Neural Network Enhancement of the Los Alamos Force Deployment Estimator

Transcription

1 Missouri University of Science and Technoogy Schoars' Mine Eectrica and Computer Engineering Facuty Research & Creative Works Eectrica and Computer Engineering Neura Network Enhancement of the Los Aamos Force Depoyment Estimator Bobby Turner Donad C. Wunsch Missouri University of Science and Technoogy, Foow this and additiona works at: Part of the Eectrica and Computer Engineering Commons Recommended Citation B. Turner and D. C. Wunsch, "Neura Network Enhancement of the Los Aamos Force Depoyment Estimator," Proceedings of the High Consequence Operations Safety Symposium (1994, Abuquerque, NM), pp , United States. Department of Energy, Jan This Artice - Conference proceedings is brought to you for free and open access by Schoars' Mine. It has been accepted for incusion in Eectrica and Computer Engineering Facuty Research & Creative Works by an authorized administrator of Schoars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use incuding reproduction for redistribution requires the permission of the copyright hoder. For more information, pease contact schoarsmine@mst.edu.

2 Neura Network Enhancement of the Los Aamos Force Depoyment Estimator Bobby Turner and Donad C. Wunsch II, Texas Tech University Abstract The Force Depoyment Estimator (FDE) is a decision support system. It aocates transportation resources given inputs such as forces to be depoyed and their desired arriva times. Other inputs are assumptions about conditions that affect performance: carrier start time, node capacity, sustainment shipping time, buk sustainment per day, ammo sustainment per day, unit start time, carrier service time, carrier round trip time, and carrier reassignment time. Outputs incude the mean and standard deviation of estimated unit arriva times versus goa times, and data fies for post-processing. However, when a goa time is not met, the simuator gives no expanation of why. This is difficut to do because of the voume of data invoved. Poor aocation choices are buried in a mountain of other decisions, whose affects are difficut to assess individuay. To find the most troubesome aocations, we separate the cases that give the worst resuts. A neura network identifies the decisions that are common to these. We appy a simiar procedure to the cases where outputs are good. We report as suspect the decisions that occur ony in the former cases. The neura network for this system needs to be capabe of custering data with no a priori knowedge of correct output categories. It aso needs to be abe to hande inexact (fuzzy) determinations of these categories. Finay, it needs to be abe to hande arge data patterns without arge sets of exampe cases. We have chosen Adaptive Resonance Theory with fuzzy input/output representation, which fits a these criteria. 1. The Force Depoyment Estimator The Force Depoyment Estimator (FDE), as depicted in Figure 1, is a decision support system to do anayses of depoyment and sustainment issues to support various war pans. Inputs to the simuator are 1) specific units to be depoyed, 2) the modes of transportation to be used for the depoyment, 3) the fina destination of the units and the avaiabe paths to get there, and 4) the goa times defined for the depoyment. FDE then produces how to best utiize the depoyment assets to achieve the goa times if a soution exists. If a feasibe soution does not exist, the simuator wi determine the best aocation possibe and wi provide information as to which goas have not been met and by how much they have been vioated. The simuator consists of three main parts. The discrete event simuator simuates the actua movement of units from node to node using the given ift assets. Upon competion of the simuation, the data required to cacuate the goa variabes is reported to the goa programming agorithm. The goa programming agorithm determines if the specified goas have been reached. It compares the current soution to the "best" soution so far. If the current soution is better, it is saved as the "best". If the goas have not been reached, the anneaing program is initiated to derive a new set of state variabes for the discrete event simuator. Simuated anneaing is a mathematica technique which is described as a biased random search over a surface wherein a series of oca minima may be -487-

3 ... WHAff ,..o"tto /1/ HOW Figure 1. FOE Simuator encountered whie attempting to find the goba minimum. This process, unfortunatey, creates an enormous amount of data. The simuator can be run in two modes, nomina or variabe. In nomina mode a scenario inputs are fixed. In variabe mode, casses of input data have been seected for variation, seven externa and three interna as outined beow. Externa carrier start time node capacity sustainment shipping time buk sustainment per day oversized sustainment per day ammo sustainment per day unit start time Interna carrier round trip time carrier reassignment time carrier service time During the simuation, the seected variabes are randomy chosen from a given distribution. For each set of externa variabes, a number of "best" soutions is produced by varying the interna variabes. The outputs of the variabe mode are ift objective histograms, unit arriva (mean & standard deviation) vs. goa time, and data fies for post processing. Variabe mode aows the user to account for uncertainty inherent in the depoyment. 2. Neura Network Impementation The FOE simuator has proven effective in both modes of operation, nomina and variabe, and its functionaity is not in question. The goa is to appy neura network techniques in the post processing and/or rea time evauation of the simuator. For exampe, when the simuator is run and a goa time is not met, this is reported to the user. Aso, soutions found using the nomina mode of the simuator are often found to have a wide variation when the variabe mode is used

4 However, the simuator gives no expanation of why the goa is not met or what is causing the variation. This is difficut to do because of the arge voume of data invoved. Identification of bottenecks, or as the miitary cas them "choke points," in the variabes that ead to undesirabe resuts woud provide significant information to users of the simuator. The neura network architecture is shown in Figure 2 with the variabe mode of FOE. It is desired to partition the sets of externa variabes into groups that produce "bad" outputs and those that produce "good" outputs and ook for patterns in both. Bad and good can be defined reative to the actua output, the variation in the output, or a combination of the two. By ooking at the difference in the patterns that produce bad outputs and those that produce good outputs, it is then possibe to extract individua parameters, or combinations of such, in the input that are most ikey to be the source of the probem. A neura network to accompish this task must possess severa important features. The first is to have the abiity to group simiar patterns with no a priori knowedge of the correct patterns or how many may exist, which represents unsupervised earning. Second, it must be abe to hande anaog input vaues. Third, it must be abe to hande arge data sets without arge sets of exampe cases. Finay, it shoud have the abiity to detect a rare occurrence of a singe event that may be embedded in a coud of simiar events. The neura network architecture chosen to accompish this is Fuzzy Adaptive Resonance Theory, or Fuzzy ART, which meets a of these criteria. Fuzzy ART incorporates the basic features of standard ART systems, notaby, pattern matching between bottom-up and top-down earned prototype vectors. This matching process eads either to a resonant state that triggers stabe prototype earning or to a sef reguating parae memory search. If the search ends by seecting an estabished category, then the category's prototype may be updated to incorporate new information in the input pattern. If the search ends by seecting an empty pattern, the earning of a new pattern takes pace[2]. This abiity to add new patterns that don't match any of the previousy earned patterns is an important asset of Fuzzy ART. A detaied mathematica discussion of Fuzzy ART can be found in reference Appication of Fuzzy ART The Fuzzy ART neura network was tested using input and output data fies from Los Aamos of actua FOE simuations. The FOE input fie used consisted of250 sets of externa variabes with each set containing 153 variabes reated to carrier start times, node capacities, buk, oversized, and ammo sustainments per day, and unit start times. The output fie was used to partition the normaized input fie into good and bad sets. First the mean for the cosure goa, one of the goas specified in the FOE simuation, for each set of soutions was cacuated. Bad was then defined as those means that were above the average of a means. The input fie coud aso be partitioned reative to the variance in the cosure goa or a combination of both mean and variance. The output of the Fuzzy ART system was the set of weight vectors that represent earned patterns in the good set and the bad set and a score for each pattern that represented how many members of the -489-

5 .X FDE Output{! n~~=v!::~m L,...., oopn!mii ; id '; d y.,.... _.'"i J,... f t.ture extraction J I mmibei- of um N-d IJ6'tf<!IM y -y f-!t!t:,,,,,.': iii nopm tim'3 ' i ~MA~d Tu~ AR'f i unwpmi:isw.. i ff>'iua.aetwod: i 11tW&I nff'ork draw 4t<t C)fint.w, writbkf, i paniio1t. d.at w: 1;:a-:;-- r~~~; f i, 9oo.iandb.d')fi... -.!... :::.. ::.:.:: :: 1'- :. ::.:::::::::: PDE Simuao Figure 2 Variabe Mode offde with Neura Network Bock Diagram input set were represented in each earned pattern. Post processing of the Fuzzy ART output was performed to put this information into a usefu form. This invoves feature extraction in the bad patterns and then coecting these features to produce a fina answer. The foowing iustrates the use of the Fuzzy ART system reative to the cosure goa. One set of extracted features that ead to an undesirabe output is shown graphicay in Figure 3. Each bar represents one of the 153 parameters in the input data fie. The graph was truncated at zero since ony the positive vaues are of interest. The combination of these bars represents a probem area with the highest bar representing the parameter that contributes most to the probem. It is apparent that this combination contains two garing choke points as shown in the figure. The task now is to decide which parameters shoud be targeted for improvement based on the earned bad patterns. This can be accompished in severa ways. It was mentioned earier that the Fuzzy ART system used a scoring system teing how many members of the input set were represented in each earned pattern. There are two cases of interest reative to the score: 1) those patterns that have the highest score, and 2) a pattern with a very ow score, most notaby a score of 1, in the midst of patterns with much higher scores. In the atter case, the pattern with a ow score ikey contains a rare event that eads to a bad output. One method of targeting parameters for improvement woud be to ook at combinations of parameters in these two cases. Another method invoves ooking at the parameters that were the maximum in each of the bad patterns and seeing which parameters were present mutipe times

6 -., O.S <; ws Carrier Start F S ; mp s, HII i I J i so I,, I ' 1 I I I oo! I g JI! -' 1 sii Figure 3 Sampe Bad Pattern for Mean of Cosure Goa The next method invoves ooking at those parameters that are most often cose to the maximum in each of the patterns. This can be accompished by ooking at those parameters that fa within x number of standard deviations of the maximum for each of the bad patterns. This method woud identify parameters that may not be the maximum in any of the bad patterns but are consistenty near the top. A fina method for identifying choke points for improvement woud be to ook at those parameters that are present in the most bad patterns. This shows which parameters consistenty ead to bad outputs. The best method depends on the particuar appication and further investigation wi have to be performed to determine the best method. 4. Concusion The peope responsibe for creating FDE asked two basic questions at the outset of this project: can a neura network be used to identify choke points and, if so, what type of neura network architecture can be used? This work shows that a neura network can identify potentia choke points when used in conjunction with the FDE system. The F uzzy ART architecture has the possibiity of being a powerfu too in the enhancement of the FDE. Further research can now be conducted to determine the effectiveness of the F uzzy ART system in the context offde and which method outined best identifies potentia choke points. If this is successfu, the F uzzy ART agorithm coud be used to search for choke points in the interna variabes, a task that has been impossibe to this time because of the enormous amount of data invoved. Athough this work shows the effectiveness of Fuzzy ART in the context of FDE, the Fuzzy ART system can be used in a variety of situations. F uzzy ART can be used to earn patterns in historica data and then be impemented to ook for these patterns in a rea time system. This is of particuar interest if a system faiure had occurred in the past and the Fuzzy ART system earned the vaues of parameters that ead to the faiure. 0.6, r r

7 References 1. "Force Depoyment Estimator (FDE) Mode," Los Aamos Nationa Laboratory, Apri Gai A. Carpenter, Stephen Grossberg, and David B. Rosen, "Fuzzy ART: Fast Stabe Learning of Anaog Patterns by an Adaptive Resonance System," Neura Networks, Vo. 4, pp , Donad C. Wunsch II, "An Optoeectronic Learning Machine," Gai Carpenter, Stephen Grossberg, Nataya Markuzon, John H. Reynods, and David B. Rosen, "Fuzzy ARTMAP: A Neura Network Architecture for Incrementa Supervised Learning of Anaog Mutidimensiona Maps," IEEE Transactions of Neura Networks, Vo. 3, No. 5, pp , September Patrick K. Simpson, "Fuzzy Min-Max Neura Networks--Part 2: Custering," IEEE Transactions of Fuzzy Systems, Vo. 1, No. 1, pp , February