Redundancy measure

Hazards that could lead to injury of company personnel. Partial redundancy is often required (For example, redundant measurements but not redundant logic). 

Diversity can be used to further advantage in redundant configurations. Where redundant measurement devices are required, different technology can be used for each. Where redundant logic is required, one can be programmed and one hard-wired. 

Typically, process data are improved using spatial, or functional, redundancies in the process model. Measurements are spatially redundant if more than enough data exist to completely define the process model at any instant, that is, the system is overdetermined and requires a solution by least squares fitting. Similarly, data improvement can be performed using temporal redundancies. Measurements are temporally redundant if past measurement values are available and can be used for estimation purposes. Dynamic models composed of algebraic and differential equations provide both spatial and temporal redundancy. 

Similarly, some of the elements of vector x of measured variables can be classified into redundant and non-redundant measured process variables (Fig. 2). 

Aggregate two nodes connected with an unmeasured stream. The resulting Reduced Balance Scheme contains only redundant measurements ... 

Finally, let us consider fi measured instead of /3. The new occurrence matrix is in Table 3. Now, we can assign all the equations by assigning Equations 1, 2, and 3 to /3, /s, and fi, respectively. In this case, all the unmeasured process variables are determinable from the available information however, there are no redundant measured variables. 

Remark 4. As indicated by Crowe et al. (1983), measured variable classification is performed by examining the matrix associated with the reconciliation equations. The zero columns of G or Gx correspond to variables that do not participate in the reconciliation, so they are nonredundant. The remaining columns correspond to redundant measurements. 

Expressions for the unmeasured process variables, as functions of the measured ones, were also obtained. These were solved sequentially after the reconciliation of the redundant measurements was completed ... 

The MIPAS-STR almost covers the entire NOy, together they cover Cl y (e.g. both HC1 and CIONO2), whereas SAFIRE-A has its strength in HOx and can obtain additional information on Bry species. Also various types of tracers and source gases can be observed. Redundant measurements will improve the quality of the corresponding trace gas distributions and allow to validate the calibration of both instruments. 

In this particular case, the actuator has two diaphragms as a redundancy measure. The existence of two diaphragms on the actuator assures continuity of valve operation even if the diaphragm fails under pressure, which, in any case, should be signalled by means of an alarm. 

Both the Parameter and Reconcile cases determine (calculate) the same set of parameters. However, these cases do not get the same values for each parameter. A Parameter case has an equal number of unknowns and equations, therefore is considered "square" in mathematical jargon. In the Parameter case, there is no objective function that drives or affects the solution. There are typically the same measurements, and typically many redundant measurements in both the Parameter and Reconcile case. In the Parameter case we determine, by engineering analysis beforehand (before commissioning an online system for instance) by looking at numerous data sets, which measurements are most reliable (consistent and accurate). We "believe" these, that is, we force the model and measurements to be exactly the same at the solution. Some of these measurements may have final control elements (valves) associated with them and others do not. The former are of FIC, TIC, PIC, AIC type whereas the latter are of FI, TI, PI, AI type. How is any model value forced to be exactly equal to the measured value The "offset" between plant and model value is forced to be zero. For normally independent variables such as plant feed rate, tower... 

The correlations between the original features of one set and the canonical variables of the second set are called inter-set loadings. They are also redundancy measures and demonstrate the possibility of describing the first data set with the features of the second set. The inter-set loadings characterize the overlapping of both sets or, in other words, the variance of the first set explained by the second set of features. 

These contributions represent the overall correlations with each canonical feature. Again we find factor patterns which are not very pronounced. The extraction and the redundancy measures are reported in Tab. 5-9. From the total values of the variance explained we see that both sets are well represented by their canonical variables. On the other hand the redundancy measure (90% or 72%) indicates that both feature sets may be of equal practical weight. 

Redundant measurement means obtaining the same process information with two like measurements or two measurements using different principles. Redundant measurements can be calculated or inferred measurements. Two like measurements would be two pressure transmitters, two temperature measurements, two level measurements, and so on. An example of inferred measurement would be using a pressure measurement and vapor pressure tables to check an actual temperature measurement. 

An important property of SP pool libraries is called redundancy, measured as the ratio between the number of beads used in the library synthesis and the number of planned library individuals. Considering a 10,000-member library, using 10,000 resin beads we could theoretically have a single bead loaded with each library individual. However, as the mix-and-split process does not count exactly the number of beads in... 

It corresponds to a redundancy measure whose maximum and minimum values are 1 and 1/n, respectively. 

M. Bagajewicz, 2005, On the defmion of Software Accuracy in Redundant Measurement Systems , AIChE Journal, Vol. 51, No. 4. 

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