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Use of Conceptual Graph-based Reasoning and Modeling to Support the Forensic Analysis of Bridges Failure

Sylvain Ndinga Okina*, Cédric Baudrit, Denys Breysse, Franck Taillandier, Paul Louzolo-Kimbembe

Higher National Polytechnic School (ENSP), Marien Ngouabi University-Brazzaville -Congo

Abstract: Despite the development of mathematical models, procedures, decision support systems, and databases, bridges are still today confronted with failures that can lead to dramatic situations. The lack of tools allowing to learn from the past failures associated with the uncertainties in its environment makes difficult the decision making in the bridge maintenance. The difficulty of maintaining the functions of bridges comes from the complexity of relationships between random hazards, the limit states of the bridge structure, and the human decisions and activities. To date, there is no generic and holistic model capable of modeling all types of bridges failure situations and capitalizing on their knowledge. This paper proposes a knowledge model of bridge failures, based on the formalism of conceptual graphs, capable of representing and capitalizing the failures of all types of bridges in a structured common vocabulary and to conduct automatic reasoning. The aim is to be able to provide explanations of failures and alerts on future projects.

Keywords: failure analysis, failure model, bridge failure, ontology of failure, forensic engineering

Received October 10, 2022; Revised November 15, 2022; Accepted November 23, 2022

Citation: Sylvain Ndinga Okina, Cédric Baudrit, Denys Breysse, Franck Taillandier, Paul Louzolo-Kimbembe, Use of Conceptual Graph-based Reasoning and Modeling to Support the Forensic Analysis of Bridges Failure. American Journal of Civil Engineering and Architecture, 10 (4). 157-168. January 2022. doi:10.12691/ajcea-10-4-1

1. Introduction

Existing bridges often fail due to the loss of an intended function of a component or its overall structure, i.e. when its performance level is unsatisfactory [1]. Understanding their failure mechanisms is necessary to avoid catastrophic socio-economic consequences, such as increased maintenance costs, traffic limitation, fatalities [2]. Forensic engineering aims, after a failure, to identify the origin and sequence of the factors that led to it in order to find explanations and lessons learned, to enrich the collective expertise and to avoid new failures [3,4]. The examination of the failure is based either on statistical analysis using information from databases (e.g. NYSDOT, ASM, Bridgeweb ...) or on qualitative analysis by describing the sequences that led to the failure in the form of a cause tree or consequence tree (approach FTA «Fault Tree Method» [5], FMEA «Failure Mode and Effects Analysis» [6]). Divers publications have shown that bridge failure is often the manifestation of multiple sources which are [4,6,7]: limited knowledge of failure modes and mechanisms, design and implementation errors, insufficient maintenance, natural hazards, accidents, overloading and material deterioration. One of the major difficulties of classical failure analysis based on traditional media is to draw conclusions from heterogeneous non-formalised data (heuristic uncertainty) which is a source of misunderstanding and risk [8]. Furthermore, the fault trees proposed in these publications only allow to represent the possibilities of an individual event or factor in the failure chain, without taking into account the interactions or correlations with a neighboring event [9]. This is due to the lack of an appropriate formalism for representation and logical reasoning to support forensic engineering analyses. Indeed, the lack of extensive data on structures and the budgetary constraints of the owners in some contexts (e.g. Congo) also represents a major bottleneck for bridge failure analysis. For example, the lack of relevant information on the failure process (e.g. mode of failure, degree of aggressiveness of the environment, severity of damage at the time of failure, etc.) of the Mouyondzi bridge (2012/24/11), Tonato bridge (2020/25/03), etc. in Congo did not allow for a causal analysis of the failure. The databases require specific information on the bridge and the failure, which is absent in some contexts. This does not allow lessons to be learned from past cases, leading to a lack of improvement in the effectiveness of the expertise and decisions to be taken. For these reasons, the modelling of bridge failures with the use of appropriate formalism such as the conceptual graph model seems promising to deduce the urgency of interventions according to different factors [10]: (a) the diversity of failure modes "corrosion, scouring, natural aging, structural defects, degradation... "(b) ageing of structures and insufficient maintenance, (c) aggressive environment "accidents, excessive loads, variable temperature and relative humidity, human errors "(d) the various structures of the bridges in their environment, etc. The description of this information by conceptual graphs allows to obtain fact bases of any type of failure, which can provide feedback and advance forensic engineering practices [11]. The knowledge model in this framework translates into a domain ontology to provide sufficient structuring of domain knowledge and facts to support failure analysis.

2. Overview of Problems on the Ontology Modeling of Bridge Analysis

The ontology formally represents and makes explicit knowledge by helping to describe and understand situations in a defined domain and to share knowledge [1,12]. Numerous publications have been made on ontology modelling for risk analysis in construction projects and in the field of bridge engineering [13,14,15,16]. These analyses have helped to capitalize on expert knowledge and its transfer between specialists to improve understanding of technical problems. Nevertheless, in the context of a lack of important data (case of the Congo bridges), ontology models can suffer from two remarkable difficulties: (1) the fragmented and specific character of the ontological structure which is usually described by an "is one" similarity relation between two concepts of the same sub-domain (e.g. Material, Concrete). Indeed, an ontological structure does not take into account the combination of concepts from different sub-domains (e.g. Material, Failure) which is important for failure analysis and decision making. Since the lack of correlation between concepts representing risk factors (e.g. high temperature) and concepts representing the system (e.g. Component) in an ontology model prevents reasoning about cause-effect or effect-cause interactions in failure analysis. The work of Jung et al. [16] and Bien et al. [13] is one example where the authors only focused on the formalisation of risk factors without describing their semantic correlation. The semantic formalisation of concepts (taxonomic classification) and the correlation between concepts of different sub-domains have long been a fundamental issue in order to propose a global vision of the structuring of facts [17]. (2) The lack of flexible rule inferences (algorithm) in ontology models capable of generating a fact base from expert analysis, which are needed to draw post-deterioration conclusions from the failure model. In the cited publications [13,14,15,16], the combination of concepts and the interpretation of the inferred knowledge on deterioration are achieved by means of rule inferences using essentially the coded language of the semantic web. This inference mechanism seems difficult to implement and interpret in practice for a civil engineer, who is familiar with graph reasoning with easily constructed and understandable rules.

The use of conceptual graphs in this respect is essential to support logical reasoning through ontologies, by constructing fault graphs and explaining them with inferences from rules or graphical queries [18]. The CG method has recently been used for the analysis and exploitation of civil engineering knowledge [2]. It has key advantages for functional and failure analysis of civil engineering structures, including, (a) a global graphical representation of knowledge used for both reasoning and fact base construction; (b) rule inference and query projection based operations to query the fact base. Finally, CGs proposes a management of the uncertainty linked to the analysis of incomplete information or information from several sources by the unification of knowledge with the logical inference of rules. This is a promising holistic method to describe and analyses the interactions between several factors (concepts) in a failure mechanism chain. The main objective of this work is a graphical description of any type of failure on bridges with incomplete data, proposing a failure fact base to support qualitative analysis in forensic engineering. The basic idea is to enable machine learning from the newly deduced factual knowledge in order to reduce expertise time and associated costs.

3. Methods

3.1. Representation Based on the Conceptual Graph Formalism

Conceptual Graph (CG) is a knowledge representation and reasoning formalism based on labeled graphs that are composed of two parts: the terminological support, which represents basic ontological knowledge, and a set of graphs, based on this support, which represents facts (data) expressing factual knowledge [19]. The formalism of CGs allows the development of querying and reasoning mechanisms to retrieve knowledge without using the language of logic but an only graphical inference. Logical formulas and requests may be encoded using these graphs, which is very interesting to the end-users because this makes it possible to explain the reasoning and the results of requests visually in a natural way. The interested reader can refer to [18,20] for more details on the representation of information and the algorithms of reasoning using the formalism of conceptual graphs.

3.1.1. Natural Representation of Knowledge

The natural formalization, notably the terminological support, consists of a partially ordered set of concepts and a partially ordered set of relations. A concept represents a set of terms or class of objects with a common meaning for the domain. For example, an « Environment » is a concept; it corresponds to an element which is external to the system but can impact its state (e.g., Natural Air…). A relation is a link that unites the concepts between them in order to structure the facts and transfer the information between these concepts. The relations are defined by their arity corresponding to the number of arguments of the relation. For example, “affected” is a binary relation (arity = 2) that describes the interdependency between concepts, «Environment» (e.g., Natural Air) and «Component» of a bridge (e.g., Abutment, Deck). The partial order defines a hierarchy relationship allowing a specialization of concepts and relations as, for instance: «Abutment, Deck» are the sub-concepts (specialization) of the top concept «Component» (Figure 1). In conceptual graph formalism, this sub-concepts inherits the properties of top concept. This detailed representation of concepts allows the incorporation of more essential and useful information for a relevant failure analysis.

Figure 1. An taxonomic representation of general concept and specialized

3.1.2. Graphical Reasoning and Automatic Interpretation of Facts

Conceptual graphs are equipped with graphical and logical rule algorithms that use first-order logic to express domain knowledge. This allows a formal structuring of facts (graph) and their practical interpretation. A fact graph expresses factual knowledge through a bipartite graph composed of two nodes, a rectangular node representing the concept (C), and an oval node representing the binary relationship (Rn) between two concepts or a unary relationship on a concept. Reasoning using conceptual graphs is a natural and visual expression of knowledge by establishing rules according to the logic, if hypothesis, then conclusion. The hypothesis and conclusion are two graphs sharing common nodes.

The hypothesis is a list of conditions (possible, certain or probable scenarios), and the conclusion is knowledge generated or inferred if the hypothesis is true. The CGs offer the possibility to manage specific data types (string, integer, float, boolean) using binary relations, allowing the integration of physical phenomena inside rules using scripts. Figure 2 and Figure 3 illustrate graph-based reasoning. Figure 2 is a graph of an elementary fact, which means that an (excessive) thermal load affects a steel bridge inducing corrosion in the deck. The black box represents the initial fact and the dark blue and red boxes represent the new knowledge deduced from the rule application (Figure 3). Figure 3 is an expert rule that deduces that the corrosion of the metal deck is due to natural air (conclusion). This rule is inspired by the FMEA method (i.e. Failure Mode and Effects Analysis) [21]. It describes the corrosion of a steel bridge as the effect of a high thermal load [22]. The labels (1 and 2) are the arguments of the binary relation "affected" that define the position of the associated concepts (Bridge -1-, Component-2- ). The symbol * is a generic marker of the concept C; i.e., a particular knowledge item for which there is an individual term in the knowledge base. The concept pair represented by C: c, for example, “Component: Steel_Deck” means that Steel_Deck is an individual of the concept “Component”).

Figure 2. Graph, description of failure mode in steel deck of bridge: corrosion

This reasoning illustrated by graphs (Figure 2, Figure 3) is explicit and gives a natural visualization, interesting a civil engineer's or expert is in the systematic analysis of observations. Also, interpreting the effect of this alteration on component or system, i.e., the failure situation by automatic learning is an interesting question for engineers. The research methodology is presented below.

Figure 3. Graph, formalized expert's rules, deducing the corrosion source in bridge structure

3.2. Conceptual Graphs Methodology to Modeled the Bridge Failure

The approach consists in building a general ontology on bridge failure, then using the ontological knowledge to structure the failure graphs and the analysis rules. In this respect, the approach is inspired by publications on knowledge models in civil engineering [12,23] and classical failure analysis methods [24]. The approach consists of four main steps illustrated in Figure 4:

Figure 4. Holistic approach for modeling and analysis the structure failure

3.2.1. Step 1: Developing the Ontology of Existing Bridges

This step consisting in the collect of the knowledge on study domain, and the formalization of failure knowledge support. Five sources were used to collect information on the failure of bridges: (1) literature (e.g., mechanical models…) [25], (2) expertise (expert knowledge) [26], (3) failures base on worldwide sources (NYSDOT) [27], (4) newspapers, and (5) knowledge bases from the available models [28]. The analysis of the information collected on failures cases and the functional modelling of type bridge allowed to define the fundamental concepts to describe the field of failure analysis. These concepts have been divided into three groups for a good organisation and understand of the technical vocabulary: (SC) concepts that inform the engineering structure (Structure, Component, Material, Function...), (EC) concepts that identify the environment of the structure (Environment...), and inform the condition of structure (Failure mode, Failure situation). From each basic concept, more specialised concepts are derived which detail the factual knowledge (e.g. "collision" is a specialised "operating environment" which represents a risk factor in existing bridges).

Formalization of the support (noted KBFA) of knowledge domain on bridges failure according to a structure of conceptual formalism consists to represents a hierarchy of basic concepts (a), and their corresponding relationships (b).

Thus, two types of relations were defined to regroup the basic concepts in the ontology on bridges: (R1) organizational relations to describe the interactions in a bridge structure (e.g. madeOf, has...), (R2) influence relations to describe on the one hand, the links between the structure, the environment (affected…) and the condition of structure (in Situation). Figure 5 shows an extract from the “KBFA” ontology with two hierarchy of selected concepts groups (SC) and (EC). The “KBFA” ontology takes into account various environments that may have an effect on the condition of the bridges and the most likely failure modes (Figure 5a). Figure 5 (b) details the elementary hierarchy of basic concepts in the bridge ontology, and (c) details the hierarchy of influence relationships.

The taxonomy relation (is-A) represented by arrows oriented upwards, indicates that all basic the components of a bridge inherits the properties of the global structure that they form. For instance, the group of concepts represented as "SC" in the ontology indicates that (Figure 5a): a component made up of material must perform a function to contribute to the functionality of the overall structure [29]; this reflects the principle of knowledge inherence in the conceptual graph formalism [20]. Thus, in a girder bridge, the deck must provide bending resistance (function) to contribute to the overall stability of the structure.

The principle of inherence in the framework of conceptual graphs is of interest in this work and allows the applied the fault tree analysis method (a top-down approach) in the modeling of failure mechanisms (graph) [30].

3.2.2. Step 2: Building a Graphical Model to Diagnoses the Bridge Condition

The expert reasoning on the elaborated bridge ontology (Figure 5) allows to build a generic graph on the failure mechanism. Indeed, a failure situation is considered as a dynamic process that can be described as a graphical chain of cause and effect with multiple interactions; for example, a corrosion of a bridge structural component coupled with a truck impact overload on the same component can lead to the collapse of the bridge. The reasoning in this framework uses the FMEA method, which is a popular and widely accepted method for failure analysis of multi-component systems such as bridges [24].

It involves the identification of components, system functions, failure modes and their source environment in order to establish corresponding graphical sequences, i.e. graphs of elementary facts. Thus, derived from the combination of the basic components and their physical relationships with the aggressive environment, the conceptual system failure model describes distinctive concepts that identify a bridge as a functional structure with conditional interactions (see illustration Figure 2). A physical relationship (causal relations here) describes the fact that aggressiveness of environment led to the deterioration of structure performance (scale of the system) or the material of components (scale of the component) up to induce an observable condition (i.e., failure situation). Consequently, the failure of a bridge structure can be described as an effect of a structure interaction with its environment, notably caused by independent random hazards (scale of the system). Also, a global failure of the bridge can be described as a joint situation of local failures [31]. Describing a global failure from the scale of a component leads to an in-depth understanding of situations dues to the modes of altering the material or the structural defaults as indicated in [32,33].

Figure 5. Excerpt of support formalized the structural relationships between concepts of different groups: (a) KBFA support, (b) details on environment of bridge, (c) details on influence relationships

In that, the graphically of the chaining of failure consists in the structuring of elementary facts represented by depending boxes (basic concepts) between the interaction of environment and structure (bridge) with its all identifiable parameters (performance, material, mode of failure).

In basing on the logic of functional analysis, we derived a reasoning model that would integrate a conjoint component. The interested reader can find more illustrations about the organization of domain knowledge and the conceptual, functional analysis of bridges in [2]. The analysis of failure modes based on the expert's knowledge and experience resulted in the retention of four terms in the form of a unary relationship in the graphical model to qualify the state of an elementary fact. For example, “excessive” means that an environment has excessive aggressiveness; “degraded” means an unacceptable decrease in performance level; “happened” means that a failure with damage has occurred; and “exists” means that a failure mode has occurred on the component. For example, «Failure (Damage)» is the observable condition after an alteration of the system.

Figure 6 presents this generic modeling, which consists of four main concepts: Structure, Component, Environment, Failure. By examining visualization and the structured facts separately, this model offers an interesting understanding of the failure chain, which is explained as follows: Black boxes (left) represent the set of risk factors which the binary combination may cause a failure situation of the bridge when the criticality of risk corresponds in the degradation of the performance of structure or component. Blue boxes (unary relationship) represent input attributes of elementary fact that qualify (model), and dark blue boxes are the state of elementary facts (output data). Red boxes (to the right) are all inferred knowledge by rules for explaining the chaining of bridge failure. In order to use the model (exploitation of the knowledge which has been formalized, Figure 5), it is necessary to inform the base with observed situations (facts) and to provide rules allowing to infer explanations (inference of expert rules, and graphical requests).

Figure 6. Graph formalizing the elementary mechanism of a bridge failure, a generic graphical model

In the following paragraph we present the formalised expert rules for using the model, and the different specific terms for creating instances of the model (step 3).

3.2.3. Step 3: Formalizing of Expert Rules to Use the Model and Automatic Explanation of Failure Chaining

In order to interpret bridge failure cases, different individual instances of concepts have been defined to specify the elementary facts being modelled (Figure 6).

Figure 7 gives an extract of the illustration of these specific terms. For example, three main types of bridges (suspension bridge, beam bridge and arch bridge) are modelled based on the existing structure. The addition of each individual bridge structure in this framework is very important to identify all their failure modes.

The main addition for our approach in this step concerns automatic integration of experience knowledge and traceability of the reasoning process based on the inference of expert rules. The developed model and rules have been implemented in CoGui to enable automatic fault analysis and learning. CoGui "Conceptual Graph editor" is a platform developed in Java for the construction and implementation of knowledge models based on Conceptual Graphs [34]. Based on examining the relationships between boxes in the model (Figure 6), we developed three rules to generate new knowledge. The reasoning for formalising rules 1# and 2# is to establish the binary product of occurrence and severity of the elementary fact condition in a system [35]. These rules are writing follows as:

Rule 1#: deduces the failure situation of bridge structure due to random hazard:

Rule 1-1: if a risk has aggressiveness (e.g., excessive load), affecting an existing structure (bridge) whose a failure mode occurs (e.g., loss of ability in loading), then its level of performance degrades (e.g., critical degradation).

Rule 1-2: if failure mode of a structure (bridge) occurred, and its level of performance degraded, then failure situation (e.g., collapse) with possible damage (e.g., structure loss and human) occurs.

Rule 2#: determines the chaining of the failure of bridge component due to alteration of the material:

Rule 2-1: if a component or structure (bridge) whose failure mode occurred (e.g., corrosion process of steel) is affected by an aggressive environment (e.g., high thermal load), then it is a degradation of the level of performance of function (e.g., load resistance) of this component.

Rule 2-2: if the failure mode of a component happens, and its level of performance is degraded (not ensured function), then the failure of this component with a possible loss of equipment occurs.

Rule 3#: an explanation of the failure situation of a structure from the local condition of its component:

If a structure composed by basic two components (a, b) is in failure situation, and these two components are in series form, then this failure is provided of the local failure of one in the two components or the two.

Figure 7. Details on the modeling of knowledge taxonomy and legend of model Figure 6

Figure 8. Excerpt of formalized generic rule R1#, 1-1 and 1-2

The reasoning of rule 3# is based on the discussion of analyzing a system series summarized by equation 1 [36]:

[picture] | (1)

With:

FS, the global failure of the bridge. LFa local failure of the primary component, LFb local failure of the secondary component (see results of model application of model). Figure 8 illustrates an excerpt of formalized rule 1#. Blue boxes are a scenario of factors (e.g., traffic collision and occurs of loss ability) that led to a failure situation of the bridge (defect of capacity). The dark blue boxes represent a new knowledge from the inference of expert's rule R1#.

The formalized and inferred knowledge (Figure 6, Figure 7, Figure 8) can be shared for different uses (expertise, decision-making, learning…). In order to demonstrate the interest of the approach, an application is provided in§4: the interpretation of past failure mechanisms by inference of rules (i.e., the analysis of bridge condition before failure), and explanation of similar bridge failure by use of graphically requests.

4. Results

4.1. Failure Case Analysed from the Formalized Generic Model

The case study 1 concerning the failure of an old bridge with a steel superstructure on Mouyondzi river. The corrosion on this structure dating from the 1960s is due to a lack of maintenance (inspection, repair, etc.) during the past period of its operation until the visible deterioration of its structural health in the year 2013. The analysis of this failure case consists at used the rules inference to detect the actual condition of bridge before failure.

In order to illustrate the model and the approach, we instantiated it to the steel deck of the Mouyondzi bridge, which is subject to corrosion. The approach is also applied to analyze the failure situation of Tonato bridge, related to the decay of its wood deck. Derived from the generic prototype and its analysis rules (Figure 6, Figure 8), the instantiated models consist in comprehensive identification of the specific mode of failures and their interpretation to a better decision. Figure 9 illustrates the failure mechanism graph of the Mouyondzi bridge. The instantiated model describes the collision scenario, which caused an unacceptable displacement of the deck (rupture), causing the loss of traffic continuity (structure scale). The failure of the deck also results from an alteration of material by very advanced corrosion and impacts its capacity to support loads [37]. Three new specific rules R4#, R5#, and R6#, interpreted the graph of failure in the Mouyondzi bridge. For example, Rule R4# explains the reasoning: aggressiveness of traffic collision affects Mouyondzi bridge if its ability at loading which has been degraded. Rule R5# translates the reasoning: the rupture of the beam deck of the Mouyondzi bridge occurs if advanced corrosion of metal and high thermal loading led to an unacceptable degradation of its loading resistance.

Figure 9. Graph, description of the collapse mechanism scenario of mouyondzi bridge

The graphs related to the collapse mechanism scenario of Mouyondzi bridge (Figure 9) and Tonato bridge described in the same way, are two instances of the facts from the fact base. We will then show how this base can be exploited to interpret what can happen in a bridge after failure (reasoning of consequence at cause).

4.2. Failure Case Analysed by Graphical Requests from a Similar Case Studied

The analysed case 2 is the failure of Lubiriha bridge. The use of graphical requests in this section permits the query of the facts base for answering questions: What type of structure? What condition of structure? Can we find similar cases in a given context? Graphical requests allow the user to query the facts base to find the causes that could have led to the failure situation.

Requests graphs deduce from the instantiated graph of facts (Figure 9) to query the base for selecting the similitude between the documented structures and their situation by the projection of graphical requests. The idea is to find a possible explanation from similar cases documented in the fact base [38]. It uses the usual diagnosis approach applied in forensic engineering, which consists of analyzing a situation and seeing what can be deduced from similar past situations.

Lubiriha bridge is a beam type structure in steel, which had a failure on 2018/12/01 under conditions similar to those of the Mouyondzi bridge in the base of facts. The similarity between the two bridges is illustrated by the used material (steel), a type deck (beam), and the failure mode of the deck (corrosion process), which are described by the same vocabulary. The projected requests q#1, q#2, q#3 (Figure 10) summarize the observations made on the Lubiriha bridge from the formalized knowledge in the graph-facts (Figure 11).

The projection of request q#1 identifies that the Lubiriha bridge documented in the facts base is similar to the Mouyondzi bridge in terms of component and failure mode (loss ability). q#2 shows that the rupture of the beam deck, which ensured the load resistance in the Lubiriha bridge, results from the corrosion process.

q3# concludes that the global collapse of the Lubiriha bridge happened while its structure was loading by excessive traffic associated with the advanced corrosion process of the steel deck. On the basis of obtained results, we provide a discussion on the proposed approach and model.

5. Discussion

The analysis of the failure modes of the three structures (Mouyondzi bridge, Tonato bridge, Lubiriha bridge) demonstrates the relevance of the developed model, notably regarding the forensic engineering field. The approach provides the efficient responses to two problems in the organization of information poorly considered in the existing works: (1) the formalization of the multi-scale functional description of bridge condition before failure including the expert knowledge by an explicit algorithm (conceptual graph). The clarified links between the occurrence of risk events, i.e., the organization of the chaining of failures, facilitating the interpretation of failure as shown in § 4.1 (Figure 7, Figure 8). (2) the interpretation of similar bridges whose information is lacking by using graphical requests and conceptual base of failures (see §4.2, Figure 9, Figure 10).

The first advantage of this model on existing models [16] is its generic attribute (Figure 5, Figure 6), which developed the specific rules of analyze. The graphical formalization allows (a) intuitive and flexible reasoning (representation, structuring knowledge…), (b) model based on the logic of conceptual graphs and the relations of field (reliability and completeness of knowledge, the possibility to express all the experience knowledge…), (c) automatic and simple analysis of the failure modes of structures...

Understanding the chaining of bridge failures on this base provides an efficient diagnostic then orient the appropriate maintenance actions.

Figure 12 illustrates how a maintenance action can be proposed with reasoning based on the effect gravity of failure (conditional maintenance) [39,40]. The expert rule reasoning is (R#mi): if a failure situation happens in one component (or bridge), and if the damage was observed is critically, then urgent repair.

Figure 10. Requests explaining possible scenarios of failure of the Lubiriha bridge

Figure 11. Graph, (a) causes of the Lubiriha bridge failure deduced by graphical requests, (b) illustration of it is in visual deterioration

Figure 12. Graph, automatic selection of the maintenance action of a bridge component by rule inference

Nevertheless, the limits of this modeling are:

- The effect of material deterioration on a component of the bridge over time is not described.

- The relations describing the mechanical mechanisms of failure are not considered, e.g., how to interpret the longitudinal exhaust of the isostatic deck?

- The interpretation of the combined modes of failure is not available, i.e., the failure depending on two components is not explicated.

An improvement of the current model by coupling it with laws of material alteration or mechanical relations could be an interesting alternative in the management maintenance of bridges.

6. Conclusions

We proposed a model to support the diagnosis of a bridge before and after a failure. Three main questions were:

• How to use rare and multi-source information to explain specific cases of bridge failure?

• How to describe the scenarios causing the failure?

• How to explain the current failure situation on a poorly documented bridge?

The formalization of the vocabulary of domain based on an ontology (Figure 5) and the developed model (Figure 6) constitutes formal supports in response to these questions, allowing formalizing, inferring, and sharing knowledge related to bridge failure. Based on the conceptual graphs, this reasoning framework can be used both in a deductive way (what can happen?) and in an explanative way (what can explain the present situation?). This approach contributes to the efficiency of practices in the forensic engineering field, or functional analysis field, based on not flexible approach (e.g., MADS, MOSAR) to describe the chaining of causes or consequences of structures failures. Such a modeling approach may be extended to other specific areas of interest in civil engineering, such as analyzing the failure of dams. The transfer of such knowledge formalized in the form of graphs may support the experts reasoning on new cases. Work will continue with the development of other hypotheses related to the quality of components to realize the quantitative analysis of bridge failures, e.g., integration of mathematical law that simulates the evolution of the material alteration process. Also, the model should integrate expert's rules related to the basic decision on conditional maintenance. The long-term objective is to achieve a complete modeling dealing with both the field of failure analysis and the maintenance of existing bridges.

Acknowledgments

CoGui platform used to implement the modeling is developed by the Montpellier Computer, Robotics and Microelectronics Laboratory-LIRMM (French).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

References

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