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This paper aims to present a multi-scale stochastic damage model (SDM) for concrete and apply it to the stochastic response analysis of reinforced concrete shear wall structures.

The proposed SDM is constructed at two scales, i.e. the macro-scale and the micro-scale. The general framework of the SDM is established on the basis of the continuum damage mechanics (CDM) at the macro-scale, whereas the detailed damage evolution is determined through a parallel fiber buddle model at the micro-scale. The parallel buddle model is made up of micro-elements with stochastic fracture strains, and a one-dimensional random field is assumed for the fracture strain distribution. To represent the random field, a random functional method is adopted to quantify the stochastic damage evolution process with only two variables; thus, the numerical efficiency is greatly enhanced. Meanwhile, the probability density evolution method (PDEM) is introduced for the structural stochastic response analysis.

By combing the SDM and PDEM, the probabilistic analysis of a shear wall structure is performed. The mean value, standard deviation and the probability density function of the shear wall responses, e.g., shear capacity, accumulated energy consumption and damage evolution, are obtained.

It is noted that the proposed method can reflect the influences of randomness from material level to structural level, and is efficient for stochastic response determination of shear wall structures.

Perils of tornado and hail cause large amounts of loss every year. Based on the data provided by Property Claims Services, since 1949, tornado, hail and straight‐line‐wind losses account for more than 40 percent of total natural losses in the USA. Given the high frequency of tornado and damaging hail in the continental USA, quantifying these risks will be an important advancement in pricing them for insurance/reinsurance purposes. In the absence of a realistic physical model, which would look at these perils on a cluster/outbreak basis, it is not possible to underwrite these risks effectively. The purpose of this paper is to focus on the tornado risk.

A tornado wind‐field model is developed based on the model used by Wen and Ang. The model is calibrated to the specifications given in the Fujita intensity scale. To estimate the tornado hazard, a historical database is generated and de‐trended using the information provided by Storm Prediction Center along with the dataset given by Grazulis. This new historical database together with a reinsurance timeframe criterion in mind was used to define outbreaks. These outbreaks are used in a Monte‐Carlo simulation process to generate a large number of outbreaks representing 35,000 years of simulated data. This event‐set is used to estimate spatial frequency contours and loss analyses.

The results focus on the spatial frequency of occurrence of tornadoes in the USA. The losses are tallied using multiple occurrences of tornado and/or hail per outbreak. The distribution of loss, both on per occurrence and on aggregate basis, are discussed.

This paper is believed to be the first one to use a tornado wind‐field model, outbreak model, and vulnerability models, which estimate both spatial distribution of hazard and location‐based distribution of losses. Estimation of losses due to hail is also provided.

The purpose of this paper is to discuss the characteristics of several stochastic simulation methods applied in computation issue of structure health monitoring (SHM).

On the basis of the previous studies, this research focusses on four promising methods: transitional Markov chain Monte Carlo (TMCMC), slice sampling, slice-Metropolis-Hasting (M-H), and TMCMC-slice algorithm. The slice-M-H is the improved slice sampling algorithm, and the TMCMC-slice is the improved TMCMC algorithm. The performances of the parameters samples generated by these four algorithms are evaluated using two examples: one is the numerical example of a cantilever plate; another is the plate experiment simulating one part of the mechanical structure.

Both the numerical example and experiment show that, identification accuracy of slice-M-H is higher than that of slice sampling; and the identification accuracy of TMCMC-slice is higher than that of TMCMC. In general, the identification accuracy of the methods based on slice (slice sampling and slice-M-H) is higher than that of the methods based on TMCMC (TMCMC and TMCMC-slice).

The stochastic simulation methods evaluated in this paper are mainly two categories of representative methods: one introduces the intermediate probability density functions, and another one is the auxiliary variable approach. This paper provides important references about the stochastic simulation methods to solve the ill-conditioned computation issue, which is commonly encountered in SHM.

This paper aims to focus on the stochastic analysis of composite rotor blades with matrix cracking in forward flight condition.

The effect of matrix cracking and uncertainties are introduced to the aeroelastic analysis through the cross-sectional stiffness properties obtained using thin-walled beam formulation, which is based on a mixed force and a displacement method. Forward flight analysis is carried out using an aeroelastic analysis methodology developed for composite rotor blades based on the finite element method in space and time. The effects of matrix cracking are introduced through the changes in the extension, extension-bending and bending matrices of composites, whereas the effect of uncertainties are introduced through the stochastic properties obtained from previous experimental and analytical studies.

The stochastic behavior of helicopter hub loads, blade root forces and blade tip responses are obtained for different crack densities. Further, assuming the behavior of progressive damage in same beam is measurable as compared to its undamaged state, the stochastic behaviors of delta values of various measurements are studied. From the stochastic analysis of forward flight behavior of composite rotor blades at various matrix cracking levels, it is observed that the histograms of these behaviors get mixed due to uncertainties. This analysis brings out the parameters which can be used for effective prediction of matrix cracking level under various uncertainties.

The behavior is useful for the development of a realistic online matrix crack prediction system.

Instead of introducing the white noise in the simulated data for testing the robustness of damage prediction algorithm, a systematic approach is developed to model uncertainties along with damage in forward flight simulation.

The front bearing mount structure in an aero engine has been severely loaded under the fan blade off (FBO) event since imbalance forces at high amplitude but low frequency is transformed to the engine front mount structure. The bearing mount structural forces are estimated by an integrated implicit-explicit analysis process of whole engine model of an aero engine. Since there are many dependent factors which are governing those predicted loads, experimental evidence on FBO is becoming necessary to validate the model used for the load prediction which is more expensive and also time consuming. This paper aims to discuss the above mentioned issues.

The current paper deals with the high impact but low probability nature of FBO load prediction on the bearing mount structure by stochastic approach which could be replaced for FBO experiments which is highly essential for current economic conditions. Several influential factors on the predicted loads have been chosen in the stochastic model and sensitive analysis has also been performed to bring down the variation involved in the predicted load.

The predicted load by proposed stochastic model is then compared with the experimental results. The conclusion on the predicted load with various dependent influential factors is matching well with certain value of damage factor from planned FBO test event.

Limitation of this paper could be that it does not cover with range of load amplitude and is only applicable for civil small and medium engines.

The high amplitude but low frequency load pattern is assessed with impact condition by stochastic model.

Combining experimental and probabilistic load prediction was never done before and read across from previous engine test program could be effectively performed with stochastic model approach.

Disaster management and humanitarian logistics (HT) play crucial roles in large-scale events such as earthquakes, floods, hurricanes and tsunamis. Well-organized disaster response is crucial for effectively managing medical centres, staff allocation and casualty distribution during emergencies. To address this issue, this study aims to introduce a multi-objective stochastic programming model to enhance disaster preparedness and response, focusing on the critical first 72 h after earthquakes. The purpose is to optimize the allocation of resources, temporary medical centres and medical staff to save lives effectively.

This study uses stochastic programming-based dynamic modelling and a discrete-time Markov Chain to address uncertainty. The model considers potential road and hospital damage and distance limits and introduces an a-reliability level for untreated casualties. It divides the initial 72 h into four periods to capture earthquake dynamics.

Using a real case study in Istanbul’s Kartal district, the model’s effectiveness is demonstrated for earthquake scenarios. Key insights include optimal medical centre locations, required capacities, necessary medical staff and casualty allocation strategies, all vital for efficient disaster response within the critical first 72 h.

This study innovates by integrating stochastic programming and dynamic modelling to tackle post-disaster medical response. The use of a Markov Chain for uncertain health conditions and focus on the immediate aftermath of earthquakes offer practical value. By optimizing resource allocation amid uncertainties, the study contributes significantly to disaster management and HT research.

The paper discusses the problems encountered in the management and quantitative evaluation of fire risk and safety in a building. Rational methods for obtaining solutions to these problems are provided by non‐deterministic mathematical models rather than deterministic models. This is due to the fact that the occurrence and spread of an accidental (not arson) fire are random phenomena affected by uncertainties caused by several factors. Non‐deterministic models discussed briefly in the paper include simple statistical and probabilistic models, regression methods, probability distributions, fault and event trees and stochastic models. The paper only provides a framework for applying these models to any type of facility. For any type, it may be necessary to modify these techniques, collect all the relevant data and perform the analyses to derive results and conclusions applicable to that type.

As the intensity of natural disasters increases, there is a need to develop policies and procedures to assist various agencies with moving aid to affected areas. One of the biggest limitations to this process is damage to transportation networks, in particular waterways. To keep waterways safe, aids to navigation (ATONs) are placed in various areas to guide mariners and ships to their final destination. If the ATONs are damaged, then the waterways are left unsafe, making it difficult to move supplies and recover from a disaster. The aim of this paper is to explore the effectiveness of pre‐positioning strategies for port recovery in response to a natural disaster.

A stochastic facility location model is presented to determine where teams and commodities should be pre‐positioned in order to maximize the number of ATONs repaired, given a constraint on response time. The first stage decisions focus on determining the location of resources. The second stage decisions consist of the distribution of supplies and teams to affected areas.

Results show the benefit of pre‐positioning and the value of coordination toward the responsiveness of restoring waterways. Furthermore, the relationship between resources, repair time, and response is characterized.

There has been extensive work addressing pre‐positioning as it relates to responding to the needs of populations affected by disasters. However, little has been done to explore pre‐positioning in the context of business recovery from severe weather events.

The use of waste polyethylene terephthalate (PET) plastics derived from shredded bottles in concrete is not formalized yet, especially in reinforced members such as beams and columns. The disposal of plastic wastes in concrete is a viable alternative to manage those wastes while minimizing the environmental impacts associated to recycling, carbon dioxide emissions and energy consumption.

This paper evaluates the suitability of 2D deterministic and stochastic finite element (FE) modeling to predict the shear strength behavior of reinforced concrete (RC) beams without stirrups. Different concrete mixtures prepared with 1.5%–4.5% PET additions, by volume, are investigated.

Test results showed that the deterministic and stochastic FE approaches are accurate to assess the maximum load of RC beams at failure and corresponding midspan deflection. However, the crack patterns observed experimentally during the different stages of loading can only be reproduced using the stochastic FE approach. This later method accounts for the concrete heterogeneity due to PET additions, allowing a statistical simulation of the effect of mechanical properties (i.e. compressive strength, tensile strength and Young’s modulus) on the output FE parameters.

Data presented in this paper can be of interest to civil and structural engineers, aiming to predict the failure mechanisms of RC beams containing plastic wastes, while minimizing the experimental time and resources needed to estimate the variability effect of concrete properties on the performance of such structures.