共查询到20条相似文献，搜索用时 31 毫秒
1.
Under certain conditions the concentration and flux of a substance moving in a stochastic flow field are described by the stochastic convection equation. A numerical method for solving the one-dimensional problem is studied here. The differential operator is replaced by a discrete linear operator based on finite differences. The resulting system of stochastic equations is then replaced by a system of equations whose solution is the mean concentration or mean flux. This final system is analysed and conditions for a stable numerical solution are obtained. Finally, numerical examples are given and are compared to an approximate analytical solution to the stochastic convection equation. 相似文献
2.
One of the problems in signal processing is estimating the impulse response function of an unknown system. The well-known Wiener filter theory has been a powerful method in attacking this problem. In comparison, the use of stochastic approximation method as an adaptive signal processor is relatively new. This adaptive scheme can often be described by a recursive equation in which the estimated impulse response parameters are adjusted according to the gradient of a predetermined error function. This paper illustrates by means of simple examples the application of stochastic approximation method as a single-channel adaptive processor. Under some conditions the expected value of its weight sequence converges to the corresponding Wiener optimum filter when the least-mean-square error criterion is used. 相似文献
3.
Under certain conditions the concentration of a substance moving in a stochastic flow field is described by the stochastic convection equation. A numerical method yielding the mean solution and variance of the two-dimensional problem is described here. First, the differential operator is replaced by a discrete linear operator based on finite differences. The resulting system of stochastic equations is then replaced by a system of equations whose solution is the mean concentration. The variance of the concentration can then be calculated. In addition, and example is given for which an approximate analytical solution and its variance is known. The numerical method is applied to the example and results compared to the approximate analytical solution and variance. 相似文献
4.
Abstract The problem of non-steady flow of water in a soil-plant system can be described by adding a sink term to the continuity equation for soil water flow. In this paper the sink term is defined in two different ways. Firstly it is considered to be dependent on the hydraulic conductivity of the soil, on the difference in pressure head between the soil and the root-soil interface and some root effectiveness function. Secondly the sink is taken to be a prescribed function of the soil water content. The partial differential equation applying to the first problem is solved by both a finite difference (FD 1) and a finite element (FE 1) technique, that applying to the second problem by a finite difference approach (FD 2). The purpose of this paper is to verify the numerical models against field measurements, to compare the results obtained by the three numerical methods and to show how the finite element method can be applied to complex but realistic two-dimensional flow situations. Two examples are given. The first concerns one-dimensional flow and it compares numerical results with those obtained experimentally in the field from water balance studies on red cabbage (Brassica oleracea L. ‘Rode Herfst’) grown on a clay soil in the presence of a water table. The second example describes two-dimensional flow in a complex field situation in the Netherlands where flow takes place under cropped field conditions through five anisotropic layers. Water is supplied to the system by infiltration from two unlined ditches and is withdrawn from the system by evapotranspiration and by leakage to an underlying pumped aquifer. 相似文献
5.
Jeen-Shang Lin 《地震工程与结构动力学》1993,22(1):75-88
This study investigated the performance, in the frequency domain, of an engineering equivalent linear method that is widely used in soil dynamics. A stochastic linear method using an extended differential equation by Wen and Baber was employed as the base line for evaluation. Stationary responses of single-degree-of-freedom non-linear systems under filtered white noise from both approaches were compared. For both a smooth nearly elasto-plastic material and soils, the study found that the engineering equivalent linear analysis underestimated rms displacements, but provided good estimates of rms acceleration responses. Furthermore, the frequency response functions of acceleration from both approaches were close at all levels of response. 相似文献
6.
The application of methods of modern theory of Brownian motion to the calculation of fluctuations of soil moisture reserve is considered. Analytical dependences of the correlation time of soil moisture reserve fluctuations and its mean on the characteristics of external stochastic and deterministic impacts are obtained for a nonlinear hydrological model of moisture reserve formation based on Langevin equation and generalized Langevin relationships. Variations of the low-frequency part of the spectrum of fast synoptic variables (the difference between precipitation and evaporation) because of interaction with moisture reserve fluctuations is examined. A new effect—an increase in the spectrum in the intermediate domain of time intervals between characteristic times—is explained by the time of variations of synoptic fluctuations and the time of variations of fluctuations of soil moisture reserve. The problem of determining a non-steady response of the mean soil moisture reserve to fluctuation of moistening regime is used to demonstrate the potentialities of a new apparatus of statistical physics-fluctuation theorems. 相似文献
7.
Verifying optimality of rainfed agriculture using a stochastic model for drought occurrence 总被引：1，自引：1，他引：0
Erfaneh Sharifi Koichi Unami Macarius Yangyuoru Masayuki Fujihara 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(5):1503-1514
It may be paradoxical but subsistence rainfed agriculture is the predominant source of food in Sub-Saharan Africa where the production uncertainty is associated with the stochastic nature of rainfall. This paper attempts to comprehend the rationale of this situation by a mathematical approach. Considering the level of drought severity as the zero-reverting Ornstein–Uhlenbeck process, optimality of rainfed agriculture is investigated in the context of stochastic control theory. Occurrence of drought terminating growth of crops is modelled with the concept of first exit time. A stochastic control problem allowing for virtual cost of irrigation, water stress to crops, and benefits of farming is formulated with irrigation effort as the control variable. The Hamilton–Jacobi–Bellman equation governing the optimal control is studied to identify the set of cost functions optimizing rainfed agriculture in an inverse problem approach. Data and information were collected in the coastal savanna agro-ecological zone of Ghana, to identify model parameters, formulate the stochastic control problem, solve the inverse problem, and then verify optimality of rainfed agriculture. The results indicated that rainfed agriculture is not optimal when the crop is more tolerant to water stress. 相似文献
8.
In this paper, we present an optimal polynomial controller for reducing the peak response quantities of seismically excited non-linear or hysteretic building systems. A performance index, that is quadratic in control and polynomial of any order in non-linear states, is considered. The performance index is minimized based on the Hamilton–Jacobi–Bellman equation using a polynomial function of non-linear states, which satisfies all the properties of a Lyapunov function. The resulting optimal controller is a summation of polynomials in non-linear states, i.e. linear, cubic, quintic, etc. Gain matrices for different parts of the controller are determined from Riccati and Lyapunov matrix equations. Numerical simulation results indicate that the percentage of reduction for the selected peak response quantity increases with the increase of the earthquake intensity. Such load adaptive properties are very desirable, since the intensity of the earthquake ground acceleration is stochastic in nature. The proposed optimal polynomial controller is an effective and viable control method for non-linear or hysteretic civil engineering structures. It is an addition to available control methods in the literature. 相似文献
9.
10.
11.
Hakan Sirin 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,20(6):381-390
Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field. 相似文献
12.
A convection-diffusion equation arises from the conservation equations in miscible and immiscible flooding, thermal recovery, and water movement through desiccated soil. When the convection term dominates the diffusion term, the equations are very difficult to solve numerically. Owing to the hyperbolic character assumed for dominating convection, inaccurate, oscillating solutions result. A new solution technique minimizes the oscillations. The differential equation is transformed into a moving coordinate system which eliminates the convection term but makes the boundary location change in time. We illustrate the new method on two one-dimensional problems: the linear convection-diffusion equation and a non-linear diffusion type equation governing water movement through desiccated soil. Transforming the linear convection diffusion equation into a moving coordinate system gives a diffusion equation with time dependent boundary conditions. We apply orthogonal collocation on finite elements with a Crank-Nicholson time discretization. Comparisons are made to schemes using fixed coordinate systems. The equation describing movement of water in dry soil is a highly non-linear diffusion-type equation with coefficients varying over six orders of magnitude. We solve the equation in a coordinate system moving with a time-dependent velocity, which is determined by the location of the largest gradient of the solution. The finite difference technique with a variable grid size is applied, and a modified Crank-Nicholson technique is used for the temporal discretization. Comparisons are made to an exact solution obtained by similarity transformation, and with an ordinary finite difference scheme on a fixed coordinate system. 相似文献
13.
Reliability‐based control algorithms for nonlinear hysteretic systems based on enhanced stochastic averaging of energy envelope 
下载免费PDF全文
下载免费PDF全文 Current reliability‐based control techniques have been successfully applied to linear systems; however, incorporation of stochastic nonlinear behavior of systems in such control designs remains a challenge. This paper presents two reliability‐based control algorithms that minimize failure probabilities of nonlinear hysteretic systems subjected to stochastic excitations. The proposed methods include constrained reliability‐based control (CRC) and unconstrained reliability‐based control (URC) algorithms. Accurate probabilistic estimates of nonlinear system responses to stochastic excitations are derived analytically using enhanced stochastic averaging of energy envelope proposed previously by the authors. Convolving these demand estimates with capacity models yields the reliability of nonlinear systems in the control design process. The CRC design employs the first‐level and second‐level optimizations sequentially where the first‐level optimization solves the Hamilton–Jacobi–Bellman equation and the second‐level optimization searches for optimal objective function parameters to minimize the probability of failure. In the URC design, a single optimization minimizes the probability of failure by directly searching for the optimal control gain. Application of the proposed control algorithms to a building on nonlinear foundation has shown noticeable improvements in system performance under various stochastic excitations. The URC design appears to be the most optimal method as it reduced the probability of slight damage to 8.7%, compared with 11.6% and 19.2% for the case of CRC and a stochastic linear quadratic regulator, respectively. Under the Kobe ground motion, the normalized peak drift displacement with respect to stochastic linear quadratic regulator is reduced to 0.78 and 0.81 for the URC and CRC cases, respectively, at comparable control force levels. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
14.
The present study deals with the non‐linear stochastic dynamic analysis of a soil–structure interacting system. The ultimate objective is to determine the risk of damage to the system due to liquefaction under a wide range of earthquake intensities. A Monte Carlo simulation approach is followed in conjunction with advanced finite element procedures. The stochastic spatial variability of soil properties and the randomness of the seismic excitation are taken into account in order to estimate the statistics of the response, measured in terms of uniform foundation settlement and tilting. Specifically, soil properties are modelled as non‐Gaussian random fields and seismic excitations as non‐stationary random processes. The probabilistic characteristics of the stochastic field modelling soil properties are established from in situ tests. The risk of damage to the soil–structure system due to liquefaction is assessed by establishing fragility curves, which are of paramount importance for risk assessment and management studies of such systems. Fragility curves express the probability of exceeding various thresholds in the response. The relative effect of the variability of various soil parameters on the variability of the response is also examined. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
15.
倾斜地层地震液化和滑移的有限元分析 总被引：1，自引：0，他引：1
应用饱和多孔介质动力学分析倾斜地层的土壤动力线性反应、液化和液化滑移问题，地下水位上的地层简化为单相介质层，饱和夹砂层看作是两相介质，水是可压缩的，采用双曲线非线性本构关系，考虑了砂土的剪胀性、刚度退化、滞回特性和土水相对运动等因素。基于土力学模型，建立了适用于分析非自由场地液化的动力方程组，基于是否考虑发生渗流问题，同时建立了两种离散形式：一种是以土骨架位移和水位移为未知量的矩阵方程，另一种是以土骨架位移、水位移和孔隙水压力为未知量的矩阵方程，初步分析了适用于多孔介质波动模拟的离散模型的人工边界问题，形成的方法将有助于问题的解决。 相似文献
16.
Koichi Unami Macarius Yangyuoru Abul Hasan Md. Badiul Alam Gordana Kranjac-Berisavljevic 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(1):77-89
Micro-dams are expected to be feasible options for water resources development in semi-arid regions such as the Guinea savanna agro-ecological zone of West Africa. An optimal water management strategy in a micro-dam irrigation scheme supplying water from an existing reservoir to a potential command area is discussed in this paper based on the framework of stochastic control. Water intake facilities are assumed to consist of photovoltaic pumping system units and hoses. The knowledge of current states of the storage volume of the reservoir and the soil moisture in the command area is fed-back to the intake flow rate. A system of two stochastic differential equations is proposed as a model for the dynamics of the micro-dam irrigation scheme, so that temporally backward solution of the Hamilton–Jacobi–Bellman equation determines an optimal control, which represents the optimal water management strategy. A computational procedure using the finite element method is successfully implemented to provide comprehensive information on the optimal control. The results indicate that the water initially stored in the reservoir can support full irrigation for about 80 days under the optimal water management strategy, which is predominantly based on the demand-side principle. However, the volatility of the soil moisture in the command area must be reasonably small. 相似文献
17.
An analytical tool which facilitates the analysis of stochastic groundwater problems without resorting to Monte Carlo analysis can be developed using an approach analogous to that used in the field of applied mathematics to investigate the propagation of waves in random media. The fundamental assumption of this approach is that the random part of the porous medium property is small compared to the non-random part. This assumption allows us to treat the problem of solving a partial differential equation with stochastic coefficients using perturbation theory. 相似文献
18.
利用连续线性系统的随机振动理论,研究非均匀地基土层地震的动力反应问题。假定土层的剪切模量随深度线性变化,得到土层的最大位移反应的均值和方差。引入结构微分算子,采用模态叠加法进行反应分析,与普通的分离变量法相比较,此方法概念明确、步骤简单。 相似文献
19.
R. J. WANG 《Geophysical Prospecting》1977,25(2):342-381
The Wiener prediction filter has been an effective tool for accomplishing dereverberation when the input data are stationary. For non-stationary data, however, the performance of the Wiener filter is often unsatisfactory. This is not surprising since it is derived under the stationarity assumption. Dereverberation of nonstationary seismic data is here accomplished with a difference equation model having time-varying coefficients. These time-varying coefficients are in turn expanded in terms of orthogonal functions. The kernels of these orthogonal functions are then determined according to the adaptive algorithm of Nagumo and Noda. It is demonstrated that the present adaptive predictive deconvolution method, which combines the time-varying difference equation model with the adaptive method of Nagumo and Noda, is a powerful tool for removing both the long- and short-period reverberations. Several examples using both synthetic and field data illustrate the application of adaptive predictive deconvolution. The results of applying the Wiener prediction filter and the adaptive predictive deconvolution on nonstationary data indicate that the adaptive method is much more effective in removing multiples. Furthermore, the criteria for selecting various input parameters are discussed. It has been found that the output trace from the adaptive predictive deconvolution is rather sensitive to some input parameters, and that the prediction distance is by far the most influential parameter. 相似文献
20.
本文讨论用分裂算法解高阶偏移方程时所用的有限差分方程与原偏微分方程的相容性和算法的稳定性。根据Lax等价原理,这种相容性和稳定性可以保证数值方程收敛于原偏微分方程。我们证明了该分裂算法满足相容性和稳定性要求。这就不但以文献[1]中的实例说明了这种算法的实用性,而且从原理上论证了算法的正确性。 相似文献