Fuzzy Rules Based System for Diagnosis of Stone Construction Cracks of Buildings

Transcription

1 Fuzzy Rules Base System for Diagnosis of Stone Construction Cracks of Builings Serhiy Shtovba, Alexaner Rotshtein* an Olga Pankevich Vinnitsa State Technical University Khmelnitskoe Shosse, 95, 21021, Vinnitsa, Ukraine Phone: , Fax: *Jerusalem College of Technology - Mahon Lev Havvaa Haleumi st., 21, 91160, Jerusalem, Israel Phone: , Fax: rot@barley.cteh.ac.il ABSTRACT: This paper presents the fuzzy expert system for intelligent support of ecision making about cause of stone construction crack of builing. The system is base on some linguistic expert expressions formalise by 9 fuzzy knowlege bases. Tuning of fuzzy rules by genetic algorithms provie a goo concorance between real causes of cracks an results of ecision making by the system. KEYWORDS: Stone Construction Crack, Diagnosis, Hierarchical Fuzzy Knowlege Bases, Tuning, Genetic Algorithms. INTRODUCTION Diagnosis (or etermination of cause) of stone construction crack is an important task of builing engineering. Instant an correct iagnosis of the stone construction cracks makes further investigations, esign an reconstruction of builings successful. The task of iagnosis may be solve correctly by high qualification engineers with large experience only. The number of such experts is lacking an in connection with this the esign of intelligent system for crack of builings iagnose is necessity. This paper presents the fuzzy expert system for ecision making support about cause of stone construction crack of builing. The approach to the system esign suggeste in this paper is base on: escription of the structure of iagnostic moel by hierarchical ecision making tree; presentation of state parameters in linguistic variable form; formalisation of linguistic terms by fuzzy sets; formalisation of expert nature language expressions about relationship «state parameters - iagnosis» by fuzzy knowlege bases; tuning of the knowlege bases by genetic optimization of membership functions parameters an weight of the rules. The approach allows to use as expert linguistic information as experimental ata reflecting interconnection between input an output parameters. The use of all available source information provies increasing of iagnostic moel quality. PROBLEM STATEMENT Different causes of stone construction cracks was classifie in the next iagnoses: 1 - static overloa; 2 - ynamic overloa; 3 - especial overloa; ESIT 2000, September 2000, Aachen, Germany 402

2 4 - efects of basis an founation; 5 - temperature influence; 6 - breach of technological process of builing. Suggeste classification accors to maximal epth of iagnosis, which can be got for case of visual investigations. Source information, which nee for ecision making, is ata of visual investigation of builing. These are values of the next factors (parameters of object state): x 1 - construction type; x 2 - work conition; x 3 - thickness of horizontal junctions; x 4 - efects of junctions filling; x 5 - efects of banaging system; x 6 - presence of unprovie holes; x 7 - efects of reinforcing; x 8 - curve of construction; x 9 - eflection from vertical line; x 10 - moistening of brickwork; x 11 - peeling of brickwork; x 12 - weathering of brickwork; x 13 - leaching of brickwork; x 14 - crumbling out of brickwork; x 15 - crack location; x 16 - crack irection; x 17 - opening of crack; x 18 - crack with; x 19 - crack length; x 20 - consequences of fair; x 21 - information about earthquakes, explosions; x 22 - presence of ynamic loa; x 23 - splitting uner straight; x 24 - crack epth; x 25 - isplacement of breast-wall; x 26 - amage of water-supply system; x 27 - quality of rains; x 28 - presence of loose soils; x 29 - present of water into basement; x 30 - presence of capacity construction close; x 31 - presence of new contiguity builings; x 32 - isplacement of straight, beam; x 33 - necessity of settle junction; x 34 - presence of settle junction; x 35 - presence of aitional loas; x 36 - presence of mechanical amage; x 37 - quality of cushions uner beams; x 38 - insufficient size of beans bearing place; x 39 - necessity of temperature junction; x 40 - presence of temperature junction; x 41 - execution work on winter; x 42 - using of heterogeneous materials. From cybernetic point of view, creation of the iagnostic moel for cause ( D ) of crack etermination is reuce to fining out the representation of this form: X = {x1,...,x 42} D {1,..., 6 }, where X is a vector of the sate parameters. DECISION MAKING TREE Hierarchical interconnection between state parameters ( X ) an cause of crack ( D ) is represente by Figure 1 in the form of ecision making tree. Graph vertices are interprete in the next way (Rotshtein, 1998): the root - cause of crack; terminal vertices - partial state parameters; nonterminal vertices (ouble circles) - fuzzy knowlege bases; Enlarge state parameters, to which graph eges correspon, as going out of nonterminal vertices are interprete in the following way: y 1 - state of construction; y 2 - estruction of brickwork; y 3 - aitional information; y 4 - possibility of basis an founation efects; y 5 - possibility of static overloa; y 6 - eman to temperature junction; y 7 - possibility of crack connecte with breach of technological processes; y 8 - eman to setle junction. The tie between state parameters an iagnosis is efine by this system of relations: D = fd (x1,x 2,y1,x15,x16,x17,x18,x19,y 3 ) ; y 1 = f y (x3,x 4,x5,x 6,y2,x 7,x8,x9,x 10 ) ; 1 y 2 = f y (x11,x12,x13,x 14 ) ; 2 y 3 = f y (y1,y5,x 20,x 21,x 22,x 23,x 24,y6,y 7 ) ; 3 ESIT 2000, September 2000, Aachen, Germany 403

3 y 4 = f y (x 25,x 26,y8,x 27,x 28,x 29,x30,x31,x 32 ) ; 4 y 5 = f y (x35,x36,x37,x 38 ) ; 5 y6 = f y (x39,x 40 ) ; 6 y7 = f y (x 41,x 42 ) ; 7 y8 = f y (x33,x34 ). 8 x 11 x 12 x 3 x 13 x 4 x 14 x 5 x 1 x 25 x 6 x 33 x 26 f y2 x 2 x 34 f y8 x 27 y 8 x 7 x 8 y 2 f y1 y 1 1 x 28 x 29 x 30 x 9 x 10 f y4 x 15 x 16 f D D x 31 y 4 x 17 6 x 32 f y5 y 5 x 18 x 35 x 20 x 36 x 21 x 19 y 3 x 37 x 22 f y3 x 38 x 23 x 39 x 24 y 6 x 40 f y6 x 41 f y7 y 7 x 42 Figure 1: Decision Making Tree LINGUISTIC VARIABLES AND FUZZY KNOWLEDGE BASES ESIT 2000, September 2000, Aachen, Germany 404

4 Accoring to our approach the state parameters was represente as linguistic variables (Zimmerman, 1996). There were 118 terms, which use for linguistic assessment of partial state parameters an 24 - for enlarge state parameters. For formalisation of linguistic terms have been employe the next membership function moel (Rotshtein an Katelnikov, 1998): t 1 µ (x) =, 2 x b 1+ c t where µ (x) - membership function of variable x to term t; b an c - tuning parameters - coorinate of maximum an concentration coefficient. Natural language expert expressions, which tie up the state parameters an output variable, were formalise in fuzzy knowlege base form. Table 1 shows a fragment of fuzzy knowlege base of top level. Total number of rules of all knowlege bases is 151. x1 x 2 y1 x15 x16 x17 x18 x19 y3 - holing - at support vertical up - - static wall with aperture holing relax across all construction eaf wall holing - between walls wall with holing - across all aperture construc- - holing itself pier holing - from monolithic inclusion overloa slanting uniform hair very long ynamic overloa slanting up - - especial overloa vertical up large scale very long absence tion normal upper part slanting up small long influence of temperature slanting up hair mile property of materials Table 1: Fragment of knowlege base about cause of crack D Definite cause of crack will be etermine by way of solving the system of fuzzy logical equations, which is isomorphic to ecision making tree an fuzzy knowlege bases (Rotshtein, 1998). Fuzzy logical evience is carrie out accoring to the following algorithm (Rotshtein, 1998): Step 1. Fix partial state parameters. Step 2. Fin partial state parameters membership egrees to linguistic terms. Step 3. Weaken foun membership egrees in fuzzy logic equations an calculate ecision membership egrees to terms 1,2,..., 6. Step 4. Choose the term from set { 1,2,...,6} with the maximum membership egree as the iagnosis. Execution of step 2 accoring to (Rotshtein an Shtovba, 1998) allows to use as quantitative as qualitative values of state parameters. SOFTWARE REALISATION AND CHECK EXAMPLE The moels an algorithms suggeste here are realise in expert system which provies intelligent support in ecion making about cause of stone construction cracks of builings. The system is realise on base of FuzzyExpert shell (Rotshtein, 1998). Illustration of propose moel an algorithms application is showe below. Let us consier the crack in wall of Mogiliv- Poilsky Machine Works builing. The next state parameters corresponing to the object: x 1=eaf wall; x 2 =holing; x 3 =normal; x 4 =absence; x 5 =sacre; x 6 =absence; x 7 =absence; x 8 =absence; x 9 =absence; x 10 =absence; x 11=absence; x 12 =absence; x 13 =absence; x 14 ==absence; x 15 =between walls; x 16 =vertical; x 17 =up; x 18 =2, mm; ESIT 2000, September 2000, Aachen, Germany 405

5 x 19 =2, m; x 20 =absence; x 21 =absence; x 22 =absence; x 23 =available; x 24 =two-sies; x 25 =absence; x 26 =available; x 27 =available; x 28 =available; x 29 =absence; x 30 =available; x 31=absence; x 32 =absence; x 33 =not necessary; x 34 =absence; x 35 =absence; x 36 =absence; x 37 =absence; x 38 =absence; x 39 =not necessary; x 40 =absence; x 41 =uncertainly; x 42 =absence. As the results of the fuzzy logic evience we obtain the following egrees of membership: 1 µ (D) = ; 2 µ (D) = ; 3 µ (D) = ; 4 µ (D) = 1 ; 5 µ (D) = ; µ 6 (D) = what correspon to solution 4 - efects of basis an founation. TUNING OF FUZZY DECISION MAKING MODEL Tuning or parametrical ientification is fining out such values of moel parameters which provie the best results of moeling. Accoring to (Rotshtein an Katelnikov, 1998) the tuning parameters of fuzzy ecision making moel are membership functions parameters an weights of fuzzy rules. For our moel the total number of this parameters (controlle variables) is 2x(118+24)+151=435. The number of the one is large, because of for solving this nonlinear large scale optimization task we employe genetic algorithms. After tuning, the results of ecision making by the system is goo concorant with real causes of cracks - the iagnostic error is less than 4%. CONCLUSION Fuzzy expert system which provies intelligent support in ecision making about cause of stone construction crack of builings is propose in this paper. The system can be useful also for the stuents corresponing subject apart from it being employe by practising builing engineering. Suggeste approach for the expert system esign may be use for creation iagnostic system in other fiels. REFERENCES Rotshtein, Alexaner, 1998 «Design an Tuning of Fuzzy Rule-Base Systems for Meical Diagnosis». In «Fuzzy an Neuro-Fuzzy in Meicine», CRC Press, USA. Rotshtein, Alexaner; Katelnikov, Denis, 1998 «Tuning of Fuzzy Rules for Nonlinear Objects Ientification with Discrete an Continuous Output», 6 th European Congress on Intelligent Techniques an Soft Computing, Aachen, Germany, pp Rotshtein, Alexaner; Shtovba, Serhiy, 1998, Preiction the Reliability of Algorithmic Processes with Fuzzy Input Data», Cybernetics an Systems Analysis #34, pp Zimmerman, Hans-Jurger, 1996, «Fuzzy Sets Theory an its Applications». Kluwer Acaemic Publisher, Dorrecht. ESIT 2000, September 2000, Aachen, Germany 406