Data interpretation numeric-symbolic mapping

KBSs can be viewed with increasing levels of commitment to problem solving. At the level described in the previous section, a KBS accomplishes symbolic-symbolic mappings between input and output variables analogous to the numeric-symbolic mappings of approaches such as neural networks and multivariate statistical interpreters. For each problem-solving task, the particular numeric-symbolic or symbolic-symbolic approach is based on the task and the knowledge and data available. 

Data Interpretation extends data analysis techniques to label assignment and considers both integrated approaches to feature extraction and feature mapping and approaches with explicit and separable extraction and mapping steps. The approaches in this section focus on those that form numeric-symbolic interpreters to map from numeric data to specific labels of interest. 

Numeric-symbolic approaches are particularly important in process applications because the time series of data is by far the dominant form of input data, and they are the methods of choice if annotated data exist to develop the interpretation system. With complete dependence on the annotated data to develop the feature mapping step, numeric-symbolic mappers can be used to assign labels directly. However, as the amount and coverage of available annotated data diminishes for the given label of interest, there is a need to integrate numeric-symbolic approaches with... 

In practice, there may not be sufficient operating experience and resultant data to develop a numeric-symbolic interpreter that can map with certainty to the labels of interest, Cl. Under these circumstances, if sufficient knowledge of process behaviors exists, it is possible to construct a KBS in place of available operating data. But the KBS maps symbolic forms of input data into the symbolic labels of interest and is therefore not sufficient in itself. A KBS depends on intermediate interpretations, ft, that can be generated with certainty from a numeric-symbolic mapper. This is shown in Fig. 4. In these cases, the burden of interpretation becomes distributed between the numeric-symbolic and symbolic-symbolic interpreters. Figure 4 retains the value of input mapping to preprocess data for the numeric-symbolic interpreter. 

General considerations of data availability lead immediately to the recognition that detection systems are more likely to be designed as comprehensive numeric-symbolic interpreters as illustrated in Fig. 3. State description systems may be configured as shown in either Fig. 3 or Fig. 4. Fault classification systems are most likely to require the symbolic-symbolic mapping to compensate for limited data as shown in Fig. 4. Many practical data interpretation problems involve all three kinds of interpreters. In all situations, there is a clear need for interpretation systems to adapt to and evolve with changing process conditions and ever-increasing experience. 

Among nonlocal methods, those based on linear projection are the most widely used for data interpretation. Owing to their limited modeling ability, linear univariate and multivariate methods are used mainly to extract the most relevant features and reduce data dimensionality. Nonlinear methods often are used to directly map the numerical inputs to the symbolic outputs, but require careful attention to avoid arbitrary extrapolation because of their global nature. 

The label of interest is Feed Injection System Problem. The if, and, and or statements relate specific process observations that can establish that there is a likelihood of an injection system problem. Injector header pressure is a process measurement and abnormal is an intermediate label of interest. The label abnormal can be determined by developing a numeric-symbolic interpreter that maps injector header pressure data as either normal or abnormal. 

As is typical of process systems, the plant runs with a very high availability and product quality is normally maintained. For diagnostic data interpretation, there is very little data for developing any kind of numeric-symbolic interpreter that maps directly from the input data to the output diagnostic conclusions. It is possible, however, to map with a great deal of confidence from the input numeric data to a set of useful intermediate interpretations. With respect to the sensor data, there is considerable information for map-... 

In addition, the GPC trace, an example of which is shown in Fig. 42, reflects the composition signature of a given product and reflects the spectrum of molecular chains that are present. Analysis of the area, height, and location of each peak provides valuable quantitative information that is used as input to a CUSUM analysis. Numeric input data from the GPC is mapped into high, normal, and low, based on variance from established normal operating experience. Both the sensor and GPC interpretations are accomplished by individual numeric-symbolic interpreters using limit checking for each individual measurement. 

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