Software and Analysis Techniques

Simulation Reduction Using the Taguchi Method: A Feasibility Study and an Analytic Model for Footprint Dispersions and its Application to Mission Design

Farrokh Mistree, Ph.D., Uwe Lautenschlager, Stein Erikstad, J.R. Jagannatha Rao, and Yi-Chao Chen, Ph.D., Department of Mechanical Engineering

This project had two distinct thrusts. In the simulation reduction study, Prof. Mistree and his colleagues used the principles of Taguchi's Robust Design Method to develop an efficient alternative to existing methods of computing reliability of simulations. In the model for footprint dispersions, J. R. Jagannatha Rao and Yi-Chao Chen developed an analytic method for computing the reliability of a space vehicle landing in a desired target area.

Mistree's team used the Taguchi method, based on a few basic concepts:

Quality should be designed into the product and not inspected into it,
Quality is best achieved by minimizing the deviation from the target. Products should be so designed that they are immune to uncontrollable environmental factors, and
The cost of quality should be measured as a function of deviation from the standard, and losses should be measured system-wide.

Taguchi designed experiments using orthogonal arrays, which make the design of the experiments easy and consistent. The power of orthogonal arrays is the ability to evaluate several factors in a minimum number of experiments. The following LifeSat tasks were identified with the components for the usual P-diagram of Taguchi method:

The quality characteristic is the ability to follow the desired trajectory and land at the desired target,
The response of the system is the actual trajectory including the deviation from the target,
The noise factors are the environmental and vehicle parameters,
The control factors are specified by the designer and, hence, are related to the vehicle, such as mass, velocity components, physical dimensions, and wind coefficients.

A simulation based on orthogonal arrays with 27 samples compared very favorably with a Monte Carlo simulation with 100 samples used to obtain the footprints of trajectories into the landing range. Statistical parameters (mean and standard deviation) of the landing range were compared for both methods, and differences were found to be small. Finally, a prototype software package implementing this method was developed and delivered.

In the analytical method developed by Jagamaatha Rao and Yi-Chao Chen, a simplified LifeSat simulation model was first implemented using the governing differential equations in the spherical coordinate system. By studying the dispersion of the footprint over a wide range of flight parameters, researchers found that the footprint dispersion was almost a linear function of parameter deviations when landing in the small target area. They reasoned that it might be possible to compute the reliability analytically by using an approximation of the footprint dispersion function.

Following this idea, a linear approximation was first used, which required only 2n simulations for the n parameter problem. The set of all admissible parameters was identified approximately, using two simple inequalities. The integral of the product of the n probability density functions over this admissible set gave the desired reliability. To facilitate the evaluation of the probability density integral, a transformation of the coordinates was introduced in such a way that the new coordinates in the parameter space were aligned with the coordinates of the target area. For normal distribution density functions, such a coordinate transformation resulted in an analytic integration in n-2 variables.

The remaining 2-dimensional integration can be executed numerically,. or even manually, with the aid of normal distribution tables.

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Measurement of Computer Software Quality

J. C. Huang, Ph.D. Department of Computer Science

Computer software is an important commodity in our modern high-technology society. Yet, there is no useful measure of software quality. Without such a measure, it is difficult to compare the usefulness of software development methods, to specify the required level of quality in a software contract, to assess the effectiveness of a quality assurance activity, and to determine the competence of a programmer. ISSO researchers are currently studying contributions to the solution of these problems.

A specimen is, by definition, a sample of substance or material for examination or study. Thus, a good specimen must exemplify the whole mass from which it is extracted. Engineers have discovered that good specimens of a computer program can be produced by applying the technique of pathwise decomposition developed in previous work on program analysis.

The main idea can be briefly described as follows:
Consider the restriction imposed by the following sentence: "The program state at this point must satisfy predicate C, or else the program becomes undefined." the phrase "program state" refers to the aggregate of values assumed by all variables involved. Since this restriction constrains the states assumable by the program, it is called a "state constraint" or a "constraint" for short and is denoted by /\C. State constraints are designed to be inserted into a program to create another program. For instance, given a program of the form:

Program 1: S1;S2

a new program can be created, as shown below:

Program 2: S1;/\C;S2

Program 2 is said to be created from program 1 by constraining the program states to C prior to execution of S2. Intuitively, program 2 is a subprogram of program 1 because its definition is that of program 1 restricted to C. Within that restriction, program 2 performs the same computation as program 1.

By inserting a different set of constraints at different points in a program, one can decompose it into a set of subprograms. To distinguish this process from the traditional method of decomposing a program into procedures and functions, the present method is called a pathwise decomposition because here the program is divided along the control flow, where as in the traditional method a program is divided across the control flow.

Experience with this methodology shows that the extent to which a given program can be simplified reflects the quality of its design as well as the quality of the source code. ISSO researchers are striving to develop different models of measurement and calibrate models and measures experimentally.

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Modular Structures for Large Rule-Based Systems

Christoph F. Eick, Ph.D., Department of Computer Science

In data-driven rule-based languages, such as OPS or CLIPS, a program consists of a global rule-set, whose rules communicate through a global fact base. However, due to the lack of information hiding, encapsulation, inheritance, and scoping concepts in these languages, it is a quite complicated process to develop large rule-based expert systems with these languages.

The objectives of the performed research are to alleviate these problems. The focus of the research is the design and implementation of a rule-based language called PICASSO (downward compatible with CLIPS) that provides encapsulation, modularization, and reuse concepts for rule-based systems.

The definition of the syntax and semantics of the language has already been completed, and a precompiler of the language has been developed in a student's thesis. Currently, investigators perform case studies that evaluate the benefits of PICASSO for the development of large rule-based systems, and work on new matching algorithms for the efficient implementation of large, modular rule-based systems.

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ISSO -- Institute for Space Systems Operations
1992-1993 Annual Report