Improved Maximum Entropy Method Research Articles

Global reliability assessment of coupled transmission tower-insulator-line systems considering soil-structure interaction subjected to multi-hazard of wind and ice

This study aims to assess the global reliability of coupled transmission tower-insulator-line systems considering soil-structure interaction (CTTILSs-SSI) subjected to multi-hazard of wind and ice. Firstly, two simplified models of CTTILSs-SSI under stochastic wind and ice loads are established, and their governing equations are derived through the Lagrange equation. On this basis, a global reliability assessment framework of CTTILSs-SSI is proposed based on the improved maximum entropy method, in which the global performance function of CTTILSs-SSI is defined via the state variable description method. Finally, a practical ultra-high voltage overhead transmission line located on the icing zone is chosen to illustrate the proposed framework. Moreover, to investigate the influence of soil-structure interaction (SSI) and soil types on the global reliability of transmission tower-insulator-line systems (TTILSs), the global reliability of CTTILSs-SSI with various soil types is compared with that of a fixed base system. The results indicate that under the in-plane wind and ice loads, the global failure probability of TTILSs is almost zero, and it is essentially not affected by the SSI effect and soil types. However, under the out-of-plane wind and ice loads, the global failure probability of CTTILSs-SSI is higher than that of the fixed base system, and the global failure probability of CTTILSs-SSI increases as the soil stiffness decreases. Accordingly, it may be more reasonable to consider the SSI effect into the global reliability analysis of TTILSs subjected to ice and out-of-plane wind loads, particularly when the soil is soft.

A point mapping strategy-based sparse grid integration method for statistical moments estimation and structural reliability analysis

The high-order moment-based method is an attractive non-intrusive approach for structural reliability analysis, while it remains a challenge to strike a balance between accuracy, efficiency, and versatility in estimating statistical moments of performance functions. In this paper, a point mapping strategy-based sparse grid integration (SGI) method is proposed for statistical moment estimation and structural reliability analysis, with improved efficiency while ensuring the accuracy. Firstly, a point mapping strategy (PMS) is developed based on the adaptive high dimensional model representation (HDMR), by which the traditional SGI is reconstructed as a sum of multiple integrations over the sparse grid point sets with different effective dimensions. With this new form of SGI, the estimation of statistical moments only requires the evaluation of the performance function at a small number of necessary reference points, once the effects of some interaction terms are negligible. The validity and feasibility of the proposed PMS-based SGI method for statistical moments estimation are verified by several numerical examples. Then, the proposed method is applied to structural reliability analysis with the aid of an improved maximum entropy method. Two engineering examples are investigated, including the strength failure problem of tubular tower K-shape connection joints and the fatigue failure problem of a marine riser resulting from the vortex-induced vibration (VIV). The results indicate that the proposed method provides a better trade-off between accuracy and efficiency in evaluating the first four order statistical moments and structural failure probability compared to conventional methods.

Time-Varying Wind-Resistance Global Reliability Analysis of In-Service Transmission Tower Using High-Order Moments-Based Improved Maximum Entropy Method

The transmission tower is an important infrastructure for transmission lines. To secure the operation of the power grid, it is particularly important to evaluate the safety of the in-service transmission tower under the action of random wind loads throughout their entire life cycle. Thus, this paper firstly establishes the time-varying equivalent performance function of the in-service transmission tower under the action of random wind loads. Then, in order to address the shortcomings of the traditional maximum entropy method, the high-order moments-based improved maximum entropy method (HM-IMEM) is proposed and extended to assess the wind resistance global reliability of the in-service transmission tower. Finally, the effectiveness of the proposed method is demonstrated evaluating the wind resistance global reliability of an in-service transmission tower in an engineering setting. Analytic results indicate that: (1) The proposed method can ensure a balance between calculation accuracy and efficiency. Compared with Monte Carlo simulation (MCS) method, the relative error is only 0.11% and the computational cost is much lower than that of the MCS method. (2) The reliability of the in-service transmission tower significantly decreased over time. In order to guide maintenance and reinforcement by predicting the time-varying performance of in-service transmission towers, it is of great engineering value to evaluate the wind resistance global reliability of the in-service transmission tower.

Structural Reliability Assessment Based on Enhanced Conjugate Unscented Transformation and Improved Maximum Entropy Method

Estimation of statistical moments remains one of the main topics of stochastic analysis whose accuracy greatly affects reliability analysis results. In this work, conjugate unscented transformation (CUT) methods, which can balance accuracy and efficiency, are introduced for the statistical moment estimation of responses. Because of the drawbacks of existing CUT methods, a family of enhanced conjugate unscented transformation (ECUT) methods, including ECUT-4, ECUT-6, and ECUT-8 methods, is proposed for statistical moment estimation by combining the original CUT, variable transformation, and exact dimension reduction method. Then the probability density function of a performance function is reconstructed by the improved maximum entropy method (IMEM) with the available statistical moments as constraints. To demonstrate the accuracy and effectiveness of the proposed methods, five numerical examples, including linear and nonlinear, low-dimensional and high-dimensional, and explicit and implicit performance functions, are investigated, in which the results obtained from the proposed methods are compared with other existing moment methods and a Monte Carlo simulation (MCS) method. The results of the examples show that the proposed ECUT-6 and ECUT-8 methods have fairly high accuracy and efficiency for structural reliability analysis.

Seismic reliability analysis of high-pier railway bridges with correlated random parameters via an improved maximum entropy method

Seismic reliability analysis is crucially important for the seismic performance evaluation and probabilistic seismic risk assessment of bridges. However, the exact and efficient computation of seismic reliability for a practical bridge with uncertainty is still challenging. This study presents a composite method of maximum entropy principle with fractional moments, partially stratified sampling, and Nataf transformation for the seismic reliability analysis of bridge with correlated random parameters, and then evaluates the impact of random variable correlation on the probabilistic seismic performance of high-pier continues rigid frame bridge (CRFB). Different from the existing maximum entropy method, a unbiased likelihood function-based maximum entropy method is proposed to compute the extreme value distribution (EVD) of structural nonlinear seismic response. To illustrate the efficiency and accuracy of the proposed method, a hysteretic nonlinear single-degree-of-freedom (SDOF) system and a simplified two-span bridge are first taken as examples. The obtained EVD is compared with the results of Monte Carlo simulation, current maximum entropy method, and widely used probability distribution model fitting. The proposed method is then applied to evaluate the seismic reliability of a practical high-pier CRFB. The influence of uncertainties and variable correlation of structural parameters on the seismic reliability of high-pier CRFB is discussed in detail. The analysis results indicate the high efficiency and accuracy of the proposed method and demonstrate the significant importance of structural parameter correlation on the probabilistic seismic performance assessment of high-pier CRFB.

Efficient seismic reliability analysis of non-linear structures under non-stationary ground motions

The seismic reliability assessment (SRA) of complex nonlinear structures which possess structural and seismic uncertainty is an open challenge for academics and practical engineers. This paper proposes an improved maximum entropy method (IMEM) for the SRA of nonlinear structures. Non-stationary ground motions are first generated via a random-function-based spectral representation method. High-dimensional random variables in the ground motion simulation are then converted into two basic random variables as the high-dimensional probability space is reduced to a low-dimensional probability space. A two-step IMEM constrained with fractional moments is deployed to estimate the extreme value distribution (EVD) of the nonlinear structural dynamic system. An improved Latin hypercube sampling approach is also established to calculate the fractional moments of the complex nonlinear dynamic system. The first-passage probability of the structural nonlinear seismic response can be computed conveniently by a numerical integration using the EVD. Two numerical examples, 1) a three-story nonlinear shear frame structure and 2) a real-world high-pier continuous rigid frame bridge model, both of which exhibit strong nonlinearity under seismic action, are analyzed to show that the proposed method is efficient and accurate.

Extreme value distribution and dynamic reliability estimation of high-pier bridges subjected to near-fault impulsive ground motions

The seismic behaviour of high-pier and long-span bridges in fault zones is significantly influenced by the near-fault impulsive effect. In view of this, this study evaluates the extreme value distribution and dynamic reliability of high-pier bridges built in fault zones. First, based on the improved maximum entropy method constrained with fractional moments, a new method is proposed to evaluate the extreme value distribution of nonlinear structure seismic response. In the proposed method, the fractional moments are evaluated by the Latin hypercube sampling, and a linear system of equations that determine the initial value of fractional exponents and Lagrange multipliers is illustrated to improve the stability of the simplex algorithm. Second, based on the obtained extreme value distribution, the seismic reliability of structure is estimated by the simple numerical integration. Two numerical examples, including a nonlinear single-degree-of-freedom system and a three-storey nonlinear shear frame, are adopted to validate the proposed method. Finally, the seismic reliability of a typical high-pier and long-span continuous rigid frame bridge located in southwest of China is evaluated by the proposed method and some critical conclusions are drawn. The results obtained from this study not only indicate the accuracy and efficiency of the proposed method but also can provide some direct guidelines for the seismic design of the high-pier and long-span bridges in fault zones.

A novel structural reliability analysis method via improved maximum entropy method based on nonlinear mapping and sparse grid numerical integration

Abstract This paper proposes an improved maximum entropy method for reliability analysis (i-MEM), in which the limit state function is transformed by a nonlinear mapping to predict the failure probability accurately. Through the nonlinear mapping, more statistical information can be obtained by the first-four statistical moments, and the truncation error originating from numerical integration is solved by the bounded limit state function after the nonlinear mapping, therefore the i-MEM can capture the tail information of the real probability distribution. In order to calculate the statistical moments in i-MEM with accuracy and efficiency, an improved sparse grid numerical integration method (i-SGNI) is developed on the basis of the normalized moment-based quadrature rule. Combining the i-MEM and i-SGNI, a novel reliability analysis method is proposed. To illustrate the accuracy, efficiency and numerical stability of the proposed method, six numerical examples and one engineering example are presented, compared with some common reliability analysis methods. The results show that the proposed method, with the combination of i-MEM and i-SGNI, can achieve a good balance between accuracy and efficiency for structural reliability analysis.

A novel approach to uncertainty analysis using methods of hybrid dimension reduction and improved maximum entropy

Methods of uncertainty analysis based on statistical moments are more convenient than methods that use a Taylor series expansion because the moments methods require neither an iteration process to locate the most probable point nor the computation of derivatives of the performance function. However, existing moments estimation methods are either computationally expensive (e.g., the full factorial numerical integration method) or produce large errors (e.g., the univariate dimension-reduction method). In this paper, a hybrid dimension-reduction method taking account of interactions among variables is presented for estimating the probability moments of the system performance function. In this method, a contribution-degree analysis with finite changes is implemented to identify the relative importance of the input variables on the output. Then, an approximate performance function is generated with the hybrid dimension-reduction method that is based on the results of contribution-degree analysis. Finally, the statistical moments of the performance function can be calculated from the approximate performance function. Once the probability moments are obtained, an improved maximum entropy method is used to generate the probability density function of the performance function. The uncertainty analysis can be implemented by using the approximation probability density function. Five illustrative numerical examples are presented, and different methods are compared in those examples. The statistical moments estimation results reveal that the proposed moments estimation method can dramatically improve efficiency and also guarantee accuracy. Compared with the other probability density function approximation methods, our improved maximum entropy method, using more statistical moments, is more accurate and robust.

An improved maximum entropy method via fractional moments with Laplace transform for reliability analysis

The fractional moment-based maximum entropy method (FM-MEM) attracts more and more attention in reliability analysis recently, comparing with the common integer moment-based maximum entropy method. In the present paper, a new approach for reliability analysis is proposed from the improvement of the fractional moment-based maximum entropy method via the Laplace transformation and dimension reduction method (DRM). Different with the traditional FM-MEM with a double-loop multivariate optimization formulation, the proposed method introduces a single-loop univariate optimization algorithm through solving a set of linear equations. Firstly, the single-loop algorithm is proposed for bounded positive random variable and then is extended to arbitrary positive random variable with the help of Laplace transform. Then, a univariate strategy is given to simplify the calculation for the unknown parameters in the single-loop algorithm. Through the improvement, not only the proposed method can predict failure probability accurately but also the computational cost is considerably reduced. Due to the univariate optimization strategy, the proposed method is more robust than common reliability analysis methods, which are sensitive to the initial points, such as the traditional FM-MEM and the first-order reliability method. Several numerical examples are studied to illustrate the efficiency, robustness, and accuracy of the proposed method for the prediction of the failure probability in comparison with other methods.

Time-variant reliability assessment for multiple failure modes and temporal parameters

Multiple failure modes and temporal parameters are usually inherent in the complicated products’ performance, which bring new challenges for conducting time-variant reliability analysis and design. This paper proposes a novel time-variant reliability analysis method for multiple failure modes and temporal parameters based on the combination of the extreme value moment method and improved maximum entropy method. Firstly, a scaling function is established to reduce the integration error of the original maximum entropy method. The improved maximum entropy method can transform an infinite interval to a limited interval for a range of integration. The extreme value moments are then obtained by employing the sparse grid technique and the extreme value theory. Finally, the probability density function (PDF) of responses can be obtained by the combination of the extreme value moment method and the improved maximum entropy method and so the time-variant reliability can be estimated. The effectiveness of the proposed method is illustrated with two examples.

Improved Maximum Entropy Method applied to Real-time Time-Dependent Density Functional Theory

The maximum entropy method (MEM) is one of the key techniques for spectral analysis. The main feature is to describe spectra in low frequency with short time-series data. We adopted MEM to analyze the spectrum from the dipole moment obtained by the time-dependent density functional theory (TDDFT) calculation in real time, which is intensively studied and applied to computing optical properties. In the MEM analysis, we proposed that we use the concatenated data set made from several-times repeated raw data together with the phase. We have applied this technique to spectral analysis of the TDDFT dipole moment of oligo-uorene with n = 8. As a result, the higher resolution can be obtained without any peak shift due to the phase jump. The peak position is in good agreement to that of FT with just raw data. This paper presents the efficiency and characteristic features of this technique.

An approach to hesitant fuzzy multi-stage multi-criterion decision making

Purpose – The purpose of this paper is to develop some weight determining methods for hesitant fuzzy multi-criterion decision making (MCDM) in which the preference information on attributes is collected over different periods. Design/methodology/approach – Based on the proposed weight determining methods and dynamic hesitant fuzzy aggregation operators, an approach is developed to solve the hesitant fuzzy multi-stage multi-attribute decision-making problem where all the preference information of attributes over different periods is represented in hesitant fuzzy values. Findings – In order to determine the weights associated with dynamic hesitant fuzzy operators, the authors propose the improved maximum entropy method and the minimum average deviation method. Research limitations/implications – This paper does not consider the multi-stage multi-criteria group decision-making problem. Practical implications – An example concerning the evaluation of rangelands is given to illustrate the validation and efficiency of the proposed approach. It should be stated that the proposed approach can also be implemented into other multi-stage MCDM problems. Originality/value – The concept of hesitant fuzzy variable (HFV) is defined. Some operational laws and properties of the HFVs are given. Moreover, to fuse the multi-stage hesitant fuzzy information, the aggregation operators of hesitant fuzzy sets are extended to that of the HFVs.

Aerial Transmission Lines Image Restoration Technology Research Based on the Improved Maximum Entropy

According to the limitations of the shooting environment, captured image exist the phenomenon of image blurring and noise. This paper proposes that the improved maximum entropy method recovery blurred image which acquire in aerial. Finally, according to the first order Markoff theory to evaluate the quality of the processed image, the results show that maximum entropy image restoration method compared to the conventional approach increase image clarity and details more better.

Comparative analysis of a randomized N-policy queue: An improved maximum entropy method

We analyze a single removable and unreliable server in an M/G/1 queueing system operating under the 〈 p, N〉-policy. As soon as the system size is greater than N, turn the server on with probability p and leave the server off with probability (1 − p). All arriving customers demand the first essential service, where only some of them demand the second optional service. He needs a startup time before providing first essential service until there are no customers in the system. The server is subject to break down according to a Poisson process and his repair time obeys a general distribution. In this queueing system, the steady-state probabilities cannot be derived explicitly. Thus, we employ an improved maximum entropy method with several well-known constraints to estimate the probability distributions of system size and the expected waiting time in the system. By a comparative analysis between the exact and approximate results, we may demonstrate that the improved maximum entropy method is accurate enough for practical purpose, and it is a useful method for solving complex queueing systems.

3A12 配向処理基板上に蒸着した液晶超薄膜の配向形成過程 : 表面SHG法と偏光紫外吸収分光法に基づく改良最大エントロピー法による解析(物理・物性)

3A12 配向処理基板上に蒸着した液晶超薄膜の配向形成過程 : 表面SHG法と偏光紫外吸収分光法に基づく改良最大エントロピー法による解析(物理・物性)