2- OPA 3D

OPA in 3 dimensions is more suitable for prediction than OPA is. In fact OPA could be employed to analyse a-posteriori a matrix (e.g. a batch), but this method is not really suitable to predict and control a new batch.

OPA 3D is more suitable in the sense that it takes into account variability of several batches and gives as outputs some prediction coefficients that are more robust and more representative of a process for instance.

This method could then be employed during process monitoring to obtain concentration profiles and/or pure spectra of a mixture.

For a scientific overview of the method, click here.


1- When pressing the "OPA3D" button in the "Factor Analysis" menu, the user gets a first window. It corresponds to the way of presenting the data.




The field "Method" is filled with MCR-ALS. This abbreviation stands for "Multivariate Curve Resolution - Alternating Least Squares", which is the method employed to resolve the data (i.e. obtaining the concentration profiles and/or pure spectra).

The field "Batch numbers" corresponds to all batches that should be analysed simulatenously. It is filled according to data that were loaded before.

The button "Initial Inputs" gives the user the possibility to load initial inputs for MCR-ALS and OPA3D. These initial inputs come ideally from OPA performed on a single matrix before but can also come from external knowledge.

When loading the data, it is important to have all matrices that have to be analysed in the same file.
The user can check that everything he loaded is correct since in this first window, the 3 first fields are filled automatically (field "initial inputs" takes the value "loaded" if initial inputs were correctly loaded).

"Column-wise" and "row-wise augmented matrix" correspond to the way of building the augmented matrix (i.e. the unfolded matrix).
The "Column-wise" augmented matrix is clicked by default since this is the most common case for batch data (mode 2 = wavelengths = same dimension for all batches).

2- The second window that appears after this corresponds more to the algorithm.





The "Maximum number of iterations" and the "Convergence criterion" are parameters of the ALS algorithm.
Default values are proposed but can be changed.

The field "All species present in all batches" (clicked by default) corresponds to the fact that all components are supposed to be present in all batches.
Once again, this is the most common case for batch process data since all batches are normally coming from the same process.
In this version of CuBatch, this restriction is applied. It means that even the other option is present, it can not be chosen "which species are present in different batches".
The last field is in fact a question so set or not some constraints with different parameters.

3-A 3rd window comes if the question "do you want to use some constraints ?" is answered "yes" (i.e. cliked).




- The 1st constraint is "Unimodality".
Unimodality allows only one maximum per profile. It can be applied for concentration and/or spectral profiles.
Different algorithlms can be applied for unimdality. From the roughest to the softest, we have vertical, horizontal, average.
The tolerance limit defines how strictly unimlodality shoud be applied.

- The 2nd constraint is "Closure".
Closure constrains the total concentration at each time to be constant (fulfilment of the mass equation).
It normalises the total concentration at each time to a fixed value (unity for instance) by dividing each element of a row of C by the sum of the elements of the row
The value of the total concentration in the closed system can be set by the user.
Closure can be applied for concentration or spectral profiles.
In this version of CuBatch, closure is restricted to one closure for the species concentrations, and this constraint is applied to all matrices.
The closure condition is also set to the "lower or equal than" condition by default.It allows for some departures of this condition, i.e, slight variations of the total concentration in the system may be allowed.
Last limitation of this version of closure constraint is that all compounds in the data set analysed belong to the closed system.

- The 3rd constraint is "Non-negativity".
Non-negativity forces the elements in a profile to be positive. It can be applied for concentration and/or spectral profiles.
The user can choose the algorithm to apply non-negativity.
- forced to zero: the negative values in a profile are updated to zero.
- nnls: non-negative least squares.
- fnnls: fast non-negative least-squares.
In this version of CuBatch, once it is chosen to apply non-negativity, it will be automatically applied to all profiles.

- The 4th and the 5th constraints are the "equality constraint".
Equality constraints for concentration and spectra : the elements from matrices C and S known beforehand replace those calculated during the optimization process.
The selection of these constraints is necessary to activate the introduction of the information in the csel and ssel matrices, when present.
When selected, they activate the use of the information in Csel and/or Ssel in the resolution process.
In this version of CuBatch, Equality forces the defined values in Csel and/or Ssel to be exactly updated in the concentration profiles and/or spectra.
or allows for some departures of this condition, i.e, values very close to the ones in Csel/Ssel are allowed.

- The last constraint is the "three-way constraint".
The three-way data structure constraints allows for selecting between a trilinear and a non-trilinear model to describe the data set. From an operational point of view, it can be said say that a trilinear structure implies a common shape for all profiles related to the same compound in the submatrices of an augmented direction (e.g., in a column-wise augmented matrix, the profile from the i th compound would have the same shape in all Ci submatrices).
The default value is "no trilinear structure" because it is recommended, in case of doubt about the trilinearity of the dataset, to choose no trilinear.
Other options are:
- trilinear, equal shape and synchronization (all species)
- trilinear without synchronization (all species) (corrects for trilinear systems with shifted, but equally shaped profiles between matrices for the same compound)
- trilinear and synchronization for only some species (allows for the application of partial trilinearity; only to some of the compounds in the data set).
- selection the mode of application of the trilinearity constraint: application to C matrix, to S matrix, or to C and S matrices.

For more details about all constraints, see the proper literature.

After this window, the iterative resolution procedure starts...