TY - BOOK

T1 - Efficient diagnostics of complex mechanical systems

AU - Grashorn, Jan

PY - 2024/9/20

Y1 - 2024/9/20

N2 - Diagnosing faults and unsafe operation conditions in machines and structures often involves inverse modeling, where a computational model is used together with data to infer the current system state. To tackle imprecise models and sensor noise, a stochastic framework can be adapted here. This allows for the quantification of uncertainties in both models and measurements, offering a more robust approach to fault diagnosis. By incorporating probability distributions, it is possible to capture a range of possible outcomes and assess their likelihood, providing deeper insights into system behavior. Inverse problems are frequently ill-posed, meaning that solutions may not be unique or stable, leading to significant uncertainties in the results. By leveraging a stochastic framework, it is possible to introduce probabilistic methods into the modeling process, allowing for a more nuanced interpretation of the data. This approach facilitates the evaluation of multiple models and states, providing a mechanism to assess their relative probabilities and identify the most likely scenarios. This work focuses on developing efficient algorithms for inverse modeling in structural and dynamical engineering systems, specifically for parameter updating. Traditional approaches to solving inverse problems in these fields often rely on Markov chain Monte Carlo (MCMC) methods within a Bayesian framework. Although effective, these methods can be computationally expensive due to the high number of model evaluations and rejected samples. Recent advancements in the field of optimal transport offer a more efficient way to tackle Bayesian inverse problems by employing a variational approach. This approach utilizes transport maps to establish a coupling between two probability distributions, enabling a direct mapping from a simple, easy-to-evaluate distribution to the complex posterior distribution used in Bayesian updating. The mapping is derived through optimization, and in this work, polynomial-based transport maps are used. However, the method is flexible, allowing for other functions such as neural networks to be used as the basis for the mapping. The thesis presents a general formulation for solving structural health monitoring problems, illustrating the advantages and disadvantages of using transport maps in this context. Moreover, the same framework is applied to parameter updating in dynamical systems, presenting an alternative to traditional filtering methods like Kalman filters or particle filters. The results demonstrate that the use of optimal transport-based methods can lead to significant reductions in computational effort while maintaining accuracy in the Bayesian parameter updating process. To support future research and experimentation, and to validate developed algorithms, an open-source framework for vibration experiments has been developed. This open-source framework offers a cost-effective solution for conducting research on dynamic behavior in engineering systems. Designed to accommodate generic signals, such as harmonic vibrations, random excitations and earthquake recordings, the framework is versatile and suitable for a wide range of applications. By using standard, readily available components, the setup significantly reduces costs compared to traditional vibration testing equipment. This accessibility makes it an excellent choice for smaller research groups and educational institutions that require reliable yet affordable experimental tools.

AB - Diagnosing faults and unsafe operation conditions in machines and structures often involves inverse modeling, where a computational model is used together with data to infer the current system state. To tackle imprecise models and sensor noise, a stochastic framework can be adapted here. This allows for the quantification of uncertainties in both models and measurements, offering a more robust approach to fault diagnosis. By incorporating probability distributions, it is possible to capture a range of possible outcomes and assess their likelihood, providing deeper insights into system behavior. Inverse problems are frequently ill-posed, meaning that solutions may not be unique or stable, leading to significant uncertainties in the results. By leveraging a stochastic framework, it is possible to introduce probabilistic methods into the modeling process, allowing for a more nuanced interpretation of the data. This approach facilitates the evaluation of multiple models and states, providing a mechanism to assess their relative probabilities and identify the most likely scenarios. This work focuses on developing efficient algorithms for inverse modeling in structural and dynamical engineering systems, specifically for parameter updating. Traditional approaches to solving inverse problems in these fields often rely on Markov chain Monte Carlo (MCMC) methods within a Bayesian framework. Although effective, these methods can be computationally expensive due to the high number of model evaluations and rejected samples. Recent advancements in the field of optimal transport offer a more efficient way to tackle Bayesian inverse problems by employing a variational approach. This approach utilizes transport maps to establish a coupling between two probability distributions, enabling a direct mapping from a simple, easy-to-evaluate distribution to the complex posterior distribution used in Bayesian updating. The mapping is derived through optimization, and in this work, polynomial-based transport maps are used. However, the method is flexible, allowing for other functions such as neural networks to be used as the basis for the mapping. The thesis presents a general formulation for solving structural health monitoring problems, illustrating the advantages and disadvantages of using transport maps in this context. Moreover, the same framework is applied to parameter updating in dynamical systems, presenting an alternative to traditional filtering methods like Kalman filters or particle filters. The results demonstrate that the use of optimal transport-based methods can lead to significant reductions in computational effort while maintaining accuracy in the Bayesian parameter updating process. To support future research and experimentation, and to validate developed algorithms, an open-source framework for vibration experiments has been developed. This open-source framework offers a cost-effective solution for conducting research on dynamic behavior in engineering systems. Designed to accommodate generic signals, such as harmonic vibrations, random excitations and earthquake recordings, the framework is versatile and suitable for a wide range of applications. By using standard, readily available components, the setup significantly reduces costs compared to traditional vibration testing equipment. This accessibility makes it an excellent choice for smaller research groups and educational institutions that require reliable yet affordable experimental tools.

U2 - 10.15488/17989

DO - 10.15488/17989

M3 - Doctoral thesis

CY - Hannover

ER -