Inferential modeling

Togkalidou, T., Braatz, R.D., Johnson, B.K., Davidson, O. and Andrews, A., 2001. Experimental design and inferential modelling in pharmaceutical crystallization. American Institution of Chemical Engineers Journal, 47(1), 160-168. 

The deposition velocity Vd for vegetative surfaces is commonly estimated by an empirical modeling approach (often called an inferential modeling... 

Brook, J. R., Di-Giovanni, F., Cakmak, S., and Meyers, T. P. (1997). Estimation of Dry Deposition Velocity Using Inferential Models and Site-Specific Meterology-Uncertainty Due to Siting of Meterological Towers. Atmos. Environ. 31(23), 3911-3919. 

Togkalidou, T, R.D. Braatz, B.K. Johnson, O.A. Davidson, and A.T Andrews (2001). Experimental design and inferential modeling in pharmaceutical crystallization. AIChE J. 47, 160-168. 

A conceptually different and relatively new example of an inferential model, motivated by human performance problems specifically, is nonlinear causal resource analysis (NCRA) [Kondraske, 1988 Vasta and Kondraske, 1994]. Quantitative task demands, in terms of performance variables that characterize the involved subsystems, are inferred from a population data set that includes measures of subsystem performance resource availabilities (e.g., speed, accuracy, etc.) and overall performance on the task in question. This method is based on the following simple concept Consider a sample of 100 people, each with a known amount of cash (e.g., a fairly even distribution from 0 to 10,000). Each person is asked to try to purchase a specific computer, the cost of which is unknown. In the subgroup that was able to make the purchase (some would not have enough cash), the individual who had the least amount of cash provides the key clue. That amount of cash availability provides an estimate of the computer s cost (i.e., the unknown value). Thus, in human performance, demand is inferred from resource availabdities. 

A conceptually different and relatively new example of an inferential model, motivated by human performance problems specifically, is nonlinear causal resource analysis (NCRA) (Vasta and Kondraske, 1994 Kondraske, 1988). Quantitative task demands, in terms of performance variables... 

Quality control laboratories may be equipped with instruments which indicate MW or MWD directly. The most common technique used for this purpose is gel permeation chromatography (GPC). Infrequent analysis is the rule. Such off-line measurements are most often used to update inferential models, or to effect open loop control of the polymerization by manual process adjustments based on GPC results. On-line GPC is available its application is not yet common in industrial practice, but applications of on-line measurement of MWD by GPC have been reported [26]. The difficulties encountered with on-line GPC are the maintenance, sampling and calibration problems associated with any process chromatography application. In addition, a compromise must be made between resolution of the MWD and time of analysis. As a rule of thumb, it is possible to determine an accurate average molecular weight in under 10 minutes. Determination of the MWD can take considerably longer. 

In the field of polymer reactor engineering, the calorimetric estimation and control problems have been extensively studied with simulations and experiments [1, 33, 37,39]. EJCF [33,37] and L [39] observers have been employed to estimate the heat generation rate, on the basis of an off-line fitted heat transfer model [38, 39]. Various control techniques have been employed among them are adaptive, inferential, model predictive, and geometric control [1, 38, 39]. The robustness of the controller is shown by its successful implementations, regardless of the particular estimation and control techniques employed. Recently [15], it has been formally established, and experimentally demonstrated, the feasibility of jointly estimating the heat generation rate and the heat transfer coefficient in an exothermic reactor. 

Measurements are made at the most fundamental level possible (single scattering events, dilute regime viscosity, spectroscopy, etc.) and these are designed to obtain model-free primary quantities, such as conversion, composition, molar mass, intrinsic viscosity, and so on. The use of empirical and inferential models and calibration schemes is thereby avoided. 

Tipnis, S.K., Penney, W.R. and Fasano, J.B., 1994. An experimental investigation to determine a scale-up method for fast competitive parallel reactions in agitated vessels. American Institute of Chemical Engineers Symposium Series, 299, 78-91. Togkalidou, T., Braatz, R.D., Johnson, B.K., Davidson, O. and Andrews, A., 2001. Experimental design and inferential modelling in pharmaceutical crystallization. American Institution of Chemical Engineers Journal, 47(1), 160-168. 

The deposition velocity 1/ for vegetative surfaces is commonly estimated by an empirical modeling approach (often called inferential modeling), which uses meteorological data and information on the surface characteristics of the vegetation (Brook et al., 1997 Hicks et al., 1987). In the ADOM model, for example, the dry deposition velocity to vegetation is estimated as the inverse of the sum of three resistances aerodynamic, laminar-layer or diffusive, and canopy. The aerodynamic resistance is... 

Frescholtz 2002). Although ongoing and new planned field and laboratory studies are designed to further test this hypothesis, we feel that it is warranted at this time to develop a pilot-scale network of aimual ecosystem fluxes of THg in TF and LF as indicators of total atmospheric deposition. These fluxes can then be compared with measured wet plus modeled diy deposition based on both inferential and regional-scale models to develop independent estimates of total atmospheric deposition for forested catchments. We also believe that this approach could eventually be applied to a national network, such as the MDN. Although this method is best aimed at forested sites, ongoing research will address methods appropriate for other ecosystems. 

The successful study of intermediates not only provides one or more signposts which help define the detailed pathway traversed by a reaction, the intermediates themselves may also provide inferential evidence about the transition states for which they are often taken as models (cf. p. 41). 

The procedures are grouped in two general classes inferential and descriptive. These labels are not an established convention, but rather, are used to highlight the fundamental difference between the completely atheoretical approach of CA and the model-guided approach of the other methods. Among the inferential methods, CCK is based on the strictest model, LCA makes fewer assumptions, and MA uses a bottom-up, fit-oriented approach. 

It is vitally important that the multivariate nature of data related to a process be assessed to develop an understanding of a process and to assess quality. Process data together with appropriate chemometric models can provide information about (1) product quality inferentially from process conditions (2) process consistency (process signature, statistical process control) (3) analyzer reliability and (4) operational knowledge that can aid in scale-up and process transfers. ... 

Inferential sensors, also known as soft sensors, are models that nse readily measurable variables to determine product properties critical to prediction of prodnct/process qnafity. Ideally the soft sensors are continuously monitored and controlled, or moiutored on a relevant time scale. They need to make predictions quickly enough to be used for feedback control to keep process variability to a minimum. 

SSDs are being routinely used for the display and interpretation of effects data (Parkhurst et al. 1996 Posthuma et al. 2002). An SSD for atrazine (shown in Figure 7.3) displays the typical S-shaped curve associated with many chemical dose-response relationships. Each point on the curve represents an LC50 for a particular species exposed to atrazine under standard toxicity test protocols. The SSD approach uses only a single statistically derived endpoint from each available toxicity test (e.g., the LC50 or EC50). In contrast, all data collected during any specific toxicity test can be used in a hierarchical model. The ability to use all available data to make inferential decisions is a marked improvement over the standard SSD effects distribution. 

Two very different approaches to inferential statistics exist the classical or fre-quentist approach and the Bayesian approach. Each approach is used to draw conclusions (or inferences) regarding the magnitude of some unknown quantity, such as the intercept and slope of a dose-response model. The key difference between classical... 

The shortcoming of all methods for predetermining cure cycles that regulate secondary variables is that they deal only in expectations and probabilities. No matter how many eventualities are anticipated, there is always one more that is unexpected. Unexpected variations in material properties, process equipment malfunctions, and changes to geometries of tool and part all contribute to the uncertainty of the outcome. As a result, in-process, inferential control is needed for the process environment as well as the boundary conditions and material state. Inferential control is relatively new to the polymer processing industry, especially in complex processes where good models are not yet common. 

The degree of inaccessability of such processes varies. For example, we could distinguish preconscious processes (which can become accessible with effort) from totally unconscious processes (which must remain forever inferential). This sort of elaboration of our model will be left for a future study. 

The analyst needs to understand that statistical models vary in their inferential utility. Linear models of some type or other are the most common and the most easily analyzed with statistical computing packages, but they may be only rough approximations of the real world. An oft-quoted aphorism of G.E.P. Box is that all models are wrong, some are useful. That is no doubt true, but it misses another level of detail of such models as follows. At the simplest level, a model fits the data. At the next level, a model predicts the data. At its most useful level, a model shows unanticipated features of the data and the research, and this is the ideal especially for biomarker research. The most exquisite characterization of association... 

One solution to this problem is to employ inferential control, where process measurements that can be obtained more rapidly are used with a mathematical model to infer the value of the controlled variable, as illustrated in Figure 12. For example, if the overhead product stream in a distillation column cannot be analysed on-line, measurement of a selected tray temperature may be used to infer the actual composition. If necessary, the parameters in the model may be updated, if composition measurement become available, as illustrated by the second measuring device in Figure 12 (dashed lines). 

The concentration of the product B, CB, is not measured on-line and a measurement is only available hourly from a lab. The control of the concentration is therefore based on inferential control in loop 4 using the reactor temperature T. The inferential controller will then, from a model of the process, infer what the concentration CB is and use this inferred measurement as the signal to the controller CC3 (where the first C refers to Concentration). 

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