Response

Library of response objects and base classes to create your own objectives and constraints.

class DeviationSquared(**kwds)

Computes the difference between a function’s current value and a desired value.

The math formula used by DeviationSquared is defined as follows:

\[Response = \frac{1}{2} \left( 1 - \frac{f_{c}}{f_{d}} \right) ^2\]

where:

• \(f_{c}\) is the current value of a function,

• \(f_{d}\) is its desired value,

• \(s\) is the error in the function.

Usage Example:

Compute the deviation of VX(22,11)@T=1 from a desired value of: 3.14159.

val = DeviationSquared (label        = "VX(22,11)@T=1",
                        signal       =  vx2211At1,
                        desiredValue = 3.14159,
                        )

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
id	Int		Auto
label	Str
measuredValue	Reference - ValueAtTime	\(\checkmark\)
plot	Bool		False
scale	Double		1.0
sensitivity	Bool		True
targetValue	Double		0.0

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

id

The id of the object.

Type=Int

label

Label string for the Response.

Type=Str

measuredValue

Value of the RV associated with DeviationSquared.

Type=Reference (ValueAtTime), Required

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

scale

Scaling factor of Response.

Type=Double, Default=1.0

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

targetValue

Desired value of the RV associated with DeviationSquared.

Type=Double, Default=0.0

class GenericResponse(**kwds)

Creates a generic response.

This response is a layer over the Rv element that links it to the plotting and optimization functionalities.

Usage Examples:

Generic Response using run time Expression.

gr = GenericResponse (label    = "Generic Response",
                      function = "(1-FZ(21,31)/501)**2",
                      scale    = 1e5
                     )

Generic Response using User written subroutine.

gr = GenericResponse (label    = "Generic Response",
                      routine  = mygenericResponse,
                      scale    = 1e5
                     )

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
end	Double
function	Function
id	Int		Auto
label	Str
plot	Bool		False
routine	Routine
scale	Double		1.0
script	Script
sensitivity	Bool		True
start	Double
useDeriv	Bool		False

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

end

Specify the end time of the window of interest.

Type=Double

function

Function expression for GenericResponse.

Type=Function

id

The id of the object.

Type=Int

label

Label string for the Response.

Type=Str

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

routine

User subroutine for GenericResponse.

Type=Routine

scale

Scaling factor of Response.

Type=Double, Default=1.0

script

Path and name of the script that contains the routine.

Type=Script

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

start

Specify the starting time of the window of interest.

Type=Double

useDeriv

True if derivative of the function is to be used as response.

Type=Bool, Default=False

class MaxVal(**kwds)

Computes the approximate maximum value of a MotionSolve expression or a user subroutine during the simulation.

The maximum is approximated by an alpha-soft function so that the analytical sensitivity can be calculated. The math formula used by MaxVal is defined as follows:

\[max(x) = \frac{ \int_{t} x(t) e^{a x{t}} dt }{ \int_{t} e^{a x{t}} dt }\]

where:

• \(a = coef > 0\)

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
alpha	Double		10.0
coef	Double		1.0
end	Double
function	Function	\(\checkmark\)
id	Int		Auto
k	Int		1
label	Str
nominal	Double		0.0
plot	Bool		False
routine	Routine
scale	Double		1.0
script	Script
sensitivity	Bool		True
start	Double
threshold	Double		2.0
wlen	Int		5

See also

See Comment 1 for more information.

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

alpha

Coef being used in the approximation of extremum.

Type=Double, Default=10.0

coef

Coefficient used in the approximation of maximum, alpha=coef.

Type=Double, Default=1.0

end

Specify the end time of the window of interest.

Type=Double

function

Solver function that defines the extremum being computed.

Type=Function, Required

id

The id of the object.

Type=Int

k

The order of the smoothing function.

Type=Int, Default=1

label

Label string for the Response.

Type=Str

nominal

Estimated value of extremum being calculated.

Type=Double, Default=0.0

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

routine

An alternative name for the user subroutine.

Type=Routine

scale

Scaling factor of Response.

Type=Double, Default=1.0

script

Path and name of the script that contains the routine.

Type=Script

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

start

Specify the starting time of the window of interest.

Type=Double

threshold

The threshold value of the sensor.

Type=Double, Default=2.0

wlen

The window length for the smoothing function.

Type=Int, Default=5

class MinVal(**kwds)

Computes the approximate minimum value of a MotionSolve expression or a user subroutine during the simulation.

The minimum is approximated by an alpha-soft function so that the analytical sensitivity can be calculated. The math formula used by MinVal is defined as follows:

\[min(x) = \frac{ \int_{t} x(t) e^{a x{t}} dt }{ \int_{t} e^{a x{t}} dt }\]

where:

• \(a = -coef > 0\)

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
alpha	Double		10.0
coef	Double		1.0
end	Double
function	Function	\(\checkmark\)
id	Int		Auto
k	Int		1
label	Str
nominal	Double		0.0
plot	Bool		False
routine	Routine
scale	Double		1.0
script	Script
sensitivity	Bool		True
start	Double
threshold	Double		2.0
wlen	Int		5

See also

See Comment 1 for more information.

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

alpha

Coef being used in the approximation of extremum.

Type=Double, Default=10.0

coef

Coefficient used in the approximation of minimum, alpha=-coef.

Type=Double, Default=1.0

end

Specify the end time of the window of interest.

Type=Double

function

Solver function that defines the extremum being computed.

Type=Function, Required

id

The id of the object.

Type=Int

k

The order of the smoothing function.

Type=Int, Default=1

label

Label string for the Response.

Type=Str

nominal

Estimated value of extremum being calculated.

Type=Double, Default=0.0

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

routine

An alternative name for the user subroutine.

Type=Routine

scale

Scaling factor of Response.

Type=Double, Default=1.0

script

Path and name of the script that contains the routine.

Type=Script

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

start

Specify the starting time of the window of interest.

Type=Double

threshold

The threshold value of the sensor.

Type=Double, Default=2.0

wlen

The window length for the smoothing function.

Type=Int, Default=5

class RMS2(**kwds)

Computes the root-mean-square area difference between a measured signal and a target curve.

The math formula used by RMS2 is defined as follows:

\[Response = \int_{0}^{T} (y-y^{*})^2 dt\]

where:

• \(y\) is the measured value,

• \(y^{*}\) is the interpolated value based on the value of the state variable.

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
end	Double
id	Int		Auto
independentVariable	Reference - Variable [0]
label	Str
mean	Double		0
measuredValue	Function
plot	Bool		False
routine	Routine
scale	Double		1
script	Script
sensitivity	Bool		True
start	Double
std	Double		0
targetValue	CurveProperty	\(\checkmark\)
xValue	Reference - RMS2

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

end

Specify the end time of the window of interest.

Type=Double

id

The id of the object.

Type=Int

independentVariable

Independent Variable in RMS2.

Type=Reference (Variable) [0]

label

Label string for the Response.

Type=Str

mean

Mean value of normal distribution used in weighting.

Type=Double, Default=0

measuredValue

Runtime function expression that defines measured value.

Type=Function

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

routine

Type=Routine

scale

Scaling factor of RMS2.

Type=Double, Default=1

script

Type=Script

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

start

Specify the starting time of the window of interest.

Type=Double

std

Standard deviation of normal distribution used in weighting.

Type=Double, Default=0

targetValue

List of datum that defines the sample points.

Type=CurveProperty, Required

xValue

Type=Reference (RMS2)

class ResponseExpression(**kwds)

Computes the value of an arbitrary function that is composed of design variables and other responses.

It employs the chain rule to compute the sensitivity using sympy to calculate the partial derivatives.

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
function	Str	\(\checkmark\)
id	Int		Auto
label	Str
plot	Bool		False
scale	Double		1.0
sensitivity	Bool		True
symbols	Property [0]	\(\checkmark\)
variables	Property [0]	\(\checkmark\)

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

function

An expression of DVs and RVs whose value is required.

Type=Str, Required

id

The id of the object.

Type=Int

label

Label string for the Response.

Type=Str

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

scale

Scaling factor of Response.

Type=Double, Default=1.0

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

symbols

Symbols used in expression.

Type=Property [0], Required

variables

Variables that are referred by Symbols.

Type=Property [0], Required

class SignalDistance(**kwds)

Computes the distance between two signals by dynamic time warping.

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
end	Double
gamma	Double		0.01
id	Int		Auto
label	Str
numPoints	Int		10
periods	Int		1
plot	Bool		False
scale	Double		1.0
sensitivity	Bool		True
signal	Reference - Variable [0]	\(\checkmark\)
start	Double
targetSignal	Property [0]	\(\checkmark\)

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

end

Specify the end time of the window of interest.

Type=Double

gamma

Type=Double, Default=0.01

id

The id of the object.

Type=Int

label

Label string for the Response.

Type=Str

numPoints

Type=Int, Default=10

periods

Type=Int, Default=1

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

scale

Scaling factor of Response.

Type=Double, Default=1.0

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

signal

Type=Reference (Variable) [0], Required

start

Specify the starting time of the window of interest.

Type=Double

targetSignal

Type=Property [0], Required

class Slope2(**kwds)

Computes the slope of a curve at a particular point of interest \(t^{*}\).

The math formula used by Slope2 is defined as follows:

\[Response = \frac{f(t_{2}) - f(t_{1})}{t_{2} - t_{1}}\]

where:

\(t_{1} < t^{*} < t_{2}\)

Usage Example:

Compute the slope of Toe vs Ride Height at design position (T=5).

val = Slope2 (label       = "Slope2",
              numerator   = "<Toe_Expression>",
              denominator = "<Ride_Height_Expression>",
              time        = 5,
              delta       = 0.1,
              interval    = 1e-3,   # Optional
             )

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
delta	Double		0.1
denominator	Function	\(\checkmark\)
id	Int		Auto
interval	Double
label	Str
numerator	Function	\(\checkmark\)
plot	Bool		False
scale	Double		1.0
sensitivity	Bool		True
time	Double	\(\checkmark\)

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

delta

Time span at the start&end of which the signal is evaluated.

Type=Double, Default=0.1

denominator

MS expression for denominator.

Type=Function, Required

id

The id of the object.

Type=Int

interval

Interval over which the signal is averaged.

Type=Double

label

Label string for the Response.

Type=Str

numerator

MS expression for numerator.

Type=Function, Required

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

scale

Scaling factor of Response.

Type=Double, Default=1.0

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

time

Time at which the slope is calculated.

Type=Double, Required, Default=0.0

class Slope2Deviation(**kwds)

Computes the square of the deviation of the slope of a curve at a certain point in time from a target value.

The math formula used by Slope2Deviation is defined as follows:

\[Response = \left( 1 - \frac{m}{m_{d}} \right) ^2\]

where:

• \(m\) is the slope of a curve at the point of interest,

• \(m_{d}\) is the target value.

It has all the properties Slope2 has plus the targetValue of the slope.

Usage Example:

Compute the deviation of the slope of TOE vs. DZ at design position (T=5) from a desired value of 3.14159.

val = Slope2Deviation(label       = "Slope2",
                      numerator   = "<Toe_Expression>",
                      denominator = "<Ride_Height_Expression>",
                      time        = 5,
                      delta       = 0.1,
                      interval    = 1e-3,    # Optional
                      targetValue = 3.14159
                      )

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
delta	Double		0.1
denominator	Function	\(\checkmark\)
id	Int		Auto
interval	Double
label	Str
numerator	Function	\(\checkmark\)
plot	Bool		False
scale	Double		1.0
sensitivity	Bool		True
targetValue	Double	\(\checkmark\)
time	Double	\(\checkmark\)

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

delta

Time span at the start&end of which the signal is evaluated.

Type=Double, Default=0.1

denominator

MS expression for denominator.

Type=Function, Required

id

The id of the object.

Type=Int

interval

Interval over which the signal is averaged.

Type=Double

label

Label string for the Response.

Type=Str

numerator

MS expression for numerator.

Type=Function, Required

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

scale

Scaling factor of Response.

Type=Double, Default=1.0

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

targetValue

Desired value of the slope.

Type=Double, Required, Default=0.0

time

Time at which the slope is calculated.

Type=Double, Required, Default=0.0

class ValueAtG(**kwds)

Computes the value of a signal, \(f\) when a second signal \(G\) achieves a certain value \(C\).

The math formula used by ValueAtG is defined as follows:

\[Response = \frac{\int_{t_{0}}^{t_{f}} f(Q,U,U_{d}) w(t) dt} {\int_{t_{0}}^{t_{f}} w(t) dt}\]

where:

• \(w(t) = Step (G, C-Delta, 0, C, 1) + Step (G, C, 1, C+Delta, 0) - 1\)

Usage Example:

Compute the steer angle difference when the steering wheel angle is ZERO.

t0      = 0
tf      = 2
delta   = 1e-3
gvalue  = 0

# Steering wheel angle
gsignal = "AZ(77,66)"

# Steering angle difference: Yaw(Left-wheel) - Yaw(right-wheel)
fsignal = "Yaw(33,22) - Yaw(55,44)"

val = ValueAtG (label   = "Steer Angle DIfference at Zero SWA",
                fsignal = fsignal,
                gsignal = gsignal,
                gvalue  = gvalue,
                delta   = delta
               )

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
delta	Double	\(\checkmark\)
fsignal	Function	\(\checkmark\)
gsignal	Function	\(\checkmark\)
gvalue	Double	\(\checkmark\)
id	Int		Auto
label	Str
plot	Bool		False
scale	Double		1.0
sensitivity	Bool		True

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

delta

The interval around ‘gvalue’ used to define the impulse function.

Type=Double, Required, Default=0.0

fsignal

Function representing a signal whose value is required.

Type=Function, Required

gsignal

The reference signal associated with fsignal.

Type=Function, Required

gvalue

Value of gsignal at which fsignal is to be computed .

Type=Double, Required, Default=0.0

id

The id of the object.

Type=Int

label

Label string for the Response.

Type=Str

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

scale

Scaling factor of Response.

Type=Double, Default=1.0

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True

class ValueAtTime(**kwds)

Computes the value of a signal at a certain time T.

The math formula used by ValueAtTime is defined as follows:

\[Response = \frac{\int_{t_{0}}^{t_{f}} f(Q, U, U_{d})w(t) dt} {\int_{t_{0}}^{t_{f}} w(t) dt} = \frac{1}{delta} \int_{t_{0}}^{t_{f}} f(Q, U, U_{d})w(t) dt\]

where:

\(w(t) = Step (Time, T-Delta, 0, T, 1) + Step (Time, T, 1, T+Delta, 0) - 1\)

Usage Example:

Compute the value of VM(22,11) @ t=1 sec.

t0     = 0
tf     = 2
t      = 1
delta  = 1e-3
w(t)   = Step (Time, t-delta, 0, t, 1) + Step (Time, t, 1, t+delta, 0) - 1
Num    = Integral ( VM(22,11) * w(t) dt, t=t0, t=tf )

# ValueAtTime = Num / delta

val = ValueAtTime (label  = "VM(22,11) @ Time=1",
                   delta         = delta,
                   atTime        = t,
                   measuredValue = "VM(22,11)",
                   )

Name	Type	Required	Default	Modifiable
active	Bool		True	\(\checkmark\)
atTime	Double	\(\checkmark\)
delta	Double	\(\checkmark\)
id	Int		Auto
label	Str
measuredValue	Function	\(\checkmark\)
plot	Bool		False
scale	Double		1.0
sensitivity	Bool		True

active

Defines the state of the object.

Type=Bool, Default=True, Modifiable

atTime

Time at which response is computed.

Type=Double, Required, Default=0.0

delta

Time interval around ‘atTime’ used to define the impulse function.

Type=Double, Required, Default=0.0

id

The id of the object.

Type=Int

label

Label string for the Response.

Type=Str

measuredValue

Function expression for ValueAtTime.

Type=Function, Required

plot

If True, a dynamic plot will be created.

Type=Bool, Default=False

scale

Scaling factor of Response.

Type=Double, Default=1.0

sensitivity

Returns a zero sensitivity vector when set to False.

Type=Bool, Default=True