Otto, K. N., and Antonsson, E. K., 1991. "Trade-off strategies in engineering design". Research in Engineering Design, 3 (2), pp. 87--104.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....assess designs; often the only real metric is the consumer s purchase which may even be biased by many other factors such as marketing and advertising. The designer needs some basis to quantify the comparison between two designs. Measuring a design is the topic of myriad research. Suh (1990) Otto and Antonsson (1991), Otto (1993) Pugh (1991) Ullman (1992) have looked at metrics in a general sense. Several researchers have focused on a single aspect of a design andshown techniques to improve a design with respect to that one performance criterion. These are known as the Design for X strategies where X can ....

K. N. Otto and E. K. Antonsson, "Trade--Off Strategies in Engineering Design", Research in Engineering Design, Vol 3, 1991, pp 87--103.

....an aggregation function P . In previous work on the M o I, aggregation functions were considered to act on preference values, not preference functions; a more precise definition of aggregation will be given in Chapter 5. At first, the M o I made use of two different aggregation functions [57], the non compensating P min (# 1 ,# 2 ) min(# 1 ,# 2 ) for situations where the overall performance is dictated by the lowest performing attribute, and the compensating P# (# 1 ,# 2 ) # # 1 # 2 , when high performance on one attribute is deemed to partly compensate for lower performance on ....

....on the individual variables. In this example, the individual design preferences were all weighted 103 0 20000 40000 60000 80000 100000 Bending Stiffness 0.0 0.2 0.4 0.6 0.8 1.0 p Figure 7. 3: Performance preference equally, and were allowed to trade off in a non compensating manner [57]. The aggregated design preference traded off in a compensating manner with the performance preference [57] In a traditional design process, the vehicle structure engineer would seek to maximize the bending stiffness, and then make trade offs from the stiffest design in response to the needs of ....

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Kevin N. Otto and Erik K. Antonsson. Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87--104, 1991.

....a basis for discussing the contributions of this thesis. The practical value of the methods developed in this work will be demonstrated to directly address French s concerns. 1. 1 Organization of Thesis This thesis builds on the work of Wood and Antonsson [66, 67, 68, 69] and Otto and Antonsson [43, 44, 46, 47, 69]. Their work has laid a broad theoretical foundation for the method of imprecision. The work described in this thesis seeks, through examining the specific rather than the general, and the practical rather than the theoretical, to bring the method closer to implementation in industry. Its two ....

....p j (p j ) p j (f j ( # d) o ( # d) P # d 1 (d 1 ) dn (d n ) p 1 (f 1 ( # d) pq (f q ( # d) # . # The aggregation function P reflects the trade off strategy, which indicates how competing attributes of the design should be traded off against each other [44, 45]. An airplane can be made lighter, but this action will probably increase manufacturing cost. One of the most difficult aspects of product development is recognizing, understanding, and managing such trade offs in a way that maximizes the success of the product. 60] p5) The trade off ....

Kevin N. Otto and Erik K. Antonsson. Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87--104, 1991.

....solution should use combination methods that are based in domain expertise; the methods of combination, like the calculation modules, should permit easy modification. Combination functions such as other weighted means (those between min and max) have been used previously in preference aggregation (Otto and Antonsson, 1991; Scott and Antonsson, 1995) and the fuzzy sets literature (Zimmermann, 1985) has an extensive treatment of t norms (less than min) and t conorms (greater than max) ffl One feature of this sort of analysis, when it is handled informally by a human designer, is that the subfunctions (or ....

Otto, K. N., and Antonsson, E. K., 1991, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp. 87--104.

....Imprecision (M o I) Wood and Antonsson, 1989) a formal method for representing and manipulating uncertainty in engineering design employing the mathematics of fuzzy sets. It has been shown that the M o I can be used to combine design information using a variety of different trade off strategies (Otto and Antonsson, 1991; Scott and Antonsson, 1995) Other references have developed the M o I for industrial application (Law and Antonsson, 1994) Current work undertakes to use the structure of the M o I to formalize the presently informal negotiation process. The mechanisms employed by the M o I for the ....

.... that maximize o , i.e. designs d such that: o ( d ) o = supf o ( d) j d 2 Xg: The aggregation function P reflects the design or tradeoff strategy, which indicates to what degree competing attributes of the design should be traded off against each other (Otto and Antonsson, 1991; Scott and Antonsson, 1995) The appropriate design strategy is dictated by the design problem. A design problem will in general require a hierarchy of different trade off strategies which successively aggregate design attributes. FORMALIZING NEGOTIATION The M o I has been applied previously as ....

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Otto, K. N., and Antonsson, E. K., 1991, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp. 87--104.

.... 1985) The design preferences d ( # d) which are specified on the DVS, can be mapped onto the PVS by use of the extension principle (Zadeh, 1975) The various preferences are then combined with an aggregation function P ; at first, the M o I made use of two different aggregation operators (Otto and Antonsson, 1991), the non compensating P min ( 1 , 2 ) min( 1 , 2 ) for situations where the overall performance is dictated by the lowestperforming attribute, and the compensating PP ( 1 , 2 ) # 1 2 , when high performance on one attribute is deemed to partly compensate for lower performance on ....

Otto, K. N., and Antonsson, E. K., 1991, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp. 87--104.

.... o = P III Gamma P I ( d1 ; dn ) P II ( p1 ; pq ) Delta = P III ( d ; p ) 1) The aggregation functions P I , P II , and P III reflect the trade off strategies for each aggregation, i.e. how competing attributes of the design should be traded off against each other (Otto and Antonsson, 1991; Scott and Antonsson, 1996) The trade off strategy formalizes the designer s balancing of conflicting goals and constraints. The choice of aggregation function is not one that the designer is free to make: the appropriate trade off strategy is usually dictated by the design problem. Although it ....

Otto, K. N., and Antonsson, E. K., 1991, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp. 87--104.

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Otto, K. N., and Antonsson, E. K., 1991. "Trade-off strategies in engineering design". Research in Engineering Design, 3 (2), pp. 87--104.

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Otto, K. N., and Antonsson, E. K., 1991. "Trade-off strategies in engineering design". Research in Engineering Design, 3 (2), pp. 87--104.

....a trade off strategy (or aggregation) determines which of the undominated (Pareto) points is selected as best satisfying the multiple criteria. Choosing an appropriate trade off strategy is a crucial part of the engineering design process, principally because it can dramatically affect the result [31]. A family of functions, appropriate for engineering design, to perform this aggregation is introduced in [39] It can be highly beneficial for the engineer to consider sets of designs [3] As the design process proceeds, the size of the set of designs under consideration is reduced, as the ....

....experience and intuition. For multi attribute problems, decision analysis methods are used to assess the performance of sets of designs (the Method of Imprecision [3, 49] and to trade off multiple competing aspects of the design (utility theory [18] matrix methods [34] and aggregation methods [31, 39]) Integrated Subdivision Modeling for Thin Shell Structures, F. Cirak, et al. 13 012345678910 x 0 1 2 3 4 5 6 7 8 9 10 x constraints undominated points 2 1 admissible region inadmissible region Figure 7: A Set of Pareto Points. Finally, engineers routinely use models of ....

OTTO, K. N., AND ANTONSSON, E. K. Trade-Off Strategies in Engineering Design. Research in Engineering Design 3, 2 (1991), 87--104.

....and Seering [20] for interval mathematics. The concept is extended here to different uncertainty forms. Modeling of Uncertainty Every uncertainty form discussed above shall be directly modeled. That is, the initial design parameter uncertainty shall be modeled using the method of imprecision [8, 22] where each design parameter value is given a rank from zero to one to indicate degree of preference. This forms a preference function over each design parameter and performance parameter indicating degree of preference for values. Co dependencies are possible, see [8] Similarly, probabilistic ....

....method of imprecision [8, 22] where each design parameter value is given a rank from zero to one to indicate degree of preference. This forms a preference function over each design parameter and performance parameter indicating degree of preference for values. Co dependencies are possible, see [8]. Similarly, probabilistic noise parameters [10] shall have their values ranked with degrees of probability. Finally, possibilistic noise parameters [10] shall have their values ranked with degrees of possibility. All these uncertainties reflect different phenomena, and consequently will have ....

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K. N. Otto and E. K. Antonsson. Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87--104, 1991.

....uncertain parameter and d is the uncertainty on variable d. They are also similar in that they all conform to the first three restrictions of Table 1. The axioms shown in Table 1 have been proposed as the minimum set of restrictions for an engineering design combination (aggregation) function P (Otto and Antonsson, 1991), where i is the uncertainty associated with the i th aspect of the design. The 1 Variational and parametric modeling systems begin to approach this, by letting the designer specify a dimension precisely, but with the idea that it will be modified later. 2 Joseph G. Gavin, Jr. discussing ....

....may contribute more heavily to the combined result than others. Combination functions are also referred to as metrics. A combination function P is a formalization of the process of trading off competing design attributes, and should satisfy the restrictions for engineering design proposed in (Otto and Antonsson, 1991) and shown in Table 1. Combination func3 0 1 d d Figure 1. Example imprecise design variable tions can be divided into two classes: compensating and non compensating. A compensating combination function (e.g . sum) will produce an overall measure of a design alternative where aspects that ....

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Otto, K. N., and Antonsson, E. K., 1991, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp. 87--104.

....and the Kepner Tregoe method (Hauser and Clausing, 1988; Pugh, 1981; Kepner and Tregoe, 1981) among others. Current research efforts are pursuing other design engineering decision making tools such as fuzzy sets, design strategies, utility theory, and interval analysis (Wood and Antonsson, 1989; Otto and Antonsson 1991; Thurston 1991; Ward and Seering, 1990) While these tools offer varying degrees of assistance to the engineering design task, none address the specific problems encountered with evaluating designs that exhibit hierarchical functional topologies, such as in the design of precision machines ....

....(Thurston, 1991) but is intended for single decision makers and vector objectives. We address hierarchical objective structures, and simplicity for team designs. Also, a more general method for preliminary computer aided design decision making has been developed (Wood and Antonsson, 1989, Wood, Otto, and Antonsson, 1991). Again, DRAFT, Marsh et al. Hierarchical Decision Making in Machine Design July 29, 1993 10 such work is intended for single decision makers. Otto and Antonsson, 1991) present methods for trading off vector criteria numerically using different strategies. In general, expansion of such ....

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Otto, K. and E. Antonsson. Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87-104, 1991.

....so we seek design configurations d such that ( d ) supf ( d) j d 2 Xg. The combination function P must satisfy continuity and annihilation i.e. P[ 1 ; 0; n q ] 0) 2] Additional restrictions that P should satisfy for engineering design have been proposed in [3]. P reflects the design strategy [3, 4] Suppose that the designer wishes to maximize his satisfaction with the least satisfactory aspect of the design. This is a conservative or non compensating design strategy. The design is judged by its lowest preference ( d i or p j ) and P is min: ....

....d such that ( d ) supf ( d) j d 2 Xg. The combination function P must satisfy continuity and annihilation i.e. P[ 1 ; 0; n q ] 0) 2] Additional restrictions that P should satisfy for engineering design have been proposed in [3] P reflects the design strategy [3, 4]. Suppose that the designer wishes to maximize his satisfaction with the least satisfactory aspect of the design. This is a conservative or non compensating design strategy. The design is judged by its lowest preference ( d i or p j ) and P is min: d) min Theta d1 ; dn ; ....

[Article contains additional citation context not shown here]

K. N. Otto and E. K. Antonsson. Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87--104, 1991.

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Otto, K. N., and Antonsson, E. K., 1991a, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp. 87--104.

....to represent the possibilities. Zadeh s extension principle, for example, can be used to propagate imprecise understanding through relevant calculations and models. A comprehensive review of modeling imprecision and uncertainty in engineering design is given in [8] Further work can be found in [6, 7, 9, 10, 11, 12]. For imprecision to be used during a design process, it must be represented. This means that a designer s understanding of the usefulness of values in a model must be represented, say with fuzzy numbers. A well defined procedure for specifying the fuzzy numbers must be given, however, for design ....

K. N. Otto and E. K. Antonsson. Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87--104, 1991.

....uncertain variable and d is the uncertainty on variable d. They are also similar in that they all conform to the first three restrictions of Table 1. The axioms shown in Table 1 have been proposed as the minimum set of restrictions for an engineering design combination (aggregation) function P [58], where i is the uncertainty associated with the i th aspect of the design. The discussion below indicates where these theories diverge among themselves and with optimization theory, matrix methods, and the MoI. Imprecision vs. Uncertainty. Uncertainty, which usually represents uncontrolled ....

....may contribute more heavily to the combined result than others. Combination functions are also referred to as metrics. A combination function P is a formalization of the process of trading off competing design attributes, and should satisfy the restrictions for engineering design proposed in [58] and shown in Table 1. Combination functions can be divided into two classes: compensating and non compensating. A compensating combination function (e.g. sum) will produce an overall measure of a design alternative where aspects that perform well can compensate for aspects that perform poorly. ....

[Article contains additional citation context not shown here]

OTTO, K. N., AND ANTONSSON, E. K. Trade-Off Strategies in Engineering Design. Research in Engineering Design 3, 2 (1991), 87--104.

No context found.

Otto, K. N., and Antonsson, E. K., 1991a, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp.

....performs a trade off, such that some aspects of a design may contribute more heavily to the combined result than others. A aggregation function P is a formalization of the process of trading off competing design attributes, and should satisfy the restrictions for engineering design proposed in [Otto and Antonsson, 1991]. Aggregation functions can be divided into two classes: compensating and non compensating. A compensating aggregation function (e.g. sum) will produce an overall measure of a design alternative where aspects that perform well can compensate for aspects that perform poorly. For example, a ....

....the customer to specify preferences over a range of values, rather than a crisp constraint that may be moved by negotiation later in the design process. Because the method was developed specifically for engineering design, the trade off combination functions meet the restrictions discussed in [Otto and Antonsson, 1991]. A choice of two basic combination functions is available to aggregate the preferences for the attributes of the design: the (non compensating) min and a (compensating) product of powers. A family of aggregation functions suitable for engineering design decision making are presented in [Scott and ....

Otto, K. N. and Antonsson, E. K. (1991). Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87--104.

....is, some form of (8) is always used to normalize each extensively measurable scale into a scale that can be relatively compared by the designer across the different objectives, or can be multiplied by a weighting factor. This holds true whether operating with utility theory [10, 30] imprecision [18, 19, 20], goal programming [3, 9] weighted sums [7] or any method that uses an overall figure of merit over real valued objectives. The discussion is now complete for numerical evaluations. There are times, however, when evaluations are made without numbers. The next section will discuss these ....

K. N. Otto and E. K. Antonsson. Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87--104, 1991.

....of Imprecision (MoI) Wood and Antonsson, 1989) a formal method for representing and manipulating uncertainty in engineering design employing the mathematics of fuzzy sets. It has been shown previously that the MoI can be used to combine design information using different trade off strategies (Otto and Antonsson, 1991). Specifically, the designer can combine preferences in a compensating or non compensating manner, using one of two aggregation functions. The MoI can handle importance weightings using these two trade off strategies (Law and Antonsson, 1995a; Otto and Antonsson, 1991) and different attributes ....

....trade off strategies (Otto and Antonsson, 1991) Specifically, the designer can combine preferences in a compensating or non compensating manner, using one of two aggregation functions. The MoI can handle importance weightings using these two trade off strategies (Law and Antonsson, 1995a; Otto and Antonsson, 1991), and different attributes can be combined hierarchically in hybrid strategies. Research applying both trade off strategies to industrial applications is ongoing (Law and Antonsson, 1994) A class of aggregation functions on fuzzy sets called t norms and t conorms has been studied in some detail ....

[Article contains additional citation context not shown here]

Otto, K. N., and Antonsson, E. K., 1991, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp. 87--104.

....parameters. These form a dependent variable space Y. There are also membership specifications, independent of those specified on X , placed on Y. Typically, all of the imprecise quantities are combined to solve the complete model; that is, select precise values for the design parameters [4]. This is calculated by maximizing the overall membership over the set of design parameters X . Examples are given in [4] However, it is usually of considerable interest to observe the design parameter membership expressed on the performance parameter space. This can be calculated using the ....

....specified on X , placed on Y. Typically, all of the imprecise quantities are combined to solve the complete model; that is, select precise values for the design parameters [4] This is calculated by maximizing the overall membership over the set of design parameters X . Examples are given in [4]. However, it is usually of considerable interest to observe the design parameter membership expressed on the performance parameter space. This can be calculated using the extension principle [8] as will be discussed subsequently. Doing so allows a comparison of the membership functions specified ....

K. N. Otto and E. K. Antonsson, Trade-Off Strategies in Engineering Design, Research in Engineering Design 3 (1991) 87--104.

....must consider a cloud of alternative designs. A computational tool that considers individual designs separately provides limited insight into the structure of the cloud of alternatives. A more systematic methodology is required: one that explicitly models imprecision. The Method of Imprecision [1, 2, 3] uses the mathematics of fuzzy sets to represent and manipulate imprecise preliminary design information. The Imprecise Design Tool [3] a computational implementation of this methodology, supports preliminary design decisions based on imprecise information, and accepts any design evaluation ....

.... the functional requirements p j (p j ) p j (f j ( d) o = P Gamma d 1 ; dn ; p 1 ; pq Delta : The combination function P reflects the design or trade off strategy, which indicates how competing attributes of the design should be traded off against each other [1]. a k a k p j a k p j min a k f j p j a k max d d d d 2 1 D DVS j y Figure 1. The Level Interval Algorithm. Imprecision Calculations After specifying design preferences d 1 ; dn and functional requirements p 1 ; pq , and identifying the appropriate design ....

Kevin N. Otto and Erik K. Antonsson. Trade-Off Strategies in Engineering Design. Research in Engineering Design, 3(2):87--104, 1991.

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Otto, K. N., and Antonsson, E. K., 1991, "Trade-Off Strategies in Engineering Design," Research in Engineering Design, Vol. 3, (No. 2), pp. 87--104.

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