Centers of probability measures without the mean

In the recent years, the notion of mixability has been developed with applications to operations research, optimal transportation, and quantitative finance. An n-tuple of distributions is said to be jointly mixable if there exist n random variables following these distributions and adding up to a constant, called center, with probability one. When the n distributions are identical, we speak of complete mixability. If each distribution has finite mean, the center is obviously the sum of the means. In this paper, we investigate the set of centers of completely and jointly mixable distributions not having a finite mean. In addition to several results, we show the (possibly counterintuitive) fact that, for each (Formula presented.), there exist n standard Cauchy random variables adding up to a constant C if and only if (Formula presented.

Inference and dynamic decision-making for deteriorating systems with probabilistic dependencies through Bayesian networks and deep reinforcement learning

In the context of modern environmental and societal concerns, there is an increasing demand for methods able to identify management strategies for civil engineering systems, minimizing structural failure risks while optimally planning inspection and maintenance (I&M) processes. Most available methods simplify the I&M decision problem to the component level due to the computational complexity associated with global optimization methodologies under joint system-level state descriptions. In this paper, we propose an efficient algorithmic framework for inference and decision-making under uncertainty for engineering systems exposed to deteriorating environments, providing optimal management strategies directly at the system level. In our approach, the decision problem is formulated as a factored partially observable Markov decision process, whose dynamics are encoded in Bayesian network conditional structures. The methodology can handle environments under equal or general, unequal deterioration correlations among components, through Gaussian hierarchical structures and dynamic Bayesian networks. In terms of policy optimization, we adopt a deep decentralized multi-agent actor-critic (DDMAC) reinforcement learning approach, in which the policies are approximated by actor neural networks guided by a critic network. By including deterioration dependence in the simulated environment, and by formulating the cost model at the system level, DDMAC policies intrinsically consider the underlying system-effects. This is demonstrated through numerical experiments conducted for both a 9-out-of-10 system and a steel frame under fatigue deterioration. Results demonstrate that DDMAC policies offer substantial benefits when compared to state-of-the-art heuristic approaches. The inherent consideration of system-effects by DDMAC strategies is also interpreted based on the learned policies

Computational performance of risk-based inspection methodologies for offshore wind support structures

Offshore wind turbines are dynamically responding structures reaching around 70 million of stress cycles per year due to the combined action of waves and wind loading. Therefore, the assessment of fatigue deterioration becomes crucial. Besides, fatigue assessment is characterized by large uncertainties associated with both fatigue loads and strength. Inspections can be undertaken to detect potential cracks and therefore improve our belief about the condition of the structure. However, offshore wind inspections are costly and complex operations, involving the deployment of ROVs or divers for the case of underwater components. Risk-based inspection aims to identify the optimal maintenance policy by balancing the risk of structural failure against maintenance efforts (inspections and repairs). Introduction of a risk-based inspection plan can lead to reductions in the expected life-cycle costs as already demonstrated in the Oil & Gas sector. Inspection planning is a complex sequential decision problem where the decision about whether to go or not for an inspection must consider the outcomes from the previous inspections. In theory, it is possible to find the optimal policy by solving a pre-posterior decision analysis. Nevertheless, for the real case of an offshore wind structure standing a lifetime of 20 years, it is not possible to solve a decision tree which is exponentially growing over time and it becomes computationally intractable. Due to the computational limitations, assumptions are generally introduced within the risk-based analysis leading to approximate optimal policies. Traditional risk-based inspection techniques encompass FORM/SORM or Monte Carlo simulations to estimate and update the probability of failure as well as the inclusion of heuristic decision rules to solve the decision problem. However, novel methods and algorithms have been proposed recently to improve the computational efficiency of the risk-based analyses such as Dynamic Bayesian Networks (DBNs) or Partially Observable Markov Decision Processes (POMDPs). The aim of this work is to compare the existing risk-based inspection planning methodologies applicable to offshore wind structures. The computational performance and life-cycle expected costs corresponding to the different methodologies are explored. Additionally, the challenges which risk-based inspection planning is facing in the present are presented and potential solutions are suggested, for instance, on how to incorporate the correlation between structural components or “system-effects” into the risk-based analysis. In order to explore the main aspects involved during the application of the existing risk-based methodologies, the following step are pursued: 1) identification of the most relevant random variables within the deterioration models, 2) calibration of SN/Miner’s fatigue model to a fracture mechanics model, 3) comparison of the methods available for updating the failure probability when information from inspections is available and 4) comparison of the methods available to solve the pre-posterior decision problem corresponding to inspection planning. The optimal inspection plan for an offshore wind tubular joint is then identified by employing the different risk-based methodologies. Thereby, the methodologies are reviewed in terms of: 1) computational time to set up the model, 2) computation time required by the simulation and 3) obtained life-cycle expected costs. The results highlight the computational advantages of modern methods such as DBNs or POMDP which facilitate the identification of more optimal inspection policies

Surfaces with Dual Functionality through Specific Coimmobilization of Self-Assembled Polymeric Nanostructures

Coimmobilization of functional, nanosized assemblies broadens the possibility to engineer dually functionalized active surfaces with a nanostructured texture. Surfaces decorated with different nanoassemblies, such as micelles, polymersomes, or nanoparticles are in high demand for various applications ranging from catalysis, biosensing up to antimicrobial surfaces. Here, we present a combination of bio-orthogonal and catalyst-free strain-promoted azide–alkyne click (SPAAC) and thiol–ene reactions to simultaneously coimmobilize various nanoassemblies; we selected polymersome–polymersome and polymersome–micelle assemblies. For the first time, the immobilization method using SPAAC reaction was studied in detail to attach soft, polymeric assemblies on a solid support. Together, the SPAAC and thiol–ene reactions successfully coimmobilized two unique self-assembled structures on the surfaces. Additionally, poly(dimethylsiloxane) (PDMS)-based polymersomes were used as “ink” for direct immobilization from a PDMS-based microstamp onto a surface creating locally defined patterns. Combining immobilization reactions has the advantage to attach any kind of nanoassembly pairs, resulting in surfaces with “desired” interfacial properties. Different nanoassemblies that encapsulate multiple active compounds coimmobilized on a surface will pave the way for the development of multifunctional surfaces with controlled properties and efficiency

Optimal Inspection and Maintenance Planning for Deteriorating Structural Components through Dynamic Bayesian Networks and Markov Decision Processes

Civil and maritime engineering systems, among others, from bridges to offshore platforms and wind turbines, must be efficiently managed as they are exposed to deterioration mechanisms throughout their operational life, such as fatigue or corrosion. Identifying optimal inspection and maintenance policies demands the solution of a complex sequential decision-making problem under uncertainty, with the main objective of efficiently controlling the risk associated with structural failures. Addressing this complexity, risk-based inspection planning methodologies, supported often by dynamic Bayesian networks, evaluate a set of pre-defined heuristic decision rules to reasonably simplify the decision problem. However, the resulting policies may be compromised by the limited space considered in the definition of the decision rules. Avoiding this limitation, Partially Observable Markov Decision Processes (POMDPs) provide a principled mathematical methodology for stochastic optimal control under uncertain action outcomes and observations, in which the optimal actions are prescribed as a function of the entire, dynamically updated, state probability distribution. In this paper, we combine dynamic Bayesian networks with POMDPs in a joint framework for optimal inspection and maintenance planning, and we provide the formulation for developing both infinite and finite horizon POMDPs in a structural reliability context. The proposed methodology is implemented and tested for the case of a structural component subject to fatigue deterioration, demonstrating the capability of state-of-the-art point-based POMDP solvers for solving the underlying planning optimization problem. Within the numerical experiments, POMDP and heuristic-based policies are thoroughly compared, and results showcase that POMDPs achieve substantially lower costs as compared to their counterparts, even for traditional problem settings