• Title/Summary/Keyword: Cover Depth

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The Effect of Freeze and Thaw for the Stabilized Soil Bottom Liners in the Landfill (폐기물 매립지 바닥층의 고화토 포설시 동결/융해 현상에 관한 연구)

  • Lee, Song;Lee, Jai-Young;Kim, Heung-Suck
    • Journal of the Korean Geotechnical Society
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    • v.16 no.1
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    • pp.179-189
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    • 2000
  • The purpose of this research is to complement the existing researches on landfill bottom liners behavior during the periods of freeze and thaw. Landfill-related researches have been typically focused on small-scale soil samples that are often compacted under conditions different from those used in the field. Although these tests have been invaluable in clarifying the problem of freeze and thaw, extending the results of such experimental studies to prototype landfills are questionable. In this investigation, the author utilized a large scale laboratory simulation allowing inclusion of the field depth of the cover systems, layered soil profiles, rainfall simulation, a cold climate and boundary conditions similar to those encountered in the landfill. The soil materials were stabilized soils (mixed clays, cements, and minerals) instead of clays. The bottom liners are made up of drainage layer (30 cm), stabilized layer (75 cm), and leach collection layer (60 cm). The stabilized layers are made up of supporting layer (45 cm) and low permeable layer (30 cm) - consisting of $P_A\; and\; P_B$ layer. As a results, depths of penetration increased by about 2~5 more centimeters at rainfall simulated designs than those at no rainfall simulated designs (that is design 3, design 5 and design 7) - it increased by about 20mm/day in the bottom liners and frost heaves also increased it by a few millimeters. Also, a few cracks appeared partly. According to these results, we can surmise that the compacted stabilized soil is more reliable than the compacted clay liners for construction of the landfill liners.

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Studies on Diplosis mori Yokopama (mulberry shoot Gall midge) on mulberry tree (뽕나무 순집이 혹파리에 관한 연구)

  • 전대략;이영렬;조철호
    • Journal of Sericultural and Entomological Science
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    • v.2
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    • pp.49-61
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    • 1962
  • The insect Diplosis mori Yokoyama is causing extensive destruction of mulberry trees in Korea with a resultant loss in silk production. This study was made to determine an effective method of control. Methods and Materials Used Preliminary studies were made to determine more exactly the life cycle of the insect. Based on this information, various control measures were tested, including the use of spray methods with BHC and control of larvae by tilling. Results Obtained 1. Life cycle studies (a) In the Suwon area, this-insect has 5 generations per year. The first starts in the later part of June and the final cycle ends in the later part of September. (b) The adult insects appear about 7: 00-8: 00 P.M. and live for 2-5 days. Females live in longer periods than the male. (c) Larvae lives inside the second and third stipules (A. B.) before mulberry leaf development. They cause extensive damage to the leaves at the point where they are attached to the stem. (d) Weather conditions considerably affect the life cycle. The pupa particularly are affected and not be able to change into the moth stage when there is a long period of no rain. (e) Larvae are large......0.3 to 2.0mm......and are milky-white immediately after hatching but turn to pinkish as the worm matures. The matured worm has a jumping ability up to 15-20cm. The worm burrows into the ground 1.5 to 3.0 cm before changing into the pupal stage. (f) The pupal stage usually lasts 7-8 days, in summer weather conditions and the pupa is surrounded with a coarse cocoon. (g) These insects, as a general rule, overwinter as pupae but sometimes as larvae. 2. Control measures (a) BHC dust applied on the ground seem most effective. It should be done 4-5 days after the worm has burrowed into the ground. For this control, it is recommended that 6kg of a 2% formation Tanbo(l0ares) be used. (b) For the effective spraying against the fly, it is recommended that a formulation of liquid BHC spray terials be used at the rate of 400-600 liters per Tanbo. (c) Tillage methods which provide a cover of soil 5cm or more in depth above infested areas will effect-maively prevent the emergence of the fly from the pupal stage. 3. Conclusions Methods of control against Diplosis mori Yokoyama can be tied more closely to the life cycle of the insect with more effective results. Further studies are needed to complete information on possible controls during or after hibernation. Economic studies on the cost of these control measures are also needed.

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Characteristics of Water Distribution and Transport Depending on Soil Evolution in the Different Forest Stands (상이(相異)한 임분(林分)의 토층분화(土層分化)에 따른 수분분포(水分分布)와 이동특성(移動特性))

  • Jin, Hyun-O;Chung, Doug-Young;Son, Yowhan;Joo, Yeong-Teuk;Oh, Jong-Min
    • Journal of Korean Society of Forest Science
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    • v.89 no.1
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    • pp.24-32
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    • 2000
  • We investigated the patterns of soil horizon evolution and its water distribution on three different forest stands covered with Larix leptolepis, Pinus koraiensis, and Qercus mongolica on the Experimental Forest of Kyunghee University, located in Kwangju, Kyunggi-Do. Compared to the properties of depths of O and A horizons evolved on the Pinus koraiensis stand, the depths of O and A horizons on the forest stands of Larix leptolepis and Qercus mongolica were shallower, indicating that the soil horizon were deeply influenced by geographical characteristics, its erosive and sedimentary distinction, vegetation cover and its population density. And the bulk densities of the sites selected were lower in the high slope gradient than that in the lower slope gradient at the same depth of soil profile. Therefore, the changes of the soil bulk densities were closely related to the soil organic matter and the vertical transport of soil particle throughout soil depths. On the other hand, the bulk density and organic matter content in soil can influence the water transport phenomena, resulting in decrease of the hydraulic conductivity as the increase in the bulk density, while the organic matter can not affect the hydraulic conductivity on the soil surface layer. For a rainfall infiltration characteristics from a lysimeter experiment established on the stand of Larix leptolepis, the bulk density and slope gradient strongly influenced the vertical transport of water, as well as the lateral movement of rainfall. Conclusively, the characteristics of water movement and distribution in the forest stand can be determined not by the geographical factor such as slope gradient but also by the bulk density and organic matter content remained in soils.

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INFLUENCE OF REBONDING PROCEDURES ON MICROLEAKAGE OF COMPOSITE RESIN RESTORATIONS (복합레진 수복 시 재접착 술식이 미세누출에 미치는 영향)

  • Lee, Mi-Ae;Seo, Duck-Kyu;Son, Ho-Hyun;Cho, Byeong-Hoon
    • Restorative Dentistry and Endodontics
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    • v.35 no.3
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    • pp.164-172
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    • 2010
  • During a composite resin restoration, an anticipating contraction gap is usually tried to seal with low-viscosity resin after successive polishing, etching, rinsing and drying steps, which as a whole is called rebonding procedure. However, the gap might already have been filled with water or debris before applying the sealing resin. We hypothesized that microleakage would decrease if the rebonding agent was applied before the polishing step, i.e., immediately after curing composite resin. On the buccal and lingual surfaces of 35 extracted human molar teeth, class V cavities were prepared with the occlusal margin in enamel and the gingival margin in dentin. They were restored with a hybrid composite resin Z250 (3M ESPE, USA) using an adhesive AdperTM Single Bond 2 (3M ESPE). As rebonding agents, BisCover LV (Bisco, USA), ScotchBond Multi-Purpose adhesive (3M ESPE) and an experimental adhesive were applied on the restoration margins before polishing step or after successive polishing and etching steps. The infiltration depth of 2% methylene blue into the margin was measured using an optical stereomicroscope. The correlation between viscosity of rebonding agents and mciroleakage was also evaluated. There were no statistically significant differences in the microleakage within the rebonding procedures, within the rebonding agents, and within the margins. However, when the restorations were not rebonded, the microleakage at gingival margin was significantly higher than those groups rebonded with 3 agents (p < 0.05). The difference was not observed at the occlusal margin. No significant correlation was found between viscosity of rebonding agents and microleakage, except very weak correlation in case of rebonding after polishing and etching at gingival margin.

Time Dependent Evaluation of Corrosion Free Life of Concrete Tunnel Structures Based on the Reliability Theory (해저 콘크리트 구조물의 신뢰성 이론에 의한 시간 의존적 내구수명 평가)

  • Pack, Seung Woo;Jung, Min Sun
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.15 no.3
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    • pp.142-154
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    • 2011
  • This study predicted the probability of corrosion initiation of reinforced concrete tunnel boxes structures using the Monte Carlo Simulation. For the inner wall and outer wall in the tunnel boxes, exposed to airborne chloride ion and seawater directly respectively, statistical values of parameters like diffusion coefficient D, surface chloride content $C_s$, cover depth c, and the chloride threshold level $C_{lim}$ were examined from experiment or literature review. Their average values accounted for $3.77{\times}10^{-12}m^2/s$, 3.0% by weight of cement, 94.7mm and 45.5mm for outer wall and inner wall, respectively, and 0.69% by weight of cement for D, $C_s$, c, and $C_{lim}$, respectively. With these parametric values, the distribution of chloride contents at rebar with time and the probability of corrosion initiation of the tunnel boxes, inner wall and outer wall, was examined by considering time dependency of chloride transport. From the examination, the histogram of chloride contents at rebar is closer to a gamma distribution, and the mean value increases with time, while the coefficient of variance decreases with time. It was found that the probability of corrosion initiation and the time to corrosion were dependent on the time dependency of chloride transport. Time independent model predicted time to corrosion initiation of inner wall and outer wall as 8 and 12 years, respectively, while 178 and 283 years of time to corrosion was calculated by time dependent model for inner wall and outer wall, respectively. For time independent model, the probability of corrosion at 100 years of exposure for inner wall and outer wall was ranged 59.5 and 95.5%, respectively, while time dependent model indicated 2.9 and 0.2% of the probability corrosion, respectively. Finally, impact of $C_{lim}$, including values specified in current codes, on the probability of corrosion initiation and corrosion free life is discussed.

Effect of a frontal impermeable layer on the excess slurry pressure during the shield tunnelling in the saturated sand (포화 사질토에서 전방 차수층이 쉴드터널 초과 이수압에 미치는영향)

  • Lee, Yong-Jun;Lee, Sang-Duk
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.13 no.4
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    • pp.347-370
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    • 2011
  • Slurry type shield would be very effective for the tunnelling in a sandy ground, when the slurry pressure would be properly adjusted. Low slurry pressure could cause a tunnel face failure or a ground settlement in front of the tunnel face. Thus, the stability of tunnel face could be maintained by applying an excess slurry pressure that is larger than the active earth pressure. However, the slurry pressure should increase properly because an excessively high slurry pressure could cause the slurry flow out or the passive failure of the frontal ground. It is possible to apply the high slurry pressure without passive failure if a horizontal impermeable layer is located in the ground in front of the tunnel face, but its location, size, and effects are not clearly known yet. In this research, two-dimensional model tests were carried out in order to find out the effect of a horizontal impermeable layer for the slurry shield tunnelling in a saturated sandy ground. In tests slurry pressure was increased until the slurry flowed out of the ground surface or the ground fails. Location and dimension of the impermeable layer were varied. As results, the maximum and the excess slurry pressure in sandy ground were linearly proportional to the cover depth. Larger slurry pressure could be applied to increase the stability of the tunnel face when the impermeable layer was located in the ground above the crown in front of the tunnel face. The most effective length of the impermeable grouting layer was 1.0 ~ 1.5D, and the location was 1.0D above the crown level. The safety factor could be suggested as the ratio of the maximum slurry pressure to the active earth pressure at the tunnel face. It could also be suggested that the slurry pressure in the magnitude of 3.5 ~4.0 times larger than the active earth pressure at the initial tunnel face could be applied if the impermeable layer was constructed at the optimal location.

Estimation of Ground-level PM10 and PM2.5 Concentrations Using Boosting-based Machine Learning from Satellite and Numerical Weather Prediction Data (부스팅 기반 기계학습기법을 이용한 지상 미세먼지 농도 산출)

  • Park, Seohui;Kim, Miae;Im, Jungho
    • Korean Journal of Remote Sensing
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    • v.37 no.2
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    • pp.321-335
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    • 2021
  • Particulate matter (PM10 and PM2.5 with a diameter less than 10 and 2.5 ㎛, respectively) can be absorbed by the human body and adversely affect human health. Although most of the PM monitoring are based on ground-based observations, they are limited to point-based measurement sites, which leads to uncertainty in PM estimation for regions without observation sites. It is possible to overcome their spatial limitation by using satellite data. In this study, we developed machine learning-based retrieval algorithm for ground-level PM10 and PM2.5 concentrations using aerosol parameters from Geostationary Ocean Color Imager (GOCI) satellite and various meteorological parameters from a numerical weather prediction model during January to December of 2019. Gradient Boosted Regression Trees (GBRT) and Light Gradient Boosting Machine (LightGBM) were used to estimate PM concentrations. The model performances were examined for two types of feature sets-all input parameters (Feature set 1) and a subset of input parameters without meteorological and land-cover parameters (Feature set 2). Both models showed higher accuracy (about 10 % higher in R2) by using the Feature set 1 than the Feature set 2. The GBRT model using Feature set 1 was chosen as the final model for further analysis(PM10: R2 = 0.82, nRMSE = 34.9 %, PM2.5: R2 = 0.75, nRMSE = 35.6 %). The spatial distribution of the seasonal and annual-averaged PM concentrations was similar with in-situ observations, except for the northeastern part of China with bright surface reflectance. Their spatial distribution and seasonal changes were well matched with in-situ measurements.

Ecological Changes of Insect-damaged Pinus densiflora Stands in the Southern Temperate Forest Zone of Korea (I) (솔잎혹파리 피해적송림(被害赤松林)의 생태학적(生態学的) 연구(研究) (I))

  • Yim, Kyong Bin;Lee, Kyong Jae;Kim, Yong Shik
    • Journal of Korean Society of Forest Science
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    • v.52 no.1
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    • pp.58-71
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    • 1981
  • Thecodiplosis japonesis is sweeping the Pinus densiflora forests from south-west to north-east direction, destroying almost all the aged large trees as well as even the young ones. The front line of infestation is moving slowly but ceaselessly norhwards as a long bottle front. Estimation is that more than 40 percent of the area of P. densiflora forest has been damaged already, however some individuals could escapes from the damage and contribute to restore the site to the previous vegetation composition. When the stands were attacked by this insect, the drastic openings of the upper story of tree canopy formed by exclusively P. densiflora are usually resulted and some environmental factors such as light, temperature, litter accumulation, soil moisture and offers were naturally modified. With these changes after insect invasion, as the time passes, phytosociologic changes of the vegetation are gradually proceeding. If we select the forest according to four categories concerning the history of the insect outbreak, namely, non-attacked (healthy forest), recently damaged (the outbreak occured about 1-2 years ago), severely damaged (occured 5-6 years ago), damage prolonged (occured 10 years ago) and restored (occured about 20 years ago), any directional changes of vegetation composition could be traced these in line with four progressive stages. To elucidate these changes, three survey districts; (1) "Gongju" where the damage was severe and it was outbroken in 1977, (2) "Buyeo" where damage prolonged and (3) "Gochang" as restored, were set, (See Tab. 1). All these were located in the south temperate forest zone which was delimited mainly due to the temporature factor and generally accepted without any opposition at present. In view of temperature, the amount and distribution of precipitation and various soil factor, the overall homogeneity of environmental conditions between survey districts might be accepted. However this did not mean that small changes of edaphic and topographic conditions and microclimates can induce any alteration of vegetation patterns. Again four survey plots were set in each district and inter plot distance was 3 to 4 km. And again four subplots were set within a survey plot. The size of a subplot was $10m{\times}10m$ for woody vegetation and $5m{\times}5m$ for ground cover vegetation which was less than 2 m high. The nested quadrat method was adopted. In sampling survey plots, the followings were taken into account: (1) Natural growth having more than 80 percent of crown density of upper canopy and more than 5 hectares of area. (2) Was not affected by both natural and artificial disturbances such as fire and thinning operation for the past three decades. (3) Lower than 500 m of altitude (4) Less than 20 degrees of slope, and (5) Northerly sited aspect. An intensive vegetation survey was undertaken during the summer of 1980. The vegetation was devided into 3 categories for sampling; the upper layer (dominated mainly by the pine trees), the middle layer composed by oak species and other broad-leaved trees as well as the pine, and the ground layer or the lower layer (shrubby form of woody plants). In this study our survey was concentrated on woody species only. For the vegetation analysis, calculated were values of intensity, frequency, covers, relative importance, species diversity, dominance and similarity and dissimilasity index when importance values were calculated, different relative weights as score were arbitrarily given to each layer, i.e., 3 points for the upper layer, 2 for the middle layer and 1 for the ground layer. Then the formula becomes as follows; $$R.I.V.=\frac{3(IV\;upper\;L.)+2(IV.\;middle\;L.)+1(IV.\;ground\;L.)}{6}$$ The values of Similarity Index were calculated on the basis of the Relative Importance Value of trees (sum of relative density, frequency and cover). The formula used is; $$S.I.=\frac{2C}{S_1+S_2}{\times}100=\frac{2C}{100+100}{\times}100=C(%)$$ Where: C = The sum of the lower of the two quantitative values for species shared by the two communities. $S_1$ = The sum of all values for the first community. $S_2$ = The sum of all values for the second community. In Tab. 3, the species composition of each plot by layer and by district is presented. Without exception, the species formed the upper layer of stands was Pinus densiflora. As seen from the table, the relative cover (%), density (number of tree per $500m^2$), the range of height and diameter at brest height and cone bearing tendency were given. For the middle layer, Quercus spp. (Q. aliena, serrata, mongolica, accutissina and variabilis) and Pinus densiflora were dominating ones. Genus Rhodedendron and Lespedeza were abundant in ground vegetation, but some oaks were involved also. (1) Gongju district The total of woody species appeared in this district was 26 and relative importance value of Pinus densiflora for the upper layer was 79.1%, but in the middle layer, the R.I.V. for Quercus acctissima, Pinus densiflora, and Quercus aliena, were 22.8%, 18.7% and 10.0%, respectively, and in ground vegetation Q. mongolica 17.0%, Q. serrata 16.8% Corylus heterophylla 11.8%, and Q. dentata 11.3% in order. (2) Buyeo district. The number of species enumerated in this district was 36 and the R.I.V. of Pinus densiflora for the uppper layer was 100%. In the middle layer, the R.I.V. of Q. variabilis and Q. serrata were 8.6% and 8.5% respectively. In the ground vegetative 24 species were counted which had no more than 5% of R.I.V. The mean R.I.V. of P.densiflora ( totaling three layers ) and averaging four plots was 57.7% in contrast to 46.9% for Gongju district. (3) Gochang-district The total number of woody species was 23 and the mean R.I.V. of Pinus densiflora was 66.0% showing greater value than those for two former districts. The next high value was 6.5% for Q. serrata. As the time passes since insect outbreak, the mean R.I.V. of P. densiflora increased as the following order, 46.9%, 57.7% and 66%. This implies that P. densiflora was getting back to its original dominat state again. The pooled importance of Genus Quercus was decreasing with the increase of that for Pinus densiflora. This trend was contradict to the facts which were surveyed at Kyonggi-do area (the central temperate forest zone) reported previously (Yim et al, 1980). Among Genus Quercus, Quercus acutissina, warm-loving species, was more abundant in the southern temperature zone to which the present research is concerned than the central temperate zone. But vice-versa was true with Q. mongolica, a cold-loving one. The species which are not common between the present survey and the previous report are Corpinus cordata, Beltala davurica, Wisturia floribunda, Weigela subsessilis, Gleditsia japonica var. koraiensis, Acer pseudosieboldianum, Euonymus japonica var. macrophylla, Ribes mandshuricum, Pyrus calleryana var. faruiei, Tilia amurensis and Pyrus pyrifolia. In Figure 4 and Table 5, Maximum species diversity (maximum H'), Species diversity (H') and Eveness (J') were presented. The Similarity indices between districts were shown in Tab. 5. Seeing Fig. 6, showing two-dimensional ordination of polts on the basis of X and Y coordinates, Ai plots aggregate at the left site, Bi plots at lower site, and Ci plots at upper-right site. The increasing and decreasing patterns as to Relative Density and Relative Importance Value by genus or species were given in Fig. 7. Some of the patterns presented here are not consistent with the previously reported ones (Yim, et al, 1980). The present authors would like to attribute this fact that two distinct types of the insect attack, one is the short war type occuring in the south temperate forest zone, which means that insect attack went for a few years only, the other one is a long-drawn was type observed at the temperate forest zone in which the insect damage went on continuously for several years. These different behaviours of infestation might have resulted the different ways of vegetational change. Analysing the similarity indices between districts, the very convincing results come out that the value of dissimilarity index between A and B was 30%, 27% between B and C and 35% between A and C (Table 6). The range of similarity index was obtained from the calculation of every possible combinations of plots between two districts. Longer time isolation between communities has brought the higher value of dissimilarity index. The main components of ground vegetation, 10 to 20 years after insect outbreak, become to be consisted of mainly Genus Lespedeza and Rhododendron. Genus Quercus which relate to the top dorminant state for a while after insect attack was giving its place to Pinus densiflora. It was implied that, provided that the soil fertility, soil moisture and soil depth were good enough, Genus Quercuss had never been so easily taken ever by the resistant speeies like Pinus densiflora which forms the edaphic climax at vast areas of forest land. Usually they refer Quercus to the representative component of the undisturbed natural forest in the central part of this country.

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Efficacy and Accuracy of Patient Specific Customize Bolus Using a 3-Dimensional Printer for Electron Beam Therapy (전자선 빔 치료 시 삼차원프린터를 이용하여 제작한 환자맞춤형 볼루스의 유용성 및 선량 정확도 평가)

  • Choi, Woo Keun;Chun, Jun Chul;Ju, Sang Gyu;Min, Byung Jun;Park, Su Yeon;Nam, Hee Rim;Hong, Chae-Seon;Kim, MinKyu;Koo, Bum Yong;Lim, Do Hoon
    • Progress in Medical Physics
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    • v.27 no.2
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    • pp.64-71
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    • 2016
  • We develop a manufacture procedure for the production of a patient specific customized bolus (PSCB) using a 3D printer (3DP). The dosimetric accuracy of the 3D-PSCB is evaluated for electron beam therapy. In order to cover the required planning target volume (PTV), we select the proper electron beam energy and the field size through initial dose calculation using a treatment planning system. The PSCB is delineated based on the initial dose distribution. The dose calculation is repeated after applying the PSCB. We iteratively fine-tune the PSCB shape until the plan quality is sufficient to meet the required clinical criteria. Then the contour data of the PSCB is transferred to an in-house conversion software through the DICOMRT protocol. This contour data is converted into the 3DP data format, STereoLithography data format and then printed using a 3DP. Two virtual patients, having concave and convex shapes, were generated with a virtual PTV and an organ at risk (OAR). Then, two corresponding electron treatment plans with and without a PSCB were generated to evaluate the dosimetric effect of the PSCB. The dosimetric characteristics and dose volume histograms for the PTV and OAR are compared in both plans. Film dosimetry is performed to verify the dosimetric accuracy of the 3D-PSCB. The calculated planar dose distribution is compared to that measured using film dosimetry taken from the beam central axis. We compare the percent depth dose curve and gamma analysis (the dose difference is 3%, and the distance to agreement is 3 mm) results. No significant difference in the PTV dose is observed in the plan with the PSCB compared to that without the PSCB. The maximum, minimum, and mean doses of the OAR in the plan with the PSCB were significantly reduced by 9.7%, 36.6%, and 28.3%, respectively, compared to those in the plan without the PSCB. By applying the PSCB, the OAR volumes receiving 90% and 80% of the prescribed dose were reduced from $14.40cm^3$ to $0.1cm^3$ and from $42.6cm^3$ to $3.7cm^3$, respectively, in comparison to that without using the PSCB. The gamma pass rates of the concave and convex plans were 95% and 98%, respectively. A new procedure of the fabrication of a PSCB is developed using a 3DP. We confirm the usefulness and dosimetric accuracy of the 3D-PSCB for the clinical use. Thus, rapidly advancing 3DP technology is able to ease and expand clinical implementation of the PSCB.

Memory Organization for a Fuzzy Controller.

  • Jee, K.D.S.;Poluzzi, R.;Russo, B.
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1993.06a
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    • pp.1041-1043
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    • 1993
  • Fuzzy logic based Control Theory has gained much interest in the industrial world, thanks to its ability to formalize and solve in a very natural way many problems that are very difficult to quantify at an analytical level. This paper shows a solution for treating membership function inside hardware circuits. The proposed hardware structure optimizes the memoried size by using particular form of the vectorial representation. The process of memorizing fuzzy sets, i.e. their membership function, has always been one of the more problematic issues for the hardware implementation, due to the quite large memory space that is needed. To simplify such an implementation, it is commonly [1,2,8,9,10,11] used to limit the membership functions either to those having triangular or trapezoidal shape, or pre-definite shape. These kinds of functions are able to cover a large spectrum of applications with a limited usage of memory, since they can be memorized by specifying very few parameters ( ight, base, critical points, etc.). This however results in a loss of computational power due to computation on the medium points. A solution to this problem is obtained by discretizing the universe of discourse U, i.e. by fixing a finite number of points and memorizing the value of the membership functions on such points [3,10,14,15]. Such a solution provides a satisfying computational speed, a very high precision of definitions and gives the users the opportunity to choose membership functions of any shape. However, a significant memory waste can as well be registered. It is indeed possible that for each of the given fuzzy sets many elements of the universe of discourse have a membership value equal to zero. It has also been noticed that almost in all cases common points among fuzzy sets, i.e. points with non null membership values are very few. More specifically, in many applications, for each element u of U, there exists at most three fuzzy sets for which the membership value is ot null [3,5,6,7,12,13]. Our proposal is based on such hypotheses. Moreover, we use a technique that even though it does not restrict the shapes of membership functions, it reduces strongly the computational time for the membership values and optimizes the function memorization. In figure 1 it is represented a term set whose characteristics are common for fuzzy controllers and to which we will refer in the following. The above term set has a universe of discourse with 128 elements (so to have a good resolution), 8 fuzzy sets that describe the term set, 32 levels of discretization for the membership values. Clearly, the number of bits necessary for the given specifications are 5 for 32 truth levels, 3 for 8 membership functions and 7 for 128 levels of resolution. The memory depth is given by the dimension of the universe of the discourse (128 in our case) and it will be represented by the memory rows. The length of a world of memory is defined by: Length = nem (dm(m)+dm(fm) Where: fm is the maximum number of non null values in every element of the universe of the discourse, dm(m) is the dimension of the values of the membership function m, dm(fm) is the dimension of the word to represent the index of the highest membership function. In our case then Length=24. The memory dimension is therefore 128*24 bits. If we had chosen to memorize all values of the membership functions we would have needed to memorize on each memory row the membership value of each element. Fuzzy sets word dimension is 8*5 bits. Therefore, the dimension of the memory would have been 128*40 bits. Coherently with our hypothesis, in fig. 1 each element of universe of the discourse has a non null membership value on at most three fuzzy sets. Focusing on the elements 32,64,96 of the universe of discourse, they will be memorized as follows: The computation of the rule weights is done by comparing those bits that represent the index of the membership function, with the word of the program memor . The output bus of the Program Memory (μCOD), is given as input a comparator (Combinatory Net). If the index is equal to the bus value then one of the non null weight derives from the rule and it is produced as output, otherwise the output is zero (fig. 2). It is clear, that the memory dimension of the antecedent is in this way reduced since only non null values are memorized. Moreover, the time performance of the system is equivalent to the performance of a system using vectorial memorization of all weights. The dimensioning of the word is influenced by some parameters of the input variable. The most important parameter is the maximum number membership functions (nfm) having a non null value in each element of the universe of discourse. From our study in the field of fuzzy system, we see that typically nfm 3 and there are at most 16 membership function. At any rate, such a value can be increased up to the physical dimensional limit of the antecedent memory. A less important role n the optimization process of the word dimension is played by the number of membership functions defined for each linguistic term. The table below shows the request word dimension as a function of such parameters and compares our proposed method with the method of vectorial memorization[10]. Summing up, the characteristics of our method are: Users are not restricted to membership functions with specific shapes. The number of the fuzzy sets and the resolution of the vertical axis have a very small influence in increasing memory space. Weight computations are done by combinatorial network and therefore the time performance of the system is equivalent to the one of the vectorial method. The number of non null membership values on any element of the universe of discourse is limited. Such a constraint is usually non very restrictive since many controllers obtain a good precision with only three non null weights. The method here briefly described has been adopted by our group in the design of an optimized version of the coprocessor described in [10].

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