves are available for each of these conditions, then it is possible to make a compressor characterization provided there is good enough variability of the Mach number.

For example, in case of gas MW changes, each gas condition can be modeled.

Then the speeds which correspond to each gas have to be manually edited at 2nd digit level; this will have no impact on performance calculations. See an example below (RPM column).

Variable Speed Map Generated with Fan Law Option

When head and flow variables for map modeling, it is possible to generate a new set of curves outside the input data set using fan law. These newly generated curves will be added to the data set used for the performance characterization.

Point the cursor on the <RPM column> in the input data set that corresponds to the speed curve which will serve as basis to calculate the new curve. Right-click and then click on <Fan law>; enter the speed value in the input box.

Extended Range Modeling

Extended range modeling (ERM) objective is to extend the predictability range determined by [(MU/MU*)|MIN : (MU/MU*)|MAX ] interval.

One (or more) off-design operating condition(s) performance map, in addition to the reference condition one (design), shall be available from the manufacturer.

The off-design operating condition must be added via the process case treeview and process data must be populated.

In the data grid area of the performance characterization tabpage, the user will use the <Condition Basis> column to assign the off-design operating condition.

The procedure is summarized as follows:

Important Note:

Prediction shall be made within the allowed Mu/Mu* range, i.e., [(MU/MU*)|MIN : (MU/MU*)|MAX ]; this range is typically set by the input dataset available speed range. User may override and widen theses limits using an extension factor (%). In practice, this means allowing extrapolation outside of the characterizer. In most cases it is not acceptable practice. The only instances where this can be accepted are:

- Extrapolating to lower speeds using standard method/linear (this will employ fan law extrapolation).

- Minor extension for plotting some speed curves defined as % of Base Speed, to account for discrepancies in speed values.

The extension feature is enabled by double clicking on the warning label as depicted just below; a warning message will be prompted.

How to Generate Performance Maps

Right-click in the <Speed Curves> treeview area. Click on <Add Speed Line>.

Write value 100 (for 100%) and click Ok. Repeat same steps for other speeds that apply, for example, 75% and 105%.

Base Speed Auto vs. Manual

If <Base Speed -> Manual> option is selected, the tool will assign this value as 100% speed specified by user for the purpose of generating new curves.

When <Base Speed -> Auto> is selected, the tool calculates the maximum operating speed among all checked case in the relevant treeview section and assigns that value as 100% speed. Thus this option requires extra computation steps.


If OEM data specifies Maximum Continuous Speed (MCS) = 10167 RPM for variable speed electric motor driver, then you can set the 100% speed to Manual and enter Base Speed as equals to 9683 RPM (use numerical value only, i.e., no string characters).

Click on the button Thermo Design run for calculating individual process section, then click on Map icon to view the curves (see an example depicted below)

How to Set Up Performance Monitoring and Trending

Click on Trend Analysis icon

This will enable icons in the toolstrip menu as depicted hereunder

Click on Sampling Settings icon

Specify the Modbus communication options based on your Modbus specification for the application under consideration.

Populate the Analog Inputs Tabpage based on Modbus specification of the considered application. As basic information, the following information mu st be supplied

By default, design condition will be used for gas mixture. This can be modified if needed.

When flow measurement unit is selected as delta P measurement (ΔP), the flow measurement device (FMD) configuration icon becomes enabled. Selecting that icon will display FMD configuration form. Populate the form based on your application parameters.

Guessed Reynolds number can be set as 1e5 as default value while Search Upper and Lower Values can be set at 1000 and 0.001 respectively.

Performance Monitoring and Trending Interface

Click on Connect icon

If the connection is successful the status as connected will be displayed

Clicking on Scan icon will launch the Monitor interface.

It is suggested to start the sampling according to the following order:

Appendix A - Thermodesign Settings

Right-click on Thermodesign settings icon will display the settings form for the active process section.

An explanation is provided hereunder for each parameter.



FI*, MU Coefficients by user

When checked, design will be calculated based on user specified/imposed values for FI* and MU* entered via the characterizer modeling section (coefficients under thermodesign).


ETAP (Polytropic Efficiency) Correction Factor.   

ETAP = ETAP * Correction Factor / 100

Default value = 100% (= no adjustment)     


TAU (Work Input Factor) Correction Factor.   

TAU= TAU * Correction Factor / 100

Default value = 100% (= no adjustment)     

volumetric shift factor

Volumetric shift by means of flow coeffiicient ratio FI1/FI1*(Design condition)

Default value = 1.00 (= no adjustment)     

mach nUMBER shift factor

Mach number shift by means of ratio MU/MU1*(Design condition)

Default value = 1.00 (= no adjustment)     


When checked, selects T2SDIV temperature method in lieu of Root Search Method (Default)


Select among 3 options, the polytropic calculation method:

  • 3-Point (Default)

  • Shultz

  • Average Suction and Discharge


When checked, configures the performance calculation output as follows:

Performance point calculation only for alternative cases.

Performance point calculation and single speed curve for design (Default).


When checked, displays a label on each speed curve of the performance map, indicating the speed in % in addition to RPM’s.


Plot the performance curves using LINES instead of SPLINES (Default).

points interval control

Change the intervals distribution of the control points used to generate the performance curves. Adequate for steep curvature near the choke region.

Default value = 1.00 (speed curves will be plotted using calculated points which are equally spaced flow wise).

operating range verification

When checked, the operating range (available turndown) of the performance curves is verified. Default value unchecked.

convergence control

When checked, convergence stabilization measure is used. The program will set minimum (floor) values for TAU and ETAP while the solver performs the iterations. Default value is unchecked.


Absolute tolerance on discharge pressure [kPa].

Stop criteria for iterations set on discharge pressure.   

Default value=0.5 kPa.

speed initial value

Initial guess INIT_RPM for speed [RPM] (Option).

If left blank, the software will attempt to calculate INIT_RPM automatically.

speed low limit

Sets lower bound of speed search interval for thermodesign solver as defined by


Default value = 0.6

speed high limit

Sets upper bound of speed search interval    for thermodesign solver as defined by


Default value = 1.15


Relative tolerance on flow [%].   

Stop criteria for iterations set on flow.   

Default value=0.01%


Defines the number of subdivisions for T2SDIV and H2SDIV methods.

Default value =1 (lower accuracy / faster).

T2SDIV = option method, returns P2, T2 that satisfies inputs HPOL, EPOL.

H2SDIV= default method, returns HPOL,T2 that satisfies inputs P2,EPOL



Speed safety margin [%].

Default value=0%.

Effects U2 and RPM values by a factor (1+SSM/100);

RPM_new = RPM_old * (1+SSM/100)

U2_new = U2_old * (1+SSM/100)

Subsequently effect the design flow coefficient and Mach number values calculated through the performance characterization procedure.


Defines if SSM margin as specified one row above is to be included in the thermodesign calculations (that is, after characterization has been performed). By default, SSM margin is not to be included.

If it is included, the speeds of each curve used for trending will be displayed with SSM margin included.


Control line to surge limit line margin [%]. Default value=10%



Specifies the mechanical losses (bearings, seals) at 10000 RPM.    The program linearly extrapolates different speeds.

Appendix B – Status Codes

Status Codes for Thermodesign




Specified flow TOO LOW (SURGE).

Flow is automatically adjusted to control line flow using recycle control.


Inlet pressure TOO LOW (VACUUM).

User should inspect the result to ensure the specified duty has been matched.


No plotting at the flagged speed.

Not enough operating margin on curve, OR

Speed TOO HIGH (exceeds the upper bound of allowed Mu/Mu* range).


No plotting at the flagged speed.

Speed TOO LOW (exceeds the lower bound of allowed Mu/Mu* range).


Specified duty cannot be matched with iterated variable set on FLOW.

No flow can satisfy the imposed duty.



Not enough operating margin on speed curve for the actual case.



Specified flow TOO HIGH (CHOKE).

Flow is automatically adjusted to chocking line.



Specified duty cannot be matched with the fixed speed motor speed.

Table B1 – Status codes for thermodesignExample of Status Code display ERR3 (Thermodesign Console):

Status Codes for Performance Monitoring and Trending




operating point (SIGNAL ACQUISITION) IS IN surge


operating point (SIGNAL ACQUISITION) IS IN choke





Table B2 – Status codes for performance monitoring and trendin


Example of Status Code display FL0SP1 (Trend Analysis):

FL0: Operating Point Status = Normal (in Envelope)

SP1: Speed is lower than characterizer range

Appendix C – Thermodynamic Methods

  1. Equations of State

In order to accurately predict gas mixtures thermodynamic properties for real-life compression applications, an equation of state is needed. There is a prominent risk of doing improper estimate of the compressor performance under assumption of ideal gas behavior.

The following equations of state are currently available:

EOS Package 1

ISO 20765 Part I (AGA8-92DC)

EOS Package 2

ISO 20765 Part II (GERG2008)

EOS Package 3


Table C – Equations of state availabl

eCTrend uses equations of state based on the Helmholtz free energy whose implementation is described in ISO-20765 standard.   

ISO-20765 methods use a standardized 21-component gas system in which all of the major and minor components of natural gas are included. Trace component present but not identified as one of the 21 specified components may be reassigned (see ISO-20765 for details).

The next paragraphs provide a brief outline of each equation of state available.

AGA8-92DC (Natural Gas and Similar Mixtures)

The AGA8-92DC equation was published in 1992 by the American Gas Association, having been designed specifically as a procedure for the high accuracy calculation of compression factor. In this respect, it is already the subject of ISO12213-2.

In order for the AGA8 equation to become useful for the calculation of all thermodynamic properties, the equation itself, published initially in a form explicit only for volumetric properties, was mathematically reformulated.    This reformulation has been the subject of the ISO 20765-part I standard which specifies a method of calculation for the volumetric and caloric properties of natural gases based on the Helmholtz free energy.

GERG2008 (Natural Gas and Similar Mixtures)

The GERG-2008 equation of state was developed by the University of Bochum in Germany as a new wide-range equation of state for the volumetric and caloric properties of natural gases and other mixtures. It is now the subject of the ISO 20765 Part II.

The ranges of temperature, pressure, and composition to which the GERG-2008 equation of state applies are much wider than the AGA-8 equation and cover an extended range of application.   

EOS-CG (CO2 and Combustion Gas like Mixtures)

This equation of state is a new Helmholtz energy mixture model for humid gases and CCS mixtures (also referred to as Equation of State for Combustion Gases and Combustion Gas like Mixtures, EOS-CG) developed by the University of Bochum in Germany.

Using the mathematical approach in the GERG-2008 with some minor adjustments, the EOS-CG improves the description for binary and multi-component mixtures of six components as follows:

Applications include Compressed Air Energy Storage (CAES) and Compression, Transport and Injection of Separated CO2 (CCS).

Density Solver - Soave-Redlich-Kwong (SRK) Equation of State

The SRK equation of state is implemented in CTrend as part of the ISO 20765 routines (density solver) and is applied in order to obtain an initial approximation of the density roots (vapor phase).

More specifically, SRK equation of state is used to narrow down the root search interval of the CTrend density solver for ISO20765 part II. For reference, SRK equation of state formulation, i.e. alpha function, mixing rules and binary interaction coefficients are those from the API Technical Data Book 6th edition.

Equation of State Accuracy

For the ISO-20765-part 1 standard (AGA8) equation of state, volumetric properties are subject to an uncertainty of calculation of about ± 0,1 % (95 % confidence interval). For caloric properties, the uncertainty of calculation is usually greater.

ISO-20765-part 2 standard (GERG2008) equation of state produces results that are at least equal or better in accuracy than AGA8 for both volumetric properties and caloric properties considering mixtures in the gas phase. The method maintains an uncertainty of = 0,1 % for volumetric properties, and is generally within 0,1 % for speed of sound.


Compressor calculations deal with gas phase.    Phase equilibrium calculations and stability test are outside the scope of CTrend.    It is User’s responsibility to verify (using for example a process simulator) that the fluid conditions at the inlet and along the compression path remain in the gaseous phase.

  1. Polytropic Head Calculation Methods

The software provides three options for compressor polytropic head calculations:

- Average Suction-Discharge;

- Shultz Method;

- 3-Point (End-Point) Method.

The 3-point method (Huntington, 1985) is known to be more accurate that the other two without incurring significant exta computational cost; thus it is the default method.

When the discharge temperature is to be calculated, the software uses two methods:

- Root Search Iterative Method (based on isentropic temperature calculation);

- Subdivision Method (more robust but less accurate).

The following flowcharts provide an overview of the thermodynamic methods for discharge temperature calculations.

Appendix D – Performance Signature (Characterization Methods)

Standard Methods

The following table provides guidance on the selection of standard methods for performance characterization.



Data Requirement





See Table 6

No User Adjustment required.

Fan Law extrapolation outside input data set speed range.

Not suitable for Extended Range Modeling (ERM).





5 ≤ NQ ≤ No. of samples, or 40 whichever is lower. Recommended NQ = 13

1 ≤ NW ≤ No. of samples, or 40 whichever is lower. Recommended NW =19


2 ≤ NCP < No. of samples.    Recommended NCP = 30.

Recommended practice:

- No of speed curves >= 5

- No of data point per curve >=11

- Speed lines provided at regular intervals

- Narrow flow intervals for higher gradient/ steep curvature

Shall not be used to extrapolate outside input data set speed range.

LRPM and URPM shall not exceed the input data set speed range (user adjustment required to obtain convergence).

Sensitive to data reading / reporting error.

Table D – Standard methods parameter


.Artificial Neural Network ANN Method (Machine Learning)

An ANN of configurable topology is offered as an alternative to the standard methods mentioned above. The ANN was adapted from JETNET 3.0 ANN package by others.

Certain considerations apply when using ANN instead of the standard methods:

- The ANN method uses a random seed for initialization.

So, when a new characterization is performed, the outcome may vary from one trial to the next. When a characterization is deemed satisfactory it is recommended to freeze it.

- The ANN method is prone to over-fitting. The RMSE (Root Mean Square Error) for a certain output could reach smaller levels without implying that ANN generalization has been attained; So, an ANN shall be configured with a number of layers and units as small as possible in order to prevent over-fitting. A tradeoff between generalization and accuracy needs to be made.

- ANN is NOT suitable for extrapolation.

ANN Configuration Parameters (Basic)

The ANN parameters are entered via the GUI mask as depicted below.

All though the ANN allows for advanced configuration, in most situations it should be sufficient to configure the network with basic options. The basic options available to choose from as are:

As default, RMSE (Root Mean Square Error) and Maximum No. of iterations can be set as follows:

RMSE = 0.001

Maximum No. of Iterations = 200000

ANN Configuration Parameters (Advanced)

Advanced tuning of the parameters is generally not required. If advanced tuning is performed, the following parameters can be configured:

Advanced configuration can be made via configuration file “SETTLEMENT.CFG” located in the application path; the parameters are defined as follows:


Default Updating Method


Default Output Mode (Multiple <1> or Single <0>)


Total No. of Layers


Scaling Factors (Min. Bound)


Scaling Factors (Max. Bound)


Activation Function, Layer 1 (ATAN <1>, LINEAR <4>)


Activation Function, Layer 2 or Output (ATAN <1>, LINEAR <4>)


Activation Function, Layer 3 or Output (ATAN <1>, LINEAR <4>)


Activation Function, Output (ATAN <1>, LINEAR <4>)


Noise Width


Noise Scale Factor


Mini-Batch Size




Learning Rate


Screen Refresh Rate


Error Measurement Method (<0> for MSE)


Initial Width


Weight Decay Simple Pruning


Single Output Mode Select (<0>    Loop, <N> Train Selected Output N)


Nt Used <0>


Select DVAR (<0> Sound Speed, <1> Isentropic Coefficient KT)


Grid No. Subdivision (Linear or Spline Densification Option)


Not Used <0>


Default Size (No. Units ) First Hidden Layer w/ Option SMALL.


Default Size (No. Units ) First Hidden Layer w/ Option NORMAL.


Default Size (No. Units ) Second Hidden Layer w/ Option LARGE.

Available updating methods and their assigned code:

  1. 0 -> Standard Back-Propagation updating

  2. 1 -> Manhattan updating

  3. 2 -> Langevin updating

  4. 3 -> Quickprop

  5. 4 -> Conjugate Gradient - Polak-Ribiere

  6. 5 -> Conjugate Gradient - Hestenes-Stiefel

  7. 6 -> Conjugate Gradient - Fletcher-Reeves

  8. 7 -> Conjugate Gradient - Shanno

  9. 10 -> Scaled Conjugate Gradient - Polak-Ribiere

  10. 11 -> Scaled Conjugate Gradient - Hestenes-Stiefel

  11. 12 -> Scaled Conjugate Gradient - Fletcher-Reeves

  12. 13 -> Scaled Conjugate Gradient - Shanno

  13. 15 -> Resilient Back-Propagation


ANN Prediction Task Procedure

  1. The network is initialized with parameters stored in file (done in the modeling step)

  2. The input vector is scaled

  3. The neural network parameters are set up

  4. The input vector is fed forward into the network

  5. The calculation results are stored in the output vector

  6. The output vector is scaled (back-transform).

Output Information

The program writes the network parameters, RMSE error and coefficient of determination in file.

STANDARD: network will write unformatted in a file “Fort.X” (X=process section)

OPTION: network writes formatted in a file “Fort.X” (X=process section)

Note that unformatted writing is machine dependant which may affect the portability of the “Fort.X “file

Appendix E – Notations and Formulas






Molecular Weight



Gas Constant = 8314.472



Actual Inlet Volume Flow



Compressibility Factor


Absolute Pressure






Speed of Sound






Shaft Speed



Corrected Shaft Speed


Mass Flowrate



Corrected Mass Flow



Polytropic Head



Total number of impellers in a process section


Isentropic Temperature Exponent


Isentropic Volume Exponent


Actual Inlet Flow Coefficient


Design Inlet Flow Coefficient

Mu (or μ)

Peripheral Mach Number

Mu* (or μ*)

Design Peripheral Mach Number

ETAP (or η)

Polytropic Efficiency

TAU (or τ or WIF)

Work Input Factor


Impeller Peripheral Tip Speed (Average)



Tip Impeller Diameter (Average)


Table E – NotationsSubscripts:

1 (or s): Inlet; 2 (or d): Outlet

Asterisk (*) denotes <Design>; example: Mu*


When 'a' suffix is omitted in units for pressure, the pressure shall be assumed as absolute (e.g., MPa, Bar)

General Formulas

The inlet flow coefficient Fi1 and the peripheral Mach number Mu are given as follows:



Where RPMC is the corrected speed and CRF is the corrected flow, given respectively by:



The work input factor TAU and polytropic efficiency ETAP are expressed as:


For multi-stage compressors, the diameter D2 is averaged based on the following formula:

Universal flow coefficient

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