International Symposium (NDT-CE 2003)Non-Destructive Testing in Civil Engineering 2003
|Start > Contributions >Lectures > Structures 1:|
Analysis and assessment of deteriorating concrete bridges using fuzzy set theoryTheda Lücken & Friedhelm Stangenberg
Institute for Reinforced and Prestressed Concrete Structures, Ruhr-Universität Bochum, Germany
This paper presents an assessment strategy for deteriorating concrete bridges. The strategy includes in-situ inspections, evaluation of inspection results and condition assessment of the bridge. Uncertainties in the inspection results originating from imprecise information or verbal descriptions as well as vagueness and expert judgement in the process of damage assessment are taken into account using the fuzzy set theory. An expert system considering fuzziness and uncertainty is developed. The application of the proposed approach is illustrated by an example.
Routine inspections are usually carried out to control the condition of existing bridges and other engineering facilities. Repair can be performed in time to prevent the degradation of possible damages and defects. But this typical procedure will not lead to success in all cases. In the case of serious damages, a detailed damage analysis is required. The detailed damage analysis is carried out in addition to routine inspections, in order to get more information about damage mechanisms, its extent and evolution as well as consequences of the damage.
The present work is based on a project of the Federal Highway Research Institute in Germany (BASt)  within a management system for structural maintenance developed by the BASt . The project deals with damage analysis on object level. On object level, each individual structure is examined whereas the entirety of all structures in a network (e.g. structures in a road network) is considered on network level (figure 1). Both levels - the object and the network level - have to be considered in maintenance management.
The analysis and evaluation of damage is a difficult process in which human judgement plays an important role. The information required for reliable damage evaluations is usually incomplete and involves uncertainties. The fuzzy set theory developed by L.A. Zadeh in 1965  yields an appropriate basis to deal with such problems.
Expert systems provide decision support in the complex process of damage analysis and evaluation. An expert system is a software tool which is intended to model human expertise or knowledge within a specific domain. It is characterised by an explicit separation of knowledge base and control mechanism
2 Approach to damage assessment
Detailed inspections as well as general information about the structure are the basis for the damage assessment and the input data for the expert system
Detailed inspections include visual inspections, non-destructive testing, laboratory tests, monitoring, numerical structural analysis, and further investigation activities.
The output of the inspections are descriptive damage data (e.g. cracks, spalling, corrosion) and measurement results (e.g. concrete cover, carbonation depth, crack width). Investigation results are evaluated by appropriate methods.
Furthermore, probable damage mechanisms are determined and damage accumulation processes are analysed. The analysis of the damage accumulation process includes service life prediction and discretisation of cumulative damage into damage states.
Based on these studies on damage mechanisms and damage accumulation, a damage assessment of the total structure is carried out. Local damages are evaluated and a condition estimate of the total structure is calculated. This kind of condition assessment is the basis for planning maintenance and repair.
3 Evaluation of investigation results
The result of an investigation can be a set of measuring data, a single value or a linguistic expression. Randomness in test results is handled by the classical probability theory. The characteristic value of a set of measuring data is estimated by the p-quantile of a statistical distribution, e.g. 5%- or 95%-quantile. Appropriate distributions are the normal and lognormal distribution. The statistical fit test is carried out in accordance to the value of the variation coefficient. The approach is checked by graphical verifications (probability paper, histogram) .
For example, the measured data of the concrete cover of a structure have to be statistically evaluated. The characteristic value is determined by the 5%-quantile of the normal or lognormal distribution.
Uncertainty can occur, for example, in a set of limited available measurement data. In those cases, a combination of fuzzy logic and probability theory is necessary.
If the input data are linguistic expressions, the definition of fuzzy sets allows an objective evaluation of these data. Therefore, linguistic variables are determined in the knowledge base according to the usual linguistic terms. Furthermore, membership functions are defined to associate linguistic expressions to numerical values . Figure 4 shows the used membership function for crack width. The chosen linguistic variables "low", "medium" and "high" are related to the numerical values of crack width in mm.
4 Condition assessment of the structure
4.1 Probable damage mechanisms
The expert knowledge of several sources is concentrated in the form of rules in the knowledge base of the expert system. Probable damage mechanisms can be determined by the input of general information about the structure, investigation results and damage data.
In the determination of probable damage mechanisms, not absolutely certain information shall also be taken into account. The degree of uncertainty is represented in the expert system by a certainty factor. This is a numerical value ranging from 0 (very uncertain) to 1 (very certain).
Furthermore, vagueness and expert judgement in the determination of damage mechanisms are processed within fuzzy set theory in the model. In the rules of the expert system, a similarity measure is calculated, if the rules operate with fuzzy data and fuzzy conclusions . The similarity measure specifies the degree of fuzziness of a rule (cp. figure 1).
A qualitative judgement can be illustrated on the example of the threshold level of chloride concentration in concrete. The corresponding membership function with linguistic variables is shown in figure 5.
Although the occurring uncertainties are implemented in the described model, the expert system cannot always yield a clearly defined statement on the damage mechanism. Therefore, an occurrence probability of each damage mechanism is specified by the expert system. The probability of occurrence P is calculated by combining the certainty factor CF and the similarity measure S  according to:P = CF · S
The expert finally determines the most probable damage mechanism. A decision is made with the results of the expert system and further information which cannot be modelled by the expert system, for example graphical representations of cracks.
An example is given in section 5.
4.2 Damage accumulation and service life prediction
Such a discretisation can be done for different deterioration mechanisms with varying numbers of damage states. Damage state 0 indicates no damage whereas state 1 defines the collapse of the structure. The number of states between 0 and 1 is chosen according to the deterioration rate. The deterioration rate defines the velocity of deterioration in dependence of the time. A damage state transition is characterised by a change of the deterioration rate (see figure 6b).
The probability distribution of damage at a particular time t based on the damage states above described is modelled using the Markov chain theory . The transition probability between the damage states is generated from the in-service data obtained during inspections.
The output of the expert system is a statement on current and future damage states as well as a prediction of service life.
4.3 Damage assessment
Initially, local damages - in contrast to cumulative damage considered before - are evaluated according to the criteria stability, traffic safety and durability as defined in .
Stability and durability depend on damage mechanisms and damage accumulation. Further, the kind and extent of damage (one or more components deteriorated) are determined to evaluate local damage according to the criteria stability and durability. The traffic safety is defined in this work in dependence of the damage accumulation process and the kind of damage. This assumption can be made if we only consider the damage of the structure (and not that of equipment). The corresponding relationships are illustrated in figure 7.
The evaluation of stability, traffic safety and durability provides the basis for the condition assessment of the total structure. The condition estimate of the total structure is calculated according to the algorithm suggested in . This assessment mark is necessary to specify a priority list on network level. On object level, a textual assessment of the damage as well as an evaluation of the total structure concerning stability, traffic safety and durability serves as input for planning repair.
5 Illustrative example
Appropriate investigation methods are applied to measure the concrete cover and the chloride concentration in the concrete in different depth.
Probable damage mechanisms should be determined. The approach is outlined in figure 8.
5.2 Evaluation of investigation results
The characteristic value of the chloride content is 0.07 mass-% of the concrete in the depth of the reinforcement.
5.3 Probable damage mechanisms
During the consultation, the surrounding humidity is asked. It is supposed to be "humid" in this example.
With the above given input data, the expert system determines the following list of probable damage mechanisms with the probability of occurrence P:
This list serves as decision support for the user and gives a check if additional investigations have to be carried out to improve the results.
The presented approach and the expert system is a reliable and practical tool for the analysis and assessment of deteriorating concrete bridges on object level. The damage analysis is based on detailed inspections and includes the evaluation of investigation results, knowledge of damage mechanisms, damage accumulation processes and the final damage assessment of the structure. Reliable inspections of the deteriorating structure with appropriate investigation activities are an important item of damage analysis.
The uncertainties in imprecise information, linguistic expressions, vagueness and qualitative judgement in the process of damage evaluation are handled by the fuzzy set theory. Furthermore, not absolutely certain information are estimated using certainty factors in the expert system.
The expert system is developed as an open and adaptive system. The knowledge base is exemplarily generated for deteriorating concrete bridges. In the future, it is necessary to enlarge the knowledge base of the expert system to enable damage analyses for all kind of bridges and other engineering facilities.
The developed strategy combined with the detailed inspection and the assessment by the expert system provides an effective decision support for maintenance management.