Patent Number: 054066050
Section: description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT Described herein is an existing analytical tag design approach which is employed in carrying out a portion of the method for designing gas tag compositions of the present invention. The first step of the design procedure is to compute a set of geometric cosines, .mu..sub.i, with the equation ##EQU1## Equation (1) is derived from angular quadrature relationships used in discrete-ordinates approximations to the neutron transport equation..sup.1 Here, N.sub.I, the number of cosines in the positive .mu. direction, is the subscript of the commonly used S.sub.n discrete-ordinates scheme. Use of Eq. (1) ensures that the resulting system of tag nodes will possess complete symmetry with respect to the origin, and that the distances between each node and all of its closest neighbors are equalized as nearly as possible. FNT B. G. CARLSON and K. D. LATHROP, in Computing Methods in Reactor Physics, p. 171, H. GREENSPAN, C. N. KELBER, and D. OKRENT, Eds., Gordon and Breach, Science Publishers, Inc., New York (1968). Using the set of .mu..sub.i generated by Eq. (1), the locations of the tag nodes for the inner sphere are determined from ##EQU2## where (X.sup.n, Y.sup.n, Z.sup.n).sub.I are the coordinates of tag node n on the surface of the inner sphere, and R.sub.I is the radius of the inner sphere. Note that as indices i and j vary from 1 to N.sub.I and from 1 to (N.sub.I -i+1), respectively, n varies from 1 to M.sub.I, where M.sub.I, the total number of nodes on the inner sphere, is equal to 4N.sub.I (N.sub.I +1). After M.sub.I nodes are specified for the inner sphere, M.sub.0 node locations are computed with the same equation for the outer sphere. The geometry of the resulting node arrangement is illustrated graphically in FIG. 1, which depicts a few nodes from the positive octants of each sphere. The relationship between the radii of the inner and outer spheres is given by ##EQU3## Use of Eq. 3 together with Eqs. (1) and (2) will minimize the overall cost of the system of tags. In general, the more spread out the system of tags becomes in tag-ratio space, the greater the enrichment requirements and, hence, the greater the overall costs for the noble gases used to create the tags. Use of Eq. (3) ensures that the system of tags will be packed as efficiently as possible into a given volume of ratio space. The last independent variable, R.sub.I, is determined by expanding the system of nodes isotropically about the (common) origin of the two spheres until the closest distance between any two nodes is greater than a minimum separation distance, .tau., thereby ensuring the ability to unambiguously identify single-element failures. The value of .tau. is left as an input variable and can be adjusted to allow for experimental uncertainties in the mass-spectrometer system used for the isotopic analyses, uncertainties associated with blending the tags, and, depending on the gases used, uncertainties in neutron burnout of the constituent isotopes..sup.2 FNT .sup.2 Recent isotopic burnout correlations used at EBR-II are described in J. D. B. LAMBERT, B. Y. C. SO, F. S. KIRN,J. R. ARMSTRONG; E. R. EBERSOLE, and M. T. LAUG, "Recent Improvements in Identifying Fission Product Sources in the Experimental Breeder Reactor II," Nucl. Technol., 39, 275 (1978). The final step of the node-design procedure is systematic elimination of certain points that violate either of the following analytical constraints: 1. No four nodes in the system may lie in the same plane unless that plane is parallel to one of the three coordinate planes. PA1 2. No tag node on the inner sphere can fall on a straight line connecting any two other tag nodes. Constraint 1 ensures that the system of tags is amenable to a recently devised multiple-failure-analysis technique..sup.3 Constraint 2 ensures that single-assembly failures cannot be confused with double-assembly failures. FNT .sup.3 K. C. GROSS, C. PASSERELLO, and A. SHAPIRO, "Barycentric Coordinates Technique for Resolution of Multiple Fuel Failures with Gas Tagging," Trans. Am. Nucl. Soc., 27,685 (1977). If the number of tags remaining after elimination is less than the total number of tags required for the given reactor, then N.sub.I and/or N.sub.0 are increased, and the procedure is repeated. When the required number of tag nodes is obtained, the entire system is translated rectilinearly to the positive octant of the Cartesian ratio space. The values of the component compositions for each node are then normalized appropriately so that the maximum value in each direction is spaced sufficiently far away from the corresponding background isotopic compositions. Unfortunately, the locations of the tag nodes specified with an analytical design such as this concentric sphere design are not precise points in composition space as discussed above. This "movement" arises from experimental variations in the tag cylinder filling process and may result in erroneous failed assembly identification and removal from the reactor's core of the wrong fuel assemblies. Although it is impossible to totally eliminate the source of all inaccuracies in the tag blending procedure, the present invention provides a method for designing gas tag compositions which substantially reduces the possibility of misidentification of leaking fuel assemblies particularly in the case of multiple leaking fuel assemblies. In accordance with the present invention, the present method for designing gas tag compositions solves the problem endemic to prior art approaches not by eliminating experimental uncertainties, but by accepting and accommodating these uncertainties with an iterative genetic algorithm approach that is run during the blending procedure. In prior art approaches, the node-design method (such as the concentric sphere method described above) would produce a table of all the target compositions for every required tag node. These target compositions would then be used to guide the gas blending operation. Unavoidable experimental uncertainties would result in small discrepancies between the target compositions and the measured final compositions. The inventive method disclosed herein starts with a table of target compositions as in earlier approaches and uses the first target composition to blend the first canister of tag gas. When that canister of tag gas is produced, its final composition is measured accurately with a mass spectrometer. This measured composition is now used as the "true" location of node #1, and nodes 2, 3 . . . , NTAG (where NTAG is the total number of tags in the system) are adjusted using a genetic algorithm approach described in the following paragraphs. Genetic algorithms are used in the analysis of complex phenomena and are derived from a simple heuristic assumption: that optimal solutions are located in regions of the search space containing relatively high numbers of good solutions, and that these solutions can be found by judicious sampling of the space. Genetic algorithms are further based upon two key axioms: (1) that non-biological structures may be described by simple bit strings and (2) that these structures may be improved by the application of simple transformations to these strings. A genetic algorithm controls the representation and alteration of such strings in order to evolve well-adapted solutions to the optimization problem under consideration. The basic approach undertaken in and operation of genetic algorithms is described in Advances in Nuclear Science and Technology, Vol. 21, J. Lewins and M. Becker (editors), Plenum Press, New York, New York (1990). Referring to FIG. 4, there is shown a flow chart illustrating the sequence of steps in carrying out the method for designing gas tag compositions of the present invention. In FIG. 4, an oval symbol indicates the start of an operational sequence, a rectangle indicates an instruction or set of instructions resulting in the performance of a control function, and a hexagon indicates a decision based upon the comparison of binary signals within a microprocessor controller which is described below. At step 76, the operation of a program stored in a microprocessor controller for designing gas tag compositions is initiated. At step 78, the microprocessor controller is initialized by resetting its control flags to an initial set of conditions whereupon the microprocessor controller is ready for controlling apparatus for manufacturing gas tags, which apparatus is described in detail below. At step 80, the program in the microprocessor controller perturbs all node positions on the inner and outer tag spheres described above in a random direction. The random direction selected is constrained in that the node does not leave the surface of the sphere on which it resides. The program next, at step 82, then computes a distance parameter, d(I), for each node on the inner sphere, where d(I) is the minimum distance to any tie-line connecting other nodes in the system. The distance d(I) is the shortest distance between a node and a tie line connecting any two other nodes, with the goal being to maximize the distance parameter at a later step in the process. At step 84, the program computes a control parameter D by taking the root-mean-square of all d(I)'s, where ##EQU4## The overall objective of the inventive method is to maximize the magnitude of the control parameter D, while adhering to the analytical constraint that the target tag nodes do not leave the surfaces of their respective spheres. The program at step 86 then selects M nodes from the population of remaining nodes that give the highest, or best, values of d(I). The selected M nodes can be on either of the concentric spheres, with d(I) connecting nodes on the inner and outer spheres. Those M nodes which give the highest values of d(I) are termed "parent" nodes and retain their positions in the subsequent generation, or during subsequent steps in the process. The program at step 88 then selects N nodes from the population of remaining nodes that give the lowest, or poorest, values of d(I) and these N node positions are marked for "death" and may be disqualified during the subsequent generation. Those nodes are designated as "children nodes". In one embodiment, M=N which simplifies calculations in carrying out the inventive method. The program then proceeds to step 90 to determine if there are any remaining nodes. If there are no remaining nodes, the program proceeds to step 92 and ends. If, at step 90, it is determined that there are remaining nodes present, the program proceeds to step 94 and holds the parent nodes fixed, while producing "mutated" children nodes by perturbing all non-parent node positions and reevaluating the new d(I) values. The new d(I) values for the mutated children nodes are recomputed at step 96 with the value of the first (J=1) remaining node determined at step 98. From step 98, the program proceeds to step 100 to determine if the J node has been marked for death. If the J node has not been marked for death, the program branches to step 84 and again computes the control parameter D of all d(I)'s. If at step 100 it is determined that the J node has been marked for death, the program, at step 102, determines whether the position of the node has improved compared to its position two generations ago. If at step 100 it is determined that the node's position has not improved as compared to its position two generations ago, the program branches to step 104 and returns the node to its original position it had two generations ago, followed by an incrementing by one of the value of J to the next node at step 106. The program then determines, at step 108, if J+1 is equal to the number of nodes remaining, or to the number of nodes which have not yet been fixed in position. If J+1 equals the number of remaining nodes, the program branches to step 84 for again computing the control parameter D for all nodes. If at step 108 it is determined that J+1 does not equal the number of nodes remaining, the program branches to step 100 to determine if the J+1 node has been marked for death. If at step 102 it is determined that the J+1 node's position has improved compared to its position two generations ago, the program branches to step 110 and fixes the position of the node at its new location. The program then increments J by one at step 112 and at step 114 determines whether the J+1 node is equal to the number of remaining nodes. If J+1 is equal to the number of remaining nodes, the program branches to step 84 and again computes the control parameter D for all nodes. If at step 114 it is determined that J+1 is not equal to the number of nodes remaining, the program branches to step 100 and determines whether the J+1 node has been marked for death. The program then proceeds as previously described. Referring to FIG. 5, there is shown a simplified schematic and block diagram of a tag gas blending system 30 for designing gas tag compositions in accordance with the method of the present invention. The present invention is not limited to use with the gas tag blending system 30 of FIG. 5, but can be used with virtually any conventional gas tag blending system. The gas tag blending system 30 of FIG. 5 is disclosed and claimed in co-pending application, Ser. No. 08/174,146, filed Dec. 28, 1993, and assigned to the assignee of the present application, the disclosure of which is hereby incorporated by reference in the present application. Tag gas blending system 30 includes a tag blending manifold 32, a vacuum system 34 and a microprocessor-based controller 36. Tag blending manifold 32 includes a stainless steel manifold 42 to which are coupled a plurality of filling gas cylinders, or canisters, 40. Each of the filling gas cylinders 40 is coupled to the tag blending manifold 32 by means of a respective microprocessor-controlled valve 38. Each of the valves 38 is coupled to and controlled by microprocessor controller 36 for opening and closing each of the individual valves and connecting its associated gas cylinder 40 to manifold 42. Microprocessor controller 36 is coupled to the tag blending manifold 32 by means of a first control/communication bus 54 by means of which control signals are provided from the microprocessor controller to each of the valves 38 and also by means of which status signals relating to each of the valves is provided to the microprocessor controller. Each of the filling gas cylinders 40 contains a feed gas having a specified composition. Manifold 32 couples each of the filling gas cylinders 40 to a blended tag canister 46 for filling the blended tag canister with metered quantities of each of the feed gases in the filling gas cylinders 40. The metering is accomplished by means of microprocessor controller 36 which also is coupled to a tag gas canister valve 52 to allow for introduction into the blended tag gas canister 46 of the required feed gases to provide a tag gas having a designated composition. Vacuum system 34 is coupled by means of a vacuum line 48 to manifold 42 within the tag blending manifold 32. A first pressure transducer 44 is coupled to manifold 42 in the tag blending manifold 32, while a second pressure transducer 50 is coupled to vacuum line 48 within vacuum system 34. Vacuum system 34 is further coupled to controller 36 by means of a second control/communication bus 56. Microprocessor controller 36 controls the operation of vacuum system 34 in forming a vacuum within manifold 42 for drawing various of the feed gases within the filling gas cylinders 40 into the blended tag canister 46. Two pumps 34a and 34b are shown in the vacuum system 34 for drawing feed gases from the filling gas cylinders 40 into the blended tag canister 46 via manifold 42. In a typical tag gas blending system, X tag isotopes for Y distinct feed gas mixtures commercially available from an enriched gas supplier are used to fill blended tag canister 46 with a tag gas having a designated composition. The procedure typically involves opening one of the valves connected to one of the filling gas cylinders, drawing off a predetermined amount of feed gas, closing the valve to the filling gas cylinder as well as the valve to the blended tag canister, and purging the gas line before introducing another feed gas to the blended tag canister in forming the tag gas blend. Microprocessor controller 36 includes a ROM 60, a clock 64, an accumulator (ACC) 68, a controller 62 and an arithmetic and logic unit (ALU) 66. Microprocessor controller 36 stores instructions and data, periodically updates the stored data, compares both stored and real-time data and makes decisions based upon these comparisons by means of logic instructions in providing control for the tag gas blending system 30. An oscillator circuit 70 external to the microprocessor controller 36 provides timing signals to clock 64 for controlling the timing of operations carried out by the microprocessor controller. Program instructions and data and the sequence of steps carried out under the control of microprocessor controller 36 are illustrated in FIG. 4 and described in detail above. There has thus been shown an improved method for designing gas tagging compositions for use in identification of failed fuel assemblies in a nuclear reactor. The inventive method employs an analytical approach wherein the final composition of a first canister of tag gas as measured by a spectrometer is designated as node #1. Lattice locations of tag nodes in multi-dimensional space are then used in calculating the compositions of a node #2 and each subsequent node so as to maximize the distance of each node from any combination of tag components which might be indistinguishable from another tag composition in a reactor fuel assembly. This is accomplished by employing a genetic algorithm which improves the gene pool with time as undesirable mutated children nodes are eliminated from consideration. The method employs a sequential approach wherein the measured compositions of tag gas numbers 1 and 2 are used to fix the locations of nodes 1 and 2, with the locations of nodes 3-N then calculated for optimum tag gas composition. The geometric space representing inter-nodal spacing is in the form of one or more concentric spheres defining lattice locations of the tag nodes. While particular embodiments of the present invention have been shown and described, it will be obvious to those skilled in the art that changes and modifications may be made without departing from the invention in its broader aspects. Therefore, the aim in the appended claims is to cover all such changes and modifications as fall within the true spirit and scope of the invention. The matter set forth in the foregoing description and accompanying drawings is offered by way of illustration only and not as a limitation. The actual scope of the invention is intended to be defined in the following claims when viewed in their proper perspective based on the prior art.