I would like to predict the switching behavior of time-dependent signals. Currently the signal has 3 states (1, 2, 3), but it could be that this will change in the future. For the moment, however, it is absolutely okay to assume three states.
I can make the following assumptions about these states (see picture):
the signals repeat periodically, possibly with variations concerning the time of day.
the duration of state 2 is always constant and relatively short for all signals.
the duration of states 1 and 3 are also constant, but vary for the different signals.
the switching sequence is always the same: 1 --> 2 --> 3 --> 2 --> 1 --> [...]
there is a constant but unknown time reference between the different signals.
There is no constant time reference between my observations for the different signals. They are simply measured one after the other, but always at different times.
I am able to rebuild my model periodically after i obtained more samples.
I have the following problems:
I can only observe one signal at a time.
I can only observe the signals at different times.
I cannot trigger my measurement with the state transition. That means, when I measure, I am always "in the middle" of a state. Therefore I don't know when this state has started and also not exactly when this state will end.
I cannot observe a certain signal for a long duration. So, i am not able to observe a complete period.
My samples (observations) are widespread in time.
I would like to get a prediction either for the state change or the current state for the current time. It is likely to happen that i will never have measured my signals for that requested time.
So far I have tested the TimeSeriesPredictor from the ML.NET Toolbox, as it seemed suitable to me. However, in my opinion, this algorithm requires that you always pass only the data of one signal. This means that assumption 5 is not included in the prediction, which is probably suboptimal. Also, in this case I had problems with the prediction not changing, which should actually happen time-dependently when I query multiple predictions. This behavior led me to believe that only the order of the values entered the model, but not the associated timestamp. If I have understood everything correctly, then exactly this timestamp is my most important "feature"...
So far, i did not do any tests on Regression-based approaches, e.g. FastTree, since my data is not linear, but keeps changing states. Maybe this assumption is not valid and regression-based methods could also be suitable?
I also don't know if a multiclassifier is required, because I had understood that the TimeSeriesPredictor would also be suitable for this, since it works with the single data type. Whether the prediction is 1.3 or exactly 1.0 would be fine for me.
To sum it up:
I am looking for a algorithm which is able to recognize the switching patterns based on lose and widespread samples. It would be okay to define boundaries, e.g. state duration 3 of signal 1 will never last longer than 30s or state duration 1 of signal 3 will never last longer 60s.
Then, after the algorithm has obtained an approximate model of the switching behaviour, i would like to request a prediction of a certain signal state for a certain time.
Which methods can I use to get the best prediction, preferably using the ML.NET toolbox or based on matlab?
Not sure if this is quite what you're looking for, but if detecting spikes and changes using signals is what you're looking for, check out the anomaly detection algorithms in ML.NET. Here are two tutorials that show how to use them.
Detect anomalies in product sales
Spike detection
Change point detection
Detect anomalies in time series
Detect anomaly period
Detect anomaly
One way to approach this would be to first determine the periodicity of each of the signals independently. This could be done by looking at the frequency distribution of time differences between measurements of state 2 only and separately for each signal.
This will give a multinomial distribution. The shortest time difference will be the duration of the switching event (after discarding time differences less than the max duration of state 2). The second shortest peak will be the duration between the end of one switching event and the start of the next.
When you have the 3 calculations of periodicity you can simply calculate the difference between each of them. Given you have the timestamps of the measurements of state 2 for each signal you should be able to calculate the time of switching for all other signals.
Related
I need to create some kind of counter, that counts how many times all of the transistors(signal_1, signal_2, signal_3, signal_4) I have used turn ON (and OFF) per second. I need to show the difference in switching frequency between 2-level and 3-level inverter, the signal is PWM. I have no clue how to do it, I'm really lost here.
This is my schematics (just 1/3 of it, other 2/3 is just doubled this).
I am trying to build a network simulation (aloha like) where n nodes decide at any instant whether they have to send or not according to an exponential distribution (exponentially distributed arrival times).
What I have done so far is: I set a master clock in a for loop which ticks and any node will start sending at this instant (tick) only if a sample I draw from a uniform [0,1] for this instant is greater than 0.99999; i.e. at any time instant a node has 0.00001 probability of sending (very close to zero as the exponential distribution requires).
Can these arrival times be considered exponentially distributed at each node and if yes with what parameter?
What you're doing is called a time-step simulation, and can be terribly inefficient. Each tick in your master clock for loop represents a delta-t increment in time, and in each tick you have a laundry list of "did this happen?" possible updates. The larger the time ticks are, the lower the resolution of your model will be. Small time ticks will give better resolution, but really bog down the execution.
To answer your direct questions, you're actually generating a geometric distribution. That will provide a discrete time approximation to the exponential distribution. The expected value of a geometric (in terms of number of ticks) is 1/p, while the expected value of an exponential with rate lambda is 1/lambda, so effectively p corresponds to the exponential's rate per whatever unit of time a tick corresponds to. For instance, with your stated value p = 0.00001, if a tick is a millisecond then you're approximating an exponential with a rate of 1 occurrence per 100 seconds, or a mean of 100 seconds between occurrences.
You'd probably do much better to adopt a discrete-event modeling viewpoint. If the time between network sends follows the exponential distribution, once a send event occurs you can schedule when the next one will occur. You maintain a priority queue of pending events, and after handling the logic of the current event you poll the priority queue to see what happens next. Pull the event notice off the queue, update the simulation clock to the time of that event, and dispatch control to a method/function corresponding to the state update logic of that event. Since nothing happens between events, you can skip over large swatches of time. That makes the discrete-event paradigm much more efficient than the time step approach unless the model state needs updating in pretty much every time step. If you want more information about how to implement such models, check out this tutorial paper.
I am new with signal processing, i have following signals which i've got after some pre-processing on original signals.
You can see some of them has some similarities with others and some doesn't. but the problem is They have various range(in this example from 1000 to 3000).
Question
How can i analysis their properties scale-free(what i mean from properties is statistical properties of signals or whatever)??
Note that i don't want to cross-comparing the signals, i just want independent signals signatures which i can run some process on them sometime later.
Anything would help.
If you want to make a filter that separates signals that follow this pattern from signals that don't, well, there's tons of things you could do!
Just think practically. As a first shot at it, you could do something like this (in this order):
Check if the signals are all-positive
Check if the first element is close in value to the last element
Check if the maximum lies "in the middle" somewhere
Check if the first value is small, then the signal grows, then shrinks again
Check if the growth rates are gradual. You could for example analyze their derivatives (after smoothing):
a. derivative should be all-positive for a while, then all-negative.
b. derivative should be smooth (no jumps greater than some tolerance)
Without additional knowledge about the signal's nature/origin, it's going to be hard to come up with more meaningful metrics than these...
I am verifying part of a design which generates pulses with precisely timed edges. I have a basic behavioral model which produces an output which is similar, but not exactly the same as the design. The differences between the two are smaller than the precision needed for the design, so my model is good enough. The problem is: how do I do a comparison between these two signals?
I tried:
assert(out1 == out1_behav);
But that fails since the two signals have edges which happen 1ps apart. The design only requires that the edges be placed with 100ps precision, so I want a pass in this situation.
I thought about using a specify block with $delay() timing checks, however this causes me other problems since I need to run with +no_timing_checks to keep my ram models from failing in this RTL sim.
Is there a simple way to check that these edges are "almost" the same?
With the design requirement for the the signals to match within 100ps you could add a compare logic will a 100ps transition delay to act as a filter.
bit match;
assign #100ps match = (out1 == out1_behav);
always #*
assert #0 (match==1);
Verilog has different ways of assigning delay: transition and transport. Transition delays control the rise, fall, and indeterminate/high-Z timing. They can act as a filter if a driving signal gives a pulse less then the delay. Transport delays will always follow the the driving signals with a time shift. When the delays are large transition and transport will look the same.
assign #delay transition = driver; // Transition delay
always #(rhs) transport <= #dealy driver; // Transport delay
example: http://www.edaplayground.com/s/6/878, click the run button to see the waveform.
If you are using Modelsim/Questa, you can still use +notimingchecks, and then use the tcl command tchech_set to turn on individual timing checks, like $fullskew
Otherwise you will have to write a behavioral block that records the timestamps of the rising and falling edges of the two signals and checks the absolute value of the difference.
I am confused by the hybrid modelling paradigm in Modelica. On one hand, events are useful, on the other hand, they are to be avoided. Let me explain my case:
I have a large model consisting of multiple buildings in a neighborhood that is simulated over 1 year. Initially, the model ran very slow. Adding noEvent() around as many if-conditions as possible drastically improved the speed.
As the development continued, the control of the model got more complicated, and I have again many events, sometimes at very short intervals. To give an idea:
Number of (model) time events : 28170
Number of (U) time events : 0
Number of state events : 22572
Number of step events : 0
These events blow up the output (for correct post-processing I need the variables at events) and slows the simulation. And moreover, I have the feeling that some of the noEvent(if...) lead to unexpected behavior.
I wonder if it would be a solution to force my events at certain time steps and prohibit them in between these time steps? Ideally, I would like to trigger these 'forced events' based on certain conditions. For example: during the day they should be every 15 minutes, at high solar radiation at every minute, during nights I don't want events at all.
Is this a good idea to do? I guess this will be faster as many of the state events will become time events? How can this be done with Modelica 3.2 (in Dymola)?
Thanks on beforehand for all answers.
Roel
A few comments.
First, if you have a simulation with lots of events (relative to the total duration of the simulation), the first thing I would encourage you to do is use a lower order integrator. The point here is that higher-order integrators normally allow you to take longer time steps. But if those steps are constantly truncated by events, they just end up being really expensive.
Second, you could try fixed-step integrators. Depending on the tool, they may implement this kind of "pool events and fire them all at once" kind of approach in the context of fixed-time step integrators. But the specification doesn't really say anything on how tools should deal with events that occur between fixed time steps.
Third, another way to approach this would be to "pool" your events yourself. The simplest way I could imagine doing this would be to take all the statements that currently generate events and wrap them in a "when sample(...,...) then" statement. This way, you could make sure that the events were only triggered at specific intervals. This would be more portable then the fixed time step approach. I think this is what you were actually proposing in your question but it is important to point out that it should not be based on time steps (the model has no concept of a time step) but rather on a model specified sampling interval (which will, in practice, be completely independent of time steps).
As you point out, using "sample(...,...)" will turn these into time events and, yes, this should be faster.