First-order Second-moment Research Articles

Probabilistic Slope Stability Analysis of Mount St. Helens Using Scoops3D and a Hybrid Intelligence Paradigm

In the past, numerous stratovolcanoes worldwide witnessed catastrophic flank collapses. One of the greatest risks associated with stratovolcanoes is a massive rock failure. On 18 May 1980, we witnessed a rock slope failure due to a volcano eruption, and a 2185.60 m high rock slope of Mount St. Helens was collapsed. Thus, from the serviceability perspective, this work presents an effective computational technique to perform probabilistic analyses of Mount St. Helens situated in Washington, USA. Using the first-order second-moment method, probability theory and statistics were employed to map the uncertainties in rock parameters. Initially, Scoops3D was used to perform slope stability analysis followed by probabilistic evaluation using a hybrid computational model of artificial neural network (ANN) and firefly algorithm (FF), i.e., ANN-FF. The performance of the ANN-FF model was examined and compared with that of conventional ANN and other hybrid ANNs built using seven additional meta-heuristic algorithms. In the validation stage, the proposed ANN-FF model was the best-fitted hybrid model with R2 = 0.9996 and RMSE = 0.0042. Under seismic and non-seismic situations, the reliability index and the probability of failure were estimated. The suggested method allows for an effective assessment of the failure probability of Mount St. Helens under various earthquake circumstances. The developed MATLAB model is also attached as a supplementary material for future studies.

Time-depending Reliability Analysis of O-ring Sealing Performance

O-rings are commonly used due to their simple structure and excellent performance. However, the time-dependent creep behavior of rubber during usage can significantly impact the working performance and service life of the O-ring. The phenomenological creep constitutive model establishes a relationship between the deformation of rubber materials under creep conditions and time, by incorporating a creep function that considers the significance of damage. Based on the phenomenological creep constitutive model, we establish a simulation model for the contact pressure of an engine O-ring. This model characterizes the time-dependent degradation process of the O-ring’s sealing performance by tracking the variation of contact pressure and contact surface width over time. To account for the randomness of rubber material model parameters and compression amount, we develop a time-dependent reliability analysis model for the O-ring using the first-order second-moment (FOSM) method. The research findings can establish a theoretical foundation for the assessment, analysis, and evaluation of O-ring sealing’s time-dependent reliability.

Chatter reliability of high speed cylindrical grinding with uncertain parameters

Cylindrical grinding is commonly used as the final process of machining, but its quality and efficiency are often limited by chatter phenomenon. Many research show that the result from conventional chatter analysis by using the deterministic parameters is not consistent with the practical working condition and the chatter reliability prediction in high speed cylindrical grinding with uncertain parameters is studied in this paper. The dynamic model of the cylindrical grinding system is established, and uncertain parameters such as mass, stiffness and damping coefficient are introduced, and the stability lobe diagrams with uncertain parameters were obtained. The reliability model of the grinding system was established, and the reliability was solved by using the Monte Carlo simulation method, the improved first-order second-moment method and the second-order second-moment method, respectively. Then, the chatter-free reliability of the system was predicted by using the reliability lobe diagram. The accuracy of the grinding reliability prediction results is verified by the experiment results. Furthermore, the Monte Carlo sensitivity analysis method is used to study the influence of random parameters on the grinding system, and the results show that the variation of modal mass has the greatest influence on the reliability of the grinding system.

A novel adaptive approach based on over-distance interval searching and precise step size determining for first-order structural reliability analysis

The first-order second-moment reliability method (FORM) is a prevalent method in the reliability analyzing community owing to its accuracy and efficiency. However, it may encounter unstable solutions such as periodic oscillation and non-convergence when a high-dimensional problem with complex performance functions is involved. In this study, a novel adaptive approach based on over-distance interval searching and precise step size determining is presented to work out a solution for the above issues. First, the relationship between the state of the iterative rotation angle and the ideal step size was noticed. Therefore, a rotation control condition is proposed to dictate the selection of step size for the algorithm. After that, the determination of the step size of the proposed method here can be realized in two stages: In the first stage, an over-distance step size interval searching approach is established to define an initial exploration interval of step size with a length of 1. In the second stage, a determination approach of adaptive precise step size is then proposed to modify the fixed step sizes to make it adaptable to changes, therefore, get the final step sizes for the proposed method. Together, an over-distance adaptive precise searching approach of step size that can generate self-adaptive step sizes both greater and less than 1 is performed by interplaying the above two stages, thus preventing an excessive amount of redundant workload and speeding up the convergence while reducing the risk of oscillations. Besides, an iterative direction modification approach is given to orient the first iteration more accurately. In addition to that, the proposed method is tested on a offshore jacket platform and other seven examples to verify its performance. The results demonstrate that the proposed method provides excellent robustness and efficiency for both low and high-nonlinearity problems, showing significant merits.

Probabilistic assessment of heavy-haul railway track using multi-gene genetic programming

This study presented a probabilistic assessment of heavy-haul railway track using a high-performance computational model called multi-gene genetic programming (MGGP). A reliability analysis (RA) method based on MGGP and the first-order second-moment method (FOSM) has been proposed in this study. First, GP was used to map the implicit performance functions; therefore, arriving at GP-based explicit performance functions. Subsequently, the developed GP model was used to perform RA of a soil slope of heavy-haul railway track under both seismic and non-seismic conditions. Using the FOSM, soil uncertainties were mapped based on the concepts of probability theory and statistics, and a ready-made expression was developed. Simulated results demonstrate that the GP-based FOSM approach can predict the probability of failure (POF) of slope with rational accuracy. The probabilistic analysis against bearing capacity failure was also investigated in this study to ensure serviceability of the soil slope. Based on the outcomes, it can be deduced that the coefficient of variation of soil properties affects the POF of slope significantly. With the aid of the developed expression, the POF of the soil slope of heavy-haul railway track can be assessed rationally and efficiently.

Reliability-based assessment of reasonable mid-tower lateral stiffness for a three-tower suspension bridge

A reasonable lateral stiffness of the bridge mid-tower should ensure that the deflection-to-span ratio and sliding resistance coefficient satisfy the design requirements. However, if this stiffness is determined by the deterministic parametric analysis, the above two verification indices may exceed the threshold due to the randomness of the high-dimensional structure and load parameters. To satisfy the structural safety requirements of a three-tower suspension bridge during its design life, this study proposes a method to quickly and accurately evaluate the reliability indices of the deflection-to-span ratio and sliding resistance coefficient of the three-tower suspension bridge. Based on advanced first-order second-moment, the proposed method transforms the reliability problem into an optimization problem with constraint functions, uses the single-cable theory to establish the limit state function, and combines the manta ray foraging optimization algorithm and penalty function to derive the reliability index. The effectiveness of the proposed method is verified by performing Latin hypercube sampling for an examplary three-tower suspension bridge. These results prove that the new technique avoids tedious finite element simulation and surrogate model fitting, ensuring the accuracy of the reliability index while improving the calculation efficiency. The study further identifies critical structural parameters by parametric analysis. Based on the inverse reliability, the dimensionless stiffness range for the mid-tower with the randomness of the parameters is derived, and the preliminary design method of the lateral stiffness of the mid-tower based on the reliability is established.

Reliability analysis of piezoelectric cantilever beam with inverse piezoelectric effect

In this paper, the mechanical output and electrical output of the piezoelectric cantilever beam under the inverse piezoelectric condition has been studied. The limit state equation for the mechanical reliability and electrical reliability of the piezoelectric cantilever beam under the inverse piezoelectric effect has been derived. The reliability of the piezoelectric cantilever beam has been predicted by using the principle of the series system with inverse piezoelectric. The proposed reliability model of the piezoelectric cantilever beam under the inverse piezoelectric state is simple, which is obtained by using the first-order second-moment method. It has been shown that the proposed model is robust and practical with validation by an engineering problem.

An efficient and non-intrusive approach for robust design optimization with the first-order second-moment method

A modified robust design optimization approach is presented, which uses the first-order second-moment method to compute the mean value and the standard deviation for arbitrary objective functions. Existing approaches compute the gradient of the variance using the adjoint method, direct differentiation or finite differences, respectively. These approaches either access to the FE-code and/or have high computational cost. In this paper, a new approach for the computation of the gradient of the variance is provided. It can be easily implemented as a non-intrusive method, which behaves similar to finite differences with the cost of only one additional objective evaluation, independent of the number of variables. Here, a step-size has to be chosen carefully and therefore, a procedure to determine a problem-independent step-size is provided. As an alternative, the approach can be implemented as an analytic method with the same cost like the adjoint method, but providing wider applicability (e.g. eigenvalue problems). The provided approach is derived, analyzed and applied to several benchmark examples.

Influence of Limit State Function’s Form of Geotechnical Structures on Approximate Analytical Reliability Methods

Approximate analytical methods have been frequently used in geotechnical engineering to estimate the reliability of geotechnical structures due to their efficiency and simplicity. The main spirit of these methods is using the moments of the limit state function to estimate the reliability index. However, the moments are strongly dependent on the form of the limit state function, resulting in the fact that these methods are sensitive to the form of limit state functions. This study aims to systematically explore how various equivalent forms of limit state functions affect the performance of several commonly used approximate analytical methods, including the first-order second-moment method, the first-order reliability method, and the point estimation method. The applicable conditions of these methods are illustrated through five typical geotechnical examples. The results indicate that the estimated accuracy for the first-order second-moment method and the point estimation method is affected by the form of the limit state functions. Although the form of the limit state function does not affect the accuracy of the first-order reliability method, it affects computational efficiency. The limit state functions with an equivalent logarithmic form are almost always favorable for the investigated examples and are thus recommended in practice.

Probabilistic damage tolerance assessment method based on the multi-scale crack growth model

The probabilistic damage tolerance analysis method, which combines the theory of damage tolerance and probabilistic fracture mechanics, can significantly improve the reliability and safety of engineering structures. In this study, the stress intensity factors under different crack sizes of experimental specimens were simulated by the finite element method, and the damage tolerance evaluation effects of three fatigue crack growth models were compared. Then, based on the multi-scale fatigue crack growth model and the first-order second-moment (FOSM) method, the reliability under the specified fatigue crack growth life was obtained. Finally, considering the uncertainty of initial crack and fracture toughness, the probabilistic damage tolerance assessment map based on the multi-scale fatigue crack growth model is established. The map provides a basis for developing a more reasonable model and establishing a more perfect and reliable damage tolerance assessment method.

ASSESSING SEISMIC SOIL LIQUEFACTION POTENTIAL USING MACHINE LEARNING APPROACH

The liquefaction vulnerability of soil is generally related to a few soil parameters which are ordinarily measured by laboratory tests on distributed and undistributed tests under distinctive test conditions. This study uses methods based on a standard penetration test to assess liquefaction criteria to appraise the liquefaction vulnerability for soil deposits of Chalus City placed in a high seismic area. To overcome the deficiencies of these experimental strategies an ANN-based model has been created utilizing the Artificial Intelligence technique to anticipate liquefaction. The proposed model is a function of the plasticity index, liquid limit, water content, and some other geotechnical parameters. Reliability index (β) and probability of liquefaction (PL) have also been determined for both the proposed methods for a superior understanding of their accuracies and strength. First-order second moment (FOSM) reliability analysis has been embraced in the present paper. The observation drawn from the study illustrates a reliable and conventional expectation rate of the regression as compared to the experimental strategy. A strong regression shown for assessing the liquefaction vulnerability, which is based on field test information for preparatory prediction, would be of extraordinary help within the field of geotechnical designing.

A generalized approach for robust topology optimization using the first-order second-moment method for arbitrary response functions

The paper presents a rigorous formulation of adjoint systems to be solved for a robust design optimization using the first-order second-moment method. This formulation allows to apply the method for any objective function, which is demonstrated by considering deformation at certain point and maximum stress as objectives subjected to random material stiffness and geometry, respectively. The presented approach requires the solution of at most three additional adjoint systems per uncertain system response, when compared to the deterministic case. Hence, the number of adjoint systems to be solved is independent of the number of random variables. This comes at the expense of accuracy, since the objective functions are assumed to be linear with respect to random parameters. However, the application to two standard cases and the validation with Monte Carlo simulations show that the approach is still able to find robust designs.

Increasing reliability of axially compressed cylinders through stiffness tailoring and optimization.

The capabilities of the rapid tow shearing (RTS) process are explored to reduce the well-known imperfection sensitivity of axially compressed cylindrical shells. RTS deposits curvilinear carbon fibre tapes with a fibre-angle-thickness coupling that enables the in situ manufacturing of embedded rings and stringers. By blending the material's elastic modulus and wall thickness smoothly across the cylindrical surface, the load paths can be redistributed favourably with a minimal-design approach that contains part count and weight while ameliorating imperfection sensitivity. A genetic algorithm that incorporates realistic manufacturing imperfections and axial stiffness penalty is used to maximize the 99.9% reliability load of straight fibre (SF) and RTS cylinders. The axial stiffness penalty ensures that reliability does not come at the expense of stiffness. The first-order second-moment method is used to calculate statistical moments that enable an estimate of the 99.9% reliability load. Due to the fibre-angle-thickness coupling of RTS, buckling data are normalized by mass and thickness. Compared to a quasi-isotropic laminate, which corresponds to the optimal eight-layer design for a perfect cylinder, the optimized SF and RTS laminates have a 6% and 8% greater 99.9% normalized reliability load. By relaxing the axial stiffness penalty, the performance benefit can be increased such that SF and RTS cylinders exceed the 99.9% normalized reliability load of an eight-layer quasi-isotropic laminate by 23% and 37%, respectively. Both improvements (with and without penalty functions) stem largely from a reduction in the variance of the buckling-load distribution, thereby demonstrating the potential of fibre-steered cylinders in reducing the imperfection sensitivity of cylindrical shells. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Assessment of uncertainties in a complex modeling chain for predicting reservoir sedimentation under changing climate

Long-term predictions of reservoir sedimentation require an objective consideration of the preceding catchment processes. In this study, we apply a complex modeling chain to predict sedimentation processes in the Banja reservoir (Albania). The modeling chain consists of the water balance model WaSiM, the soil erosion and sediment transport model combination RUSLE-SEDD, and the 3d hydro-morphodynamic reservoir model SSIIM2 to accurately represent all relevant physical processes. Furthermore, an ensemble of climate models is used to analyze future scenarios. Although the capabilities of each model enable us to obtain satisfying results, the propagation of uncertainties in the modeling chain cannot be neglected. Hence, approximate model parameter uncertainties are quantified with the First-Order Second-Moment (FOSM) method. Another source of uncertainty for long-term predictions is the spread of climate projections. Thus, we compared both sources of uncertainties and found that the uncertainties generated by climate projections are 408% (for runoff), 539% (for sediment yield), and 272% (for bed elevation in the reservoir) larger than the model parameter uncertainties. We conclude that (i) FOSM is a suitable method for quantifying approximate parameter uncertainties in a complex modeling chain, (ii) the model parameter uncertainties are smaller than the spread of climate projections, and (iii) these uncertainties are of the same order of magnitude as the change signal for the investigated low-emission scenario. Thus, the proposed method might support modelers to communicate different sources of uncertainty in complex modeling chains, including climate impact models.

"Reliability Analysis of Axially Compressed Steel Columns "

"In the past, the evaluation of the strength and safety of compressed steel columns has primarily relied on deterministic concepts. However, these concepts fail to account for the significant variability observed in buckling strength test results. This study aims to address this limitation by adopting a probabilistic approach to assess the buckling strength of steel columns; following the Indian standard specification IS 800-2007. In this investigation, the statistically variable nature of the material properties is considered by treating them as random variables and assuming a normal distribution. By incorporating this variability, a more comprehensive evaluation of the buckling strength can be achieved. The buckling strength of the steel column is computed using Merchant Rankine's formula, which takes into account deductive uncertainty. This formula considers various factors such as the slenderness ratio, live load to dead load ratio, and other relevant parameters to estimate the buckling strength of the column. Furthermore, the reliability of axially loaded columns is assessed using the First Order Second Moment (FOSM) technique. The effects of the slenderness ratio and the live load-to-dead load ratio on the reliability of the columns are specifically investigated and discussed. Overall, this study contributes to a more comprehensive understanding of the buckling strength of steel columns, incorporating statistical variability and providing insights into the reliability assessment of such structural elements."

Application of a first-order method to estimate the failure probability of component subjected to thermal transients for optimization of design parameters

The Japan Atomic Energy Agency has been developing “Advanced Reactor Knowledge- and AI-aided Design Integration Approach through the whole plant lifecycle (ARKADIA)” to offer the best solutions for challenges in the design and operation of nuclear plants. A part of ARKADIA for design study, which included design optimization of components, is named as ARKADIA-Design. In the development of ARKADIA-Design, we have been developing a process to automatically optimize design parameters of structural components subjected to various kinds of loads, including thermal transients. In this paper, we propose a simplified procedure to estimate the failure probability of components subjected to thermal transients for design optimization. An objective function of this optimization is defined on the basis of failure probability of the components, because failure probability can be commonly used as an indicator of component integrity for various mechanisms, and it helps future introductions of a risk-informed performance-based approach to component design. To enable the necessary number of estimations for design optimization with practical calculation time, we aimed to reduce the number of analyses required for one estimation. For this purpose, we adopted the first-order second-moment (FOSM) method as the estimation method for failure probability in the process of optimization. An orthogonal table in the experiment design method is utilized to define the conditions of the analyses for evaluation of the mean and variance of thermal transient stress, which are used as inputs in the FOSM method. The superposition of ramp responses is also utilized to evaluate the time history of thermal transient stress instead of finite element analysis. The proposed procedure was applied in a demonstration study to optimize the thickness of a cylindrical vessel subjected to thermal transients derived from shutdown. We confirmed that the procedure can evaluate the failure probability depending on the cylinder thickness with practical calculation time.

Probabilistic Soil Liquefaction Assessment: A Case Study for Agartala City in Tripura in North-East India

A sudden increase in pore water pressure causes the effective stress to decrease significantly, which in turn causes a loss of shear strength and the subsequent outcome of allowing the soil to behave as a liquid, resulting in soil liquefaction. Agartala, the capital of Tripura, is located in northeastern India, and the entire region is considered seismically active according to the seismic zoning map of India as per IS 1893:2002 (Part 1); the entire region is classified as Zone-V. Significant earthquakes have struck this region, including the 1897 Shillong and 1950 Assam earthquakes. The city is vulnerable to liquefaction due to alluvial soil and a low groundwater table. Several parameters are involved in assessing liquefaction potential in the deterministic method and have different input parameter uncertainties, resulting in inconsistent outcomes. As a result, evaluating liquefaction susceptibility requires a thorough probability approach that considers parameter uncertainty. In this work, the soil liquefaction potential of Agartala City is assessed using fuzzy logic and compared to the conventional Reliability technique using the first-order second-moment method. Soil liquefaction potential was properly calculated using both approaches for the 71 boreholes in and around Agartala city. The outcomes are shown as contour maps representing spatial variations of the probability of liquefaction at different depths. In this study, Fuzzy logic is used to model the relationships between different soil parameters, which can help better understand the soil\'s behaviour during liquefaction. This developed method can assess the vulnerability of liquefaction potential and select appropriate materials and construction processes.

Generalized first-order second-moment method for uncertain random structures

<abstract> <p>In this paper, a new reliability assessing method for structures influenced by both aleatory and epistemic uncertainty simultaneously is developed. To handle hybrid types of uncertainties, chance theory is introduced to define a new hybrid reliability index. By mathematical derivation and theorems proofs, the new index is showed to be effective and compatible with hybrid types of uncertainties. Correspondingly, a generalized first-order second-moment (GFOSM) algorithm is established for practical reliability assessment of structures with hybrid uncertainties. Based on the first two moments of basic variables, the GFOSM method can perform fast and effective reliability assessment without large-scale integration operations and can be considered as an extension and expansion of the traditional FOSM method. Two numerical cases further illustrate the effectiveness and practicability of the proposed method from different perspectives.</p> </abstract>

A fatigue reliability assessment model for welded structures based on the structural stress method

Since many factors affect the fatigue life of welded structures and the relationships between them are complex, finding effective ways to improve the fatigue reliability of welded structures has always been a challenge for the industry. A fatigue reliability assessment model and design method for welded structures based on the structural stress method is proposed. According to the limit state equation of the model, the design-life fatigue reliability and the service fatigue reliability assessment approaches are presented. Then, a first-order second-moment method is employed to reveal quantitative fatigue reliability for welded joints and structures. The relationships between the fatigue reliability and the influence variables are used to analyze and improve the welded structure design. Fatigue reliability of T-joint examples was assessed by accounting for weld leg sizes, plate thicknesses, penetration depths, and single-sided and double-sided forms. Furthermore, the assessment model was verified with a welded bogie frame. The fatigue reliability of the frame was improved based on the evaluation results. The model and method can be applied to other types of welded joints and welded structures.

Reliability analysis of compressed timber studs on the buckling criterion

Introduction. Ensuring safety is a priority goal in the design, construction and operation of building and structures. A quantitative assessment of safety can be the failure probability of a structural element. The article presents algorithms for reliability analysis of timber studs by the buckling criterion under central compression force.
 
 Materials and methods. The FOSM (First Order Second Moment) method is a classic approach for solving many reliability analyses tasks in the engineering sector. This method uses the second statistical moments of random variables (mathematical expectation and variance) and the method of statistical linearization with the decomposition of the function into a Taylor series of the first order. However, it is often necessary to deal with nonlinear limit state functions, where the statistical linearization method can lead to incorrect results. In this case, it is necessary to use other algorithms for reliability analysis: the Hasofer – Lind method, SORM (Second Order Reliability Method), etc.
 
 Results. The numerical example of reliability analysis for compressed timber studs on the buckling criterion is considered. To illustrate the problem of the research, the dimensions of the cross-section of the studs and the strength of the wood are taken as random variables, and the load is considered a deterministic value. In the following, an algorithm for reliability analysis is described for a timber studs under random load. The classical FOSM approach showed an overestimated reliability index by 35 % compared to the results of the Monte Carlo numerical experiment and the analytical solution using the Hasofer – Lind algorithm.
 
 Conclusions. The use of the traditional FOSM method for reliability analysis of wooden studs according to the buckling criterion can lead to overestimated reliability index estimates. It is unacceptable from the point of view of the structural safety. The calculation and analysis of the reliability of timber studs should be carried out on the basis of the Hasofer – Lind algorithm, the SORM method or other optimization methods.