An expert system, ETUDES - Expert Time integration control Using DEep and Surface Knowledge System, which addresses the determination of the timestep for time integration of linear structural dynamic equations, is described. This timestep may be also be applicable for a moderately nonlinear simulation of the same structure. The system also determines whether an explicit or implicit method is most efficient for the particular simulation. A production rule programming system written in OPS5 is used for the implementation of this prototype expert system. Issues relating to the expert system architecture for this application, such as knowledge representation, reasoning mechanisms, and structure are discussed. Two types of knowledge representations are used, one to hold information which uniquely identifies a simulation (scenario) and another type which encodes the causal knowledge used to obtain the scenario. The reasoning mechanism is a hybrid of computational and heuristic processes. The domain of this expert system has the characteristic of being rich in data but sparse in knowledge therefore it is found in the knowledge acquisition process that there exists no golden rule that can be applied for every simulation and that each simulation has unique attributes which require special attention when setting a timestep and its corresponding integrator. The domain is thus subdivided into subdomains such that within a restricted neighborhood of an abstract simulation space, sets of parameters may be safely interpolated so that the result is robust and reproducible. Since the system uses deep knowledge from the domain of structural dynamics, relationships from that domain are used to structure the knowledge so that different simulations can be compared and arbitrary simulations can be controlled with equivalent degrees of accuracy. The surface component interpolates the data within a restricted subdomain by utilizing a heuristic knowledge structure defined as a scenario. A scenario is defined as a discretized spectrum of n bands whereby a band is defined to have homogeneous dynamic characteristics and/or similar importance to the overall result within the band. Although the setting of the timestep is overall not a procedural process, the subtasks needed to navigate in tht: domain are procedural and thus the computational process forms part of the reasoning mechanism. Thus, the concept of computational artificial intelligence is introduced. Essentially, heuristic measures are used to estimate the effects of factors affecting the response and thus the error. These factors are; the load distribution, the stiffness distribution, and the load-structure interaction distribution. The key feature is that only distributions are needed since all parameters are referenced to the energy of the system defined in terms of the response. Thus, absolute quantities which would be known only a postiori are not needed.

The domain knowledge is comprised of the analysis of error in time integration and the behavior of structural dynamic systems. Error arising in numerical simulations is categorized into method-dependent (arising from the discrete aspect of the integrator) and method-independent (arising from implementation of algorithm on a finite precision machine and the spatial discretization error). For the purposes of analysis, method-independent errors are assumed and verified to be negligible. The various types of method-dependent time integration errors; frequency distortion (a nonlinear compression/expansion of the temporal axis) and amplitude attenuation (a numerical damping which can differ from the actual system damping), and methods for measuring their effects are examined. These measures vary in terms of their domain of measure; some measure error over the entire spatial domain others only at a point in space. The same can be said for the temporal domain. From these four combinations the measure over the time domain for the entire simulation length for one point in space is chosen as being the best trade-off between accuracy and computational complexity and is called the cumulative squared error. The point in space is ideally the point at which the spectral displacement occurs. Two types of approximations are introduced: a truncated spectrum model and a reduced band spectrum. The truncated model references estimates of the first n modes of the system whereas the reduced band spectrum approximates between the modes of the system, thus corresponding to a reduction in the degrees of freedom in the frequency domain. Mathematical inequalities on the aggregate effect of each component are then used to bound the error. Error estimation using a priori information is considered and described within the framework of the discrete spectrum models. The conditions governing the definition of an appropriate scenario are derived from the standpoint of structural dynamics, in particular modal analysis. Considerations which effect the setting of error tolerances are introduced such as response spectrum content, spectrum information content, and external error masking. Two general types of algorithms are proposed for the setting of the timestep once the scenario is heuristically defined; - an iterative model which accounts for the current characteristics of the simulation and a single-iterate model which produces a pareto-optimal result based on variations of a typical simulation. The prototype is evaluated by measuring its performance in various benchmark model problems. Currently available methods are used as a basis of reference to show the expert system's sensitivity to various parameters which affect the error in a simulation. The results prove to be robust for reasonable subdomains. The limitations of the system and future research directions are given with regard to increasing the amount of knowledge extraction that can be effected on the user input and to the degree of applicability for this system for more nonlinear systems.

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