PARÁMETROS CARACTERÍSTICOS DE LOS INTERCAMBIADORES

A discussion o f the relevant software analysis methods to apply to on-line monitoring and control is necessary here. While a large amount o f effort over the past decade has been spent to extract the maximum amount o f information possible from the ill-posed data set, the methods used are not always straightforward to implement in an autonomous manner which is required for hands-off operations in an automatic control or monitoring situation. Also in the present application there is additional information available to the algorithms. This reduces some o f the advantages programs might have over others and brings them closer together in terms o f their use in monitoring and control. In this situation it is advantageous to choose those easiest to implement without compromising the resulting distribution. In this comparative discussion o f the techniques used the following points need to be considered:

1. Algorithm speed and storage requirements.

2. Amount o f user information required to find the best solution.

3. Past experience o f performance o f methods in similar situations as the present application ie. peaky and mult imodal distributions.

4. The performance o f the algorithms in the presence o f noisy data.

Each point will be considered in turn:

1. Algorithm speed and storage requirements.

Algorithm speed and storage space are o f prime importance when the result is sought in the shortest possible time and particularly when the data processing step is the longest part o f the experimental set-up (see §1.02). Very high speed processor chips are now available but at a relatively high cost. Cheap computer power is however on the increase and it can be assumed that within the next few years processing power/cost will increase dramatically. Thus the choice o f algorithm suitability due to speed is not o f overriding importance as development o f the technique will go hand in hand with an increase in computer advancement and consequently a reduction in algorithm execution time.

Currently it is sensible in a monitoring and control application to choose methods without large amounts o f re-iterative convergence tests. Many methods seem to produce several solutions for the same data set with different starting information and choose the best result based on a goodness-of-fit criterion. However cheaper parallel processing hardware which perform many calculations simultaneously will reduce the time for such methods.

Storage space again is not o f overriding concern as the cost o f memory is dropping along with all solid-state equipment and computers now come equipped with more memory than most techniques described in this section will ever require in this application. It does become an issue however where large amounts o f storage and retrieval affect the analysis time.

2. Amount of user information required.

This is one o f the most important issues for an autonomous monitoring and control situation. Many o f the methods described require a user to input values at the beginning or during processing to start or continue the algorithm. The main concern is mid-process information which must be based on user interaction with the program. This is not effective for use in monitoring and control as the human element has not been removed from the control loop. Methods should be chosen which perform well with no user interaction.

3. Past experience of method performance.

Performance in conditions prescribed by the system o f interest is necessary in considering algorithm choice. The system o f primary concern is one broad peak with a narrow spike at a defined size to simulate the presence o f particle o f defined size next to a broad distribution o f particles (ie. virus-like particles in yeast homogenate. See § 1.2). There are some programs notably constrained régularisation which might oversmooth the solution. Alternatively in this case a different regularising matrix could be sought to allow for a "spiky” solution. This would probably be subject to instability in the presence o f noise which often causes over-oscillatory solutions.

The analysis methods that are o f interest are those where it is easy and theoretically sensible to include a-priori information into the starting matrices. This information may be the noise level in the data if this can be experimentally assessed (see § 1.42), the range o f sizes to be covered (this is easy to include in all cases) or a weighting o f the parameters in the algorithm so as to bias the result towards a desired direction. Weighting o f the data points themselves is a different issue. It has been shown that it is advantageous to weight the points inversely as the square o f the standard deviation o f the data points.

In least squares methods it is quite straightforward to weight certain columns o f the matrix to bias the solution to certain areas o f size or decay constant. The range o f size analysed is also simple to include. Since it is generally found that the range o f F can significantly affect the solution reached this is important starting information to include.

4. Robustness to noise.

In the software analysis assessment, chapter 5, noise is simulated by adding or subtracting a random number o f counts to each data channel to a predetermined level. This simulates photon-counting noise. Noise due to dust and flare (see §1.42) will depend upon the sample cleanliness and system alignment. In real experiments there is no way to determine the contribution to the noise from each source. Dust is unquantifiable and thus cannot be simulated, flare can be minimised by careful alignment but its actual contribution is unknown (Madani and Kaler 1991). Chapter 7 on intemodal light scattering offers a possible eradication o f such noise contributions to the correlogram by holding large dust particles out o f the beam. This and other applications are discussed.

Thus the performance o f analysis methods in the presence o f simulated noise is only an indication o f their robustness and not an absolute measure o f suitability. A table o f the methods described in § 1.43 is shown on the next page.