CBR-Conveyor: Solving the Inverse and Constraint Problems to Assist the Design of Pneumatic Conveyors

Abstract

Summary In this paper, we describe a system to assist the engineer in solving the design problem of pneumatic conveyors. The system is an example of how case-based reasoning (CBR) systems can collaborate with numerical models in order to increase their usability. It is shown how the CBR system is produced from a numerical model, and how it can solve several problems not directly addressed by the numerical model alone. These problems are those of inverse queries, and queries in the presence of constraints. The paper also discusses the solution to several difficulties which arose in querying the CBR system. These are connected with interpolation over nominal values and with interpolation in the presence of constraints. These problems are discussed generally, and examples of their solution for the pneumatic conveyor are presented in detail. This paper describes a CBR system developed on the back of a numerical model for pneumatic conveyors. Computational models of physical processes are an important tool for engineers in many the design of physical systems. They are often complex pieces of software, needing a considerable degree of knowledge and understanding to solve a specific engineering problem. The models are often deterministic in nature, so that they produce unknown outputs, from given specified inputs. The engineer will often use considerable skill in using such the model to solve a particular problem. Sometimes the model will be used in a trial and error fashion, attempting to find the right inputs for a given set of outputs ( i.e. the inverse problem). Often only some of the inputs and some of the outputs will be known, or simple constraints on inputs and outputs may apply. In all of these cases, the usability of the software is of importance. Usability is defined [1] as: The extent to which a product can be used by specified users to achieve specified goals with effectiveness, efficiency and satisfaction in a specified context of use. One way to improve usability is simply to build a database from a given numerical model and use the database to solve the queries. However, this is often not a practical alternative. Firstly, the dimensionality of the model is often too great to permit a feasible database from being produced with any satisfactory accuracy. Secondly, the model may take a long time to run, and the time expense involved in the production of a full database may be prohibitive. However, these problems may be overcome to a great extent by using only partial databases, as are common in case based reasoning systems. These systems employ comparatively small databases with well chosen cases. They rely for their accuracy on the retrieval of a set of near cases, and interpolating in some way, in order to construct the required solution. The paper gives illustrative examples of the use of a system called CBR-conveyor. The section gives selected output from the system, in answering some interesting queries. The paper also discusses how a CBR-conveyor can be derived from a numerical model, and then used to answer queries of the types given above. The basic problem associated with a general system of this type is that of interpolation. This problem is described in the paper. It consists of three sub problems: how do we interpolate over nominal values? How do we interpolate over multi valued mappings? And, how do we interpolate with constraints? The solutions to each of these problems are discussed. A brief description of the pneumatic conveyor problem and the numerical model used to simulate its action, are included. Several interesting problems have been solved to overcome this construction. The construction of a dissimilarity matrix for nominal parameters has been solved using the value difference method technique [1]. The solution of the interpolation over nominal values has been solved using the generalised Shephard nearest neighbour technique [2]. The examples show that the system gives a good solution to inverse and constraint problems, which can be confirmed by model runs.