Research Article. Research on environmental prediction based on linear regression model

Transcription

1 Avalable onlne Journal of Chemcal and Pharmaceutcal Research, 06, 8(6): Research Artcle ISSN : CODEN(USA) : JCPRC5 Research on envronmental predcton based on lnear regresson model Fang Chen, Jnglun Lu and Le Lu 3 Chongqnng Normal Unversty, Chongqng, , Chna Baoshan Unversty, Yunnan, , Chna 3 Zhaotong Unversty, Yunnan, , Chna ABSTRACT Envronmental predcton n metal mne has been the man problem whch nterferes wth mnng workng at depth. And ts correspondng formaton mechansm s so complcated that the envronmental predcton theory cannot come up wth the practcal engneerng research. So t s necessary to establsh the correspondng geologcal structure stress model of the mnng area studed, analyze ts mechansm and put forward the predcton of envronmental predcton locaton n mnng area. Based on the correspondng geologcal structure stress data of chongqng mne n Schuan, ths paper establshes the three-dmensonal fnte element modelng wth numercal smulaton, n order to calculate, analyze and predct the structure stress and the locaton where the envronmental predcton may occur wthn the range of 3 klometers n ths mne. Keywords: Metal mne; envronmental predcton; lnear regresson model INTRODUCTION Envronmental predcton s a natural dsaster whch loses dynamc balance. Due to the great geostress, the excavaton load leads to the dfferentaton of stress and the sudden release of the elastc energy n rock mass. Drectly affects the workng effcency of the metal mnng enterprses, ncreases ts economc costs, and even leads to safety accdents. How to forecast envronmental predcton n mnng process effectvely, has become one of the challenges faced by the underground project worldwde. envronmental predcton predcton s manly based on the formng mechansm of envronmental predcton from the qualtatve or quanttatve analyss of the envronmental predcton orentaton, and the research methods manly nclude the theory analyss and the feld measurement method. Currently, a completed and mature set of theory and method has not yet formed ether at home or abroad. Wth the development of computer scence and technology, the applcatons of artfcal ntellgence, expert system and numercal analyss have become an mportant drecton n envronmental predcton predcton []. Ths paper studes the envronmental predcton of mnng at depth n chongqng mne, Schuan. The man method s the applcaton of ANSYS fnte element analyss smulaton tools, settng up the three-dmensonal geostress model, analyzng the regon stress and local mnng roadway by fnte element, combned wth the correspondng numercal analyss structure, studyng ts mnng energy dstrbuton law of surroundng rocks. Whether the burst would come out or not and the correspondng damage degree are predcted n terms of the related crtera of envronmental predcton. Through ths method, the envronmental predcton poston and destructon area can be determned n the practcal engneerng process of mnng at depth, provdng the correspondng regonal stress feld dstrbuton and the correspondng bass for safety producton, whch guarantees the safety of staff underground as a result. Analyss of tectonc stress envronment of chongqng mne n Schuan After 30 years of mnng n chongqng mne, the man mnng ste s deeper than 500m, and the correspondng development engneerng has reached the depth of 00m. Accordng to the relevant engneerng experence, the 443

2 explot depth has been near the crtcal pont of envronmental predcton. Its man feature s the tectonc stress of mnng area s very hgh, and the shallow horzontal stress on the surface s greater than gravty stress. Because of the nfluence of the correspondng mnng work, stress concentraton area has emerged n ths regon, large energy s gathered nsde the rock mass, and the condton of envronmental predcton has developed. On the bass of geologcal and stress data untl now, the resdual tectonc stress on horzontal drecton s huge, and two horzontal stress of ts weght, have separately become a maxmum and mnmum prncpal stress, that s: σ = σ = (0.5~0.40)σ z, gravty maxmum vertcal stress becomes a prncpal stress stress feld under the condton of gravty: σ = σ z. The east sde of chongqng mne: σ = (.7~3.33)γh, σ 3 = (0.33~0.59)γh; The west sde of chongqng mne:σ = (.7~.6)γh, σ 3 = (0.7~0.59)γh. The planar projecton of the man ore body of chongqng mne s shown n fgure. Fg. Planar Projecton of Ore Body n chongqng Mne Numercal modelng for chongqng mne Numercal modelng of fnte element. In the process of deep mnng, msestmatng the stress of the surroundng rock mass wll make the envronmental predcton suddenly, mpactng the producton progress and the safety of the staff; Under estmatng the strength of the surroundng rock mass wll make the mnng and project desgn too conservatve, ncrease the mnng cost, whch leads to waste the correspondng fnancal and materal resources. Because the analyss of the mne stress feld s a complex result combned wth multple factors, the three-dmensonal fnte element model s chosen for analyss and calculaton accordng to the actual stuaton of engneerng n chongqng mne area. Settng the measured geostress nformaton as the calculaton reference ponts of the fnte element numercal smulaton method, makes the correspondng structure closer to the actual stuaton. The establshment of fnte element three-dmensonal modelng The :5000 prospectng lne secton map, :5000 present stuaton map of the mnng envronment and :000 geographcal cross-secton dagram between -430m and -640m level are collected as the man geologcal data of chongqng mne. Takng computer processng speed and accuracy requrements nto account, a total range of 3 klometers s chosen from the mne, east to the producton department, and west to X Wang Chong. Mnng depth selecton s manly based on the followng two aspects, one s to assume the coordnaton of the model sze, therefore, -000m s selected as the alttude; The other s for the reference of related documents and to calculate the structure, only -430m~800m need to be consdered. Bottomless sublevel cavng mnng s applyng n chongqng mne. In the modelng process, due to the nfluence of strata subsdence zone, -48m~50m s approxmately set as the subsdence zone, whose upper angle of -430m level s 55 and lower angle 65. The fnte element model of chongqng mnng area s shown n fgure. 444

3 Fg. Fnte Element Modelng of chongqng Mne Yeld crteron. Mohr-Coulomb yeld surface has some defects n practcal engneerng applcaton. When the stress s located n or near the corners, t s so hard to determne the outer normal dervatve of yeld functon along the surface that the numercal calculaton for vscoplastc stran rate cannot be accurate. Drucker-Praher modfed t based on Mohr-Coulomb and Mses crtera: f = α I + J K 0 () = In the above formula: I and J are the frst constant of stress tensor and the second constant of stress devator respectvely. α and K are nternal frcton angle of rock and expermental constant of cohesve force respectvely: α snϕ = () 3(3 snϕ) 6cosϕ K = (3) 3 ( 3 snϕ) Fnte element modelng of stress n mnng area. The dstrbuton nephograms of vertcal maxmum prncpal stress σ both n mnng area and ore body are shown n fgure 3 and fgure 4. After mnng at -430m level, large tensle stress exsts at -500m level, the maxmum stress s 4.5 MPa. The man reason s that nfluenced by the upper mnng and engneerng, large mned-out areas or loose coverng layers appear and the concentrated underground stress comes out. Wth the mnng depth ncreasng, the tensle stress changes nto compressve stress, and ts quantty ncreases. The three-dmensonal smulaton results show that there exsts a hgh geostress feld n chongqng mnng area, whose depth s 000m and the maxmum value 44 MPa. Fg.3 Vertcal maxmum stress nephogram of the mnng area Fg.4 Vertcal maxmum stress nephogram of the ore body LINEAR REGRESSION MODEL The theory-orented lectures cover sngle lnear regresson and multple lnear regressons. Students learn what regresson s, how to create ts mode, how to estmate the parameters of the model (Estmaton Usng Least Squares), understandng the assumptons of establshng the condtons for the model, what the regresson coeffcents are, how to compare the models, and predctng and controllng usng regresson model. Teachers start thers lectures wth a 445

4 dscusson of smple regresson, then, move on to multple lnear regresson. Ths s qute reasonable from a pedagogcal pont of vew, snce smple regresson has the great advantage of beng easy to understand graphcally. Students should place a lot of emphass on the smple lnear regresson analyss and understandng ts mathematcal expressons and be open to more sophstcated concepts. It s dffcult for students to study multple lnear regresson analyss. However, t s a prmary tool n the analyss of real data. Thereby, sngle lnear regresson s taught n sx sessons, whle multple lnear regresson requres four sessons. A sesson s 90 mnutes duraton. Sngle lnear model descrbes a lnear relatonshp between two varables. One s called the target, response or dependent varable, and s usually represented. Another s called the predctng or ndependent varables, and s usually represented by x. Gven ( x, x,λ, xn ), the smple lnear regresson model s descrbed as: C mn N = k + C X + [ Y ( j + )] h. = X + Y ( j) Y ( j + ) ( + δ) q = 0, R where the data, x, y, represent a random sample from a larger populaton, whch consst of n set of observatons, the coeffcents are unknown parameters, and are random error or dsturbance terms. FEEDBACK EXERCISES In the sprng semester of the 0/03 term, a total of 60 junor students came from two majors,, joned the course at the Xnxang Unversty, Xnxang, Chna. These students already had joned some prevous courses, such as mathematcal analyss, advanced algebra, probablty and statstcs, etc [5]. They also demonstrated a certan level of operatng computer software capablty. A survey questonnare wth sx feedback questons was admnstered to all of these students (shown n Table ). Tab.: Feedback questons Majors Questons Computerscence Mathematcs (students30) (students30) Mean I becamenterestedndataanalyssthroughthsclass. 7 (90%) 8 (93%) 9% I understandtheconceptoflnearregresson. 4 (80%) 6 (87%) 83% 3 I performedthelnearregressonusngmatlabprogram. 7 (90%) 6 (87%) 88% 4 I performedthelnearregressonusngmsexcel. 9 (97%) 9 (97%) 97% 5 I thnkthepractces usefultounderstandtheconceptof lnearregresson. 30 (00%) 30 (00%) 00% 6 I canapplymyknowledgeof mathematcsbyperformng theexperment. 4 (80%) 5 (83%) 8% There are too many formulatons about regresson analyss. It s often dffcult to understand these concepts of regresson analyss, sad some students. As can be seen from student feedback, only 80% of computer scence students can understand regresson, whle 87% of mathematcs students can do so. However, almost students fnshed ther experments, and all of them thnk the practce s very useful to understand those concepts. Ths nformaton shows that students' nterest wll be enthused f theory s combned wth practce, and as long as theory explanaton s not gnored. Its objectve s to strengthen ther statstcal sklls. One of the authors receved and accepted the teachng load. Hence, sharng the teachng experence s the objectve of ths artcle. THEORY TEACHING The theory-orented lectures cover sngle lnear regresson and multple lnear regressons. Students learn what regresson s, how to create ts mode, how to estmate the parameters of the model (Estmaton Usng Least Squares), understandng the assumptons of establshng the condtons for the model, what the regresson coeffcents are, how to compare the models, and predctng and controllng usng regresson model. Teachers start thers lectures wth a dscusson of smple regresson, then, move on to multple lnear regresson. Ths s qute reasonable from a pedagogcal pont of vew, snce smple regresson has the great advantage of beng easy to understand graphcally. Students should place a lot of emphass on the smple lnear regresson analyss and understandng ts mathematcal expressons and be open to more sophstcated concepts. It s dffcult for students to study multple lnear regresson analyss. However, t s a prmary tool n the analyss of real data. Thereby, sngle lnear regresson s taught n sx sessons, whle multple lnear regresson requres four sessons. A sesson s 90 mnutes duraton. 446

5 SINGLE LINEAR REGRESSION MODEL Sngle lnear model descrbes a lnear relatonshp between two varables. One s called the target, response or dependent varable, and s usually represented by y. Another s called the predctng or ndependent varables, and s usually represented by x. Gven y = β0 + βx + ε ε ~ N(0, σ ) and cov( ε, ε { } where the data x, y ( x, x K xn ), the smple lnear regresson model s descrbed as: ) = 0 when j j, represent a random sample from a larger populaton, whch consst of n set of observatons, () the β coeffcents are unknown parameters, and β are random error or dsturbance terms. LEAST SQUARE ESTIMATION A prmary goal of a regresson analyss s to estmate the relatonshp between the predctor and the target varables or equvalently, to estmate the unknown parameter β. Ths requres a data-based rule or crteron that wll gve a reasonable estmate. The standard approach s least squares regresson whch s a convex optmsaton problem wth no constrants. The objectve s a sum of squares of terms of the form that are chosen to mnmse: n = y ( β0 + βx )] [ () The scatter dagram gves a graphcal representaton of least squares, whch can help students to understand regresson graphcally. If the ftted regresson equaton has been obtaned, t s a lne gven by: E( y) = β + β x (3) 0 y Resduals are defned as the dfference between the observed value and the ftted value. Equaton () mnmses the sum of squares of the resduals f the coeffcents β β take as the ftted coeffcent. By mnmsng Equaton (), the regresson coeffcents are obtaned by: β β 0 = y β x = S xy / S xx x = x, =, = ( ) y y S xx x x, S XY = ( x x)( y y) where n n (4) Evaluaton of envronmental predcton Suffcent and necessary condtons of envronmental predcton n mnes are as follows. Frstly, the rock tself can store a lot of elastc stran energy; secondly, there exsts the related envronment to produce hgh stress and accumulate energy. Based on the fnte element calculaton and analyss, the dstrbuton features and quantty of the elastc stran energy n surroundng rocks after deep mnng can be obtaned, the calculaton formula s: = ( σ ω + σ ω + σ )/ W (4) e 3ω3 In the above formula: σ, ε, σ, ε, σ 3, ε 3 are the prncpal stress and stran of rock unt respectvely. Related researches at home and abroad as well as the feld montorng show that, f the nternal elastc energy of rock mass reaches or exceeds J m 3, correspondng mpact ground pressure and envronmental predcton wll happen. Fgure 5 s the elastc stran energy dstrbuton nephogram of mnng area at -430m level, and the related calculaton results show that the rock mass has hgh horzontal elastc energy at -500m, as shown n fgure 6. When mnng below -500m, there wll be the phenomenon of envronmental predcton and ejecton. 447

6 Fg.5 Varaton nephogram of elastc energy n -430m mne area Fg.6 Varaton nephogram of elastc energy n -500m mne area CONCLUSION Amng at the structure stress crcumstances of chongqng mnng area, applyng numercal smulaton of fnte element method, establshng the three-dmensonal fnte element model of chongqng mne, settng the correspondng yeld crteron, the expermental results show that the maxmum tensle stress s 44 MPa at -000m n chongqng mne. On ths bass, ths paper studes the locaton where the envronmental predcton may occur n the mne area. Through the correspondng judgng crtera of envronmental predcton, contnual mnng under -500m n the mne area wll lead to envronmental predcton or rock ejecton for sure. REFERENCES [] Guo L. The model to dynamcally predct envronmental predcton proneness of hard rock at depth and ts applcaton, D. Central South Unversty, Changsha. (009) -. [] Gu De-sheng, L X-bn. Scence problems and research state of deep mnng n metal and nonferrous mnes, C. The ffth academc annual conference papers of Chna Nonferrous Metal Insttute. Mnng research and development magazne, Changsha. (00) -4. [3] He Man-chao, Xe He-png, Peng Su-png. J. Chnese Journal of Rock Mechancs and Engneerng. 4 (009) [4] Mu Xao-jun, Wu J-mn, L Jng-bo. Causes of envronmental predcton n crcular chambers and ts geologcal dsaster analyss, J. Journal of Hoha Unversty (Natural Scences). 30 (0) [5] Zhu Q-hu, Lu Wen-bo, Sun Jn-shan. J. Engneerng Journal of Wuhan Unversty. 40 (007)