Stephan Rudolph

On topology, size and generalization of non-linear feed-forward neural networks

Abstract The use of similarity transforms in the design and the interpretation of feed-forward neural networks is proposed. The method is based on the so-called Buckingham Theorem or Pi Theorem and is valid for all neural network function approximation problems which belong to the class of dimensionally homogeneous equations. The new design method allows the a priori determination of a minimal topology size of the first and last network layer. Finally, the correct and unique pointwise generalization capability of the new so-called similarity network topology is proved and illustrated using two examples.

On a Grammar-Based Design Language That Supports Automated Design Generation and Creativity

One of the major obstacles towards the realization of automated creative design lies in the restricting design frames explicitly or implicitly imposed by common means for design representation. In this paper it is proposed to extend these frames by improving the design representation with a description technique that is more suitable to capture conceptual decisions taking place in engineering during early design phases. In this context especially the description of topological arrangements or functional dependencies is emphasized. It is shown that the application of grammar techniques known from formal languages is well suited for the development of a compact description language for engineering design objects. This is illustrated in an example for a formal language of truss designs. Furthermore it is investigated how this new design representation approach can support “creative” engineering and where possible future research along these lines can be done.

DESIGN LANGUAGE FOR AIRPLANE GEOMETRIES USING THE UNIFIED MODELING LANGUAGE

The design language allows the construction of a variety of airplan designs. The syntax of the design language relies on the standardized Unified Modeling Language (UML) and consists of an object-oriented vocabulary (i.e. points, lines, profiles, wings, etc.) comparable to building blocks, and design rules (i.e. building laws) which represent the building knowledge used. In the terminology of graph-based design languages, the building blocks are the information objects which represent the static aspects of the design because they represent indivisible design entities. They are represented as UML classes and instances and their interrelation forms an object-oriented class hierarchy. The design rules represent the dynamic aspects of the design and express the building knowledge as stepwise activities. Finally, a production system (i.e. a specific rule set) is able to create an airplane geometry and generates design variants through manual modifications of the production system.Copyright

Optimized time-frequency distributions for acoustic signal classification

Successful acoustic signal classification requires the choice of an appropriate problem-adapted signal representation and the extraction of an invariant feature vector for classification. The two scientific core questions however, what is the best signal representation and what is acoustic resemblance, are theoretically still unanswered. Both the definitions of an optimum time-frequency representation (TFD) and of the correct acoustic invariants need some a priori knowledge about the inherent structure and symmetries of the acoustic time series as well as some knowledge about the differences between the classes to be distinguished. In this work, the central parts are a data-driven optimization of the parameterized TFD by maximizing the distance measure of the different sound classes and a geometric similarity concept based on dimensional analysis for defining dimensionless acoustic invariants. Starting from a parameterized TFD of the acoustic signals the joint moments are calculated. Dimensional analysis is used for defining dimensionless invariants under geometric transformations of the TFDs. The significance of these invariants is shown on the basis of the acoustic class of whistling and booming noise (WBN). Using these geometric invariants, the detection rate of WBN can be improved. However, the detection rate is heavily dependent on the chosen TFD. By maximizing the distance measure of the sound classes as a function of two TFD-kernel parameters, the optimum TFD in the sense of the available signal structure can be found and is exemplified by means of an industrial WBN dataset. For validation purpose of the kernel optimization, some acoustic signals in the sense of analytically known asymptotic limit cases with predetermined behavior are given.

An Evolutionary Approach to the Inverse Problem in Rule-Based Design Representations

In this paper design grammars as a rule-based representation formalism for design generation are discussed and used for the construction of transmission towers. In the context of such a rule-based representation technique several theoretical questions such as the completeness and capacity of a representation are still unanswered. Especially the question whether a given design object can be generated within a certain design grammar is still open and is known as the inverse problem. In the framework of the transmission tower design grammar an evolutionary approach for the solution of the inverse problem, i.e. the identification of a grammar that generates a predetermined pylon, is shown. The solution of the inverse problem is based on an evolutionary search algorithm whereby the fitness function is applied on the geometry of the design object and is therefore independent of the specific implementation of the design grammar. The design grammar search algorithm uses a combination of design space exploration techniques together with methods from pattern recognition and is shown in two simulation examples.

Exploiting Similarity Theory for Case-Based Reasoning in Real-Valued Engineering Design Problems

The framework of dimensional analysis is used for case-based reasoning. For all case descriptions in engineering and physics consisting of real-valued quantities with physical units, the Pi-Theorem of Buckingham can be shown to derive appropriate similarity conditions and provide an appropriate case adaptation.

On Engineering Design Generation with XML-based Knowledge-Enhanced Grammars

One of the bottlenecks in conceptual engineering design is the pure amount of design information which the design engineer needs to take into consideration. The design information is heterogeneous and consists of the design object behavior (i.e. the physics), its intended geometrical form and composition (i.e. the geometry) and miscellaneous other information pieces concerning manufacturing cost and more.

From data to models: synergies of a joint data mining and similarity theory approach

Successful model building techniques in the natural sciences can usually be classified into the two categories of inductive and deductive methods. If numerical data is the only source of available knowledge in a certain problem, then it is obvious that inductive techniques seem to be the method of choice. Recently, data mining has received much attention to extract hidden knowledge from very large databases, and is, therefore, in this framework considered to be an inductive approach. Deductive methods, on the contrary, rely on a rigorous application and the explicit knowledge of the underlying domain, using first principles to establish a mathematical model of the problem, typically yielding governing equations. This paper focuses on the establishment of an intermediate knowledge representation level, between inductive and deductive knowledge identification techniques. This intermediate knowledge representation level is based on the notion of group transforms, and can be shown to be a mathematically necessary condition in the existence of any correct model representation. The synergy effect of using group transforms in both the inductive data mining and the deductive similarity theory approach can be demonstrated to be conceptually advantageous and is observed to be numerically superior to conventional techniques. The limitations and underlying assumptions of the approach are identified and discussed using example.

ON A SYMBOLIC CAD FRONT-END FOR DESIGN EVALUATION BASED ON THE PI-THEOREM

The current implementation and theoretical foundation of a possible symbolic front-end for CAD systems for the evaluation of engineering design objects during the design process is described. Based on implicit functional descriptions of the design object (i.e. the design parameters contained in the database of the solid modeler), the Pi-Theorem is used to derive the associated dimensionless groups. Based on the assumed validity of the evaluation hypothesis that “any minimal description in the sense of the Pi-Theorem is an evaluation”, these automatically generated dimensionless groups serve then as a symbolic representation for the purpose of design object evaluation.

Design computing and cognition (dcc'10)

† Assessing the Impact of Complexity Science in Design † Design Communication † Understanding Functions † Computational Design Synthesis: Knowledge Representation † Conceptual Computational Design Tools: Bridging the Gap Between Abstract Requirements and Concrete Implementation Strategies † Design Creativity † Shape Grammar Implementation: From Theory to Useable Software † Research Methods for Design Cognition