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2.12. MATCHMODSchuette and Pevear MatchMod departs from both the neural network approach and the symbolic tradition cut-out by PROSPECTOR in mineral analysis. Schuette and Pevear (Schuette 95) pioneered evolutionary computing in interpretation of X-ray diffraction patterns. Their research effort was essentially motivated by the need to develop diagnostic systems that could handle uncertainty and nonlinearity differently from the more established approaches. The application developed estimates of the composition and structure of a clay sample given its X-ray diffraction (XRD) pattern. This pattern is produced through a process where a clay sample is rotated in front of an X-ray source. The plot creates a pattern along in a two-dimensional system. The x-axis represents the rotational angle. The range is given along the y-axis. This defines interference from various atomic planes in the mineral crystal structure. The XRD pattern is a function of the combination of mineral present in the clay as well as the relative proportions of minerals. The peaks and valleys of the plot is the subject for interpretation. The interpreted result is used for Illite Age Analysis (IAA). This is a sample dating technique that distinguishes between illite of different ages. However, the classification process poses a challenge and is not very well taken care of by traditional means. There are two common ways to interpret the structure of minerals using XRD patterns. The so called "Rietveld" method and a manual expertise guided trial-and-error search. The former is a deterministic least-squares method that is useful for compositional judgment. The latter is a heuristic-driven method where the user is trying to minimize error. MatchMod is a new approach that applies a stochastic optimization technique based on ideas from biology. Genetic algorithms (GA) are optimization techniques inspired by our understanding of how nature deals with the issue of staying alive: survival of the fittest, genetic recombination, and mutation. In a GA, new possibilities are explored by letting genetic operators modify known elements to produce new ones. The process is guided by fitness measures related to population of possibilities. In contrast to other stochastic methods, GA use the fitness criteria as the engine rather than a random generator. Its ability to do radical non-local leaps in the search space distinguishes it from the more traditional approaches. Moreover, it pursues the objective function along a wide front. For more information on GA, see Goldberg (89). Schuette and Pevear exploit the strengths of GAs in MatchMod. The system is a forward-driven process where known references are established and instantiated in order to produce new tentative patterns. These areas are crossed and the results tested against the existing log pattern, which serves as the objective function. MatchMod consists of six components:
The four models represent MatchMod's knowledge about X-ray crystallography and clay mineralogy. All four models use information about the chemical composition of clays and their crystal structures to estimate the XRD pattern produced by a sample of that clay. They encompass parameters such as the number of iron atoms added to the crystal structure, the sequence of mixed-phase layering, the characteristics of the crystals, and more. Some of them are specific to the laboratory used; others are more general. In MatchMod, 15 parameters are manipulated by the genetic algorithm. The combiner creates new patterns based on the instantiated models given as input. The weighted output XRD pattern is matched against the original pattern. The relative goodness of the new patterns produced is highlighted before the user, who may intervene in several ways. Parameters such as "degree of preferred crystal organization" and "percentage of illite in illite/smectite component" are represented by a bit vector representing its range of values. Hence, a paramater can be expressed as #(0 1 0 1 1 0 0 1 1 1 00). Contribution from two parent vector elements are concatenated and a so called "crossover point" selected. Thus, for each parameter, MatchMod swaps the bits after the crossover point in a parent, element with the corresponding bits in the other parent, as: In this manner, a new generation of patterns is produced. MatchMod applies multiple crossover points. This increases the diversity from one generation to the next. The fitness function applied is a standard error minimizing model: F = 1/(1 + err) where err is the sum of squares error measured at each calculated angle in the XRD pattern, and F is at its maximum when err is at its minimum. MatchMod has been used to match several hundred patterns of many types. Compared to the manual expert method, MatchMod produced equal or better quality results. In one example, illite, known to be 400 to 500 million years old, was estimated to be 218 million years old in the best manual try. MatchMod came out with a result of 439 million years. In addition to precision MatchMod computes its result in a fraction of time compared to that of a person. Due to its independence from its user, a person can be relieved of as much as a full day's work using MatchMod.
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