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This paper establishes the model basis regarding the ultimate limit state consisting of structural, loading, and probabilistic models of the support structure of offshore wind energy converters together with a sensitivity study. The model basis is part of a risk based assessment and monitoring framework and will be applied for establishing the 'as designed and constructed' reliability as prior information for the assessment and as a basis for designing a monitoring system. The model basis is derived considering the constitutive physical equations and the methodology of solving these which then in combination with the ultimate limit state requirements leads to the specific constitutive relations. As a result finite element models based on shell elements incorporating a structural and a loading model are introduced and described in detail. Applying these models the ultimate capacity of the support structure and the tripod structure are determined with a geometrically and materially nonlinear finite element analysis. The observed failure mechanisms are the basis for the definition of the ultimate limit state responses. A probabilistic model accounting for the uncertainties involved is derived on the basis of literature review and measurement data from a prototype Multibrid M5000 support structure. In combination with the developed structural and loading models, sensitivity analyses in regard to the responses are performed to enhance the understanding and to refine the developed models. To this end, as the developed models necessitate substantial numerical efforts for the probabilistic response analysis predetermined designs of numerical experiments are applied for the calculation of the sensitivities using the Spearman rank correlation coefficient. With this quantification of the sensitivity of the random variables on the responses including nonlinearity the refinement of the model is performed on a quantitative basis.
Fatigue and serviceability limit state model basis for assessment of offshore wind energy converters
(2012)
This paper develops the models for the structural performance of the loading and probabilistic characterization for the fatigue and the serviceability limit states for the support structure of offshore wind energy converters. These models and a sensitivity study are part of a risk based assessment and monitoring framework and will be applied for establishing the 'as designed and constructed' reliability as prior information for the assessment and the design of monitoring systems. The constitutive physical equations are introduced in combination with the fatigue and serviceability limit state requirements as the starting point for the development of the structural performance and loading models. With these models introduced in detail, several modeling aspects for both limit states are analyzed. This includes analyses of the influence on the hot spot stresses by applying a contact formulation for the pile guide brace connection and the application of a finite element formulation using solid elements. Further, the comparison of the natural frequencies of a discrete rotor model with a continuous rotor model is documented. To account for uncertainties associated with the structural and loading models, a probabilistic model is derived on the basis of literature review and measurement data from a prototype Multibrid M5000 support structure. The sensitivity study is based on the calculation of a nonlinear coefficient of correlation in conjunction with predetermined designs of experiments. This is conducted by a systematic analysis of the influence of the random variables on limit state responses and hence on the structural reliability. Integrating the analyses and sensitivity studies of the fatigue and serviceability limit state models developed in this paper as well as the ultimate limit state models in Thöns et al. ('Ultimate Limit State Model Basis for Assessment of Offshore Wind Energy Converters,' ASME J. Offshore Mech. Arct. Eng.), the model basis for the assessment is completed. The process of establishing and analyzing such a model basis contributes to a detailed understanding of the deterministic and probabilistic characteristics of the structure and provides valuable insights in regard to the significance of available data.
Structural health monitoring systems have been widely implemented to provide real-time continuous data support and to ensure structural safety in the context of structural integrity management. However, the quantification of the potential benefits of structural health monitoring systems has not yet attracted widespread attention. At the same time, there is an urgent need to develop strategies, such as optimizing the monitoring period, monitoring variables, and other factors, to maximize the potential benefits of structural health monitoring systems. Considering the continuity of structural health monitoring information, a framework is developed in this article to support decision-making for structural Health monitoring systems arrangement in the context of structural integrity management, which integrates the concepts of value of information and risk-based inspection planning based on an approach which utilizes a conjugate prior probability distribution for updating of the probabilistic models of structural performances based on structural health Monitoring information. An example considering fatigue degradation of steel structures is investigated to illustrate the application of the proposed framework. The considered example shows that the choice of monitoring variables, the Monitoring period, and the monitoring quality may be consistently optimized by the application of the proposed framework and approach. Finally, discussions and conclusions are provided to clarify the potential benefits of the proposed Framework with a special view to practical applications of structural health monitoring systems.
Reclassification of bridges, i.e., a change in load rating, using reliability-based methods and a direct update with proof load information has been presented by many authors. However, bridge reclassification has hardly been studied from a decision analytic perspective, i.e., with quantification of the risks and benefits of different classification choices, and the expected benefit gain from proof loading. We derive, explain and exemplify a decision analytic approach for bridge reclassification along with models for (1) elastic and ultimate capacity and their adaptation with proof load information, (2) proof load information with classification outcomes accounting for target reliabilities and, (3) utilities including socio-economic benefits from reclassification. The approach and models are exemplified with a case study based on reclassification of bridges with a low existing classification. Decision rules, for practical use by a highway authority to find the optimal classification, are identified and documented based on: (1) the measurement of the capacity at elastic limit by proof loading, (2) the bridge reclassification benefits, and, (3) the required annual reliability level. From a Value of Information analysis, it is concluded that the proof load information is highly valuable for reclassification in cases of high socio-economic benefits and high reliability requirements.
This article introduces an approach and framework for the quantification of the value of structural health monitoring (SHM) in the context of the structural risk and integrity management for systems. The quantification of the value of SHM builds upon the Bayesian decision and utility theory, which facilitates the assessment of the value of information associated with SHM. The principal approach for the quantification of the value of SHM is formulated by modeling the fundamental decision of performing SHM or not in conjunction with their expected utilities. The expected utilities are calculated accounting for the probabilistic performance of a system in conjunction with the associated structural integrity and risk management actions throughout the life cycle, the associated benefits, structural risks, and costs and when performing SHM, the SHM information, their probabilistic outcomes, and costs. The calculation of the expected utilities necessitates a comprehensive and rigorous modeling, which is introduced close to the original formulations and for which analysis characteristics and simplifications are described and derived. The framework provides the basis for the optimization of the structural risk and integrity management based on utility gains including or excluding SHM and inspection information. Studies of fatigue deteriorating structural Systems and their characteristics (1) provide decision Support for the performance of SHM, (2) explicate the influence of the structural component and system characteristics on the value of SHM, and (3) demonstrate how an integral optimization of SHM and inspection strategies for an efficient structural risk and integrity management can be performed.
A method to determine the influencing parameters of a structural and damage detection system is proposed based on the value of Information analysis. The value of information analysis utilizes the Bayesian pre-posterior decision theory to quantify the value of damage detection system for the structural integrity management during service life. First, the influencing parameters of the structural system, such as deterioration type and rate are introduced for the performance of the prior probabilistic system model. Then the influencing parameters on the damage detection system performance, including number of sensors, sensor locations, measurement noise, and the Type-I error are investigated. The preposterior probabilistic model is computed utilizing the Bayes’ theorem to update the prior system model with the damage indication information. Finally, the value of damage detection system is quantified as the difference between the maximum utility obtained in pre-posterior and prior analysis based on the decision tree analysis, comprising structural probabilistic models, consequences, as well as benefit and costs analysis associated with and without monitoring. With the developed approach, a case study on a statically determinate Pratt truss bridge girder is carried out to validate the method. The analysis shows that the deterioration rate is the most sensitive parameter on the effect of relative value of information over the whole service life. Furthermore, it shows that more sensors do not necessarily lead to a higher relative value of information; only specific sensor locations near the highest utilized components lead to a high relative value of information; measurement noise and the Type-I error should be controlled and be as small as possible. An optimal sensor employment with highest relative value of information is found. Moreover, it is found that the proposed method can be a powerful tool to develop optimal service life maintenance strategies—before implementation—for similar bridges and to optimize the damage detection system settings and sensor configuration for minimum expected Costs and risks.
We analyse the performance of risk reduction strategies for Terrorist attacks with Improvised Explosive Devices (IEDs) for large governmental building structures in terms of cost-efficiency, significance and effectiveness Accounting for life safety in conjunction with societal preferences and capabilities. The approach builds upon an extended Bayesian pre-posterior decision analysis and the principles of the marginal lifesaving costs based on the Life Quality Index (LQI). The decision scenario is formulated for a decision maker responsible for the safety of governmental or large commercial buildings and consequently the direct risks, the indirect risks due to fatalities and economical importance of the building beside the expected cost for the individual risk reduction strategies are modelled, aggregated and optimised. The considered risk reduction strategies encompass an explicit consideration and distinction of information and actions such as (i) threat surveillance may trigger the temporary evacuation of the building, (ii) the implementation of protection provisions provided by codes and guidelines, (iii) a detailed progressive collapse assessment and specific protection measures and (iv) the combination of protection and surveillance. All considered strategies are found to contribute to risk reduction and can be costefficient, especially for higher threat probabilities. The risk reduction strategies comply with societal macroeconomic and demographical characteristics and societal preferences according to the LQI. The progressive collapse assessment with targeted protection measures is found to be the most cost-efficient, significant and effective counter-terrorism strategy. This finding points to the necessity for a comprehensive utilisation of scientific methods and sophisticated engineering for progressive collapse assessment to determine targeted protection measures.
A prototype of wind turbines in 5 megawatt dass was built and tested at the first German offshore wind energy test fteld in the North Sea. In order to investigate dynamic behaviors under a complex state of loads, a continuous dynamic monitoring System was implemented by Federal Institute for Material Research and Testing (BAM). It recorded structural responses and environmental/operational variables from November 2007 to October 2009.
This paper presents significant resonance phenomenon due to the interaction in the tower-nacelle System under operational conditions. Modal parameters are automatically estimated by the poly reference Least Square Complex Frequency domain (p-LSCF) method. Campbell plot demonstrates that a three-blade passage frequency and its multiples f3n match with the natural frequencies of the wind turbine System in several modal Orders. The damping estimates decrease and the Vibration amplitude increase significantly. A control System is necessary to minimize the excessive vibrations.
Wind turbines on offshore sites (OWECs) are subjected to combined loads from wind and waves. These dynamic loads, with a frequency content within the range of the natural frequencies of the structures, cause fatigue-effective stresses in the substructures of wind turbines. Therefore, the examination of natural frequencies is an important part within the design process of wind turbines. The quality of the numerical models for such calculations is of great importance, since the certification guidelines permit only small uncertainties in modal analysis results. The accuracy of the parameters of the numerical model can only be achieved through a comparison of simulation results with corresponding test results. Therefore, it is necessary to measure the dynamic behaviour of all components of the wind turbines simultaneously. This is true not only for the design verification, but also for monitoring the OWECs in operation. The potential of integrated systems for monitoring-based maintenance optimisation should thus be used.
Vibration-based structural health monitoring of a wind turbine system. Part I: Resonance phenomenon
(2015)
This paper is focused on a resonance phenomenon of a wind turbine system in 5 MW class, on the basis of dynamic signals acquired continuously from the tubular tower under normal operational conditions during two years.
Firstly, technique specifications of the wind turbine system are introduced and a finite element model is developed to characterize the structural dynamic properties. The following part describes the continuous dynamic monitoring system integrated with an automated operational modal analysis procedure using the poly-reference Least Squares Complex Frequency domain (p-LSCF) method. Subsequently, variations and mutual relationships of environmental/operational factors such as vibration amplitude, temperature, wind speed, rotation speed of blades, pitch angle and nacelle direction are also presented. Finally, significant resonance is observed due to the fundamental frequency of the tower matching with the harmonic frequency induced by the rotation of three blades. As the rotation speed of rotor approaches to 8 rpm, the vibration amplitude of the tower increases significantly and the corresponding damping value decreases. With the further rising wind velocity, the rotation speed of blades stops increasing and the input energy just contribute to accumulate the vibration amplitude of tower. Such observation indicates the Sommerfeld effect that aggravates the resonance phenomenon. A vibration control device is necessary to minimize the excessive structural responses.
A companion paper will further discuss the environmental/operational effects on dynamic properties of the wind turbine system under the operational conditions.
The second part of these companion papers mainly researches environmental/operational influences on structural dynamic properties under normal operational conditions during two years, in order to extract a statistical based damage-sensitive indicator for health monitoring of a wind turbine system.
The correlation analyses between experimental identified frequencies, damping values as well as mode shapes and environmental/operational factors such as rotation speed of blades, wind speed, pitch angle, temperature and nacelle direction are presented. It is observed that the frequency estimates are influenced by the nacelle position, the activation of rotor, the rotation speed of blades and the wind speed as well as the temperature. Regarding to the damping estimates, they are mainly associated with variation of the aerodynamic damping due to the increasing wind speed. Besides, the resonance phenomenon is also observed in higher modes. The harmonic frequencies due to blades passing by tower are found and the corresponding damping value decreases. Moreover, the mode shapes in some modes are strongly affected by the position of the nacelle.
Subsequently, two types of simulated damage including the reduction of stiffness in both the rotor blade and the tubular tower are successfully detected by applying the Principal Component Analysis (PCA) based methods to these temperature-sensitive frequency estimates. Comparison of change of the extracted health features indicates that they are more sensitive with the tower damage.
An efficient approach to reliability analysis of deteriorating structural systems is presented, which considers stochastic dependence among element deterioration. Information on a deteriorating structure obtained through inspection or monitoring is included in the reliability assessment through Bayesian updating of the system deterioration model. The updated system reliability is then obtained through coupling the updated deterioration model with a probabilistic structural model. The underlying high-dimensional structural reliability problems are solved using subset simulation, which is an efficient and robust sampling-based algorithm suitable for such analyses. The approach is demonstrated in two case studies considering a steel frame structure and a Daniels system subjected to high-cycle fatigue.
The fatigue deterioration modeling for welded steel structures subjected to high cycle fatigue is presented in the current document. The aim of this paper is to formulate approaches based on actual Research results for the phases fatigue crack initiation, fatigue propagation and fatigue failure. The physical characteristics of the approaches are discussed in combination with the associated uncertainties and the probabilistic modeling of this time variant reliability problem. The fatigue deterioration modeling documented here serve as a basis for a reliability-based approach to inspection planning.
A reliability-based approach to inspection planning for welded steel structures subjected to high cycle fatigue is presented in the current document. Inspections are an effective means to control the Progress of fatigue deterioration and the presented approach allows to determine the minimum required inspection effort so that the considered structure complies with the given risk acceptance criteria in terms of target reliability throughout its service life.
In the present paper, an approach for updating the continuous stress range distribution of a welded connection of a wind turbine support structure with predicted information from strain measurements is presented. Environmental conditions, such as wind or, in offshore fields, waves and currents, in combination with rotor excitations generate cyclic stresses affecting the reliability of welded joints of the support structure over the service life. Using strain measurements, these conditions can be monitored, and the resulting stress ranges, under consideration of measurement, mechanical and material uncertainties, can be reconstructed. These stress ranges can be used as an input for updating the prior probability density function (PDF) of the stress ranges predicted by the overall dynamics and a detailed design analysis. Applying Bayesian probability theory and decision theoretical implications, the predicted posterior probability density of the stress ranges is calculated based on the design information and uncertainties. This approach is exemplified, and it is shown how the predicted stress ranges and the design stress ranges are distributed. The prior and the predicted posterior stress ranges are used for a reliability calculation for potentially entering a pre-posterior decision analysis
Proof load testing may be performed to confirm the reliability of the bridge for an existing classification or to prove the reliability for a higher classification. In this paper, a probabilistic decision analysis approach is applied to the scenario for the evaluation of target proof load in the situation where information on the bridge resistance model is lacking. In this case, the resistance model is established by proof loading and taking very basic prior knowledge into account. The decision scenario is modelled in the context of the proof load test planner who shall choose the required load level for assessment of a bridge. The choice of the load level depends on the risks due to the testing and the expected benefit gain from the test. Information acquired about the loading response from monitoring during the proof load testing is modelled by taking basis in the model uncertainty formulation. The optimal proof load level for classification of a single lane, simply supported bridge of 8m span subjected to live load from very heavy (gross weight > 80 tons) transport vehicles was calculated. The optimal proof load level was identified as leading to a positive expected benefit gain to the decision maker while also satisfying target reliability criteria for remaining service life. The analysis was performed for the evaluation of bridge performance with respect to five classifications of very heavy transport vehicles with different vehicle weights and configurations.
The use of load and structural performance measurement information is vital for efficient structural integrity management and for the cost of energy production with Offshore Wind Turbines (OWTs). OWTs are dynamically sensitive structures subject to an interaction with a control unit exposed to repeated cyclic wind and wave loads causing deterioration and fatigue. This study focuses on the quantification of the value of structural and environmental information on the integrity management of OWT structures, with the focus on fatigue of welded joints. By utilizing decision analysis, structural reliability methods, measurement data, as well as the cost-benefit models, a Value of Information (VoI) analysis can be performed to quantify the most beneficial measurement strategy. The VoI assessment is demonstrated for the integrity management of a butt welded joint of a monopile support structure for a 3 MW OWT with a hub height of approximately 71m. The conditional value of three-year measured oceanographic information and one-year strain monitoring information is quantified posteriori in conjunction with an inspection and repair planning. This paper provides insights on how much benefits can be achieved through structural and environmental information, with practical relevance on reliability-based maintenance of OWT structures.