After inserting 1D-variable in the workflow editor, its options have to be set up for running of the experiment. Select one item of the 1D-variables in the explorer to edit its options in the property window.
Name
It is the name of the node. This name may be defined basically once time for the entire experiment.
Comment
The comment for the node.
Domain
There are 3 domain types for signal processing of the 1D-variable: Time Domain, FFT Frequency Amplitude and FFT Frequency Phase.
Output Value
The output value from the value array of Y-Axis can be selected here for the output of the 1D-variable. That is to arrange how the value of a output link can be calculated from the values list of the Y-result. There are several types as Last Value, Minimal Value, Maximal Value, Mean Value, Sum, Absolute Sum, Bandwidth, Standard Deviation and Integral. There are also some special cases for this value accumulations:
Constraints: 1D-signal has to be fitted to the constraints defined in the tab "Constraints". The value accumulates from the constraints violation.
Data Fitting: 1D-signal has to be fitted to the imported data in the tab "Data". The value accumulates from the integral difference between signal und data curve.
X-Value by Y-Point: If the option is chosen, an additional input field "By Value" will be displayed being edited. The output value is the value of X-axis at the value given in the field "By Value" on the Y-axis.
Y-Value by X-Point: If the option is chosen, an additional input field "By Value" will be displayed being edited. The output value is the value of Y-axis at the value given in the field "By Value" on the X-axis.
X-Value by X-Leap: If the option is chosen, an additional input field "By Value" will be displayed being edited. The output value is the first value of X-axis (i) at the leap (i) to (i+1) on the X-axis, which absolute value is greater or equal than the absolute value given in the field "By Value".
X-Value by Y-Leap: If the option is chosen, an additional input field "By Value" will be displayed being edited. The output value is the first value of X-axis (i) at the leap (i) to (i+1) on the Y-axis, which absolute value is greater or equal than the absolute value given in the field "By Value".
Y-Value by X-Leap: If the option is chosen, an additional input field "By Value" will be displayed being edited. The output value is the first value of Y-axis (i) at the leap (i) to (i+1) on the X-axis, which absolute value is greater or equal than the absolute value given in the field "By Value".
Y-Value by Y-Leap: If the option is chosen, an additional input field "By Value" will be displayed being edited. The output value is the first value of Y-axis (i) at the leap (i) to (i+1) on the Y-axis, which absolute value is greater or equal than the absolute value given in the field "By Value".
X-Value by Angle: If the option is chosen, an additional input field "By Value" will be displayed being edited. The output value is the first value of X-axis (i) at the angles difference between 2 lines (i-1) to (i) and (i) to (i+1), which absolute value is greater or equal than the absolute value in degree given in the field "By Value".
Y-Value by Angle: If the option is chosen, an additional input field "By Value" will be displayed being edited. The output value is the first value of Y-axis (i) at the angles difference between 2 lines (i-1) to (i) and (i) to (i+1), which absolute value is greater or equal than the absolute value in degree given in the field "By Value".
By Value
This is the value for the option "Value Accumulation" by some special cases. If it is an angle, the unit will be degree.
X-Limit
There are 3 options: "Total X-Axis", "Limited X-Axis" or "Fix X-Points". If the option "Total X-Axis" is used, the approximation will be applied on the total X-axis. It is sometimes very computing intensive for the approximation of the total X-axis. Therefore, it is better to approximate only a interested range of X-axis. In this case, the option "Limited X-Axis" has been chosen. The Approximation will be applied only inside the range:
Xmin ≤ X ≤ Xmax
If the option is "Fix X-Points", An additional field will display for user to input a list of values, which represent the fix points on the X-axis.
Xmin
The option is only visible, if the "Boundary" is "Limited X-Axis". The value is the lower boundary for the approximation range on the X-axis:
Xmin ≤ X ≤ Xmax
Xmax
The option is only visible, if the "Boundary" is "Limited X-Axis". The value is the upper boundary for the approximation range on the X-axis:
Xmin ≤ X ≤ Xmax
X-Step Control
User can define the step control on the X-axis for approximation. There are 3 options "Automatic", "Controlled" and "Constant". By "Automatic", the step of X-axis will be automatically calculated depending on the simulation of original model. The controlling factor for the step control can be set if "Controlled" is used. User can define the fixed step for the X-axis if "Constant" is chosen.
S/A-Factor
The option is only visible by the option "Controlled" for X-Step Controll. User can define the speed-accuracy-control-factor on the X-axis of approximation. the option is set normally to 50. If its value is smaller, the computing speed will be increased, but the accuracy of meta-modeling will be decreased. Otherway, if the value is greater, the speed will be decreased and the accuracy increased.
X-Step
The option is only visible, if the option "Constant" for X-Step Controll is chosen. User can define the fixed step on the X-axis for equal distant discrete points on the X-axis for approximation.
Approximation
The method of approximation can be setup individually. There are 3 possible methods Polynomial, Gaussian Process or Hilbert Space to choose. The defult setting is "Non-Approximation".
Include All Parameters
If the option is selected, all stochastic parameters of the experiment will be input parameter for the approximation (metamodel). If it is not selected, user can choose any stochastic parameters as input parameter from all stochastic parameters of the experiment for the approximation.
Gaussian Process
Covariance Function
If the approximation is set to "Gaussian Process", this option will be available. They are different implemented covariance functions for the Gaussian process being selected: "Best Covariance", "Square Exponential", "Exponential", "Gamma-Exponential", "Matern Class 3/2", "Matern Class 5/2", "Rational Quadratic" and "Periodic". The covariance function represents the interpolation between support points in the design space. It is an assumption and a critical factor of the Gaussian process. The option is normally set to "Best Covariance". In this case, the all availble covariances will be calculated to choose the best covariance for this variable.
X-Approximation
For approximation of 1D-Variable, special methods are required, because they are value lists. There are 2 options: "Principal Component Analysis" and "Randomized Algorithms". The signal of the 1D-variable will be extract as principal components being approximated. The method "Principal Component Analysis" should be choosen for small data and the method "Randomized Algorithms" for large data.
X-Approximation Rank [%]
This option allows users to input the exact rank of the input matrix by low-rank approximation. This rank is caculated by percentage of the full input matrix size. If the value is 100, the full input matrix will be used for Gaussian process. If the value is 50, the half of the input matrix will be taken. If the both options "Approximation Rank" and "Approximation Error" are given, the used low-rank of the input matrix will be the min. rank of both calculation cases.
X-Approximation Error [%]
This option allows users to input the exact error of the low-rank approximation. This error is caculated by percentage of the maximal eigenvalue of the input matrix. All eigenvalues of the matrix will be cut off, if they are smaller then this approximation error. If the value is zero, all ranks of the input matrix is used for least square. If the value is 100, only 1 rank is used. If the both options "Approximation Rank" and "Approximation Error" are given, the used low-rank of the input matrix will be the min. rank of both calculation cases.
Gaussian Noise [%]
This option is only visible if the option "Noise Optimization" = False for design of experiment. The value is defined as procentage of the absolute difference |Ymax-Ymin| of the criterion. The Gaussian noise is very important for the meta-model. It decides about the smoothness, accuracy and existence of the meta-model. if the Gaussin noise is big, the model is very smooth, but the accuracy is bad. If the Gaussian noise is smaller, the smoothness of the meta-model is worse, but the auccuracy is better. Depending on the concrete data, if the Gaussian noise is too small, the solution of the Gaussian process cannot be found. All parameters and covariances are zero. If the noise optimzation for design of experiment is on, the optimal Gaussian noise will be found automatically.
Polynom
Polynomial Type
This is the order type of the polynomial regression for the approximation. There are 3 options to choose "Best Order", "Uniform Order" and "Manual Order". If "Uniform Order" is selected, user can set the same polynomial order for all parameters. Otherwise, different polynomial orders can be set for single parameters if "Manual Order" is selected. By "Best Order", the best polynomial order for different parameters will be calculated autmatically.
Polynomial Order
User can set here the order for the uniform polynomial regression.All parameters will have got the same polynomial order.
Low-Rank Approximation
There are 2 available options: "Full Matrix" and "Low-Rank Matrix". By "Low-Rank Matrix", the low-rank approximation will be ued for regularization of the least square method.Other option takes the full matrix for calculation of least square.
Approximation Error [%]
This option allows users to reduce the rank of input matrix at the low-rank approximation. This apprximation error is caculated by percentage of the maximal eigenvalue of the input matrix. All eigenvalues of the matrix will be cut off, if they are smaller then this approximation error. If the value is zero, all ranks of the input matrix is used for least square. If the value is 100, only 1 rank is used.
Hilbert Space
Include X-Axis
If the option is selected, The X-axis will be an input parameter for the metamodel.
Include 1D-Variable
If the option is selected, user can select any 1D-Variables as input parameters for the metamodel.
X-Nonlinearity
There are 2 options: "None" and "Autoregressive Exogenous Model". The Autoregressive Exogenous Model will show more options:
X-Input Order
This is the max. value of the forward delay order for input parameter.
All X-Input Orders
If the option is selected, the input order will be fully from 1 to the max. value. Otherwise, user can select single order individually.
X-Output Order
This is the max. value of the backward delay order for output parameter.
All X-Output Orders
If the option is selected, the output order will be fully from 1 to the max. value. Otherwise, user can select single order individually.
Uniform Space
If the option is selected, all input parameters of the metamodel will have got the same covariance function and the same number of features or same polynomial order. Otherwise, user can define different covariance function and number of features for different input parameters.
Covariance Function
They are covariance functions for the Hilbert Space being selected: "Square Exponential", "Exponential", "Gamma-Exponential", "Matern Class 3/2", "Matern Class 5/2", "Polynomial" and "User-Defined". By "User-Defined", mathematical expressions for the feature can be modeled individually. Also parameters can be defined and used for training this user-defined feature by the option "Parameter". If the operator of integration of this feature will be used in partial differential equation or state variables, user must select the option "Integral", than derivate and input these integral terms self here for the feature. Otherway, the option "Integral" does not need to be selected.
Number of Features
It is the number of the mathematical terms for the input parameter vector (feature vector) of the metamodel.
Order of Features
It is the order of the polynomial feature.
Approximation Error [%]
This option allows users to input the exact error of the low-rank approximation for kernel method. This error is caculated by percentage of the maximal eigenvalue of the input matrix. All eigenvalues of the matrix will be cut off, if they are smaller then this approximation error. If the value is zero, all ranks of the input matrix is used for least square. If the value is 100, only 1 rank is used. If the both options "Approximation Rank" and "Approximation Error" are given, the used low-rank of the input matrix will be the min. rank of both calculation cases.
Gaussian Noise [%]
This option is only visible if the option "Noise Optimization" for design of experiment ist not selected. The value is defined as procentage of the absolute difference |Ymax-Ymin| of the criterion. The Gaussian noise is very important for the meta-model. It decides about the smoothness, accuracy and existence of the meta-model. if the Gaussin noise is big, the model is very smooth, but the accuracy is bad. If the Gaussian noise is smaller, the smoothness of the meta-model is worse, but the auccuracy is better. Depending on the concrete data, if the Gaussian noise is too small, the solution of the Gaussian process cannot be found. All parameters and covariances are zero. If the noise optimzation for design of experiment is on, the optimal Gaussian noise will be found automatically.
Regularization Weight
This is the weight of the regularization term on the training process for nonlinear methods.
Include DOE
If the opption is selected, the DOE data will be used for approximation. Otherwise, the DOE data will be not considered.
Weight
It is the weight for optimization of the training process. if the option "Weight Optimization" in the design of experiment is selected, this value will be used as start value for the optimization process.
Partial Differential Equation
If the opption is selected, user can define a partial differential equation (PDE).
PDE
A dialog will be opend to input the partial differential equation for physics-informed machine learning.
Linear
The option is selected, if the partial differential equation is linear
Sampling Level
The partial differential equation will be sampled to generate the data for training the metamodel. The parameter space will be divided into a grid and each parameter will be sampled in number of Sampling Level.
Weight
It is the weight for optimization of the training process. if the option "Weight Optimization" in the design of experiment is selected, this value will be used as start value for the optimization process.
User-Defined
If the option is selected, user can define and import the sampling data for PDE.
Boundary Conditions
If the opption is selected, user can define boundary conditions.
Number of Boundaries
This is the number of boundary conditions.
Boundary Function / Initial Value
A dialog will be open to input the mathematical expression for the boundary condition.
Number of fixed Values
This is the number of fiexed values for the boundary conditions.
Fixed Parameter
User can select the input parameter which will be fixed for the boundary condition. If the fixed parameter is the X-axis, the boundary condition will be initial condition.
Value
The value for the fixed parameter.
Sampling Level
The boundary conditions will be sampled to generate the data for training the metamodel. The parameter space will be divided into a grid and each parameter will be sampled in number of Sampling Level.
Weight
It is the weight for optimization of the training process. if the option "Weight Optimization" in the design of experiment is selected, this value will be used as start value for the optimization process.
User-Defined
If the option is selected, user can define and import the sampling data for bounbdary conditions.
Constraints
If the opption is selected, user can define constraints.
Number of Constraints
This is the number of constraints.
Constraint Function
A dialog will be open to input the mathematical expression for the constraint.
Type
The constraint fuction can be greater than, smaller than or equal the Value.
Value
The value for comparison of the constraint function
Sampling Level
The boundary conditions will be sampled to generate the data for training the metamodel. The parameter space will be divided into a grid and each parameter will be sampled in number of Sampling Level.
Weight
It is the weight for optimization of the training process. if the option "Weight Optimization" in the design of experiment is selected, this value will be used as start value for the optimization process.
Parameters
If the opption is selected, user can define parameters which can be used in state variables, partial differential equation, boundary conditions or constraints above. These parameters will be considered as unknown input parameters for the physics model. They will be optimized by the machine learning training process to get optimal values.
Number of Parameters
This is the number of parameters.
Name
The name of the parameter.
Value
The value for the parameter. The value will be start value by optimization.
Fixed
If the option is selected, the parameter will be fixed for training process. Otherwise, the parameter will be optimized getting optimal value.
Lower Boundary
This is the lower boundary for the optimization process.
Upper Boundary
This is the upper boundary for the optimization process.
Global Parameter
If it is selected, the parameter value will be synchronized with the same global parameter in other D1-variables. The parameter is global in all D1-variables.
Virtual Design
- This is the virtual value of the X-axis. It used to compute Histogram, Section Diagram, Residual Plot, Probability Density, Cumulative Distribution, Sensitivity Chart, Interaction Chart based on the meta model for this 1D-variable at this point on the X-axis.
- This is the DOE Index for comparison with response surface.
Design Goal
This is the same option as "Output Value". It is used however only for virtual design optimization or meta-modeling based on the meta model of 1D-variable.