Synthesis of flexible inter-plant heat exchanger networks:A decomposition method considering intermedium fluid circles

The traditional methods for synthesizing flexible heat exchanger networks(HENs)are not directly applicable to inter-plant HEN challenges,primarily due to the spread of system uncertainty across plants via intermedium fluid circles.This complicates the synthesis process significantly.To tackle this issue,this study proposes a decomposed stepwise methodology to facilitate the flexible synthesis of the interplant HENs performing indirect heat integration.A decomposition strategy is proposed to divide the overall network into manageable sub-networks by dissecting the intermedium fluid circles.To address the variability in intermedium fluid temperatures,a temperature fluctuation analysis approach is developed and a heuristic rule is introduced to maintain the temperature feasibility of the intermedium fluids.To ensure adequate flexibility and cost-effectiveness of the designed networks,flexibility analysis and network retrofit steps are conducted through model-based optimization techniques.The efficacy of the method is demonstrated through two case studies,showing its potential in achieving the desired operational flexibility for inter-plant HENs.

A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method

The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.

Application of probability integral method in ground deformation prediction

In order to study the law of mining subsidence and ground movement, to provide the basis of coal mining under building, railway and water, we used the probability integration method to make comprehensive evaluation of ground stability. Take Yingcheng Coal Mine of Jiutai as an example. Mining-induced movement and horizontal movement are analyzed on the basis of the measurement data. The resuhs of prediction can pro- vide reference and basis for prevention of coal mining subsidence and future restoration and treatment.

Application of Choquet Integral-Importance-Performance Analysis and TOPSIS Methods in Approaching the Preference Factors of Calligraphy and Seal Engraving Imagery

Classical Chinese characters,presented through calligraphy,seal engraving,or painting,can exhibit different aesthetics and essences of Chinese characters,making them the most important asset of the Chinese people.Calligraphy and seal engraving,as two closely related systems in traditional Chinese art,have developed through the ages.Due to changes in lifestyle and advancements in modern technology,their original functions of daily writing and verification have gradually diminished.Instead,they have increasingly played a significant role in commercial art.This study utilizes the Evaluation Grid Method(EGM)and the Analytic Hierarchy Process(AHP)to research the key preference factors in the application of calligraphy and seal engraving imagery.Different from the traditional 5-point equal interval semantic questionnaire,this study employs a non-equal interval semantic questionnaire with a golden ratio scale,distinguishing the importance ratio of adjacent semantic meanings and highlighting the weighted emphasis on visual aesthetics.Additionally,the study uses Importance-Performance Analysis(IPA)and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)to obtain the key preference sequence of calligraphy and seal engraving culture.Plus,the Choquet integral comprehensive evaluation is used as a reference for IPA comparison.It is hoped that this study can provide cultural imagery references and research methods,injecting further creativity into industrial design.

A model for extracting large deformation mining subsidence using D-InSAR technique and probability integral method

Due to the difficulties in obtaining large deformation mining subsidence using differential Interferometric Synthetic Aperture Radar （D-InSAR） alone, a new algorithm was proposed to extract large deformation mining subsidence using D-InSAR technique and probability integral method. The details of the algorithm are as follows：the control points set, containing correct phase unwrapping points on the subsidence basin edge generated by D-InSAR and several observation points （near the maximum subsidence and inflection points）, was established at first; genetic algorithm （GA） was then used to optimize the parameters of probability integral method; at last, the surface subsidence was deduced according to the optimum parameters. The results of the experiment in Huaibei mining area, China, show that the presented method can generate the correct mining subsidence basin with a few surface observations, and the relative error of maximum subsidence point is about 8.3%, which is much better than that of conventional D-InSAR （relative error is 68.0%）.

An integrated method of selecting environmental covariates for predictive soil depth mapping

Environmental covariates are the basis of predictive soil mapping.Their selection determines the performance of soil mapping to a great extent,especially in cases where the number of soil samples is limited but soil spatial heterogeneity is high.In this study,we proposed an integrated method to select environmental covariates for predictive soil depth mapping.First,candidate variables that may influence the development of soil depth were selected based on pedogenetic knowledge.Second,three conventional methods(Pearson correlation analysis(PsCA),generalized additive models(GAMs),and Random Forest(RF))were used to generate optimal combinations of environmental covariates.Finally,three optimal combinations were integrated to produce a final combination based on the importance and occurrence frequency of each environmental covariate.We tested this method for soil depth mapping in the upper reaches of the Heihe River Basin in Northwest China.A total of 129 soil sampling sites were collected using a representative sampling strategy,and RF and support vector machine(SVM)models were used to map soil depth.The results showed that compared to the set of environmental covariates selected by the three conventional selection methods,the set of environmental covariates selected by the proposed method achieved higher mapping accuracy.The combination from the proposed method obtained a root mean square error(RMSE)of 11.88 cm,which was 2.25–7.64 cm lower than the other methods,and an R^2 value of 0.76,which was 0.08–0.26 higher than the other methods.The results suggest that our method can be used as an alternative to the conventional methods for soil depth mapping and may also be effective for mapping other soil properties.

A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.

Resources calculation of cobalt-rich crusts with the grid subdivision and integral method

On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the central Pacific Ocean. The formulas of this method are deduced and the interface of program module is designed. The method is carried out in the software ＂Auto mapping system of submarine topography and geomorphology MBChart＂. This method and program will possibly become a potential tool to calculate the resources of seamounts and determine the target diggings for China＇ s next Five-year Plan.

Initial support distance of a non-circular tunnel based on convergence constraint method and integral failure criteria of rock

For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.

Longitudinal integral response deformation method for the seismic analysis of a tunnel structure

For the longitudinal seismic response analysis of a tunnel structure under asynchronous earthquake excitations,a longitudinal integral response deformation method classified as a practical approach is proposed in this paper.The determinations of the structural critical moments when maximal deformations and internal forces in the longitudinal direction occur are deduced as well.When applying the proposed method,the static analysis of the free-field computation model subjected to the least favorable free-field deformation at the tunnel buried depth is performed first to calculate the equivalent input seismic loads.Then,the equivalent input seismic loads are imposed on the integral tunnel-foundation computation model to conduct the static calculation.Afterwards,the critical longitudinal seismic responses of the tunnel are obtained.The applicability of the new method is verified by comparing the seismic responses of a shield tunnel structure in Beijing,determined by the proposed procedure and by a dynamic time-history analysis under a series of obliquely incident out-of-plane and in-plane waves.The results show that the proposed method has a clear concept with high accuracy and simple progress.Meanwhile,this method provides a feasible way to determine the critical moments of the longitudinal seismic responses of a tunnel structure.Therefore,the proposed method can be effectively applied to analyze the seismic response of a long-line underground structure subjected to non-uniform excitations.

A Method for Solving Fredholm Integral Equations of the First Kind Based on Chebyshev Wavelets

In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.

Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.

Multistage Numerical Picard Iteration Methods for Nonlinear Volterra Integral Equations of the Second Kind

Using the Picard iteration method and treating the involved integration by numerical quadrature formulas, we propose a numerical scheme for the second kind nonlinear Volterra integral equations. For enlarging the convergence region of the Picard iteration method, multistage algorithm is devised. We also introduce an algorithm for problems with some singularities at the limits of integration including fractional integral equations. Numerical tests verify the validity of the proposed schemes.

First Integral Method: A General Formula for Nonlinear Fractional Klein-Gordon Equation Using Advanced Computing Language

In this article, a general formula of the first integral method has been extended to celebrate the exact solution of nonlinear time-space differential equations of fractional orders. The proposed method is easy, direct and concise as compared with other existent methods.

Research and application of sidewall stability predic-tion method based on analytic hierarchy process and fuzzy integrative evaluation method

As a difficult problem, sidewall instability has been beset drilling workers all the time. Not only does it cause huge economic losses, but also it determines the success or failure of drilling engineering. Due to complex relationship between various factors which influence sidewall stability, it hasn’t been found a widely applied method to predicate sidewall stability so far. Therefore, in order to formulate corresponding measures to ensure successful drilling, searching for a kind of better method to forecast sidewall stability before drilling becomes an imperative and significant topic for drilling engineering. On the basis of traditional sidewall stability analytical method, we have put forward the Fuzzy Comprehensive Evaluation Method to forecast sidewall stability regulation using physico-chemical performance parameters of the clay mineral. This method has been improved by introducing the Analytic Hierarchy Process (AHP) and the Maximum Subjection Principle in the application process. After introducing Analytic Hierarchy Process to identify weight, and Maximum Subjection Principle to obtain evaluation results, it has reduced the influence of human factors and enhanced the accuracy of the fuzzy evaluation results. The application in Hailaer Area indicates that this method can predict sidewall stability of gas-oil well with high credibility and strong practicability.

RESEARCH ON THE COMPANION SOLUTION FOR A THIN PLATE IN THE MESHLESS LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless local boundary integral equation method is a currently developed numerical method, which combines the advantageous features of Galerkin finite element method(GFEM), boundary element method(BEM) and element free Galerkin method(EFGM), and is a truly meshless method possessing wide prospects in engineering applications. The companion solution and all the other formulas required in the meshless local boundary integral equation for a thin plate were presented, in order to make this method apply to solve the thin plate problem.

Resolving Domain Integral Issues in Isogeometric Boundary Element Methods via Radial Integration:A Study of Thermoelastic Analysis

The paper applied the isogeometric boundary element method(IGABEM)to thermoelastic problems.The Non-Uniform Rational B-splines(NURBS)used to construct geometric models are employed to discretize the boundary integral formulation of the governing equation.Due to the existence of thermal stress,the domain integral term appears in the boundary integral equation.We resolve this problem by incorporating radial integration method into IGABEM which converts the domain integral to the boundary integral.In this way,IGABEM can maintain its advantages in dimensionality reduction and more importantly,seamless integration of CAD and numerical analysis based on boundary representation.The algorithm is verified by numerical examples.

Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations

In this paper, we present a new method, a mixture of homotopy perturbation method and a new integral transform to solve some nonlinear partial differential equations. The proposed method introduces also He’s polynomials [1]. The analytical results of examples are calculated in terms of convergent series with easily computed components [2].

Extrapolation Method for Cauchy Principal Value Integral with Classical Rectangle Rule on Interval

In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.