INVESTIGATION OF THE INVERSE MONTE CARLO METHOD AND ITS APPLICATION TO NUCLEAR GAUGING

THE INVERSE MONTE CARLO (IMC) METHOD IS A NOVEL APPLICATION OF DIRECT MONTE CARLO (MC) THAT ALLOWS A RATHER LARGE CLASS OF INVERSE PROBLEMS TO BE SOLVED IN A NONITERATIVE MANNER. DIRECT MC CAN BE VIEWED AS A MEANS OF ESTIMATING DEFINITE INTEGRALS; IMC, ON THE OTHER HAND, CAN BE VIEWED AS A MEANS OF SOLVING INVERSE PROBLEMS POSED AS FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND. IN BOTH CASES, THE TECHNIQUES CAN BE APPLIED WITHOUT EXPLICITLY USING THE INTEGRAL FORMULATION AS LONG AS THE PHYSICS OF THE PROCESS ARE KNOWN.IMC IS IMPLEMENTED BY HYPOTHESIZING FORMS FOR THE UNKNOWN DISTRIBUTIONS, EXECUTING A DIRECT MC SIMULATION AND APPLYINGWEIGHT FACTORS THAT CONTAIN THE UNKNOWN PARAMETERS. BY EQUATING THE RESULTING MC ESTIMATOR TO KNOWN OR MEASURED RESPONSES, A SYSTEM OF ALGEBRAIC EQUATIONS IS FORMED THAT CAN, IN PRINCIPLE, BE SOLVED BY STANDARD METHODS FOR THE UNKNOWN PARAMETERS. ADVANTAGES OF THE IMC METHOD INCLUDE THE FACTS THAT IT IS NONITERATIVE, IN THE SENSE THAT THE SIMULATION NEED BE PERFORMED ONLY ONCE, AND THAT IT CAN BE APPLIED TO HIGHLY COMPLEX PROBLEMS WHERE STANDARD TECHNIQUESFAIL. IN PHASE I, THE PRACTICAL FEASIBILITY OF THE METHOD WILL BE INVESTIGATED AND ITS APPLICATION TO NUCLEAR GAUGING WILL BE CONSIDERED, WITH SPECIAL EMPHASIS ON ENERGY-DISPERSIVE X-RAYFLUORESCENCE GAUGING. IN ADDITION, EXTENSION OF THE METHOD TO THE SOLUTION OF OPTIMIZTION PROBLEMS, SUCH AS ARISE IN DESIGN OF GAUGING SYSTEMS, WILL BE INVESTIGATED AND ATTEMPTSWILL BE MADE TO ESTABLISH A MATHEMATICAL BASIS FOR THE METHOD. IF PHASE I IS SUCCESSFUL, THE DEVELOPMENT OF A PROTOTYPE GAUGE, SUCH AS AN X-RAY FLUORESCENCE ANALYZER, BASED ON THE IMC METHOD WILL BE PROPOSED FOR A PHASE II EFFORT.