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.

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 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.

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.

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.

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.

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.

Passivity analysis for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

The problem of passivity analysis is investigated for uncertain stochastic neural networks with discrete interval and distributed time-varying delays.The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belongs to a given interval,which means that the lower and upper bounds of interval time-varying delays are available.By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique,new delay-dependent passivity conditions are derived in terms of linear matrix inequalities（LMIs）.Finally,numerical examples are given to show the less conservatism of the proposed conditions.

“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.

Estimation of the amount of erosion at unconformities in the last stage of the Eocene Sanduo period in the Subei Basin,China

Strata erosion is a widespread phenomenon in sedimentary basins. The generation, migration, and accumulation of hydrocarbon is influenced by the scale of erosion, so estimating the amount of erosion is essential in the analysis of oil and gas bearing basins. According to the geological features in the Subei Basin and the actual data, using the integrated method, we estimated the level of erosion at the unconformities caused by the Sanduo event. By using the mudstone interval transit time method and the vitrinite reflectance method on data from typical wells, it can be concluded that the Gaoyou, Jinhu, and Hongze depressions suffered strong strata erosion from the late Eocene to Oligocene, and the total strata erosion thickness was 300–1,100 m. Different tectonic units in the same depression have extremely uneven erosion intensity: the low convex regions have the maximum erosion thickness, amounting to 800–1,100 m; the slope regions have an erosion thickness of generally 600–800 m; the erosion thickness of the slope-hollow transition zone is 300–500 m. For the whole basin, we used the strata thickness trend analysis method combined with the interval transit time and vitrinite reflectance methods to estimate the erosion thickness in the Sanduo period. The results show that the most severe erosion of the Sanduo event in the Subei Basin is between 1,000 m to 1,200 m, mainly located in depressions around the Jianhu Uplift; the deep hollow area has the least erosion, generally about 300–600 m, and the erosion in the slope area is about 600–900 m. Compared with the northern part, the southern part has relatively little erosion. It is also proved that the Sanduo movement has heterogeneous intensity, and the western region has greater intensity than the eastern region.

INTERVAL FINITE VOLUME METHOD FOR UNCERTAINTY SIMULATION OF TWO-DIMENSIONAL RIVER WATER QUALITY

Under the interval uncertainties, by incorporating the discretization form offinite volume method and interval algebra theory, an Interval Finite Volume Method (IF-VM) wasdeveloped to solve water quality simulation issues for two-dimensional river when lacking effectivedata of flow velocity and flow quantity. The IFVM was practically applied to a segment of theXiangjiang River because the Project of Hunan Inland Waterway Multipurpose must be started workingafter the environmental impact assessment for it. The simulation results suggest that there existrather apparent pollution zones of BOD_5 downstream the Dongqiaogang discharger and that of CODdownstream Xiaoxiangjie discharger, but the pollution sources have no impact on the safety of thethree water plants located in this river segment. Although the developed IFVM is to be perfected, itis still a powerful tool under interval uncertainties for water environmental impact assessment,risk analysis, and water quality planning, etc. besides water quality simulation studied in thispaper.

An interval finite element method for electromagnetic problems with spatially uncertain parameters

During the manufacturing process of dielectric materials used in electromagnetic engineering, the electromagnetic parameters are often spatially uncertain due to the processing technology, environmental temperature, personal operations, etc. Traditionally,the random field model can be used to measure the spatial uncertainties, but its construction requires a large number of samples.On the contrary, the interval field model only needs the upper and lower bounds of the spatially uncertain parameters, which requires much less samples and furthermore is easy to understand and use for engineers. Therefore, in this paper, the interval field model is introduced to describe the spatial uncertainties of dielectric materials, and then an interval finite element method(IFEM) is proposed to calculate the upper and lower bounds of electromagnetic responses. Firstly, the interval field of the dielectric material is represented by the interval K-L expansion and inserted into the scalar Helmholtz wave equations, and thus the interval equilibrium equations are constructed according to the node-based finite element method. Secondly, a perturbation interval finite element method is developed for calculating the upper and lower bounds of electromagnetic responses such as the electric strength and magnetic strength. Finally, the effectiveness of the proposed method is verified by three numerical examples.

Non-probabilistic information fusion technique for structural damage identification based on measured dynamic data with uncertainty

Based on measured natural frequencies and acceleration responses,a non-probabilistic information fusion technique is proposed for the structural damage detection by adopting the set-membership identification（SMI） and twostep model updating procedure.Due to the insufficiency and uncertainty of information obtained from measurements,the uncertain problem of damage identification is addressed with interval variables in this paper.Based on the first-order Taylor series expansion,the interval bounds of the elemental stiffness parameters in undamaged and damaged models are estimated,respectively.The possibility of damage existence（PoDE） in elements is proposed as the quantitative measure of structural damage probability,which is more reasonable in the condition of insufficient measurement data.In comparison with the identification method based on a single kind of information,the SMI method will improve the accuracy in damage identification,which reflects the information fusion concept based on the non-probabilistic set.A numerical example is performed to demonstrate the feasibility and effectiveness of the proposed technique.