Performance criteria, generalized

Thickener control philosophies are usually based on the idea that the Iindertlow density obtained is the most important performance criterion. The o ertlow clarity is also a consideration, but this is generally not as critical. Additional factors which must be considered are optimization of tlocciilant usage and protection of the raking mechanism. 

The selection of cluster number, which is generally not known beforehand, represents the primary performance criterion. Optimization of performance therefore requires trial-and-error adjustment of the number of clusters. Once the cluster number is established, the neural network structure is used as a way to determine the linear discriminant for interpretation. In effect, the RBFN makes use of known transformed features space defined in terms of prototypes of similar patterns as a result of applying /c-means clustering. 

Sections of specifications dealing with application may be very brief if a performance criterion is used otherwise the scope of the contractor procedural responsibilities must be completely spelled out. These will vary considerably from job to job. A general guide appears in Ref. [1], excerpted here ... 

Since the design/retrofit problem embeds batch plant scheduling, it systematically includes the determination of the production sequence and the equipment sizes based on a performance criterion. Equipment sizes are considered either as continuous variables or as discrete ones and so the problem can involve either discrete variables or a set of mixed ones. Most of the existing literature has focused on single objectives involving a cost criterion typically based on capital investment. This criterion is generally expressed as a non-linear function of the size of the equipment, following the six-tenths rule. 

Analytical techniques generally involve two areas. The first is the direct solution of the system differential equations in the Aime domain, usually by state variables. The second area is optimization of a specific performance criterion. The criteria for optimization by analytical techniques usually involve minimum response time or an integral time-cost function. 

Schweickhardt and Allgower in Chapter A3 mainly concentrate on the nonlinearity assessment of processes. A comprehensive overview of general nonlinearity measures and a thorough investigation of the predictive and computational dimension of open loop measures are presented. As the main objective becomes the development of a tool to judge whether a nonlinear controller should be benefieial or needed for a particular process with specific nonlinear characteristics, the controller relevant nonlinearity is quantified. The selected measure is based on the relative differences between the output of nonlinear state feedback law and that of an equivalent linear state feedback law. The controller relevant nonlinearity measure depends not only on the plant dynamics and region of operation but also on the performance criterion used in the derivation of the controller law. 

The first two points are valid for open-loop process nonlinearity measures as well. The third point is new in control-relevant nonlinearity quantification. In a more general context, one has not only to consider the performance criterion but additionally mention the controller design method. Following the idea of Ref 24, optimal control theory with an integral performance criterion will be used here as it represents a benchmark for any achievable performance. Considering nonlinear internal model control with different filter time constants is also possible, see for example Ref 23. 

PM strategy General data Dependability data Economical data Performance criterion... 

Hunter and Reimer (1965) proposed the simple Divergence criterion that can readily be extended to multi-response situations. In general, if we have performed N experiments the experimental conditions xN+] for the next one are obtained by maximizing the weighted Divergence between the rival models, defined as... 

It is well known that cubic equations of state may predict erroneous binary vapor liquid equilibria when using interaction parameter estimates from an unconstrained regression of binary VLE data (Schwartzentruber et al.. 1987 Englezos et al. 1989). In other words, the liquid phase stability criterion is violated. Modell and Reid (1983) discuss extensively the phase stability criteria. A general method to alleviate the problem is to perform the least squares estimation subject to satisfying the liquid phase stability criterion. In other... 

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