GOSPODARKA SUROWCAMI MINERALNYMI Tom 24 2008 Zeszyt 3/1 AGNIESZKA MALINOWSKA* Fuzzy logic-based approach to building damage risk assessment considering the social and economic value Introduction The underground mining impact creates a serious problem in Poland, especially that most of the areas are intensely managed. Therefore, the correct determining of the underground mining-induced hazard is a key problem enabling proper prevention of objects in these areas. Dynamic mining exploitation has been carried out for years in Poland. The mining-induced areas vary in their countryside and urban development. Buildings elevated over years differ in the construction materials and the construction techniques themselves. They also differ in their usability. Therefore, when assessing the damage risk of objects it is crucial to know their importance (utility value, destination and economic value). Fig. 1. Buildings with different social and economic importance Rys. 1. Budynki o ró nych wartoœciach spo³ecznych i ekonomicznych * AGH University of Science and Technology Faculty of Mining Surveying and Environmental Engineering, Kraków, Poland.
76 Three methods of accounting for the importance of surface objects when assessing their underground mining-induced damage hazard are presented and compared in the paper. The presently applied in Poland method of assessing damage hazard of buildings without accounting for the object importance is introduced in Chapter 1.1. A concept of three novel solutions employing the object importance factor is discussed in the three successive Chapters. All these methods correspond with the currently applied classic method. The extended point method (Chapter 1.2) is very close to the presently applied typical point method. The two other approaches, based on fuzzy logic (Chapters 1.3 and 1.4) are the author s alternative for damage risk assessment with a point method. The fuzzy inference block construed in these methods enables continuous interpretation of surface objects. A practical example of evaluation of damage risk of two buildings of similar strength and different importance, which created good bases for comparing these three methods, is presented in Chapter 2. 1. Evaluation of strength of objects construed in Poland 1.1. Classic evaluation of building damage risk The point method is most frequently applied for assessing building damage risk in the mining areas applied in Poland [7]. With this expert method the cubature strength of household objects can be approximated. This method makes use of such parameters as: foundation type, shape of the object, existing protection, technical wearing, construction elements; this created basis for determining the number of points corresponding to the influence of a given property on the strength of the object. The ultimate strength value is determined by summing up points characteristic of a given property. The average sum of the points ranges 20 to 70. The higher is the number of points, the less resistant is the object to the mining impact. It should be stressed that the surface hazard with continuous deformations generated by underground exploitation is characterized by deformation factors, i.e.: subsidence w, tilt T, horizontal strain. These factors are predicted with the use of the Knothe method, which enables obtaining more reliable terrain deformation results. It should be emphasized that the strength of surface objects is characterized by a sum of points, being a result of construction properties; on the other hand, the hazard is described by horizontal strain, expressed in mm/m. For employing these two diverse characteristics together, the points describing the strength of objects have been categorized according to admissible horizontal strain, which a given building can bear. The final value of the building damage risk is determined by comparing terrain hazard category and the object strength category. Unfortunately, no guidelines are available, on the basis of which potential damage in a specific object could be defined. One thing is certain: the bigger is the difference between terrain hazard category and the object strength category, the higher is the risk of damage of the object. Legal standards necessitate specifying objects, the strength category of which is
lower or equal to the terrain hazard category [8]. According to instruction [3], objects having strength category lower than the terrain category by one or more grades, need protection. In practice, however, all the mines have their own protection rules, not always congruent with the legal regulations. The presented method has been used for mass evaluation of surface objects in most of the Polish mines. However, only approximated values were obtained with this method. Disadvantageously, in this method of building damage risk assessment only one risk factor, i.e. horizontal strain, is accounted for. Moreover, the point evaluation strongly relies on the construction experts opinions and experience. No decision diagram is defined for undertaking measures in the case of possible object hazard situations. In the process of hazard evaluation, one of the crucial factors, i.e. importance of objects has not been accounted for. Only some disadvantages of the presently applied method have been discussed. One of the most common counter arguments is the lack of the building importance factor in the hazard evaluation. It has a significant influence on the cost of repairs and frequency of damages claimed. Therefore, it is necessary to diversify the present approach by, e.g. accounting for importance in the object s strength evaluation. Three approaches to building damage risk evaluation are presented in the following sections. The two last ones are author s proposals. 77 1.2. Extended point method for surface objects strength evaluation The method presented by an expert team: Gil-Kleczenska, Mika, Soczawa proposed in the ningtees broadening the modified point method by properties accounting for object s destination, usability and existence of construction elements sensitive to the mining impact [1]. This method relies on the point method, which in turn, created preliminary bases for determining object strength. Then the importance of a building is accounted for by increasing or decreasing the total number of points, depending on the properties presented in the following table. Extension of point method [1] Rozwiniêcie metody punktowej TABLE 1 TABELA 1 Factors supplementing the points Buildings where human beings do not stay permanently, which are unheated (e.g., barns, pigsties Buildings where human beings stay temporarily (workshops, storages, garages) Public utility buildings where large groups of children, youth, disabled or ill persons stay permanently or temporarily Buildings having equipment sensitive to mining exploitation Points 12 6 +12 +6
78 These elements were indicated by experts on the basis of their knowledge and experience. The maximum and minimum number of points by which the total number of points determining the object strength can be increased and decreased is 18 and 12, respectively. Bearing in mind the average range of points for objects in the mining areas (20 to 70), the importance of a building may constitute 25% to 90% of the total strength of an object. With this method the importance factor can be quickly and easily accounted for when assessing the strength of an object. Two importance categories were established. The first one accounts for public utility. The duration of stay of human beings and the functionality of buildings are accounted for in the first of them. The ultimate summaric value of strength here can be diminished by 6 or 12, and increased by 12. The second class enables adding 6 points for the vulnerable construction elements or equipment. 1.3. Fuzzy assessment of building damage risk, accounting for rule-based importance factor A method worked out on the basis of fuzzy inference, accounting for the importance of objects when assessing their strength to mining impact is an author s alternative [2]. Fuzzy systems enable undertaking decisions in uncertain conditions, where no probability knowledge on the errors with which the input data and the final result are burdened is available. The fuzzy inference process consists of a few stages [3, 5, 9]. At the first of them, the so-called fuzzification process, the rigid values of input variables, e.g. terrain hazard characterized by the predicted horizontal strain value and object strength expressed in points, become fuzzy. Their membership in the fuzzy sets, describing input data and object strength, is defined. At the successive stage of inference, basing on the fuzzy input data, there is determined the degree to which the premises, being the basis for meeting conclusions for the specific rules, are met. As a result of the aggregation process, an output membership function is formed. At the last stage of inference (defuzzification process) rigid value characterizing the object hazard are determined. The importance of buildings has been accounted for at the stage of establishing rule bases. The most important element of the fuzzy-logic inference system is a rule base, where all dependences between input and output variables are defined. The buildings have been divided into three importance classes. Three linguistic values were ascribed to the linguistic variable importance: low, medium and high. Among the public utility buildings are houses, buildings having equipment sensitive to mining exploitation, high-value objects. The objects of medium importance are garages, household objects, which are in a good technical condition and which have high utility value. Low importance objects are low utility household objects, in bad technical condition and of low value. A separate rule-base has been construed for each of these classes. For linguistic variables surface structures vulnerability (v) five linguistic values were defined: v = {VL (very low), L (low), M (medium), H (high), VH (very high)} and for surface hazard (h) six linguistic values were determined h = {VL (very low), L (low), M (medium), H (high), VH (very high), EH (extremely high)}.
79 Fig. 2. Rule bases for different building importance Rys. 2. Podstawy regu³owe dla ró nych wartoœci budynków For high-importance objects the most restrictive rule base has been established, where assumption was made that a building undergoes a medium risk of damage if the category strength equals to the terrain category (Fig. 2). The rule base for low-importance objects assumes that an object having strength lower than the terrain category by more than 2 may be damaged. Three risk surfaces were generated for three importance classes on the bases of base rules (Fig. 3.). As a result of the presented fuzzy model inference it is possible to determine the damage risk of an object having a specific strength and importance, staying in an area of future Fig. 3. Risk surfaces Rys. 3. P³aszczyzny zagro enia
80 horizontal strain. A high variability of importance of the object is disadvantageous, therefore a more continuous approach to the importance factor was undertaken in the next method. 1.4. Building damage risk fuzzy assessment, accounting for importance by output weighing This author s method is based on fuzzy induction. The introduction of weighing output induction value enables more continuously accounting for the building importance. The induction process is analogous to that in the previously presented method. It is also the predicted horizontal strain and building strength, expressed in points, which are input variables. The inference process follows one rule base. The importance of buildings is accounted for by ascribing the relevant output weigh to the building s mining hazard degree. Basing on an extended point method (Chapter 1.2) it was stated that the maximum influence of importance on the final assessment of mining-induced damage risk with continuous deformations should not exceed 30% of the fuzzy-logic value. This signifies that in the case of a very important building, the fuzzy-logic risk of damage can be increased by 30%. On the other hand, when the object has low importance, the risk can be lowered by 30%. 2. Application and comparison of building damage risk assessment methods For comparison s sake, two endangered buildings in an area threatened with the same deformations of 4.5 mm/m (III cat.) were compared. The strength of both buildings was assumed to be very similar, therefore both objects were classified to the 2 category of strength (34 and 36 points, respectively). These objects significantly differ in importance: the first one is a new recreation building, where integration meetings of school children are organized. This object has mining-sensitive construction elements and its market value is very high. The other building is a farm object used for growing animals, without any mining-sensitive construction elements. Its market value is much lower than in the first case. 2.1. Modified point method The strength of the first building was assessed to 36 points, and the second one to 34 points. Accounting for the importance factor in the extended point method (Chapter 1.2), the first object was classified as public utility building where large groups of children, youth, disabled or ill persons stay permanently or temporarily. The second object is object where human beings stay only temporarily; unheated (farm) object. Therefore, to the strength of the first object was increased by 48 (1 category of strength), and the strength of the second object was lowered to 22 (3 category of strength). The comparison of the strength category and the hazard category reveals that the farm object is not threatened, whereas the recreation building is subjected to a higher damage risk.
81 Fig. 4. Analysed buildings with different importance Rys. 4. Badane budynki charakteryzuj¹ce siê ró nymi wartoœciami Fig. 5. Buildings damage risk assessment with the use of modified point method Rys. 5. Ocena zagro enia uszkodzeniem budynków przy zastosowaniu zmodyfikowanej metody punktowej
82 2.2. Fuzzy-logic inference assessment of building damage risk The building 1 was ascribed to the group of high importance objects, therefore rule based inference was carried out for particularly important objects (Fig. 6). The farm object was classified as low importance building, therefore the inference was based on a less restrictive rule base. Fig. 6. Buildings damage risk assessment with the use of fuzzy-logic inference system Rys. 6. Ocena zagro enia uszkodzeniem budynków przy zastosowaniu systemu interferencji opartego na logice rozmytej The ultimate risk value for the house and for the farm object was 62.4 and 18.4, respectively. 2.3. Fuzzy model assessment with final result weighing The following damage risk values were obtained for the fuzzy inference: building 40.3, farm object 37.6, respectively. These results do not account for the importance of both objects. The weighs for objects were determined on the basis of expert evaluation of objects in view of their destination, usefulness value, finish-off elements and value. The risk value was increased by 25% for the house, and decreased by 15% for the farm object. The ultimate value of risk for these objects was 50.4 and 32.0 for the house and the farm object, respectively (Fig. 7.). The comparison of the results obtained with three methods reveal a disadvantage lying in the fact that the extended point method accounts for the building importance mainly as a result of the usefulness function. Besides the values by which the strength of the object can be increased or decreased (6 and 12) are rigid, and the high discretization of the final result. The approach in which the construction elements sensitivity to mining impact is accounted for, is an interesting alternative. Unfortunately, the building strength cannot be lowered in view of that factor. Moreover, no clearly defined criteria exist, on the basis of which the
83 Fig. 7. Buildings damage risk assessment with the use of fuzzy-logic inference system with final result weighing Rys. 7. Ocena zagro enia uszkodzeniem budynków przy zastosowaniu systemu interferencji opartego na logice rozmytej z ocen¹ koñcowego wyniku object hazard could be defined. It follows from the presented example (Fig. 5) that the hazard assessment result is only the difference between the terrain hazard category and the strength category. There is no definite degree to which a given object is hazarded. Consequently, the basic disadvantage of this method lies in a high discreteness in accounting for the importance of a building and lack of clear criteria thanks to which the hazard can be graded. The fuzzy inference method with a three-class importance classes enables more coherent assessment of building s damage risk caused by continuous deformations. The fuzzy system enabled creating dependences between input variables (strength of the object, terrain deformations), on the basis of which the risk is assessed continuously. The division of importance into three categories enabled making an arbitrary interpretation of importance in view of economic and usability factors. However, the introduction of three classes of importance leads a high discretization of the final result. The damage risk of an important object is at a level of 62.4, whereas the low-importance object has only 18.4 points (Fig. 6). Hence, the fuzzy method with output result weighing is an optimum solution (third of the discussed methods). It enables most continuous accounting for the importance of an object. The results of hazard assessment are burdened with importance; however, accounting for importance factor has not drastically affected the results (Fig. 7). A high impact of the expert on the evaluation of the building importance is a considerable shortcoming of the method. Besides, the importance weight directly modifies the final result of risk assessment. The optimum solution lies in continuous introduction of importance at a level when the strength of the object is specified. This approach is under study within a research project (grant N524 026 32/2620). The research reporter in this paper has been supported by the Ministry of Science and Higher Education under grant N524 026 32/2620
84 REFERENCES [1] Gil-Kleczenska B., Mika W., Soczawa., 1990 Modified point method of building strength assessment to surface deformation. Materia³y V Konferencji naukowo technicznej: Budownictwo na Terenach Górniczych. Katowice Kamieñ k. Rybnika, maj 1990 (polish). [2] H e j m a n o w s k i R., M a l i n o w s k a A., 2000 A fuzzy logic approach for the building damage assessment on the mining area. XIII International Congress of the International Society for Mine Surveying 24 28 September 2007. [3] Instruction No. 12. Rules of expliotation possibilities asssessment taking into consideration safety of the buildings. Katowice 2000 (polish). [4] K a c p r z y k J., 1986 Fuzzy sets in the systems analysis. PWN, Warszawa (polish). [5] K l i r G.J., Y u a n B., 1995 Fuzzy sets and fuzzy logic theory and applications. Prentice Hall PTR, New Jersey 1995. [6] K w i a t e k J., 1998 Building protection on mining areas. Wyd. GIG, Katowice 1998 (polish). [7] Collective work: Rules of substitute building on mining areas. Wydawnictwo Œl¹sk. Katowice 1969 (polish). [8] Law 1994: Geological and mining law. Act 4th february 1994. (Dz.U. z 2005 r. Nr 228, poz. 1947) (polish). [9] The MathWorks: http://www.mathworks.com/access/helpdesk/help/toolbox/fuzzy/ METODA OCENY ZAGRO ENIA USZKODZENIEM BUDYNKÓW OPARTA NA LOGICE ROZMYTEJ, Z UWZGLÊDNIENIEM WARTOŒCI SPO ECZNYCH ORAZ EKONOMICZNYCH S³owa kluczowe Ocena zagro enia uszkodzeniem budynku, logika rozmyta, wartoœæ budynku Streszczenie Pewna ocena oddzia³ywania ruchów pod³o a, spowodowanych eksploatacj¹, na konstrukcje budynków stanowi w Polsce znacz¹cy problem. W zwi¹zku z brakiem dok³adnych metod oceny zagro enia uszkodzeniem budynków, kopalnie ponosz¹ wysokie koszta zwi¹zane z napraw¹ oraz zabezpieczaniem budynków. Problem ten wynika z faktu, i optymalne modelowanie potencjalnego uszkodzenia budynków wymaga wykorzystania licznych czynników, które trudno zastosowaæ jest przy tworzeniu modeli prognozowania ze wzglêdu na ich ciê kie do sprecyzowania i niejednoznaczne w³aœciwoœci. Zastosowanie logiki rozmytej pomaga w radzeniu sobie z niepewnoœci¹ i nieprecyzyjnoœci¹ przy podejmowaniu decyzji. Niniejszy artyku³ omawia metodê wykorzystuj¹c¹ system interferencji rozmytej w celu oceny stopnia zagro enia uszkodzeniem konstrukcji, przy uwzglêdnieniu wartoœci spo³ecznej i ekonomicznej budynku. Po zakreœleniu ram teoretycznych, artyku³ przedstawia przyk³ad zastosowania modelu interferencji rozmytej przy ocenie zagro enia uszkodzeniem konstrukcji na terenie jednej z polskich kopalni.
85 FUZZY LOGIC-BASED APPROACH TO BUILDING DAMAGE RISK ASSESSMENT CONSIDERING THE SOCIAL AND ECONOMIC VALUE Key words Building damage risk assessment, fuzzy logic, building importance Abstract Reliable assessing of mining-induced ground movement impact on building structures poses significant problem in Poland. Due to the lack of accurate methods of building damage risk assessment, mines bear high costs of building reparation and protection. This problem results from the fact that optimum modeling of potential building damage requires numerous factors which, due to their imprecise and vague characteristics, are difficult to implement into prediction models. With the application of fuzzy logic, dealing with uncertainty and imprecision in decision-making becomes possible. This paper discusses a method that uses a fuzzy inference system to evaluate the degree of structural damage with regard to a building s social and economic value. After summarizing the theoretical framework, the paper provides an example of an application of a fuzzy inference model to structural damage risk assessment in one of the Polish mining areas.