A direct probabilistic approach to solve state equations for nonlinear systems under random excitation

In this paper, a direct probabilistic approach（DPA） is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process.The proposed method has the advantage of obtaining the response＇s moments directly from the initial conditions and statistical characteristics of the corresponding external excitations. First, the response＇s moment equations are directly derived based on a DPA, which is completely independent of the It？/filtering approach since no specific assumptions regarding the correlation structure of excitation are made.By solving them under Gaussian closure, the response＇s moments can be obtained. Subsequently, a multiscale algorithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo（MC） simulation gives good agreement.Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.

Predictability of well construction time with multivariate probabilistic approach

Current univariate approach to predict the probability of well construction time has limited accuracy due to the fact that it ignores key factors affecting the time.In this study,we propose a multivariate probabilistic approach to predict the risks of well construction time.It takes advantage of an extended multi-dimensional Bernacchia–Pigolotti kernel density estimation technique and combines probability distributions by means of Monte-Carlo simulations to establish a depth-dependent probabilistic model.This method is applied to predict the durations of drilling phases of 192 wells,most of which are located in the AustraliaAsia region.Despite the challenge of gappy records,our model shows an excellent statistical agreement with the observed data.Our results suggested that the total time is longer than the trouble-free time by at least 4 days,and at most 12 days within the 10%–90% confidence interval.This model allows us to derive the likelihoods of duration for each phase at a certain depth and to generate inputs for training data-driven models,facilitating evaluation and prediction of the risks of an entire drilling operation.

Road Network Analysis with GIS and GRASS-GIS:A Probabilistic Approach

In this paper we show how it can be useful to the probability of intersections in the determination of a classification rule for raster conversions in Geographical Information System(GIS)and GRASS GIS for the Road Network Analysis(RNA).We use a geometric probabilities approach for irregular path considering these results for transportation planning operations.We study two particular problems with irregular tessellations,in order to have a situation more realistic respect to map GIS and considering also the maximum value of probability to narrow the range of possible probability values.

Development of a DFN-based probabilistic block theory approach for bench face angle design in open pit mining

In open pit mining,uncontrolled block instabilities have serious social,economic and regulatory consequences,such as casualties,disruption of operation and increased regulation difficulties.For this reason,bench face angle,as one of the controlling parameters associated with block instabilities,should be carefully designed for sustainable mining.This study introduces a discrete fracture network(DFN)-based probabilistic block theory approach for the fast design of the bench face angle.A major advantage is the explicit incorporation of discontinuity size and spatial distribution in the procedure of key blocks testing.The proposed approach was applied to a granite mine in China.First,DFN models were generated from a multi-step modeling procedure to simulate the complex structural characteristics of pit slopes.Then,a modified key blocks searching method was applied to the slope faces modeled,and a cumulative probability of failure was obtained for each sector.Finally,a bench face angle was determined commensurate with an acceptable risk level of stability.The simulation results have shown that the number of hazardous traces exposed on the slope face can be significantly reduced when the suggested bench face angle is adopted,indicating an extremely low risk of uncontrolled block instabilities.

Lychrel Numbers in Base 10: A Probabilistic Approach

For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.

PROBABILISTIC APPROACH TO SEMILINEAR AND GENERALIZED MIXED BOUNDARY VALUE PROBLEMS

A probabilistic approach is developed to solve semilinear and generalized mixed boundaryvalue problems involving Schrodinger operators. The results obtained in this paper generalize thecorresponding results of [1] and partly generalize the result of [2] as well.

Assessment of rock slope stability by probabilistic-based Slope Stability Probability Classification method along highway cut slopes in Adilcevaz-Bitlis(Turkey)

Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property.In rock slope engineering,stability evaluations are commonly performed by means of analytical or numerical analyses,principally considering the factor of safety concept.As a matter of fact,the probabilistic assessment of slope stability is progressively getting popularity due to difficulties in assigning the most appropriate values to design parameters in analytical or numerical methods.Additionally,the effect of heterogeneities in rock masses and discontinuities on the analysis results is minimized through the probabilistic concept.In this study,slope stability of high and steep sedimentary rock cut slopes along a state highway in AdilcevazBitlis(Turkey) was evaluated on the basis of probabilistic approach using the Slope Stability Probability Classification(SSPC) system.The probabilistic assessment indicates major slope stability problems because of discontinuity controlled and discontinuity orientation independent mass movements.Almost all studied cut slopes suffer from orientation-independent stability problems with very low stability probabilities.Additionally,the probability of planar and toppling failures issignificantly high with respect to the SSPC system.The stability problems along the investigated rock slopes were also verified by field reconnaissance.Remedial measures such as slope re-design and reinforcement at the studied locations should be taken to prevent hazardous events along the highway.On the other hand,the probabilistic approach may be a useful tool during rock slope engineering to overcome numerous uncertainties when probabilistic and analytic results are compared.

Forward-Kinematics-Based Approaches for Pose Accuracy of Docking Mechanism with Joint Clearance

Joint clearance,as an important stochastic factor,can significantly deteriorate positioning and repeatability accuracies and lower assembly quality of a 6-DOF docking mechanism.Considering pose accuracy with traditional error model that possesses inherent imprecision,both probabilistic and deterministic approaches based on forward kinematics are presented to analyze comprehensive pose error(CPE)in simulation.Results indicate an identical trend emerges for each CPE with both approaches,and both CPEs perform opposite variations as the moving platform upgrades.The findings provide theoretical reference for refinement of assembly quality evaluation of this mechanism.

Analysis Approach to Durability Based on Material Initial Fatigue Quality and S-N Curve

Based on probabilistic fracture mechanics approach, a new concept of material initial fatigue quality （MIFQ） is developed. Then, the relation between S-N curve and crack propagation curve is studied. From the study, a new durability analysis method is presented. In this method, S-N curve is used to determine crack growth rate under constant amplitude loading and evaluate the effects of different factors on durability and then the structural durability is analyzed. The tests and analyses indicate that this method has lower dependence on testing, and higher accuracy, reliability and generality and is convenient for application.

Seismic risk analysis of coastal area of Pakistan

Estimation of seismic hazard for the fast developing coastal area of Pakistan is carried out using deterministic and probabilistic approaches. On the basis of seismotectonics and geology, eleven faults are recognized in five seismic provinces as potential hazard sources. Maximum magnitude potential for each of these sources is calculated. Peak ground acceleration (PGA) values at the seven coastal cities due to the maximum credible earthquake on the relevant source are also obtained. Cities of Gwadar and Ormara with acceleration values of 0.21g and 0.25g respectively fall in the high seismic risk area. Cities of Turbat and Karachi lie in low seismic risk area with acceleration values of less than 0.1g. The Probabilistic PGA maps with contour interval of 0.05g for 50 and 100 years return period with 90% probability of non-exceedance are also compiled.

Analysing post-earthquake landslide susceptibility using multi-temporal landslide inventories——a case study in Miansi Town of China

The earthquake that occurred on May 12, 2008, in Wenchuan County aroused a great deal of research on co-seismic landslide susceptibility assessment, but there is still a lack of an evaluation method that considers the activity state of the landslide itself. Therefore, this paper establishes a new susceptibility evaluation model that superimposes the active landslide state based on previous susceptibility evaluation models. Based on a multi-phase landslide database, the probabilistic approach was used to evaluate landslide susceptibility in the Miansi town over many years. We chose the elevation, slope, aspect, and distance from the channel as trigger factors and then used the probability comprehensive discrimination method to calculate the probability of landslide occurrence. Then, the susceptibility results of each period were calculated by superposition with the activity rate. The results show that between 2008 and 2014, the proportion of areas with low landslide susceptibility in the study area was the largest, and the proportionof areas with the highest susceptibility was minimal. The landslide area with highest susceptibility gradually decreased from 2014 to 2017. However, in 2017, 15.06% of the area was still with high susceptibility, and relevant disaster prevention and reduction measures should be taken in these areas. The larger area under the receiver operating characteristic curve(AUC) indicates that the results of the landslide susceptibility assessment in this study are more objective and reliable than those of previous models. The difference in the AUC values over many years shows that the accuracy of the evaluation results of this model is not constant, and a greater number of landslides or higher landslide activity corresponds to a higher accuracy of the evaluation results.

Seismic Hazard Assessment of District Mansehra,Khyber Pakhtoonkhawa,Pakistan

The site of Mansehra is located seismically in an active regime, known as the Crystalline Nappe Zone and Hazara-Kashmir Syntaxis in NW Himalayas, Pakistan. Seismic Hazard Assessment （SHA） for the site has been carried out by considering the earthquake source zones, selection of appropriate attenuation equations, near fault effects and maximum potential magnitude estimation. The Mansehra Thrust, Oghi Fault, Banna Thrust, Balakot Shear Zone, Main Boundary Thrust, Panjal Thrust, Jhelum Fault and Muzaffarabad Fault and, further to the south, the Sanghargali, Nathiagali, and Thandiani Thrusts are the most critical tectonic features within the 50 km radius of Mansehra. Using the available instrumental seismological data from 1904 to 2007, SHA has been carried out. Other reactivated critical tectonic features in the area have been investigated. Among them the Balakot-Bagh fault, with the fault length of 120 km from Balakot to Poonch, has been considered as the most critical tectonic feature on the basis of geological/structural/seismological data. The potential earthquake of maximum magnitude 7.8 has been assigned to the Balakot-Bagh fault using four regression relations. The peak ground acceleration value of 0.25 g （10% probability of exceedance for 50 years） and 0.5 g has been calculated with the help of the attenuation equation using probabilistic and deterministic approaches.

A probabilistic-based method to evaluate hygrothermal performance of an internally insulated brick wall

Uncertainty exists in many aspects of building simulation.A deterministic hygrothermal analysis may not sufficiently give a reliable guidance if a number of input variables are subject to uncertainty.In this paper,a probabilistic-based method was developed to evaluate the hygrothermal performance of building components.The approach accounts for the uncertainties from model inputs and propagates them to the outputs through the simulation model,thus it provides a likelihood of performance risk.Latin hypercube sampling technique,incorporated with correlation structure among the inputs,was applied to generate the random samples that follows the intrinsic relations.The performance of an internally insulated masonry wall was evaluated by applying the proposed approach against different criteria.Thermal performance,condensation and mould growth potential of the renovated wall can overall satisfy the requirements stipulated in multifold standards.The most influential inputs were identified by the standardized regression sensitivity analysis and partial correlation technique.Both methods deliver the same key parameters for the single and time-dependent output variables in the case study.The probabilistic method can provide a comprehensive risk analysis and support the decision-maker and engineer in the design and optimization of building components.

PROBABILISTIC DAMAGE IDENTIFICATION OF STRUCTURES WITH UNCERTAINTY BASED ON DYNAMIC RESPONSES

The probabilistic damage identification problem with uncertainty in the FE model parameters, external-excitations and measured acceleration responses is studied. The uncertainty in the system is concerned with normally distributed random variables with zero mean value and given covariance. Based on the theoretical model and the measured acceleration responses, the probabilistic structural models in undamaged and damaged states are obtained by two-stage model updating, and then the Probabilities of Damage Existence （PDE） of each element are calculated as the damage criterion. The influences of the location of sensors on the damage identification results are also discussed, where one of the optimal sensor placement techniques, the effective independence method, is used to choose the nodes for measurement. The damage identification results by different numbers of measured nodes and different damage criterions are compared in the numerical example.

Evaluating diverse patterns of occupant behavior regarding control-based activities in energy performance simulation

Simulation is recognized as an effective tool for building energy performance assessment during design or retrofit processes. Nevertheless, simulation models yield deviating outcomes from the actual building performance and a significant portion of this deviation originates from the dynamic nature of occupant behavior. Literature on occupant behavior indicates that occupant behavior is not integrated into building energy performance assessment procedures with appropriate resolution, instead they are accepted as assumed and fixed data sets that usually represent the presence of occupants. This study attempts to evaluate the effect of diverse patterns of occupant behavior on energy performance simulation for office buildings. Diverse levels of sensitivity of occupant behavior on control-based activities such as using lighting apparatus, adjusting thermostat settings, and presence in space are employed through three diverse occupant behavior patterns. These occupancy patterns are correlated with three identical office spaces simulated within a conceptual office building. EDSL Tas is used to run building energy performance simulations. Effects of occupant behavior patterns on simulation outcomes are compared for five sample winter and summer workdays, with respect to heating and cooling loads. Results present findings on how diversity of occupancy profiles influences the consumption outcomes.