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Cancer is a worldwide illness that causes significant morbidity and death and imposes an immense cost on global public health. Modelling such a phenomenon is complex because of the non-stationarity and complexity of cancer waves. Apply modern novel statistical methods directly to raw clinical data. To estimate extreme cancer death rate likelihood at any period in any location of interest. Traditional statistical methodologies that deal with temporal observations of multi-regional processes cannot adequately deal with substantial regional dimensionality and cross-correlation of various regional variables. Setting: multicenter, population-based, medical survey data-based biostatistical approach. Due to the non-stationarity and complicated nature of cancer, it is challenging to model such a phenomenon. This paper offers a unique bio-system dependability technique suited for multi-regional environmental and health systems. When monitored over a significant period, it yields a reliable long-term projection of the chance of an exceptional cancer mortality rate. Traditional statistical approaches dealing with temporal observations of multi-regional processes cannot effectively deal with large regional dimensionality and cross-correlation between multiple regional data. The provided approach may be employed in numerous public health applications, depending on their clinical survey data.

Two novel methods are being outlined that, when combined, can be used for spatiotemporal analysis of wind speeds and wave heights, thus contributing to global climate studies. First, the authors provide a unique reliability approach that is especially suited for multi-dimensional structural and environmental dynamic system responses that have been numerically simulated or observed over a substantial time range, yielding representative ergodic time series. Next, this work introduces a novel deconvolution extrapolation technique applicable to a wide range of environmental and engineering applications. Classical reliability approaches cannot cope with dynamic systems with high dimensionality and responses with complicated cross-correlation. The combined study of wind speed and wave height is notoriously difficult, since they comprise a very complex, multi-dimensional, non-linear environmental system. Additionally, global warming is a significant element influencing ocean waves throughout the years. Furthermore, the environmental system reliability method is crucial for structures working in any particular region of interest and facing actual and often harsh weather conditions. This research demonstrates the effectiveness of our approach by applying it to the concurrent prediction of wind speeds and wave heights from NOAA buoys in the North Pacific. This study aims to evaluate the state-of-the-art approach that extracts essential information about the extreme responses from observed time histories.

In contrast to well-known bivariate statistical approach, which is known to properly forecast extreme response levels for two-dimensional systems, the research validates innovative structural reliability method, which is particularly appropriate for multi-dimensional structural responses. The disadvantage of dealing with large system dimensionality and cross-correlation across multiple dimensions is not a benefit of traditional dependability approaches that deal with time series. Since offshore constructions are built to handle extremely high wind and wave loads, understanding these severe stresses is essential, e.g. wind turbines should be built and operated with the least amount of inconvenience. In the first scenario, the blade root flapwise bending moment is examined, whereas in the second, the tower bottom fore-aft bending moment is examined. The FAST simulation program was utilized to generate the empirical bending moments for this investigation with the load instances activated at under-rated, rated, and above-rated speeds. The novel reliability approach, in contrast to conventional reliability methods, does not call for the study of a multi-dimensional reliability function in the case of numerical simulation. As demonstrated in this work, it is now possible to assess multi-degree-of-freedom nonlinear system failure probability, in the case when only limited system measurements are available.

This paper demonstrates the validity of the Naess–Gadai method for extrapolating extreme value statistics of second-order Volterra series processes through application on a representative model of a deep water small size tension leg platform (TLP), with specific focus on wave sum frequency effects affecting restrained modes: heave, roll and pitch. The wave loading was estimated from a second order diffraction code WAMIT, and the stochastic TLP structural response in a random sea state was calculated exactly using Volterra series representation of the TLP corner vertical displacement, chosen as a response process. Although the wave loading was assumed to be a second order (non-linear) process, the dynamic system was modelled as a linear damped mass-spring system. Next, the mean up-crossing rate based extrapolation method (Naess–Gaidai method) was applied to calculate response levels at low probability levels. Since exact solution was available via Volterra series representation, both predictions were compared in this study, namely the exact Volterra and the approximate one. The latter gave a consistent way to estimate efficiency and accuracy of Naess–Gaidai extrapolation method. Therefore the main goal of this study was to validate Naess–Gaidai extrapolation method by available analytical-based exact solution. Moreover, this paper highlights limitations of mean up-crossing rate based extrapolation methods for the case of narrow band effects, such as clustering, typically included in the springing type of response.

The Floating Production Storage and Offloading unit (FPSO) is an offshore unit producing and storing crude oil prior to tanker transport. An important design concern is an accurate prediction of risky dynamic hawser tensions during FPSO offloading operations. Bivariate extreme hawser tension contours are important for selecting proper design values. This paper employed the AQWA hydrodynamic software to analyze vessel hydrodynamic wave loads dynamic response, acting on FPSO vessels under realistic sea state conditions. This paper presents an efficient method for estimating FPSO bivariate response statistics based on numerical simulations validated by various experiments. The bivariate Average Conditional Exceedance Rate (ACER2D) method offers an accurate bivariate extreme value probability distribution and return period contours estimation, utilizing available data efficiently. The two-dimensional probability contours, corresponding to low probability return periods, are easily obtained by the ACER2D method. The performance of the presented method has shown that the ACER2D method provides an efficient and accurate prediction of extreme return period contours. The suggested approach may be used for FPSO vessel design, minimizing potential FPSO hawser damage. Bivariate contours yield bivariate design points, as opposed to a pair of uncoupled univariate design points with the same return period as currently adopted in the industry.

This article provides two unique methodologies that may be coupled to study the dependability of multidimensional nonlinear dynamic systems. First, the structural reliability approach is well suited for multidimensional environmental and structural reactions and is either measured or numerically simulated over sufficient time, yielding lengthy ergodic time series. Second, a unique approach to predicting extreme values has technical and environmental implications. In the event of measurable environmental loads, it is also feasible to calculate the probability of system failure, as shown in this research. In addition, traditional probability approaches for time series cannot cope effectively with the system's high dimensionality and cross-correlation across dimensions. It is common knowledge that wind speeds represent a complex, nonlinear, multidimensional, and cross-correlated dynamic environmental system that is always difficult to analyze. Additionally, global warming is a significant element influencing ocean waves throughout time. This section aims to demonstrate the efficacy of the previously mentioned technique by applying a novel method to the Norwegian offshore data set for the greatest daily wind cast speeds in the vicinity of the Landvik wind station. This study aims to evaluate the state-of-the-art approach for extracting essential information about the extreme reaction from observed time histories. The approach provided in this research enables the simple and efficient prediction of failure probability for the whole nonlinear multidimensional dynamic system.

Safety and reliability are essential engineering concerns for energy-harvesting installations. In the case of the piezoelectric galloping energy harvester, there is a risk that excessive wake galloping may lead to instability, overload, and thus damage. With this in mind, this paper studies bivariate statistics of the extreme, experimental galloping energy harvester dynamic response under realistic environmental conditions. The bivariate statistics were extracted from experimental wind tunnel results, specifically for the voltage-force data set. Authors advocate a novel general-purpose reliability approach that may be applied to a wide range of dynamic systems, including micro-machines. Both experimental and numerically simulated dynamic responses can be used as input for the suggested structural reliability analysis. The statistical analysis proposed in this study may be used at the design stage, supplying proper characteristic values and safeguarding the dynamic system from overload, thus extending the machine’s lifetime. This work introduces a novel bivariate technique for reliability analysis instead of the more general univariate design approaches.

As a result of global warming, the area of the polar pack ice is diminishing, making merchant travel more practical. Even if Arctic ice thickness reduced in the summer, fractured ice is still presenting operational risks to the future navigation. The intricate process of ship-ice interaction includes stochastic ice loading on the vessel hull. In order to properly construct a vessel, the severe bow forces that arise must be accurately anticipated using statistical extrapolation techniques. This study examines the severe bow forces that an oil tanker encounters when sailing in the Arctic Ocean. Two stages are taken in the analysis. Then, using the FEM program ANSYS/LS-DYNA, the oil tanker bow force distribution is estimated. Second, in order to estimate the bow force levels connected with extended return periods, the average conditional exceedance rate approach is used to anticipate severe bow forces. The vessel’s itinerary was planned to take advantage of the weaker ice. As a result, the Arctic Ocean passage took a meandering route rather than a linear one. As a result, the ship route data that was investigated was inaccurate with regard to the ice thickness data encountered by a vessel yet skewed with regard to the ice thickness distribution in the region. This research intends to demonstrate the effective application of an exact reliability approach to an oil tanker with severe bow forces on a particular route.

Green renewable energy is produced by floating offshore wind turbines (FOWT), a crucial component of the modern offshore wind energy industry. It is a safety concern to accurately evaluate excessive weights while the FOWT operates in adverse weather conditions. Under certain water conditions, dangerous structural bending moments may result in operational concerns. Using commercial FAST software, the study's hydrodynamic ambient wave loads were calculated and converted into FOWT structural loads. This article suggests a Monte Carlo‐based engineering technique that, depending on simulations or observations, is computationally effective for predicting extreme statistics of either the load or the response process. The innovative deconvolution technique has been thoroughly explained. The suggested approach effectively uses the entire set of data to produce a clear but accurate estimate for severe response values and fatigue life. In this study, estimated extreme values obtained using a novel deconvolution approach were compared to identical values produced using the modified Weibull technique. It is expected that the enhanced new de‐convolution methodology may offer a dependable and correct forecast of severe structural loads based on the overall performance of the advised de‐convolution approach due to environmental wave loading. This article promotes a computationally effective engineering technique based on Monte Carlo for predicting extreme statistics of either the load or the response process, depending on either simulations or observations. The innovative deconvolution technique has been thoroughly explained. The suggested technique effectively makes use of the entire collection of data while providing a straightforward and accurate extreme value forecast.

This research presents two unique techniques for engineering system reliability analysis of multi-dimensional non-linear dynamic structures. First, the structural reliability technique works best for multi-dimensional structural responses that have been either numerically simulated or measured over a long enough length to produce an ergodic time series. Second, a novel extreme value prediction method that can be used in various engineering applications is proposed. In contrast to those currently used in engineering reliability methodologies, the novel method is easy to use, and even a limited amount of data can still be used to obtain robust system failure estimates. As demonstrated in this work, proposed methods also provide accurate confidence bands for system failure levels in the case of real-life measured structural response. Additionally, traditional reliability approaches that deal with time series do not have the benefit of being able to handle a system's high dimensionality and cross-correlation across several dimensions readily. Container ship that experiences significant deck panel pressures and high roll angles when travelling in bad weather was selected as the example for this study. The main concern for ship transportation is the potential loss of cargo owing to violent movements. Simulating such a situation is difficult since waves and ship motions are non-stationary and complicatedly non-linear. Extreme movements greatly enhance the role of nonlinearities, activating effects of second and higher order. Furthermore, laboratory testing may also be called into doubt due to the scale and the choice of the sea state. Therefore, data collected from actual ships during difficult weather journeys offer a unique perspective on the statistics of ship movements. This work aims to benchmark state-of-the-art methods, making it possible to extract necessary information about the extreme response from available on-board measured time histories. Both suggested methods can be used in combination, making them attractive and ready to use for engineers. Methods proposed in this paper open up possibilities to predict simply yet efficiently system failure probability for non-linear multi-dimensional dynamic structure.