Performance criteria

In many cases, the methods used to solve identification problems are based on an iterative minimization of some performance criterion measuring the dissimilarity between the experimental and the synthetic data (generated by the current estimate of the direct model). In our case, direct quantitative comparison of two Bscan images at the pixels level is a very difficult task and involves the solution of a very difficult optimization problem, which can be also ill-behaved. Moreover, it would lead to a tremendous amount of computational burden. Segmented Bscan images may be used as concentrated representations of the useful... 

Elastic Properties. The abiUty of a fiber to deform under below-mpture loads and to return to its original configuration or dimension upon load removal is an important performance criterion. Permanent deformation may be as detrimental as actual breakage, rendering a product inadequate for further use. Thus, the repeated stress or strain characteristics are of significance in predicting or evaluating functional properties. 

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. 

Control philosophies for clarifiers are based on the idea that the overflow is the most important performance criterion. Underflow density or suspended sohds content is a consideration, as is optimal use of flocculation and pH control reagents. Automated controls are of three basic types (I) control loops that optimize coagulant, flocculant, and pH control reagent additions (2) those that regulate underflow removal and (3) rake drive controls. Equahzation of the feed is provided in some installations, but the clarifier feed is usually not a controlled variable with respect to the clarifier operation. 

Control of pollutants by oxidation is another exothermic process in which high conversion is the most important performance criterion. Interest in efficiency is limited to minimize byproduct formation the byproducts can be more damaging and more refractory than the original pollutants were. Commercially, most adiabatic reactors used for pollution control are of the least expensive construction. 

An alternative procedure is the dynamic programming method of Bellman (1957) which is based on the principle of optimality and the imbedding approach. The principle of optimality yields the Hamilton-Jacobi partial differential equation, whose solution results in an optimal control policy. Euler-Lagrange and Pontrya-gin s equations are applicable to systems with non-linear, time-varying state equations and non-quadratic, time varying performance criteria. The Hamilton-Jacobi equation is usually solved for the important and special case of the linear time-invariant plant with quadratic performance criterion (called the performance index), which takes the form of the matrix Riccati (1724) equation. This produces an optimal control law as a linear function of the state vector components which is always stable, providing the system is controllable. 

This could occur if the separation ratio of another solute pair, although larger, was very close to that of the critical pair but contained solutes, for example, of widely different molecular weight (and, consequently, very different diffusivities). Fortunately, the possibility of this situation arising is remote in practice, and will not be considered in this discussion. It follows that the efficiency required to separate the critical pair, numerically defined, is the first performance criterion. 

A third performance criterion developed for combined heat and power plant involves compari.son between the fuel required to meet the given loads of electricity and heat in the CHP plant with that required in a reference system . The latter involves conventional plants that meet the same load demands (indicated by subscript D), for example, in a conventional electric power station and in a heat only boiler. 

Performance criterion, ft. The quality of any potential solution, X, is determined by the average system performance achieved within the zone of the decision space identified by X, ftiX), not by the individual performance obtained at any particular point x, ftin). 

All conventional approaches (mathematical and stochastic programming, parametric and nonparametric regression analysis) adopt as a common solution format real vectors, x and as performance criterion,... 

For the reasons already discussed in Section III, our solution space consists of hyperrectangles in the decision space, X g I, not single points, X. The corresponding performance criterion used to evaluate solutions, i/i, is the expected y value within X ... 

In the previous paragraphs we defined the solution format f, performance criterion i/r, mapping procedure /, and performance metric y that characterize our learning methodology for systems with a quantitative metric y. Here we will assemble all these pieces together and briefly discuss the search procedure, S (further details can be found in Saraiva... 

The most commonly used family of methods for cluster seeking uses optimization of a squared-error performance criterion in the form... 

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. 

Although the ability to minimize percolation is a performance criterion for final cover systems, limited data are available about percolation performance for final cover systems for both conventional and alternative designs. Most of the recent data on flux rates have been generated by two federal research programs, the Alternative Landfill Cover Demonstration (ALCD)84 and the Alternative Cover Assessment Program (ACAP). From these programs, flux rate performance data are available for 14 sites with demonstration-scale ET cover systems.5,39,85... 

Maintaining the effectiveness of the cover system for an extended period of time is another important performance criterion for ET covers as well as conventional covers. Short- and long-term... 

Optimization pervades the fields of science, engineering, and business. In physics, many different optimal principles have been enunciated, describing natural phenomena in the fields of optics and classical mechanics. The field of statistics treats various principles termed maximum likelihood, minimum loss, and least squares, and business makes use of maximum profit, minimum cost, maximum use of resources, minimum effort, in its efforts to increase profits. A typical engineering problem can be posed as follows A process can be represented by some equations or perhaps solely by experimental data. You have a single performance criterion in mind such as minimum cost. The goal of optimization is to find the values of the variables in the process that yield the best value of the performance criterion. A trade-off usually exists between capital and operating costs. The described factors—process or model and the performance criterion—constitute the optimization problem. ... 

Figure El.2a illustrates the trade-offs between efficiency and emissions, suggesting that more than one performance criterion may exist We are forced to consider maximizing efficiency versus minimizing emissions, resulting in some compromise of the two objectives.

There is a trade-off between energy expenditure and tracking quality in sensor networks [31]. Sensor activation strategies are naive activation in which all the sensors are active, randomized activation in which a random subset of the sensors are active, selective activation in which a subset of the sensors are chosen according to some performance criterion,... 

The steadystate error is another time-domain specification. It is not a dynamic specification, but it is an important performance criterion. In many loops (but not all) a steadystate error of zero is desired, i.e, the value of the controlled variable should eventually level out at the setpoint. 

This literature suggests two conclusions with respect to the role of growth as a primary performance criterion. First, it is only one of many that have been identified, and second, even in this context it is usually addressed as an adjunct to constraints on profitability. 

The ICLS model contains pure spectra of caustic, salt, water, and temperature. The conclusion of the model validation is that the ICLS model adequately describes the water peak shape changes due to caustic, salt, and temperature. Furthermore, it meets the required performance criterion for the prediction of caustic. The measures of performance are as follows (see Table 5.1 for a description of these figures of merit) ... 

The principle uses of the zinc borate Zn[B304(0H)3] are as a polymer additive and preservative for wood composites, such as oriented strand board (OSB). As a polymer additive it functions as a fire retardant synergist and modifier of electrical and optical properties. Its function as a fire retardant additive is discussed further below. A substantial amount of Zn[B304(0H)3] is used to improve the tracking index, which is an important performance criterion for polymers, such as polyamides (nylon) and polybutyl teraphtha-lates (PBT), used in electrical applications. 

Jones uses an integrated squared error loss value [L(x) as the performance criterion ... 

An optimization problem is a mathematical model which in addition to the aforementioned elements contains one or multiple performance criteria. The performance criterion is denoted as objective function, and it can be the minimization of cost, the maximization of profit or yield of a process for instance. If we have multiple performance criteria then the problem is classified as multi-objective optimization problem. A well defined optimization problem features a number of variables greater than the number of equality constraints, which implies that there exist degrees of freedom upon which we optimize. If the number of variables equals the number of equality constraints, then the optimization problem reduces to a solution of nonlinear systems of equations with additional inequality constraints. 

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