Selection performance index

The decision on the type of performance index to be selected depends upon the nature of the control problem. Consider the design of an autopilot for a racing yacth. 

A simplified performance index for stiffness is readily obtained from the essentials of micromechanics theory (see, for example. Chapter 3). The fundamental engineering constants for a unidirectionally reinforced lamina, ., 2, v.,2, and G.,2, are easily analyzed with simple back-of-the-envelope calculations that reveal which engineering constants are dominated by the fiber properties, which by the matrix properties, and which are not dominated by either fiber or matrix properties. Recall that the fiber-direction modulus, is fiber-dominated. Moreover, both the modulus transverse to the fibers, 2, and the shear modulus, G12. are matrix-dominated. Finally, the Poisson s ratio, v.,2, is neither fiber-dominated nor matrix-dominated. Accordingly, if for design purposes the matrix has been selected but the value of 1 is insufficient, then another more-capable fiber system is necessary. Flowever, if 2 and/or G12 are insufficient, then selection of a different fiber system will do no practical good. The actual problem is the matrix systemi The same arguments apply to variations in the relative percentages of fiber and matrix for a fixed material system. 

Our goal is to estimate the function P(r) from the set of discrete observations Y(tj). We use a nonparametric approach, whereby we seek to estimate the function without supposing a particular functional form or parameterization. We require that our estimated function be relatively smooth, yet consistent with the measured data. These competing properties are satisfied by selecting the function that minimizes, for an appropriate value of the regularization parameter X, the performance index ... 

In order to ensure successful minimization of the performance index and to enhance our ability to determine the global optimum, we select the corresponding finite-dimensional representation in a different manner than before. We again use B-splines to represent the unknown functions ... 

The effects of non-uniform distribution of the catalytic material within the support in the performance of catalyst pellets started receiving attention in the late 60 s (cf 1-4). These, as well as later studies, both theoretical and experimental, demonstrated that non-uniformly distributed catalysts can offer superior conversion, selectivity, durability, and thermal sensitivity characteristics over those wherein the activity is uniform. Work in this area has been reviewed by Gavriilidis et al. (5). Recently, Wu et al. (6) showed that for any catalyst performance index (i.e. conversion, selectivity or yield) and for the most general case of an arbitrary number of reactions, following arbitrary kinetics, occurring in a non-isothermal pellet, with finite external mass and heat transfer resistances, the optimal catalyst distribution remains a Dirac-delta function. 

The problem is stated as a minimax problem, where the maximum value of the performance index with respect to selection of the uncertain parameter values is minimized with respect to the control variables, the design decisions and the structural parameters. 

The performance indexes, which define an optimal catalyst distribution, include effectiveness, selectivity, yield and deactivation rate. The key parameters, affecting the choice of the optimal catalyst profile, are the reaction kinetics, the transport resistances, and the production cost of the catalyst. An extensive review of the theoretical and experimental developments in this area is available [20]. Two typical examples to demonstrate the importance of an appropriate distribution of the active components are now described. 

One possible compromise here would be to develop an index based on the performance of a neutral agent that only mechanically removes viruses from hands. In the past, nonmedicated soaps have often been used for this purpose. However, soaps on the market differ widely, especially in properties such as pH and detergent action. Tap water also differs at different geographical locations. Therefore, a simple, safe, and readily available solution such as standard hard water (e.g., with 200 ppm hardness) could be used to establish the reference point for this index. Product efficacy claims could then be allowed at a certain differential above the mechanical virus removal with hard water. Manufacturers could publish the performance index of their formulation on the label to aid in product selection. To prevent minor differences in indices being used as a sales feature, a simple product classitication scheme could be developed. 

Certain properties, such as cost or density, are always included in a hierarchical classification. Other properties are selected by elimination on the basis of a limit value - such is often the case for temperature resistance. However, many limit values are difficult to determine. Indeed, these values would require the use of an often-complex model, limited to a specific use case. If we do not have a limit value, to avoid introducing an arbitraiy limit value, we are forced to feed the properly in question into a performance index. This technique enables us to take account of that property, but it is liable to favor materials whose performances may be excessive in relation to the function required of them. There are material properties, which are not subject to a quantitative physical measurement, or which are subject to a crade qualitative classification. In this case, the limit value can only be fixed arbitrarily by a classification relative to other materials whose performances are knowa... 

To compare the performance of various materials and to select the most appropriate candidates for a given application or a specific design, a novel approach was introduced by Michael F. Ashby that consists in combining several relevant properties (e.g., mechanical, thermal, or electrical) to yield a performance index. Then plotting one property against another onto a log-log plot, together with the relevant performance indices, allows one to do the following ... 

The data in Table 5.5 indicate that the separation characteristics of each feed are quite different. By repeated use of the automated selection procedures in FDS, the information shown in Table 5.6 can be produced. The numbers listed under the subheadings D and W indicate the relative performance index of the equipment as a solids dewatering or cake washing device respectively (better performance is associated with greater index values). A indicates that the equipment is not suitable for the particular separation. 

Lavan Method The Levy and Lavan (2006) fully stressed analysis/redesign procedure uses a single active ground motion, selected based on its high displacement or energy demands. A response analysis is performed using this ground motion, and the objective function, or performance index, is calculated as the value of a chosen response parameter at story / normalised by an allowable value. In this study the parameter chosen is the interstory drift 8-. 

Pi/i has been selected as a basis for the evaluation of the performance index since it can be determined a priori and without any previous knowledge of the measurements. The parameters required for its computation are R, Q and Po- The measurement error covariance R is given by the quality of the sensors while the process noise covariance Q is generally more difficult to determine because one does not have the ability to directly observe the process. If an ideal process is assumed, where all variability sources are included in the model, Q = 0. Finally, the value of Po is selected to be equal to R (practical initialisation for the filtering process). Under conditions where Q and R are constant, both the estimations of P i error covariance and the Kalman gain ki stabilise quickly and then remain constant. Therefore, the asymptotic value of Pi/i can also be used as performance measure. In fact, when the Kalman filter is applied to a system that is continuous and dynamic, the latter is preferred, whereas when conditions reflect short lived batch systems the former is more appropriate. 

Based on the fact that past and present control actions affect the future response of the system, a receding-time horizon is selected. The trajectory of the system is predicted and compared to the desired trajectory. The control actions are then determined from the minimisation of a performance index over the given time horizon, r ... 

In order to calculate J as a function of r, the Tin that yields the maximum catalyst temperature allowed at r = 0 for each of r values selected was first calculated. This allows calculation of J with the procedures in Figure 10.21. The smallest value of 4>g was 2.S, and therefore, Q can be set to zero. Values of the performance index J were then calculated using the procedures of Figure 10.21 for the selected r values. The values of J normalized with respect to that of J for r of 20 seconds are plotted in Figure 10.22 for 6 = 2 X 10 min (1.4 days) and various values... 

Inspections of the workplaces at randomly selected intervals to observe the items and whether the performance is correct or not. Plotting the safety performance index on a control chart. The safety performance index is defined as the percentage of the observed items that are judged as correct. 

Both shape and materials selections should be carried out together since shaping depends on the type of material - for example ceramics are more difficult to shape than metals. Let us concentrate on mechanics, which is the focus of the book, and more precisely now on the mechanical design that has been extensively reviewed by Ashby (2001). Several performance indices are listed in Table 2.5 according to the application. At this stage, these indices do not yet consider shape. Let us take an example to determine the performance index and determine how shape influences this performance. This will allow us to introduce the shape factor and hence understand how shape contributes to object strength. 

Then the charts can be used to select shaped materials that are placed on the chart as artificial ones at coordinates E =EI. A shaped material is positioned relative to the unshaped one on the chart as shown in Figure 2.14. As expected, a shaped material offers better performance than an unshaped one. In fact, on this chart, the performance index E Ip that corresponds to a beam with minimum weight and stiffness prescribed is represented by lines of slopes +2 (as the performance usually is identical on the same line). It is then observed that the shaped material is positioned towards the left and bottom side as compared to the unshaped one. The magnitude of the achieved improvement can be predicted plotting the (E, p ) position. Interestingly, composites like wood having natural microshapes show the best performance for the designed beam. 

GORE. The CORE Electronic Chemistry Library is a joint project of Cornell University, OCLC (On-line Computer Library Center), Bell Communications Research (Bellcore), and the American Chemical Society. The CORE database will contain the full text of American Chemical Society Journals from 1980, associated information from Chemical Abstracts Service, and selected reference texts. It will provide machine-readable text that can be searched and displayed, graphical representations of equations and figures, and full-page document images. The project will examine the performance obtained by the use of a traditional printed index as compared with a hypertext system (SUPERBOOK) and a document retrieval system (Pixlook) (6,116). 

However, in general these fabrication and performance advantages are common to all plastics and so a decision has to be made in regard to which plastic would be best for a particular application. Rather than compare the basic raw material costs it is better to use a cost index on the basis of the cost to achieve a certain performance. Consider again the material selection procedures illustrated in Section 1.4.1 in relation to strength and stiffness. 

A third parameter to consider is the column construction. Thus the sample applicator should provide optimal sample application to give the most performance possible out of the packed bed. Constructions should also allow simple, fast, and reproducible packing of the column. Because costs for repacking of columns are a substantial operating cost item in industrial chromatography, the selection of column construction from this point of view is also important. Some novel column constructions allow very simple procedures both for laboratory and for industrial scale (e.g., INdEX columns, see Section V). 

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