Second Moment Method Research Articles

Reliability Analysis and Experimental Verification of Landing-Gear Steering Mechanism Considering Environmental Temperature

The rack-and-pinion steering mechanism of a nose landing gear, which is applied to a regional turboprop aircraft being developed, is chosen as the research object in this paper. First, the finite element analysis of the key components of the steering mechanism is carried out. Second, the reliability of the steering mechanism is analyzed through combining the dynamic simulation model and the first-order second-moment method based on an artificial neural network. Additionally, the analytical results of reliability and parameter sensitivity show that the steering mechanism has very high reliability, and the turning moment and load torque are the factors that have great influence on the reliability of the steering mechanism. Third, an environmental test system is designed for the reliability test of this nose landing gear. After 300,000 different-temperature environmental tests, the high reliability of the landing-gear steering mechanism is verified. It can be known from the test data that the failure data of the steering mechanism are in accordance with the bathtub curve law in each environmental test, and the temperature has a significant impact on the reliability of the steering mechanism. This paper’s work provides a consolidated test basis and method for analyzing and verifying the performance and reliability of other aircraft landing-gear systems.

Reliability analysis of the steel-tube umbilical cable cross section in ocean engineering

Umbilical cable is one of the key control equipments during the exploitation of ocean oil and gas, which is named as the “nerve line” in subsea production system. So it is necessary to carry out the reasonable design and accurate analysis of the umbilical cable to meet the safty requirements. The cross section of steel-tube umbilical cable at the top of configuration undertakes the most dangerous loading case during operation. The current design of umbilical cable is based on the safety factor without enough consideration of the influence of random factors. Concerning the importance of umbilical and the particularity of application environment, it is unreasonable to ignore the uncertainty. Firstly, the uncertainty of components in the section is investigated, and the strength of the cross section under the operation condition is analyzed. Based on above content, the limit state equation is established. Then the reliability of the umbilical cable is calculated by improved first-order second-moment method and Monte Carlo method, respectively. The reliability analysis results show that the randomness of the structure has an important impact on the strength of the umbilical cable. It is necessary to add the reliability research in the design of umbilical cable.

Uncertainty analysis through development of seismic fragility curve for a SMRF structure using adaptive neuro-fuzzy inference system based on fuzzy c-means algorithm

The present study is focused mainly on development of the fragility curves for the sidesway collapse limit state. One important aspect of deriving fragility curves is how uncertainties are blended and incorporated into the model under seismic conditions. The collapse fragility curve is in uenced by di erent uncertainty sources. In this paper, in order to reduce the dispersion of uncertainties, Adaptive Neuro Fuzzy Inference System (ANFIS)based on the fuzzy C-means algorithm is used to derive structural collapse fragility curve, considering e ects of epistemic and aleatory uncertainties associated with seismic loads and structural modeling. This approach is applied to a Steel Moment-Resisting Frame (SMRF) structural model whose relevant uncertainties have not been yet considered by others in particular by using ANFIS method for collapse damage state. The results show the superiority of ANFIS solution in comparison with excising probabilistic methods, e.g., First- Order Second-Moment Method (FOSM) and Monte Carlo (MC)/Response Surface Method (RSM) to incorporate epistemic uncertainty in terms of reducing computational e ort and increasing calculation accuracy. As a result, it can be concluded that, in comparison with the proposed method rather than Monte Carlo method, the mean and standard deviation are increased by 2.2% and 10%, respectively.

Probabilistic Modeling of Seismic Risk Based Design for a Dual System Structure

The dual system structure concept has gained popularity in the construction of high-rise buildings over the last decades. Meanwhile, earthquake engineering design provisions for buildings have moved from the uniform hazard concept to the uniform risk concept upon recognizing the uncertainties involved in the earthquake resistance of concrete structures. In this study, a probabilistic model for the evaluation of such risk is proposed for a dual system structure consisting of shear walls or core walls and a moment frame structure as earthquake resistant structure. Uncertainties in the earthquake resistance of the dual system structure due to record-to-record variability, limited amount of data, material variability and structure modeling are included in the formulation by means of the first-order second-moment method. The statistics of resistance against earthquake forces are estimated by making use of incremental nonlinear time history analysis using 10 recorded earthquake histories. Then, adopting the total probability theorem, the reliability of the structure is evaluated through a risk integral scheme by combining the earthquake resistance of the structure with the annual probability of exceedance for a given location where the building is being constructed.

Parametric sensitivity study on regional seismic damage prediction of reinforced masonry buildings based on time-history analysis

Regional seismic damage prediction is an important approach to discover the weakness of a city so as to effectively mitigate seismic losses. A major proportion of regional seismic losses is caused by masonry buildings. As a result, an accurate prediction of the regional seismic damage to masonry buildings has significant engineering and scientific values. Various parameters of the computational models for regional seismic damage predictions usually involve considerable uncertainty, especially for masonry buildings. Therefore, a parametric sensitivity analysis for the regional seismic damage prediction of reinforced masonry buildings is performed in some detail in this study. Damage to this kind of buildings is predicted through nonlinear time-history analysis using the multiple-degree-of-freedom shear model, which can better represent the features of different buildings and ground motions. In the sensitivity analysis, two widely used methods, the first-order second-moment (FOSM) method and the Monte Carlo method, are adopted and their prediction results are compared. The outcomes of this study indicate that the uncertainty of parameters has a small influence on the analysis results when the total number of regional buildings is large. However the uncertainty cannot be neglected for individual building analysis. In addition, the FOSM method, which is more time-saving, can achieve a similar level of prediction as the Monte Carlo simulation.

A reliability analysis method for rock slope controlled by weak structural surface

Catastrophic landslides maybe occur in rock slope due to the effect of strong earthquakes or heavy rainfall. The stability of rock slope is usually controlled by different scales of weak structural surfaces, which are uncertain and randomly exist in the rock slope. According to the geological characteristics of rock slope, two typical failure modes – plane and wedge are possible. A second-order second-moment (SOSM) method is presented to calculate the reliability index and the failure probability of rock slope, which is an improvement over the first-order second-moment (FOSM) method, and performance functions are built up with the classic limit equilibrium method. The presented method is applied to analyze the failure probability of two rock slopes at the Jinping I Hydropower Station and is compared with the Monte Carlo method and the FOSM method. The computed results show that for plane failure, the reliability index and the failure probability determined by the presented method are 0.563 and 28.7%, respectively, and the reliability index and the failure probability determined by Monte Carlo method are 0.677 and 24.9%, respectively. However, for the FOSM method, the reliability index and failure probability are –0.025 and 51.0%, respectively. For both plane failure and wedge failure, the difference between the presented method and the Monte Carlo method is very small, but the failure probability of plane failure determined by FOSM method is larger than that of the other two methods. The presented method can provide a useful tool to evaluate the failure probability of rock slope.

Methodology to evaluate reliability of performance of second-order automatic control system

Reliability evaluation plays a more and more important role in nuclear engineering, aviation industry, and so on. Due to the special integrity of a control system, traditional reliability methods, such as the reliability block diagram and fault tree analysis, are not proper to make a reasonable and accurate reliability evaluation on a control system. However, a systematic methodology to predict performance reliability of a control system is rarely reported. In this article, a methodology of performance reliability based on the performance requirement for an automatic control system, not just limited to the stability reliability or probabilistic robustness evaluation, is first proposed. A solution to evaluate control performance reliability is introduced with analytical approximation approach called first-order second-moment method. Also, a robust iterative algorithm is adopted to overcome the bifurcation and chaos problems encountered when searching the most probable point for highly nonlinear limit state function. An elaborate example based on a servo motor control system is presented to calculate performance reliability of the settling time of the control system with first-order second-moment method. Its numerical approximation is demonstrated to be accurate through Monte Carlo simulation.

Nondestructive Evaluation and Reliability Analysis for Determining the Mechanical Properties of Old Wood of Ancient Timber Structure

The objective of this study was to evaluate the mechanical properties of ancient wood of Abies fabri (Mast.) Craib based on the nondestructive tests and reliability analysis. Nondestructive tests including resistograph and stress wave test, and destructive tests were conducted on the wood specimens. Results indicated that there were significant linear correlations between the resistance amplitude (F) and green density (ρ), the dynamic modulus of elasticity (ED) and static modulus of elasticity (MOE), modulus of rupture (MOR), and ultimate compressive strength (UCS) of wood specimens. The cumulative distribution of the predicted MOR and UCS based on the nondestructive tests could be well fitted by the normal distribution according to the χ2 test. Moreover, a reliability analysis program based on the first-order second-moment method was developed. Reliability analysis results showed that the reliability index increased nonlinearly with the increase of the live-to-dead load ratio, and decreased nonlinearly with the increase of the design values for all the simulation load cases. According to the minimum reliability index requirements of the Chinese national standard, it is suggested that the design value of MOR and UCS be 14.0 and 10.7 MPa, respectively.

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.

Uncertainty effects of soil and structural properties on the buckling of flexible pipes shallowly buried in Winkler foundation

The failure of civil engineering systems is a consequence of decision making under uncertain conditions. Generally, buried flexible pipes are designed for their transversal behavior to prevent from the important failure mode of buckling. However, the interaction effects between soil and pipe are neglected and the uncertainties in their properties are usually not considered in pipe design. In this regard, the present research paper evaluates the effects of these uncertainties on the uncertainty of the critical buckling hoop force of flexible pipes shallowly buried using the subgrade reaction theory (Winkler model) and First-Order Second-Moment (FOSM) method. The results show that the structural uncertainties of the studied pipes and those of the soil properties have a significant effect on the uncertainty of the critical buckling hoop force, and therefore taking into account these latter in the design of the shallowly flexible pipes for their buckling behavior is required.

Uncertainty Evaluation for Constrained State Estimation in Water Distribution Systems

AbstractIn this paper, an alternative uncertainty treatment for the traditional unconstrained weighted-least-squares (WLS) method is presented. This treatment enables hydraulic constraints (i.e., null demands at transit nodes or null flows at closed pipes, pumps, or valves, etc.), high-precision measurements, and upper and lower variable bounds (i.e., head levels at tanks) to be included within the state estimation (SE) problem for water distribution systems. With this approach, there is no need to choose appropriate weights associated with these types of measurements in order to correctly assess uncertainty for the SE problem. The method set out herein tackles these as constraints and works with the linear system of equations derived from imposing first-order optimality conditions for the constrained SE problem. This approach enables general quantification of the SE uncertainty for all the hydraulic variables within the water system by applying the first-order second-moment (FOSM) method. Moreover, it en...

Mechanical Properties Evaluation of Two Wood Species of Ancient Timber Structure with Nondestructive Testing Methods

Mechanical properties of wood were evaluated using nondestructive test methods. The tests were conducted using the stress wave timing and resistance drilling machine, while static mechanical tests were conducted by an Instron universal testing machine. Both nondestructive and static mechanical tests were performed on wood specimens for Chinese fir (Cunninghamia lanceolata (Lamb.) Hook) and elm (Ulmus rubra). There were strong linear correlations between density (ρ) and resistance amplitude (F), static modulus of elasticity (MOE) and dynamic modulus of elasticity (ED), modulus of rupture (MOR) and ED, and ultimate compressive strength (UCS) and ED. Additionally, an algorithm of the reliability index was developed with the first-order second-moment method. The reliability analysis indicated that the reliability index increased with the decreased design value for both Chinese fir and elm, but it increased as the live-to-dead load ratio (ρ) increased. To achieve the reliability index requirements of the Chinese national code, the MOR design value should be set to 12.6 and 21.7 MPa, while the UCS design value should be set to 10.2 and 13.4 MPa for Chinese fir and elm, respectively.

Chatter reliability of milling system based on first-order second-moment method

In this paper, reliability analysis for dynamic structural system is presented to predict chatter vibration in a milling system. Chatter reliability is defined to represent the probability of stability (no chatter occurs) of milling system. Probability model (reliability model) of chatter vibration is established to predict milling chatter vibration, in which structural parameters and spindle speed are considered as random variables. Choosing chatter frequency as an intermediate variable, the reliability model is built. The first-order second-moment method is adopted to solve the reliability model of the milling process system to obtain the reliability level of the system. The reliability lobe diagram (RLD), which is a contour line with a specified reliability level as a function of spindle speed and cutting depth, is presented to designate the reliable region for chatter vibration prediction. A numerical example is used to demonstrate the method for reliability analysis. The reliability of milling chatter system was calculated using first-order second-moment (FOSM) method and compared to the Monte Carlo simulation method. The results from the FOSM method and Monte Carlo method were found to be similar. Comparing the results with the traditional stability lobe digram (SLD) method, chatter reliability of milling process system can be used to judge the probability of stability of milling process system. It can be concluded that RLD can be efficiently used to predict reliability in workshop applications.

Reliability Analysis of Left-Turn Sight Distance at Signalized Intersections

The current method for the analysis of sight distance for left-turn vehicles at signalized intersections assumes that all component variables are deterministic. This paper presents a probabilistic approach based on such random variables as major-road speed, time gap required for left-turn vehicle, vehicle width, lateral position of left-turn vehicle, distance between driver eye of left-turn vehicle and its front, and lateral and longitudinal positions of positioned opposing left-turn vehicle. A safety margin is defined as the difference between available and required sight distances. Relationships for the mean and standard deviation of the safety margin were developed using the first-order second-moment (FOSM) method. This method identifies the offset (distance between left edge of the left-turn lane and right edge of the opposing left-turn lane) at signalized intersections for a desired probability of noncompliance based on intersection and traffic characteristics. The proposed reliability method was validated using Monte Carlo simulation, and design graphs were established. The results show that the deterministic method provides very conservative offsets and that the offset is most sensitive to vehicle width and lateral distance-related variables and less sensitive to longitudinal distance-related variables.

Evaluation of load and resistance factors for the reliability-based design of the main cables of earth-anchored suspension bridges

This paper presents load and resistance factors for the reliability-based design of the main cables of earth-anchored suspension bridges for the Strength I Limit State defined in the AASHTO LRFD Bridge Design Specifications. Reliability analyses are performed for three suspension bridges in Korea with main span lengths ranging from 650 m to 1545 m, and the reliability indices and the Most Probable Failure Points (MPFP) of random variables are evaluated. The strength, load and stiffness parameters are taken into account as random variables. The advanced first-order second-moment method is employed to evaluate the reliability indices and the MPFP of the random variables. The elastic catenary cable element is utilized to discretize the main cables. Load factors are proposed based on the normalized MPFP of each load component considered in the Strength I Limit State. The resistance factor that yields the reference target reliability index for the main cable is found as 0.53. Two alternative resistance factors, which give lower and higher reliability indices than the reference value, are also proposed. The proposed load and resistance factors lead to a uniform reliability level for a main cable regardless of the length of the main span of a suspension bridge.

Seismic Reliability Analysis of Long-Span Cable-stayed Bridges

Earthquake motion is a random process, and thus, analyzing the seismic responses and dynamic reliability of cable-stayed bridges based on the random vibration theory is important. In this paper, dynamic reliability is investigated under earthquake loads by applying the stochastic vibration theory to the Sutong Yangtze River Highway Bridge. The response statistics are obtained from random vibration analyses, and the dynamic reliability of the normal stress of several key cross sections in the bridge is analyzed using the first-order second-moment method and the first-passage failure theory. The dynamic reliability analysis shows that the reliability index changes with girder section location and meets the design requirements. The analysis shows that the Sutong Bridge has adequate earthquake resistance ability. The structure’s earthquake resistance is appraised to provide an important theoretical reference for improving the seismic resistance design methods.

Simplified probabilistic voltage stability evaluation considering variable renewable distributed generation in distribution systems

This study investigates the evaluation of static voltage stability using a two-point estimation method (2PEM) and continuation power flow (CPF) in distribution systems. The stochastic distribution generation (DG) units have been considered with their respective probability density function (PDF). The proposed static voltage stability evaluation method first chooses several sample points to replace the PDFs using 2PEM. Then, based on each sample point, the critical static voltage stability value is calculated by CPF. On the basis of the critical values corresponding to all selected sample points, Cornish–Fisher series are used to evaluate the PDF of the critical static voltage stability, and then the static voltage stability state can be obtained. The proposed method has been tested on IEEE 33-bus, PG&E 69-bus and a real case with two stochastic DG units. Comparisons have been made with the Monte Carlo simulation and the first-order second-moment method. The results show that the proposed method has better efficiency and accuracy.

Landslide-risk zonation along mountainous highway considering rock mass classification

Landslide and especially rockfall hazard widely occurs along cut slopes in mountainous regions. The risk assessment of mass movements is still one of most challenging problems in slope engineering geology. We propose a routine method to assess rock slide and rockfall risk of cut slopes essentially based on slope properties and rock mass structure. The method is a lean low-cost path to a risk estimate. Rock block size is simplified into two classes, {small} with a volume less than 1.0 m3 and {large}, greater than 1.0 m3. Studies indicate that for a slope with n small-medium rock blocks, the possibility of rockfalls can be estimated by 1 − (1 − P) n , in which P is the likelihood of one {small} rock block fall. The possibility of other types of mass movement can be determined by the first-order second-moment (FOSM) method. Based on this, an exponent equation was adopted to evaluate the consequence and the risk. The methodology is demonstrated by a case study from the mountains of Mentougou district, Beijing, China. Based on the investigations of geological conditions (i.e., lithology, weathering and rock mass structure) and some historical mass movement data of the cut slopes, a zonation map for rockfall and rock slide risk along a 17-km section of a road is presented. The result is supported by mass movement event observations in the recent 2 years.

Reliability Analysis of Pre-Stressed Concrete Continuous Girder Bridges Using Cantilever Construction on Different Codes

The object of this paper analyzes the reliability level of pre-stressed concrete continuous girder bridges designed with the Chinese codes including the code for design of highway reinforced concrete and pre-stressed concrete bridges and culverts of JTG D62-2004 and JTJ 023-85 using cantilever construction method. Typical cross-sections used in the example bridge are considered at service stage. Load and resistance parameters are treated as random variables. The statistical parameters are based on the available literature, test data and survey results. Reliability indices are calculated by iterations using the first-order second-moment method. The calculated results indicate that the reliability indices on the code of D62-2004 vary considerably to the code of JTJ 023-85. And it could provide the references for the reinforcement of old bridges and the design of new bridges using the cantilever construction.

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.