In engineering design, customers usually provide product requirements in the form of a natural language while computer-aided design systems may prefer more formal and structured specifications. In this paper, a formalisation process is proposed to transform product requirements from its natural language descriptions to a formal specification. The formal specification is based on the product environment and the formulation of design problem, which identifies the components included in a design problem in terms of the product environment. Through the lexical, syntactic, and structure analysis of natural language descriptions of a design problem, the formalisation process identifies the product to be designed, its environment components, and their relations. A software prototype is developed to validate the formalisation process. An example of rivet setting tool design shows that both the formalisation process and software prototype are feasible.
A new bifurcation critical criterion of flip-Neimark-Sacker bifurcation is proposed for detecting or anticontrolling this type of codimension-two bifurcation of discrete systems in a general sense. The criterion is built on the properties of coefficients of characteristic equations instead of the properties of eigenvalues of Jacobian matrix of nonlinear system, which is formulated using a set of simple equalities and inequalities consisting of the coefficients of characteristic polynomial equation. The inequality conditions enable us to easily pick off the fake parameter domain whereas the equality conditions are used to accurately locate the critical bifurcation point. In particular, after the bifurcation parameter piont is determined, the inequality conditions can be used to figure out the feasible region of other system parameters. Thus, the criterion is suitable for two-parameterized family ofn-dimensional discrete systems. As compared with the classical critical criterion (or definition) of flip-Neimark-Sacker bifurcation stated in terms of the properties of eigenvalues, the proposed criterion is preferable in anticontrolling or detecting the existence of flip-Neimark-Sacker bifurcation in high-dimension nonlinear systems, due to its explicit parameter mechanism of the bifurcation.
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