Mean-value First-order Second-moment Research Articles

Friction-induced vibration reliability and sensitivity analysis of a braking system

In this study, reliability and sensitivity analyses are performed for the behavior of friction-induced vibration based on automotive braking systems. In this paper, a friction-induced vibration model of the braking system is developed using Newton’s second law. The accuracy of the vibration model is verified through experiments. The displacement response of the braking system is theoretically derived by convolution integration. The function of maximum displacement is obtained by solving the stationary point of displacement response. Based on this function, the limit state function of the maximum limit of friction-induced vibration displacement is established, and the reliability and sensitivity of the friction-induced vibration of the braking system are evaluated by using the Mean Value First Order Second Moment (MVFOSM) method. The results show that the reliability of the braking system increases with the increase of the mathematical expectation of the equivalent stiffness and decreases with the increase of the mathematical expectation of the system friction coefficient, normal force, and damping ratio. In addition, the sensitivity of the reliability varies significantly with the mathematical expectation of the system friction coefficient and damping ratio. Therefore, the system friction coefficient and damping ratio are the key parameters for the reliability design of the braking system.

Reliability Analysis of Passenger Ship Structure Conversion in Bali Straits

LCT conversion passenger ships have been widely operated in the waters of the Bali Strait. Ship operations in the Bali Strait result in repeated loads on the structure. Repeated loading produces vertical and horizontal bending moments that act randomly due to waves. Based on this, it is necessary to analyze the structure of the ship. The purpose of this study was to analyze the reliability value of the ship structure operating in undulating waters. Wave analysis is performed using the spectral method to determine the value of the load acting on the ship, while the reliability calculation uses the Mean Value First Order Second Moment (MVFOSM) method to determine the reliability value. The analysis was carried out on a full load and an empty load. The value of the reliability of the structure at full load is 0.913615 and at empty load is 0.88948.

Enhanced Reliability Method for the Two-Way Shear Provisions of the European Code for Lightweight Concrete

The two-way shear failure of concrete elements is sudden; thus, reliable design codes are a must. In this current study, three reliability methods were implemented, namely: the Mean Value First Order Second Moment (MVFOSM), the First-Order Second Moment Method (FOSM), and the Rackwitez-Fiessler procedure (RFHL-FOSM) on the two-way shear provisions of the European design code for lightweight concrete. A brief state-of-the-art review of existing reliability methods is presented and compared. An extensive experimental database of lightweight concrete slabs testing under two-way shear loading was gathered. The reliability index was calculated for the design code. This index was compared with the target values set by international standards. For two-way shear of lightweight concrete, the European design code was found to achieve the target of reliability. The MVFOSM was found to provide a better reliability index than using the FOSM.

On computation of reliability index for tensile membrane structures based on limit state of deflection

PurposeThe present study is based on finding the structural response of a tensile membrane structure (TMS) through deformation. The intention of the present research is to develop a basic understanding of reliability analysis and deflection behavior of a pre-tensioned TMS. The mean value first-order second-moment method (MVFOSM) method is used here to evaluate stochastic moments of a performance function with random input variables. Results suggest the influence of modulus of elasticity, the thickness of the membrane, and edge span length are significant for reliability based TMS design.Design/methodology/approachA simple TMS is designed and simulated by applying external forces (along with prestress), as a manifestation of wind and snow load. A nonlinear analysis is executed to evaluate TMS deflection, followed by calculating the reliability index. Parametric study is done to consider the effect of membrane material, thickness and load location. First-order second moment (FOSM) is used to evaluative the reliability. A comparison of reliability index is done and deflection variations from μ − 3s to μ + 3s are accounted for in this approach.FindingsThe effectiveness of deflection is highlighted for the reliability assessment of TMS. Reliability and parametric study collectively examine the proposed geometry and material to facilitate infield design requirements. The estimated β value indicates that most suitable fabric material for a simple TMS should possess an elasticity modulus in the range of 1,000–1,500 MPa, the thickness may be considered to be around 1.00 mm, and additional adjustment of around 5–10 mm is suggested for edge length. The loading position in case of TMS structures can be a sensitive aspect where the rigidity of the surface is dependent on the pre-tensioning of the membrane.Research limitations/implicationsThe significance of the parametric study on material and loading for deflection of TMS is emphasized. Due to the lack of consolidated literature in the field combining reliability with deflection limits of a TMS, this work can be very useful for researchers.Practical implicationsThe present work outcome may facilitate practitioners in determining effective design methodology and material selection for TMS construction.Originality/valueThe significance of parametric study for serviceability criteria is emphasized. Parameters like pre-stress can be included in future parametric studies to witness in depth behavior of TMS. Due to lack of consolidated literature in the field combining reliability with deflection limits of a TMS, this work can be very useful for the researchers. The present work outcome may facilitate practitioners in determining effective design methodology and material selection for TMS construction.

Punching Shear Strength of FRP-Reinforced Concrete Slabs without Shear Reinforcements: A Reliability Assessment.

The recent failure of buildings because of punching shear has alerted researchers to assess the reliability of the punching shear design models. However, most of the current research studies focus on model uncertainty compared to experimentally measured strength, while very limited studies consider the variability of the basic variables included in the model and the experimental measurements. This paper discusses the reliability of FRP-reinforced concrete slabs’ existing punching shear models. First, more than 180 specimens were gathered. Second, available design codes and simplified models were selected and used in the calculation. Third, several reliability methods were conducted; therefore, three methods were implemented, including the mean-value first-order second moment (MVFOSM) method, the first-order second moment (FOSM) method, and the second-order reliability method (SORM). A comparison between the three methods showed that the reliability index calculated using the FOSM is quite similar to that using SORM. However, FOSM is simpler than SORM. Finally, the reliability and sensitivity of the existing strength models were assessed. At the same design point, the reliability index varied significantly. For example, the most reliable was the JSCE, with a reliability index value of 4.78, while the Elgendy-a was the least reliable, with a reliability index of 1.03. The model accuracy is the most significant parameter compared to other parameters, where the sensitivity factor varied between 67% and 80%. On the other hand, the column dimension and flexure reinforcement are the least significant parameters compared to other parameters where the sensitivity factor was 0.4% and 0.3%, respectively.

Reliability Analysis for Retaining Pile in Foundation Pit Based on Bayesian Principle

Moso bamboo has the advantages of high short-term strength and reproducibility, appropriating for temporary supporting structure of shallow foundation pit. According to the displacement of the pile top from an indoor model test, the reliability of the supporting effect of the moso bamboo pile was analyzed. First, the calculation formula of reliability index was deduced based on the mean-value first-order second-moment (MVFOSM)method and probability theory under ultimate limit state and serviceability limit state. Then, the dimensionless bias factor (the ratio of the measured value to the calculated value) was introduced to normalize the displacement. The mathematical characteristics of the displacement were estimated and optimized based on Bayesian theory. Finally, taking 2.5 as the design reliability index, the effect of safety factor, tolerable limit displacement, and the ratio of the ultimate limit displacement to the tolerable on reliability index was analyzed. The results show that the safety level of the supporting pile can be increased by 1–2 levels when the safety factor increases by 0.5. When the coefficient of variation of tolerable limit displacement is less than 0.3, the safety factor can be 2–2.5. And the ratio of the ultimate limit displacement to the tolerable has a great influence on the reliability index, when the soil conditions is well, the ratio can be 1.2–1.3.

Probabilistic Risk Evaluation for Overall Stability of Composite Caisson Breakwaters in Korea

In the present study, the overall stability of typical Korean composite caisson breakwaters that were initially designed following the conventional deterministic approach is investigated using reliability approaches. Therefore, the sensitivity of critical uncertainties regarding breakwater safety is analyzed. Uncertainty sources related to the structure, ocean conditions, and properties of the subsoil and rubble mound are considered in the reliability analysis. Sliding and overturning failures are presented as explicit equations, and three reliability methods, i.e., the mean value first-order second-moment, first-order reliability method, and Monte Carlo simulation, are applied in the evaluation process. Furthermore, the bearing capacity of the rubble mound and subsoil are analyzed using the discrete slice method conjugated with the Monte Carlo simulation. The results of this study establish that the sliding failure generally is the most frequent failure occurring among the above-mentioned overall stability failures (around 15 times more common than failures observed in the foundation). Additionally, it is found that the horizontal wave force primarily contributes to the sliding of the caisson body, whereas the friction coefficient is the main factor producing the resistance force. Furthermore, a much small probability of overturning failure implies that the overturning of a caisson around its heels uncommonly occurs during their lifetime, unlike other overall failure modes. Moreover, the failure in foundations may commonly encounter in the breakwater that has a high rubble mound structure compared with sliding mode. Particularly, the performance function of the all foundation bearing capacities presents a nonlinear behavior and positively skewed distribution when using the Monte Carlo simulation method. This phenomenon proves that simulation methods might be an appropriate approach to evaluate the bearing capacity of a breakwater foundation that can overcome several drawbacks of the conventional design approach.

Reliability Analysis of Reinforced Concrete Frame by Finite Element Method with Implicit Limit State Functions

Since the prediction of the seismic response of structures is highly uncertain, the need for the probabilistic approach is clear, especially for the estimation of critical seismic response parameters. Considering the uncertainties present in the material and geometric form of reinforced concrete (RC) structures, reliability analyses using the Finite Element Method (FEM) were performed in the context of Performance-Based Earthquake Engineering (PBEE). This study presented and compared the possibilities of nonlinear modelling of the reinforced concrete (RC) planar frame and its reliability analysis using different numerical methods, Mean-Value First-Order Second-Moment (MVFOSM), First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM) and Monte Carlo simulation (MCS). The calibrated numerical models used were based on the previous experimental test of a planar RC frame subjected to cyclic horizontal load. Numerical models were upgraded by random variable (RV) parameters for reliability analysis purposes and, using implicit limit state function (LSF), pushover analyses were performed by controlling the horizontal inter-storey drift ratio (IDR). Reliability results were found to be sensitive to the reliability analysis method. The results of reliability analysis reveal that, in a nonlinear region, after exceeding the yield strength of the longitudinal reinforcement, the cross-sectional geometry parameters were of greater importance compared to the parameters of the material characteristics. The results also show that epistemic (knowledge-based) uncertainties significantly affected dispersion and on the median estimate parameter response. The MCS sampling method is recommended, but the First-Order Reliability Method (FORM) applied on a response model can be used with good accuracy. Reliability analysis using the FEM proved to be suitable for the direct implementation of geometric and material nonlinearities to cover epistemic (knowledge-based) uncertainties.

Reliability and Failure Analysis of Jet Vane TVC System

Structural and system reliability of a typical jet vane (JV) thrust vector control (TVC) subsystem subjected to stochastic loadings is investigated. Jet vane TVC (JVTVC) is used in many aerospace liquid and solid propulsion systems. For the purpose of this work, JVTVC structural reliability of a solid rocket propulsion system is computed using an explicit closed-form limit state function. The JV structure is influenced by the internal ballistic loads emanating out of the solid rocket propulsion internal ballistic, whose performance is modeled via a one-dimensional uniform flow assumption at the engine steady operating condition. Subsequently, JV structural reliability is predicted using the methods of mean value first-order second-moment as well as the first- and second-order reliability methods. The reliability results of the analytical methods are compared with Monte Carlo simulation for verification purposes. Finally, a comprehensive sensitivity analysis is performed to identify the key JVTVC and solid rocket propulsion design parameters affecting the TVC total system reliability. The parameters considered for sensitivity analysis include the JV geometric and structural properties as well as the solid rocket propulsion ballistic and geometric features. It turned out that the vane support arm radius and the vane area are the most important strength and load design variables, respectively, that impact the JVTVC failure reliability.

Probabilistic finite element method for large tumor radiofrequency ablation simulation and planning

A challenging problem of radiofrequency ablation (RFA) in liver surgery is to accurately estimate the shapes and sizes of RFA lesions whose formation depends on intrinsic variations of the thermal–electrical properties of soft tissue. Large tumors, which can be as long as 10 cm or more, further complicate the problem. In this paper, a probabilistic bio-heating finite element (FE) model is proposed and developed to predict RFA lesions. Uncertainties of RFA lesions are caused by the probabilistic nature of five thermal–electrical liver properties: thermal conductivity, liver tissue density, specific heat, blood perfusion rate and electrical conductivity. Confidence levels of shapes and sizes of lesions are generated by the FE model incorporated with the mean-value first-order second-moment (MVFOSM) method. Based on the probabilistic FE method, a workflow of RFA planning is introduced to enable clinicians to preoperatively view the predicted RFA lesions in three-dimension (3D) within a hepatic environment. Accurate planning of the RFA needle placements can then be achieved based on the interactive simulation and confidence level selection.

Simplified procedure for reliability-based robust geotechnical design of drilled shafts in clay using spreadsheet

ABSTRACTThis paper provides a simplified procedure for reliability-based robust geotechnical design (RGD) using spreadsheet. In the RGD methodology, design robustness is achieved by adjusting “design parameters” without reducing the uncertainties in noise factors. This design approach generally involves a multi-objective optimisation, which is computationally challenging. To improve the efficiency of the RGD methodology, the design robustness is evaluated in terms of sensitivity index and the safety requirement is evaluated using mean value first order second moment (MFOSM). To ease the concern that the reliability index obtained with MFOSM may not be sufficiently accurate, a mapping function that relates MFOSM to a more accurate method such as first order reliability method is introduced. To further improve the efficiency of the proposed simplified RGD method, a new simplified procedure along with a more accurate robustness measure is developed that eliminates the need for multi-objective optimisation. With these modifications, the proposed simplified RGD method can efficiently be implemented in a single Excel spreadsheet. The proposed simplified method, which goes beyond any existing reliability-based RGD methods in terms of ease of use and computational efficiency, is illustrated in this paper with an example of robust design of drilled shaft in clay.

Modeling of human artery tissue with probabilistic approach

Accurate modeling of biological soft tissue properties is vital for realistic medical simulation. Mechanical response of biological soft tissue always exhibits a strong variability due to the complex microstructure and different loading conditions. The inhomogeneity in human artery tissue is modeled with a computational probabilistic approach by assuming that the instantaneous stress at a specific strain varies according to normal distribution. Material parameters of the artery tissue which are modeled with a combined logarithmic and polynomial energy equation are represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters are determined using genetic algorithm (GA) and inverse mean-value first-order second-moment (IMVFOSM) method, respectively. This nondeterministic approach was verified using computer simulation based on the Monte-Carlo (MC) method. Cumulative distribution function (CDF) of the MC simulation corresponds well with that of the experimental stress–strain data and the probabilistic approach is further validated using data from other studies. By taking into account the inhomogeneous mechanical properties of human biological tissue, the proposed method is suitable for realistic virtual simulation as well as an accurate computational approach for medical device validation.

Target reliability index for serviceability limit state of single piles

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state (SLS) of single piles. This contributes to conducting the SLS reliability-based design (RBD) of piles. Based on a two-parameter, hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index (βsls) is obtained using the mean value first order second moment (MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation (MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement (slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety (FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

Incorporating serviceability limit state requirements into reliability-based analysis and design of piles

This study develops a novel reliability-based approach for the analysis and design of piles by incorporating Serviceability Limit State (SLS) requirements into Load and Resistance Factor Design (LRFD) for Ultimate Limit States (ULS). Three methods for reliability-based analysis and design, namely the Mean Value First Order Second Moment (MVFOSM) method, the Advanced First Order Second Moment (AFOSM) method, and the Monte Carlo Simulation (MCS) method, are employed for comparison. In order to expediently quantify model uncertainties for SLS and incorporate them into the process of reliability-based analysis and design of piles, the SLS model factor (or bias factor) is established based on a two-parameter, hyperbolic curve-fitting equation describing the load-settlement relation. Herein, the limiting tolerable foundation settlement (slt) is treated as a random variable. Four load test databases from South Africa presented by Dithinde et al. (2011) are compiled again to conduct reliability analysis and calculate resistance factors. The case studies illustrate that the AFOSM method has the higher accuracy than the MVFOSM method as verified using the MCS method. This study recommends the AFOSM method to perform reliability analysis and determine resistance factors for Reliability-Based Design (RBD).

Mean-value first-order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty

Reliability-based multidisciplinary design optimization (RBMDO) has received increasing attention in engineering design for achieving high reliability and safety in complex and coupling systems (e.g., multidisciplinary systems). Mean-value first-order saddlepoint approximation (MVFOSA) is introduced in this paper and is combined with the collaborative optimization (CO) method for reliability analysis under aleatory uncertainty in RBMDO. Similar to the mean-value first-order second moment (MVFOSM) method, MVFOSA approximated the performance function with the first-order Taylor expansion at the mean values of random variables. MVFOSA uses saddlepoint approximation rather than the first two moments of the random variables to estimate the probability density and cumulative distribution functions. MVFOSA-based CO (MVFOSA-CO) is also formulated and proposed. Two examples are provided to show the accuracy and efficiency of the MVFOSA-CO method.

Liver tissue characterization from uniaxial stress–strain data using probabilistic and inverse finite element methods

Biological soft tissue is highly inhomogeneous with scattered stress–strain curves. Assuming that the instantaneous strain at a specific stress varies according to a normal distribution, a nondeterministic approach is proposed to model the scattered stress–strain relationship of the tissue samples under compression. Material parameters of the liver tissue modeled using Mooney–Rivlin hyperelastic constitutive equation were represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters were determined using inverse finite element method and inverse mean-value first-order second-moment (IMVFOSM) method respectively. This method was verified using computer simulation based on direct Monte-Carlo (MC) method. The simulated cumulative distribution function (CDF) corresponded well with that of the experimental stress–strain data. The resultant nondeterministic material parameters were able to model the stress–strain curves from other separately conducted liver tissue compression tests. Stress–strain data from these new tests could be predicted using the nondeterministic material parameters.

Solution method of overtopping risk model for earth dams

Hydrologic risk analysis relies on a series of probabilistic analyses, and it is a complex problem in estimating the probability distributions of multiple independent and random variables. The goal of this study is to presents the procedure and application of a probability-based risk analysis methodology to evaluate earth dam overtopping risk that induced by concurrent flood and wind. The uncertainty arising from initial water surface level, flood, wind velocity, and dam height are discussed in this research. The improved Monte Carlo simulation and mean-value first-order second-moment method are used to solve the proposed dam overtopping risk model, respectively. The nonparametric kernel density estimation method, which can better learn the complex multimodal characteristic of probability density function than that of traditional parametric estimation method, is employed to improve the probability density function of initial water surface level. The latin hypercube sampling is introduced to generate uniform random number, which improves the efficient and stability compared with simple random sampling. Afterward, an application to the Dongwushi Reservoir in China illustrates that the dam overtopping risk computed using the improved Monte Carlo simulation is lower than that using mean-value first-order second-moment method. Furthermore, the sensitivity analysis show that initial water surface level is more sensitive to overtopping risk than wind velocity.

Reliability Sensitivity Analysis Based on Mean Value First Order Esscher's Approximation

A simple and effective computational procedure is presented for computing probability of failure of mechanical and structural systems with linear limit state function by using convolution theorem,fast probability integration and Esscher's approximation.An efficient and accurate mean-value first order Esscher's approximation method(MVFOEA) is proposed by approximating a performance function with the first order Taylor expansion at the mean-value point of random input variables.By combining MVFOEA with sensitivity analysis technique,a new reliability sensitivity analysis method is proposed.Because of the use of complete distribution information,MVFOEA is generally more accurate than mean value first order second moment(MVFOSM).MVFOEA requires the basic random variables should be independent for each other and have moment generating functions.The features of the proposed method are demonstrated with three numerical examples.

Reliability analyses of slope stability

ABSTRACT This paper proposes the coupling of reliability analysis methods with various mechanical approaches, for a slope stability assessment. Probabilistic strategies include Monte Carlo Simulation method (MCS), First and Second Order Reliability Methods (FORM, SORM), Mean-Value First-Order Second-Moment method (MFOSM) and Quadrature method (QM). Three mechanical models are considered: a Caquot-Taylor formula, a limit equilibrium method of Bishop and a finite element (FE) model based on the strength reduction method (SRM). The present study assumes both the cohesion and friction angle of the soil as uncertain input parameters, to be modelled as correlated random variables. The dependence of the slope reliability on the mechanical modelling and used probabilistic strategies is highlighted.

Mean value first order second moment analysis of buckling of axially loaded thin plates with random geometrical imperfections

Buckling strength of thin plate structures under axial compression is more dominantly affected by the initial geometric imperfections than the other types of imperfections present in them. Since these initial geometric imperfections are random in nature, the collapse strength distribution will also be random. Hence a probabilistic approach is required for reliable design of these thin plate structures. In this paper, by keeping the variance of imperfections of all the models at assumed manufacturing tolerance of 1.71 mm and maintaining the maximum amplitude of imperfections within ±8 mm, 1024 random geometrical imperfect plate models are generated by the linear combination of first 10 eigen affine mode shapes using 2k factorial design. These imperfect models are analysed using ANSYS non-linear FE buckling analysis including both geometrical and material non-linearities. From these FE analysis results, the strength distribution of the plate is obtained and reliability analysis is carried out using Mean Value First Order Second Moment (MVFOSM) method. Keywords: Buckling strength, Thin plates, Geometrical imperfections, Random modeling, Reliability based design, MVFOSM.