Uncertain Multidisciplinary Design Optimization on Next Generation Subsea Production System by Using Surrogate Model and Interval Method

The innovative Next Generation Subsea Production System(NextGen SPS)concept is a newly proposed petroleum development solution in ultra-deep water areas.The definition of NextGen SPS involves several disciplines,which makes the design process difficult.In this paper,the definition of NextGen SPS is modeled as an uncertain multidisciplinary design optimization(MDO)problem.The deterministic optimization model is formulated,and three concerning disciplines—cost calculation,hydrodynamic analysis and global performance analysis are presented.Surrogate model technique is applied in the latter two disciplines.Collaborative optimization(CO)architecture is utilized to organize the concerning disciplines.A deterministic CO framework with two disciplinelevel optimizations is proposed firstly.Then the uncertainties of design parameters and surrogate models are incorporated by using interval method,and uncertain CO frameworks with triple loop and double loop optimization structure are established respectively.The optimization results illustrate that,although the deterministic MDO result achieves higher reduction in objective function than the uncertain MDO result,the latter is more reliable than the former.

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

AN INTERVAL METHOD FOR STUDYING THE RELATIONSHIP BETWEEN THE AUSTRALIAN DOLLAR EXCHANGE RATE AND THE GOLD PRICE

This paper proposes an interval method to explore the relationship between the exchange rate of Australian dollar against US dollar and the gold price, using weekly, monthly and quarterly data. With the interval method, interval sample data are formed to present the volatility of variables. The ILS approach is extended to multi-model estimation and the computational schemes are provided. The empirical evidence suggests that the ILS estimates well characterize how the exchange rate relates to the gold price, both in the long-run and short-run. The comparison between the interval and point methods indicates that the difference between the OLS and the ILS estimates is increasing from weekly data to quarterly data, since the lowest frequency point data lost the most information of volatility.

A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

Interval finite element method and its application on anti-slide stability analysis

The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.

INTERVAL ARITHMETIC AND STATIC INTERVAL FINITE ELEMENT METHOD

When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method (FEM). The two parameters, median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. ne solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.

Interval finite difference method for steady-state temperature field prediction with interval parameters

A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters.

Application of Interval Newton Method to Solve Nonlinear Equations and Global Optimization

The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced.The prototype algorithm can not find any zero in an interval that has zero sometimes,that is,it is instable.So the prototype relaxation procedure is improved in this paper.Additionally,an immediate test of the existence of a solution following branch_and_bound is proposed,which avoids unwanted computations in those intervals that have no solution.The numerical results demonstrat that the improved interval Newton method is superior to prototype algorithm in terms of solution quality,stability and convergent speed.

Sensitivity and inverse analysis methods for parameter intervals

This paper proposes a sensitivity analysis method for engineering parameters using interval analyses.This method substantially extends the application of interval analysis method.In this scheme,parameter intervals and decision-making target intervals are determined using the interval analysis method.As an example,an inverse analysis method for uncertainty is presented.The intervals of unknown parameters can be obtained by sampling measured data.Even for limited measured data,robust results can also be obtained with the inverse analysis method,which can be intuitively evaluated by the uncertainty expressed in terms of an interval.For complex nonlinear problems,an iteratively optimized inverse analysis model is proposed.In a given set of loose parameter intervals,all the unknown parameter intervals that satisfy the measured information can be obtained by an iteratively optimized inverse analysis model.The influences of measured precisions and the number of parameters on the results of the inverse analysis are evaluated.Finally,the uniqueness of the interval inverse analysis method is discussed.

Energy density response prediction of structures with uncertainty using interval analysis method

Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method is applied to the control equation to obtain the range of energy density responses of structures with interval parameters. A cantilever beam with interval-valued damping coefficient is exemplified to carry out a simulation. The result shows that the mean value of energy density from the interval analysis method is the same as that from a probabilistic method which validates the interval analysis method. Besides, the response range from the interval analysis method is wider and includes that from the probabilistic method which indicates the interval analysis method is a more conservative method and is safer in realistic engineering structures.

Sensitivity analysis of soil parameters based on interval

Interval analysis is a new uncertainty analysis method for engineering structures. In this paper, a new sensitivity analysis method is presented by introducing interval analysis which can expand applications of the interval analysis method. The interval analysis process of sensitivity factor matrix of soil parameters is given. A method of parameter intervals and decision-making target intervals is given according to the interval analysis method. With FEM, secondary developments are done for Marc and the Duncan-Chang nonlinear elastic model. Mutual transfer between FORTRAN and Marc is implemented. With practial examples, rationality and feasibility are validated. Comparison is made with some published results.

FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.

Flexural wave bandgap properties of phononic crystal beams with interval parameters

Uncertainties are unavoidable in practical engineering,and phononic crystals are no exception.In this paper,the uncertainties are treated as the interval parameters,and an interval phononic crystal beam model is established.A perturbation-based interval finite element method(P-IFEM)and an affine-based interval finite element method(A-IFEM)are proposed to study the dynamic response of this interval phononic crystal beam,based on which an interval vibration transmission analysis can be easily implemented and the safe bandgap can be defined.Finally,two numerical examples are investigated to demonstrate the effectiveness and accuracy of the P-IFEM and A-IFEM.Results show that the safe bandgap range may even decrease by 10%compared with the deterministic bandgap without considering the uncertainties.

“粒度分析法”在小流域泥沙来源研究中的应用

小流域泥沙来源是土壤侵蚀研究的重点内容 ,目前 ,国内外主要利用径流泥沙资料 ,采用统计分析方法来确定小流域不同地貌部位及不同侵蚀类型的产沙量。研究采用“粒度分折法”,对砒砂岩不同侵蚀类型区典型小流域泥沙来源进行了分析计算 ,结果表明 :砒砂岩区小流域泥沙主要来源于沟谷地 ,占小流域总产沙量的 79.39%～84 .89% ;沟间地产沙量占总产沙量的 15 .86 %～ 2 0 .6 1%。

用Coifman区间尺度函数求解电磁场积分方程

该文采用Coifman区间尺度函数作为矩量法中的展开函数和权函数,求解电磁场积分方程,利用Coifman尺度函数的消失矩特性,减少计算矩阵元素的双重积分次数,同时对两个具有不同积分核的方程,提出了不同的消失矩近似方法。

Development of a Fuzzy Fire Risk Evaluation Model for Building Construction Sites in Hong Kong

Earlier research works on fire risk evaluation indicated that an objective,reliable,comprehensive,and practical fire risk evaluation model is essential for mitigating fire occurrence in building construction sites.Nevertheless,real empirical studies in this research area are quite limited.This journal paper gives an account of the second stage of a research study aiming at developing a fuzzy fire risk evaluation model for building construction sites in Hong Kong.The empirical research findings showed that the overall fire risk level of building construction sites is 3.6427,which can be interpreted as“moderate risk”.Also,the survey respondents perceived that“Restrictions for On-Site Personnel”is the most vital fire risk factor;with“Storage of Flammable Liquids or Dangerous Goods”being the second;and“Attitude of Main Contractor”the third.The proposed fuzzy fire risk evaluation model for building construction sites can be used to assess the overall fire risk level for a building construction site,and to identify improvement areas needed.Although the fuzzy fire risk evaluation model was developed domestically in Hong Kong,the research could be reproduced in other nations to develop similar models for international comparisons.Such an extension would provide a deeper understanding of the fire risk management on building construction sites.

Economic Dispatch of Power Systems with Virtual Power Plant Based Interval Optimization Method

Load prediction and power prediction uncertainties are inevitable aspects of a virtual power plant(VPP).In power system economic dispatch(ED)modeling,the interval is used to describe prediction uncertainties.An ED model with interval uncertainty is established in this paper.The probability degree definition is adopted to convert the interval-based economic dispatch model into a deterministic model for the purposes of solving the modeling problem.Simulation tests are performed on a 10-machine system using professional optimization software(LINGO).The simulation results verify the validity of the proposed interval-based scheme for the economic dispatch of a power system with VPP.

An interval effective independence method for optimal sensor placement based on non-probabilistic approach

This paper presents an interval effective independence method for optimal sensor placement, which contains uncertain structural information. To overcome the lack of insufficient statistic description of uncertain parameters, this paper treats uncertainties as non-probability intervals. Based on the iterative process of classical effective independence method, the proposed study considers the eliminating steps with uncertain cases. Therefore, this method with Fisher information matrix is extended to interval numbers, which could conform to actual engineering. As long as we know the bounds of uncertainties, the interval Fisher information matrix could be obtained conveniently by interval analysis technology. Moreover, due to the definition and calculation of the interval relationship, the possibilities of eliminating candidate sensors in each iterative process and the final layout of sensor placement are both presented in this paper. Finally, two numerical examples, including a five-storey shear structure and a truss structure are proposed respectively in this paper. Compared with Monte Carlo simulation, both of them can indicate the veracity of the interval effective independence method.

Modified perturbation method for eigenvalues of structure with interval parameters

In overcoming the drawbacks of traditional interval perturbation method due to the unpredictable effect of ignoring higher order terms,a modified parameter perturbation method is presented to predict the eigenvalue intervals of the uncertain structures with interval parameters.In the proposed method,interval variables are used to quantitatively describe all the uncertain parameters.Different order perturbations in both eigenvalues and eigenvectors are fully considered.By retaining higher order terms,the original dynamic eigenvalue equations are transformed into interval linear equations based on the orthogonality and regularization conditions of eigenvectors.The eigenvalue ranges and corresponding eigenvectors can be approximately predicted by the parameter combinatorial approach.Compared with the Monte Carlo method,two numerical examples are given to demonstrate the accuracy and efficiency of the proposed algorithm to solve both the real eigenvalue problem and complex eigenvalue problem.