Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

A novel adaptive support vector machine method for reliability analysis

For the structural reliability analysis, although many methods have been proposed, they still suffer from substantial computational cost or slow convergence rate for complex structures, the limit state function of which are highly non-linear, high dimensional, or implicit. A novel adaptive surrogate model method is proposed by combining support vector machine (SVM) and Monte Carlo simulation (MCS) to improve the computational efficiency of estimating structural failure probability in this paper. In the proposed method, a new adaptive learning method is established based on the kernel function of the SVM, and a new stop criterion is constructed by measuring the relative position between sample points and the margin of SVM. Then, MCS is employed to estimate failure probability based on the convergent SVM model instead of the actual limit state function. Due to the introduction of adaptive learning function, the effectiveness of the proposed method is significantly higher than those that employed random training set to construct the SVM model only once. Compared with the existing adaptive SVM combined with MCS, the proposed method avoids information loss caused by inconsistent distance scales and the normalization of the learning function, and the proposed convergence criterion is also more concise than that employed in the existing method. The examples in the paper show that the proposed method is more efficient and has broader applicability than other similar surrogate methods.

Heuristic Operator for Reliability Assessment of Frame Structures

In structural design of steel frames, in order to achieve proper safety, the effect of uncertainties in the design and loading parameters of the structure must be considered. This approach is obtained by defining a reliability index. In this study, the Modified Dolphin Monitoring (MDM) operator was used to evaluate the reliability index of three well-known steel frame structures based on the Hasofer-Lind method. The reliability index was evaluated using the EVPS and VPS algorithms and with considering the MDM operator on them. The constraint of the last story drift is considered as limit state function. The random variables consist of external loads, modulus of elasticity, moment of inertia and cross-sectional areas. According to the number of evaluations of the limit state function, the results show the efficiency of this method in comparison to the Monte Carlo simulation method. Also, the values of the most probable point (MPP) are examined.

A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

(1) Background: in practical applications, probabilistic and non-probabilistic information often simultaneously exit. For a complex system with a nonlinear limit-state function, the analysis and evaluation of the reliability are imperative yet challenging tasks. (2) Methods: an improved second-order method is proposed for reliability analysis in the presence of both random and interval variables, where a novel polar transformation is employed. This method enables a unified reliability analysis taking both random variables and bounded intervals into account, simplifying the calculation by transforming a high-dimension limit-state function into a bivariate state function. The obtained nonlinear probability density functions of two variables in the function inherit the statistic characteristics of interval and random variables. The proposed method does not require any strong assumptions and so it can be used in various practical engineering applications. (3) Results: the proposed method is validated via two numerical examples. A comparative study towards a contemporary algorithm in state-of-the-art literature is carried out to demonstrate the benefits of our method. (4) Conclusions: the proposed method outperforms existing methods both in efficiency and accuracy, especially for cases with strong nonlinearity.

Expected Uncertainty Reduction for Sequential Kriging-Based Reliability Analysis

Several acquisition functions have been proposed to identify an optimal sequence of samples in sequential kriging-based reliability analysis. However, no single acquisition function provides better performance over the others in all cases. To address this problem, this paper proposes a new acquisition function, namely expected uncertainty reduction (EUR), that serves as a meta-criterion to select the best sample from a set of optimal samples, each identified from a large number of candidate samples according to the criterion of an acquisition function. EUR directly quantifies the expected reduction of the uncertainty in the prediction of limit-state function by adding an optimal sample. The uncertainty reduction is quantified by sampling over the kriging posterior. In the proposed EUR-based sequential sampling framework, a portfolio that consists of four acquisition functions is first employed to suggest four optimal samples at each iteration of sequential sampling. Then, EUR is employed as the meta-criterion to identify the best sample among those optimal samples. The results from two mathematical case studies show that (1) EUR-based sequential sampling can perform as well as or outperform the single use of any acquisition function in the portfolio, and (2) the best-performing acquisition function may change from one problem to another or even from one iteration to the next within a problem.

Dimensioning of silicone adhesive joints: Eurocode-compliant, mesh-independent approach using the FEM

This paper deals with the application of the semi-probabilistic design concept (level I, DIN EN 1990) to structural silicone adhesives in order to calibrate partial material safety factors for a stretch-based limit state equation. Based on the current legal situation for the application of structural sealants in façades, a new Eurocode-compliant design concept is introduced and compared to existing design codes (ETAG 002). This is followed by some background information on semi-probabilistic reliability modeling and the general framework of the Eurocode for the derivation of partial material safety factors at Level I. Within this paper, a specific partial material safety factor is derived for DOWSIL 993 silicone on the basis of experimental data. The data were then further evaluated under a stretch-based limit state function to obtain a partial material safety factor for that specific limit state function. This safety factor is then extended to the application in finite element calculation programs in such a way that it is possible for the first time to perform mesh-independent static calculations of silicone adhesive joints. This procedure thus allows for great optimization of structural sealant design with potentially high economical as well as sustainability benefits. An example for the static verification of a bonded façade construction by means of finite element calculation shows (i) the application of EC 0 to silicone adhesives and (ii) the transfer of the EC 0 method to the finite element method with the result that mesh-independent ultimate loads can be determined.

Structural Reliability Algorithms of Kriging Model Based on Improved Learning Strategy

Aiming at the problems of implicit and highly nonlinear limit state function in the process of reliability analysis of mechanical products, a reliability analysis method of mechanical structures based on Kriging model and improved EGO active learning strategy is proposed. For the problem that the traditional EGO method cannot effectively select points in the limit state surface region, an improved EGO method is proposed. By dealing with the predicted values of sample point model with absolute values and assume that the distribution state of response values remains the same, the work focus of active learning selection points is moved to the vicinity, where the points are with larger prediction variance or close to the limit state surface. Three examples show that, compared with the classical active learning method, the proposed method has good global and local search ability, and can estimate the exact failure probability value under the condition of less calculation of the limit state function.