separating stationary and non stationary parts of univariate signal
All these algorithms are based on the determination of a new basis (i.e. a new set of basis vectors), chosen according to a given constrain (to maximize the variance of each component in PCA for instance). 

If you have only one signal, you have only one basis vector. So you cannot use these algorithms because you don't have enough information.

In lower dimensions, you can think of it as the calculation of the arithmetic mean from a set of noisy values corresponding to the same measurement. You need multiple measurement to be sure to get close to the "true" value of the measurement. What you are asking is how to get the "true" value from only one measurement without any repetition. That cannot be done because you don't have enough information even to do anything.



However, depending on you signal and its specific noise, there might be other ways to achieve what you want. Actually, all you have to do is to identify a way to differentiate noise from signal.

Their distributions are obviously different, but these are mere projections, so again, you have too few data to use them.

One working possibility is to filter your data to remove high frequency components (to remove most of the noise) and very low frequency components (to remove pink noise, but usually pink noise is really not a problem). But that would work only if you have an idea of the bandwidth of your signal (the maximum frequency beyond which your signal has no meaning anymore). 



What you describe won't work. If I continue my analogy of the average over noisy measurement data, it is like saying that you will split the result of you unique measurement (say, 15 = 12 + 3) and use that result (12 and 3) to calculate the mean (7.5). I hope you understand that this makes no sense (the mean of 15 is at best undefined, or at worst 15). And even if it did, your decomposition would be quite arbitrary (why not use 10+5 or 20-5 or 13264585120-13264585105?). Again, you won't get more information by decomposition of your signal.



Final word:

If you really want us to help you or to give you more details about why this won't work as you expect, please open a new question, provide actual data and explain your setup.