Assessment of the existing reinforced concrete structures with usage of the fuzzy logic – based expert system

Fuzzy logic is the useful tool when assessing the existing reinforced concrete structures. The introduction of expert system in assessing the technical condition of the existing structures built on the fuzzy logic represents a transition to a new and higher-quality level for survey of constructions sites. As a result, it is seen that the assessment of the existing building with usage of the proposed expert system is in compliance with the estimation of the qualified experts.


Introduction
Assessment of existing reinforced concrete structures is becoming a most important but complicated engineering task. General principles of sustainable development regularly lead to the need for an extension of a life of a structure, in most practical cases with severe economic constraints.
As it was shown in [1] visual inspection becomes the dominant practice in the management of maintenance, even when the importance of the structural elements are significant. Subjectivity heavily affects the process of assessment of degradation degree based on the results of visual inspection. Most of assessment approaches and methods are similar in principle, but vary in the details.
In order to use the visual inspection as a robust and reliable instrument to evaluate the safety level of an existing structural element, we decided to take advantage of the ability of Fuzzy Logic to treat uncertainty as expressed by linguistic judgements [2,3].
In order to develop the multilevel expert system for existing structures assessment a Fuzzy Logic-based algorithm is proposed, which used the Fuzzy Logic Toolbox package of MatLab Software [1].
As it pointed in [1], «a Fuzzy Logic is a versatile tool, particularly suitable for the management of decisional trees involving the processing of data endowed with «vague» nature (both numerical and qualitative one), and is naturally able to provide a linguistic, qualitative assessment of the health conditions of the building».
In this context, the Fuzzy Logic appears the most qualified tool for the processing of numerical data and uncertain information in order to obtain a linguistic description of structural damage.

Rule-based Fuzzy model/Expert system development
The stages of development of the Fuzzy Logic System are presented in details in [4,5]. For the development of the fuzzy production model for assessing of the existing structures performance it is necessary to formulate set, consisting the basic variables (see Table 1) which are characterized performance of element and set, characterizing (present) damage level (see Table 2).  As it was shown above, in the damage assessment of an existing buildings (structures), several input data are required (crack width and propagation, residual strength of materials, amount and condition of the steel reinforcement, deflection, corrosion level et al.) that will all be treated, according to previous remarks, as fuzzy sets. The common structure deficiencies associated with the deterioration of the structural element are corrosion of steel reinforcement and the cracking, scaling and spalling concrete, deflections. The ranges for basic variables and correlation function were adopted based on the own numerical and experimental studies [4][5][6].

Realization of the Fuzzy production model for assessment of existing structures in MatLab Software
Step 1: Fuzzification -Input Fuzzy. At this stage, we adopted the membership function for term-sets of input and output linguistic variables, as shown in Table 3. The most commonly used membership functions are the trapezoidal and triangular ones. These membership functions will be indeed the functions adopted in the proposed algorithm. Step 2: Setting Fuzzy Rules in accordance with Table 4. The base of the Rules of the Fuzzy production model is defined as a structure with an appropriate member of inputs x i and one output y i .
Step 3: Aggregation is the process by which the fuzzy set that represent the outputs of each rule are combined into a single fuzzy set. A rule premise in general is a compound fuzzy proposition. Aggregation only occurs once for each output variable, which is before the final defuzzification step. According to the original proposal of Zadeh for aggregation of the confidence level of assumption min-conjuction is used: Step 4: Activation. A fuzzy «IF-THEN» rule is a connection of two (compound) fuzzy propositions. Hence, this connective has to be interpreted within the framework of set theoretic or logical operators. The simplest interpretation is that of the conjuction of premise and conclusion, such that the appropriate operation is the minimum: Step 5: Accumulation. Usually, a rule base is interpreted as a disjunction of rules, i.e. rules are seen as independent «experts». Accumulation has the task to combine the individual «expert statements», which actually are fuzzy sets of recommended output values. Consequently, an appropriate accumulation operation is the maximum: Step 6: Defuzzification -from a fuzzy decision to real decision. As inference results in a fuzzy set, the task of defuzzification is to find the numerical value which «best» comprehends the information contained in this fuzzy set. A frequently used method is the so-called Center-of-Gravity defuzzification (CoG, also called Center-of-Area defuzzification CoA): dy y dy y y y   (4) which chooses the y' -coordinate of the center of gravity of the area below the graph μ(y). This defuzzification can be interpreted as a weighted mean, i.e. each value y weighted with μ(y) and integral in the denominator serves for normalization.

Implementation of the Assessment Algorithm of the Proposed Expert System
According to [1] the whole phase is managed by a nested fuzzy algorithm: starting from the assessment of the single structural elements, and progressively proceeding through the structural hierarchy (element/storey/building), input data are processed and collated in order to obtain the new Phase -assessment of the whole building. It is worth remarking that part of the results provided by the preliminary investigation could be used also at this stage.
The starting point, as it has pointed out in numerious publications [7][8][9][10], is the availability of an inventory of data and information derived from the investigation on the analyzed building, the collecting and organization of which is performed by using the survey diagnostic forms, as it shown in [5].
As an example of the implementation of the proposed expert system results of the assessment of the existing building with precast concrete elements is presented.
Results of the Visual Inspection and Basic Testing are presented in Diagnostic Protocol Example (Table 5). General view of the structural element are presented in Figure 1. Results of the assessment with usage of the proposed algorithm are listed in Table 6 and are in compliance with the estimation of the qualified experts.