I revive this question because
1) Michael says the Base and the CustomizedClass are not necessary. I could not figure out how to eliminate them. You basically need a customised model, where you override the equation. How can this be done without these additional constructs Base and CustomizedClass?
2) most importantly - How would the example work for several variables/ equations? Let's say you have 3 equations. How can you override only 1 or 2 of them - without redeclaring the 3rd one?
Or to reformulate the question: How can a model - including all the equations - be redeclared/overridden by a model which redefines only parts of its equations?
Thanks in advance.
Related
I wanted to vectorize this piece of code. Is it possible to do this? I tried finding a solution, but I was not able to find any good result on google.
for pos=length1+1:length
X1(pos) = sim(net1, [demandPred(pos), demand(pos-1), X1(pos-1), X1(pos-2)]')';
X2(pos) = sim(net1, [demandPred(pos), demand(pos-1), X2(pos-1), X2(pos-2)]')';
end
Thanks in advance. :)
Edit 1:
The model which I am going to simulate is a simple GRNN.
net1 = newgrnn([demand(169:trainElem), demand(169-1:trainElem-1), X1(169 - 1:trainElem - 1), X1(169 - 2:trainElem - 2)]', 0.09);
Can Simulink models be vectorized? Sometimes.
Can your Simulink model be vectorised? It's impossible to tell without seeing the model -- and how it is being called from m-code (as you've shown in your question) is no indication.
An example of vectorization would be: consider a model with signal s1 that gets added to constant K, and assume that you need to run the models for different values if K. You could use a loop (like the m-code you show) and run the model for each individual required value for K. Alternatively, you can make K a vector, in which case all values would get added to s1 and the result would be a vector of signals s1+K(1), s1+K(2),..., s1+K(n), and the model only needs to be executed once for all of these summations to occur.
But, whether that sort of thing can be done in your model cannot be determined without seeing the model.
I seem to struggle with a modeling problem in Modelica (using Dymola), and I hereby seek your help. The idea is this:
I have modeled some components (models) that I want to connect together through their ports. The models are working. The thing is I want to connect several of the same unit (called myUnit in the pseudo code below) in a series. If the number of units were, let's say, only 5 then I could easily dragged them out 1-by-1 and connected them in a standard manner, but let's say I want 100 units. Is there an easy and elegant way to do this? I don't believe for loops to be working outside the equation part of the model, and I want an elegant way of naming the units. I'll try to illustrate this by doing a pseudo code below, explaining what I wish to achieve:
model someModel
parameter Integer n = 100 "Length of series";
parameter Real optionValue = 123;
myLibrary.myStartUnit startUnit(someOption = optionValue); // First unit
for i in 2:n-1 loop
myLibrary.myUnit unit_'num2str(i)'(someOption = optionValue); // i'th unit
end for;
myLibrary.myEndUnit endUnit(someOption = optionValue); // Last unit
equation
connect(startUnit.outPort,unit_1.inPort);
for i in 2:n-1 loop
connect(unit_'num2str(i)'.outPort,unit_'num2str(i+1)'.inPort)
end for;
connect(unit_'num2str(n-1)'.outPort,endUnit.inport);
end someModel;
I hope I've managed to explain my problem properly, now.
Any tips for solving this problem? I greatly appreciate both strategic advice as to solve the problem as well as purely syntactic advice.
In advance, thanks for all help. :)
You can use arrays to achieve this. For example, using models of the Modelica standard library:
model ArrayDemo
parameter Integer n = 10 "Number of springs/masses";
Modelica.Mechanics.Translational.Sources.ConstantForce constantForce(f_constant=100);
Modelica.Mechanics.Translational.Components.Spring springs[n];
Modelica.Mechanics.Translational.Components.Mass masses[n];
Modelica.Mechanics.Translational.Components.Fixed fixed;
equation
connect(constantForce.flange, springs[1].flange_a);
for i in 1 : n - 1 loop
connect(springs[i].flange_b, masses[i].flange_a);
connect(masses[i].flange_b, springs[i + 1].flange_a);
end for;
connect(springs[n].flange_b, masses[n].flange_a);
connect(masses[n].flange_b, fixed.flange);
end ArrayDemo;
The idea is to declare the components using arrays and then connect them using for loops.
first a little background. I'm a psychology student so my background in coding isn't on par with you guys :-)
My problem is as follow and the most important observation is that curve fitting with 2 different programs gives completly different results for my parameters, altough my graphs stay the same. The main program we have used to fit my longitudinal data is kaleidagraph and this should be seen as kinda the 'golden standard', the program I'm trying to modify is matlab.
I was trying to be smart and wrote some code (a lot at least for me) and the goal of that code was the following:
1. Taking an individual longitudinal datafile
2. curve fitting this data on a non-parametric model using lsqcurvefit
3. obtaining figures and the points where f' and f'' are zero
This all worked well (woohoo :-)) but when I started comparing the function parameters both programs generate there is a huge difference. The kaleidagraph program stays close to it's original starting values. Matlab wanders off and sometimes gets larger by a factor 1000. The graphs stay however more or less the same in both situations and both fit the data well. However it would be lovely if I would know how to make the matlab curve fitting more 'conservative' and more located near it's original starting values.
validFitPersons = true(nbValidPersons,1);
for i=1:nbValidPersons
personalData = data{validPersons(i),3};
personalData = personalData(personalData(:,1)>=minAge,:);
% Fit a specific model for all valid persons
try
opts = optimoptions(#lsqcurvefit, 'Algorithm', 'levenberg-marquardt');
[personalParams,personalRes,personalResidual] = lsqcurvefit(heightModel,initialValues,personalData(:,1),personalData(:,2),[],[],opts);
catch
x=1;
end
Above is a the part of the code i've written to fit the datafiles into a specific model.
Below is an example of a non-parametric model i use with its function parameters.
elseif strcmpi(model,'jpa2')
% y = a.*(1-1/(1+(b_1(t+e))^c_1+(b_2(t+e))^c_2+(b_3(t+e))^c_3))
heightModel = #(params,ages) abs(params(1).*(1-1./(1+(params(2).* (ages+params(8) )).^params(5) +(params(3).* (ages+params(8) )).^params(6) +(params(4) .*(ages+params(8) )).^params(7) )));
modelStrings = {'a','b1','b2','b3','c1','c2','c3','e'};
% Define initial values
if strcmpi('male',gender)
initialValues = [176.76 0.339 0.1199 0.0764 0.42287 2.818 18.52 0.4363];
else
initialValues = [161.92 0.4173 0.1354 0.090 0.540 2.87 14.281 0.3701];
end
I've tried to mimick the curve fitting process in kaleidagraph as good as possible. There I've found they use the levenberg-marquardt algorithm which I've selected. However results still vary and I don't have any more clues about how I can change this.
Some extra adjustments:
The idea for this code was the following:
I'm trying to compare different fitting models (they are designed for this purpose). So what I do is I have 5 models with different parameters and different starting values ( the second part of my code) and next I have the general curve fitting file. Since there are different models it would be interesting if I could put restrictions into how far my starting values could wander off.
Anyone any idea how this could be done?
Anybody willing to help a psychology student?
Cheers
This is a common issue when dealing with non-linear models.
If I were, you, I would try to check if you can remove some parameters from the model in order to simplify it.
If you really want to keep your solution not too far from the initial point, you can use upper bounds and lower bounds for each variable:
x = lsqcurvefit(fun,x0,xdata,ydata,lb,ub)
defines a set of lower and upper bounds on the design variables in x so that the solution is always in the range lb ≤ x ≤ ub.
Cheers
You state:
I'm trying to compare different fitting models (they are designed for
this purpose). So what I do is I have 5 models with different
parameters and different starting values ( the second part of my code)
and next I have the general curve fitting file.
You will presumably compare the statistics from fits with different models, to see whether reductions in the fitting error are unlikely to be due to chance. You may want to rely on that comparison to pick the model that not only fits your data suitably but is also simplest (which is often referred to as the principle of parsimony).
The problem is really with the model you have shown resulting in correlated parameters and therefore overfitting, as mentioned by #David. Again, this should be resolved when you compare different models and find that some do just as well (statistically speaking) even though they involve fewer parameters.
edit
To drive the point home regarding the problem with the choice of model, here are (1) results of a trial fit using simulated data (2) the correlation matrix of the parameters in graphical form:
Note that absolute values of the correlation close to 1 indicate strongly correlated parameters, which is highly undesirable. Note also that the trend in the data is practically linear over a long portion of the dataset, which implies that 2 parameters might suffice over that stretch, so using 8 parameters to describe it seems like overkill.
Rheological models are usually build using three (or four) basics elements, which are :
The spring (existing in Modelica.Mechanics.Translational.Components for example). Its equation is f = c * (s_rel - s_rel0);
The damper (dashpot) (also existing in Modelica.Mechanics.Translational.Components). Its equation is f = d * v_rel; for a linear damper, an could be easily modified to model a non-linear damper : f = d * v_rel^(1/n);
The slider, not existing (as far as I know) in this library... It's equation is abs(f)<= flim. Unfortunately, I don't really understand how I could write the corresponding Modelica model...
I think this model should extend Modelica.Mechanics.Translational.Interfaces.PartialCompliant, but the problem is that f (the force measured between flange_b and flange_a) should be modified only when it's greater than flim...
If the slider extends PartialCompliant, it means that it already follows the equations flange_b.f = f; and flange_a.f = -f;
Adding the equation f = if abs(f)>flim then sign(f)*flim else f; gives me an error "An independent subset of the model has imbalanced number of equations and variables", which I couldn't really explain, even if I understand that if abs(f)<=flim, the equation f = f is useless...
Actually, the slider element doesn't generate a new force (just like the spring does, depending on its strain, or just like the damper does, depending on its strain rate). The force is an input for the slider element, which is sometime modified (when this force becomes greater than the limit allowed by the element). That's why I don't really understand if I should define this force as an input or an output....
If you have any suggestion, I would greatly appreciate it ! Thanks
After the first two comments, I decided to add a picture that, I hope, will help you to understand the behaviour I'm trying to model.
On the left, you can see the four elements used to develop rheological models :
a : the spring
b : the linear damper (dashpot)
c : the non-linear damper
d : the slider
On the right, you can see the behaviour I'm trying to reproduce : a and b are two associations with springs and c and d are respectively the expected stress / strain curves. I'm trying to model the same behaviour, except that I'm thinking in terms of force and not stress. As i said in the comment to Marco's answer, the curve a reminds me the behaviour of a diode :
if the force applied to the component is less than the sliding limit, there is no relative displacement between the two flanges
if the force becomes greater than the sliding limit, the force transmitted by the system equals the limit and there is relative displacement between flanges
I can't be sure, but I suspect what you are really trying to model here is Coulomb friction (i.e. a constant force that always opposes the direction of motion). If so, there is already a component in the Modelica Standard Library, called MassWithStopAndFriction, that models that (and several other flavors of friction). The wrinkle is that it is bundled with inertia.
If you don't want the inertia effect it might be possible to set the inertia to zero. I suspect that could cause a singularity. One way you might be able to avoid the singularity is to "evaluate" the parameter (at least that is what it is called in Dymola when you set the Evaluate flat to be true in the command line). No promises whether that will work since it is model and tool dependent whether such a simplification can be properly handled.
If Coulomb friction is what you want and you really don't want inertia and the approach above doesn't work, let me know and I think I can create a simple model that will work (so long as you don't have inertia).
A few considerations:
- The force is not an input and neither an output, but it is just a relation that you add into the component in order to define how the force will be propagated between the two translational flanges of the component. When you deal with acausal connectors I think it is better to think about the degrees of freedom of your component instead of inputs and outputs. In this case you have two connectors and independently at which one of the two frames you will recieve informations about the force, the equation you implement will define how that information will be propagated to the other frame.
- I tested this:
model slider
extends
Modelica.Mechanics.Translational.Interfaces.PartialCompliantWithRelativeStates;
parameter Real flim = 1;
equation
f = if abs(f)>flim then sign(f)*flim else f;
end slider;
on Dymola and it works. It is correct modelica code so it should be work also in OpenModelica, I can't think of a reason why it should be seen as an unbalance mathematical model.
I hope this helps,
Marco
Just starting with Modelica and having trouble understanding how it works.
In the below 'method' of the model, qInflow and qOutflow are used in the second line to evaluate der(h), but they have not received a value yet! (they were not defined in the 'data' of the method)? In what order is the code executed.
equation
assert(minV >= 0, "minV must be greater or equal to zero");
der(h)=(qInflow - qOutflow)/area;
qInflow=if time > 150 then 3*flowLevel else flowLevel;
qOutflow=Functions.LimitValue(minV, maxV, -flowGain*outCtr);
error=ref - h;
der(x)=error/T;
outCtr=K*(error + x);
end FlatTank;
From http://www.mathcore.com/resources/documents/ie_tank_system.pdf
This is an understandable point of confusion when coming from languages and systems that utilize imperative semantics. But Modelica doesn't work like that.
When working with Modelica it is important to understand that an equation section contains equations, not assignments. Consider this, if I gave you the following equations:
x + y = 3;
x + 2*y = 5;
If you understand that this is a mathematical context, you can then determine that x must have a value of 1 and y must have a value of 2. In other words, you have to solve a system of simultaneous equations. You'll note that the left hand side of these equations are not variables (in general), they are expressions. An equation is simply a relationship that equates one expression, on the left hand side, with another expression, on the right hand side. Furthermore, this relationship is always true and so order is irrelevant.
This is quite different from imperative programming languages with imperative semantics. But it is also very powerful because you can state these relationships (linear systems of equations, non-linear systems of equations, implicit equations, etc) and the compiler will work out the most efficient way to solve them.
Getting back to your example, when you look at the code in your question you are interpreting those equations as assignment statements. This notion is reinforced because they just happen to have variables on the left hand sides. But they are really equations. In an equation based system, you do not worry about whether a given variable has been assigned to previously. Instead, the requirement is simply that for every variable there exists (somewhere) an equation and that there are no extra equations. In other words, you should have the same number of variables as unknowns and that the system of equations has a unique solution. That is all that Modelica requires.
Now, Modelica supports the kind of imperative semantics you are used to. But they are only to be used in special cases because they constrain the interpretation of the mathematical behavior in such a way that it interferes with the symbolic manipulation that allows Modelica compilers to generate really fast code. So it is more than a question of style. You should use equations if at all possible and algorithms in Modelica should only be used as a last resort.
One last note. Some people may be wondering "Are you telling me that these equations will be put into some giant system of equations and solved by matrix inversion or Newton-Raphson or something? Why make it so complicated when it could obviously be solved in a much easier way!" But it will not be solved as a giant system of equations. If it can be solved as a simple set of assignments it will. That is one (among many) of the different symbolic manipulation techniques that will be applied. In fact, this is a key point about Modelica...you don't need to worry about optimizing the solution method, the tool will take care of that. And more importantly, if you connect components in such a way that a simultaneous system does arise, you don't need to worry about that either. Modelica tools can handle such "algebraic loops" for you, they will optimize it to find the most computationally efficient formulation and won't depend on you reformulating your model for those cases.
Does that help?
You cannot know the execution order of the equations in a Modelica model until you run a Modelica tool on it (you can re-order any equation in the source model and get the same result). And then the order is only true for this tool with the settings you used.
This was the order chosen by the OpenModelica compiler (omc +s +simCodeTarget=Dump model.mo):
error = ref - h;
outCtr = K * (error + x);
der(x) = DIVISION(error, T, #SHARED_LITERAL_2(String#);
qOutflow = LimitValue(minV, maxV, (-flowGain) * outCtr);
qInflow = if time > 150.0 then 3.0 * flowLevel else flowLevel;
der(h) = DIVISION(qInflow - qOutflow, area, #SHARED_LITERAL_3(String#);
This example was a little boring because the left and right sides of no equation changed place (h = error - ref would be viable if h was not chosen as a state variable, etc).