John Dalsgaard Sørensen

Reliability-based optimization in structural engineering

Abstract In this paper reliability-based optimization problems in structural engineering are formulated on the basis of the classical decision theory. Several formulations are presented: Reliability-based optimal design of structural systems with component or systems reliability constraints, reliability-based optimal inspection planning and reliability-based experiment planning. It is explained how these optimization problems can be solved by application of similar techniques. The reliability estimation is limited to first order reliability methods (FORM) for both component and systems reliability evaluation. The solution strategies applying first order non-linear optimization algorithms are described in detail with special attention to sensitivity analysis and stability of the optimization process. Furthermore, several practical aspects are treated as: Development of the reliability-based optimization model, inclusion of the finite element method as the response evaluation tool and how the size of the problem can be made practicable. Finally, the important task of model evaluation and sensitivity analysis of the optimal solution is treated including a strategy for model-making with both pre and post-analysis.

On risk-based operation and maintenance of offshore wind turbine components

Operation and maintenance are significant contributors to the cost of energy for offshore wind turbines. Optimal planning could rationally be based on Bayesian pre-posterior decision theory, and all costs through the lifetime of the structures should be included. This paper contains a study of a generic case where the costs are evaluated for a single wind turbine with a single component. Costs due to inspections, repairs, and lost production are included in the model. The costs are compared for two distinct maintenance strategies, namely with and without inclusion of periodic imperfect inspections. Finally the influence of different important parameters, e.g. failure rate, reliability of inspections, inspection interval, and decision rule for repairs, is evaluated.

An Expert System for Concrete Bridge Management

The importance of bridge repair versus new bridge construction has risen in recent decades due to high deterioration rates that have been observed in these structures. Budgets both for building new bridges and keeping the existing ones are always limited. To help rational decision-making, bridge management systems are presently being implemented by bridge authorities in several countries. The prototype of an expert system for concrete bridge management is presented in this paper, with its functionality relying on two modules. The inspection module relies on a periodic acquisition of field information complemented by a knowledge-based interactive system, BRIDGE-1. To optimize management strategies at the headquarters, the BRIDGE-2 module was implemented, including three submodules: inspection strategy, maintenance and repair.

A probabilistic model for chloride-ingress and initiation of corrosion in reinforced concrete structures

Corrosion of the reinforcement is a major problem for a large number of reinforced concrete structures because it can lead to a substantial decrease of the load-bearing capacity. One mode of corrosion initiation is that the chloride content around the reinforcement exceeds a critical threshold value. In the present paper a statistical model by which the chloride content in a reinforced concrete structure can be predicted, is developed. The model parameters are estimated on the basis of measurements. The distribution of the time to initiation of corrosion can now be estimated by traditional FORM/SORM-analysis. The model can also be used to determine optimal repair and maintenance strategies. In a number of examples these applications are illustrated.

Indicators for inspection and maintenance planning of concrete structures

Based on an idea introduced by Benjamin and Cornell (1970. Probability, statistics and decision for civil engineers. New York: McGaw Hill) and previous works by the authors it is demonstrated how condition indicators may be formulated for the general purpose of quality control and for assessment and inspection planning in particular. The formulation facilitates quality control based on sampling of indirect information about the condition of the considered components. This allows for a Bayesian formulation of the indicators whereby the experience and expertise of the inspection personnel may be fully utilized and consistently updated as frequentistic information is collected. The approach is illustrated on an example considering a concrete structure subject to corrosion. It is shown how half-cell potential measurements may be utilized to update the probability of excessive repair after 50 years. Furthermore in the same example it is shown how the concept of condition indicators might be applied to develop a cost optimal maintenance strategy composed of preventive and corrective repair measures.

Optimal reliability-based code calibration

Abstract Calibration of partial safety factors is considered in general, including classes of structures where no code exists beforehand. The partial safety factors are determined such that the difference between the reliability for the different structures in the class considered and a target reliability level is minimized. Code calibration on a decision theoretical basis is also considered and it is shown how target reliability indices can be calibrated. Results from code calibration for rubble mound breakwater designs are shown.

Field Implementation of RBI for Jacket Structures

After a brief outline of the simplified and generic approach to reliability- and risk-based inspection planning, focus is set on a recent application of the methodology for the planning of in-service NDT inspections of fixed offshore steel jacket structures in the Danish part of the North Sea. The study includes a sensitivity analysis performed for the identification of relevant generic parameters such as the bending to membrane stress ratio, the design fatigue life, and the material thickness. Based on the results of the sensitivity analysis, a significant number of inspection plans were computed for fixed generic parameters (predefined generic plans) and a database named iPlan was developed from which inspection plans may be obtained by interpolation between the predefined generic plans. The iPlan database facilitates the straightforward production of large numbers of inspection plans for structural details subject to fatigue deterioration, as illustrated by an example in the paper.

Calibration Methods for Reliability-Based Design Codes

The calibration methods are applied to define the optimal code format according to some target safety levels. The calibration procedure can be seen as a specific optimization process where the control variables are the partial factors of the code. Different methods are available in the literature, but the choice of an appropriate method is not usually an easy task. Each method can be shown to have a better performance for a particular kind of problems. The scope of this paper is to underline the advantages and disadvantages of the classical methods, to define their domain of validity and to propose new efficient methods. In our approach, the accuracy is balanced with time efficiency by the mean of iterative scheme using approximate methods. The presented ideas are clarified by four numerical examples of parabolic performance function, column buckling, stability of submarine shells and structural elements.

Sensitivities in Structural Maintenance Planning

A general description of optimal inspection and maintenance planning based on the classical decision theory and the modern reliability theory is given. A number of simplifications to this description is given leading to more appropriate formulations for practical applications. Sensitivities of both optimal inspection and maintenance plans as well as the associated costs are given with respect to the assumptions on which the planning has been performed. These sensitivities indicate the significance of the individual assumptions and may be used as a decision tool to reject particular optimal inspection and maintenance plans showing too large sensitivity. An example from the offshore industry is given to indicate how the methodologies can be used in practical applications.

Cost optimal reliability based inspection and replacement planning of piping subjected to CO2 corrosion

Abstract A methodology for cost optimal reliability based inspection and replacement planning of piping subjected to CO 2 corrosion is described. Both initial (design phase) and in-service planning are dealt with. The methodology is based on the application of methods for structural reliability analysis within the framework of Bayesian decision theory. The planning problem is formulated as an optimization problem where the expected lifetime costs are minimized with a constraint on the minimum acceptable reliability level. The optimization parameters are the number of inspections in the expected lifetime, the inspection times and methods. In the design phase the nominal design wall thickness is also treated as an optimization parameter. The most important benefits gained through the application of the methodology are consistent evaluation of the consequences of different inspection and replacement plans, consistent incorporation and handling of uncertainties, and consistent updating of inspection and replacement plans based on inspection results. The latter is achieved through application of Bayesian statistics for updating in combination with structural reliability methods.