ProSensus, Inc.

Whenever one is looking at any data, pre-processing is an important first step. Regardless of the methodology that one will eventually use to analyze the data, it is important to pre-process the data into the most meaningful form - for example, frequency based information via FFT's or wavelets rather than time based, nonlinear transformations, etc. This would be the case whether using some traditional data approaches or multivariate statistical approaches.

Key advantages of multivariate statistical approaches that use latent variables include the following:

1. They are the most powerful way of handling very large ill-conditioned industrial data sets due to their very efficient projection and visualization of the data in low dimensional latent variable spaces where all the information is contained. These methods now form the basis of the most advanced and powerful system identification methods used for modeling dynamic systems for control, namely sub-space identification. These subspace identification methods are supplanting most prior methods for even moderate sized problems.
   
   The multivariate latent variable approaches are also becoming the most widely used data-based methods for the analysis, monitoring and optimization of very large processes with large numbers of correlated variables. Other typical methods that rely upon methods such as Kalman filters, Bayesian networks, neural networks, etc. are much less amenable to the handling of very large numbers of variables.
   
   
2. A most important aspect of these methods is their very powerful imputation methods that allow them to transparently and automatically handle missing data. Missing data are almost always present in industrial databases due to missed samples, bad measurements, different sampling frequencies of various instruments, etc. It is not uncommon for many databases to have 10-30% of the data missing and for some variables (due to less frequent sampling, etc) to have up to 90% missing.
   
   Most regression and neural network methods do not have the ability to easily handle these missing data. Handling missing data allows our soft sensor and monitoring (fault detection and isolation, FDI) systems that use latent methods to continue to work a very high percentage of the time even in the presence of missing data.
   
   
3. The multivariate latent variable methods do something no other regression based methods do – they provide simultaneous models of both the X space (regressor variable space) and the Y space (response space), rather than just the response space (Y). This is critically important for the analysis of nearly all industrial data, except those cases in which all the regressor variables come from designed experiments.
   
   In the case where there is independent variation in all the regressor variables (e.g., designed experiments), there is no need for a model of the X space. In that case the X space is of full statistical rank and uniquely defined by the X variables themselves. However, in nearly every industrial data-based problem today, large numbers of highly correlated variables are being collected that vary in a natural way from the operation of the process (not from designed experiments). In these situations, even though hundreds to thousands of variables are being measured, they are all being driven by only a few underlying events in the process, and hence the statistical rank of the data is very low. In these situations, if one does not have a model of the low dimensional X space as well as the Y space, then the model is almost useless for practical use.
   
   The advantages of using both and X and Y-space model, vs using only a Y-space model are:
   1. The simultaneous modeling of both the X and Y spaces by latent variable methods provides a unique solution to the regression problem, as opposed to the infinite number of solutions for the Y space model provided by other regression approaches (resulting in very low confidence for the estimated model parameters and predictions).
   2. This allows for interpretation of the model in the unique latent variable subspaces, i.e. which group of regressors (X) influence which group of Y’s, which group of X’s are related to a shift in the process over a period of time, etc. No such unique interpretation is possible with other regression based methods.
   3. One has causal information only in the reduced rank space of the inputs (not on each individual process variable) and the latent variable methods extract this causal subspace.
   4. It allows for monitoring the process in these low dimensional subspaces with only a few multivariate statistics that test whether the process is continuing to operate in that subspace.
   5. It allows for process control and optimization to be performed in these low dimensional subspaces. This cannot be done in the full X variable space because that space is not of full rank and is not a causal space.
   6. For soft sensors (inferential predictive models) this feature allows for:

   1. For soft sensors, the advantages of multivariate methods are the ability to handle missing data, to test the validity of new incoming data used to make the prediction, and the ability to compute realistic and valid confidence intervals on the predictions.

      1. Handling missing data in both training data used when building the model and in future multivariate observations when using the model.
      2. Testing the validity of all new incoming data (does it fall in the reduced dimensional space defined by the data used to build the model?) If the data are valid, then the soft sensor can reliably be used. If new data are not valid, then the soft sensor is not valid. The latent variable methods allow one to then test which variables are exhibiting abnormal behavior. If only a few variables are flagged, then, the soft sensor can continue by flagging them as missing data. Regression based methods, or neural network methods that do not model the X space cannot provide these checks.
      3. Computing realistic and valid confidence intervals on the predictions of the Y’s.


4. Powerful multi-block latent variable methods exist that are excellent for combining data from many different sources or from many different sections in a large plant.
   1. In the case of combining multiple sensors (for example, digital images, process measurements, acoustic sensors) it allows the important information on the problem to be extracted from blocks of data from all sensor groups or on different process sections and simultaneously fused into a complete plant model. It easily shows which sensors blocks are most influential for the problem. Then it allows further exploration within each block to show which of the variables from each sensor block contribute the most.
   2. These multi-block methods are currently the trend in plant-wide process monitoring and soft sensors. They allow for much easier long-term maintenance (only those blocks for individual plant sections need updating if equipment or other changes occur in that section). They also allow for much easier diagnosis of problems by the engineers and operators in that only meaningful plant subsections need to be interpreted.