基于BP神经网络与马尔可夫链的污水处理厂脱氮效果模拟预测

在实际污水处理厂运行过程中,其最终出水水质会受多种因素影响制约,而基于生物反应机理的活性污泥数学模型(ASM)并未将这些生物反应以外的因素考虑在内,由此带来一些不足.对此,本文提出可通过基于数据挖掘技术的黑箱模型对污水厂处理效果进行模拟预测.结合具体实际分析,提出可将BP神经网络与马尔可夫链组合应用于污水处理脱氮效果预测中.首先,通过BP神经网络模型对北京某大型污水处理厂实际进出水数据和工艺参数进行粗略拟合;其次,利用马尔可夫链对拟合结果及误差进行状态划分以进一步提高预测精确度;最后,运用基于BP神经网络与马尔可夫链的组合模型预测分析了该厂的实际出水水质.试验结果表明,BP神经网络适用于污水处理脱氮过程的拟合计算,而通过与马尔可夫链组合,可以提高模拟预测的精度和可靠性.     

基于范例推理的灾害性地震应急物资需求预测研究

基于范例推理(CBR)理论,利用最近相邻法和粗糙集理论搜索相似度最高的主震历史范例,分析各主要物资需求量的影响因素,预测当前范例主震期应急物资需求量。通过序贯决策,采用马尔科夫预测模型预测余震类型,进而搜索余震历史范例,预测余震期应急物资需求量。以"玉树"地震为例,运用该方法估算地震发生后食物类、生活用品类、药品类、工程机械类的需求量。     

Social network analysis and valid Markov chain Monte Carlo tests of null models

Analyses of animal social networks derived from group-based associations often rely on randomisation methods developed in ecology (Manly, Ecology 76:1109–1115, 1995) and made available to the animal behaviour community through implementation of a pair-wise swapping algorithm by Bejder et al. (Anim Behav 56:719–725, 1998). We report a correctable flaw in this method and point the reader to a wider literature on the subject of null models in the ecology literature. We illustrate the importance of correcting the method using a toy network and use it to make a preliminary analysis of a network of associations among eagle rays.

Hierarchical modeling for extreme values observed over space and time

We propose a hierarchical modeling approach for explaining a collection of spatially referenced time series of extreme values. We assume that the observations follow generalized extreme value (GEV) distributions whose locations and scales are jointly spatially dependent where the dependence is captured using multivariate Markov random field models specified through coregionalization. In addition, there is temporal dependence in the locations. There are various ways to provide appropriate specifications; we consider four choices. The models can be fitted using a Markov Chain Monte Carlo (MCMC) algorithm to enable inference for parameters and to provide spatio–temporal predictions. We fit the models to a set of gridded interpolated precipitation data collected over a 50-year period for the Cape Floristic Region in South Africa, summarizing results for what appears to be the best choice of model.

应用灰色模糊马尔科夫链预测海河水质变化趋势

灰色GM(1,1)模型在水质预测中得到了较为广泛的运用,但其存在灰色偏差与抗干扰能力弱的局限性,针对这一问题,将马尔科夫链理论与模糊集合理论引入灰色GM(1,1)预测模型,并应用该模型对海河三岔口断面的DO、CODMn和NH3-N 3项指标2012~2016年的浓度变化趋势进行预测.结果表明,2004~2016年,DO及NH3-N浓度大致呈上升趋势,预计2016年分别可达9.15,1.47mg/L;CODMn浓度呈下降趋势,预计2016年可达3.91mg/L.以2012年的数据做验证,灰色模糊马尔科夫链模型的预测精度最高,可作为科学的水质预测方法.     

How sensitive are elasticities of long-run stochastic growth to how environmental variability is modelled?

A variable environment leaves a signature in a population's dynamics. Deriving statistical and mathematical models of how environmental variability affects population projections has - in the wake of reports of substantial climatic fluctuations - received much recent attention. If the model changes, then so too does the population projection. This is because a different model of environmental variability changes estimates of long-run stochastic growth, which is a function of demographic rates and their temporal sequence. Decomposing elasticities of long-run stochastic growth into constituent parts can assess the relative influence of different components. Here, we investigate the consequences of changing the environmental state definition, and therefore altering the shape of demographic rate distributions and their temporal sequence, by using age-structured matrix models to project vertebrate populations into the future under a range of environmental scenarios. The identity of the most influential demographic rate was consistent among all approaches that perturbed only the mean, but was not when only the variance was perturbed. Furthermore, the influence of each demographic rate fluctuated among projections by up to factors of six and two for changes to the variance and mean, respectively. These changes in influence depend in part upon how environmental variability - in particular, the color of environmental noise - is incorporated. In the light of predictions of increasing climatic variability in the future, these results suggest caution when drawing quantitative conclusions from stochastic population projections.     

Analytical methods for a stochastic mainland-island metapopulation model

We study a class of chain-binomial metapopulation models, giving special attention to the ‘mainland-island’ configuration, where patches receive immigrants from an external source. We evaluate the distribution of the number n_t of occupied patches at any census time t and establish a law of large numbers that identifies a deterministic trajectory which can be used to approximate the process when the number of patches is large. We also establish a central limit law, which shows that the fluctuations about this trajectory are approximately normally distributed. We describe briefly much finer results that can be used for model calibration.     

Identifying fishing trip behaviour and estimating fishing effort from VMS data using Bayesian Hidden Markov Models

Recent advances in technologies have lead to a vast influx of data on movements, based on discrete recorded position of animals or fishing boats, opening new horizons for future analyses. However, most of the potential interest of tracking data depends on the ability to develop suitable modelling strategies to analyze trajectories from discrete recorded positions. A serious modelling challenge is to infer the evolution of the true position and the associated spatio-temporal distribution of behavioural states using discrete, error-prone and incomplete observations. In this paper, a Bayesian Hierarchical Model (HBM) using Hidden Markov Process (HMP) is proposed as a template for analyzing fishing boats trajectories based on data available from satellite-based vessel monitoring systems (VMS). The analysis seeks to enhance the definition of the fishing pressure exerted on fish stocks, by discriminating between the different behavioural states of a fishing trip, and also by quantifying the relative importance of each of these states during a fishing trip. The HBM approach is tested to analyse the behaviour of pelagic trawlers in the Bay of Biscay. A hidden Markov chain with a regular discrete time step is used to model transitions between successive behavioural states (e.g., fishing, steaming, stopping (at Port or at sea)) of each vessel. The parameters of the movement process (speed and turning angles) are defined conditionally upon the behavioural states. Bayesian methods are used to integrate the available data (typically VMS position recorded at discrete time) and to draw inferences on any unknown parameters of the model. The model is first tested on simulated data with different parameters structures. Results provide insights on the potential of HBM with HMP to analyze VMS data. They show that if VMS positions are recorded synchronously with the instants at which the process switch from one behavioural state to another, the estimation method provides unbiased and precise inferences on behavioural states and on associated movement parameters. However, if the observations are not gathered with a sufficiently high frequency, the performance of the estimation method could be drastically impacted when the discrete observations are not synchronous with the switching instants. The model is then applied to real pathways to estimate variables of interest such as the number of operations per trip, time and distance spent fishing or travelling.     

Conservation decision-making in large state spaces

When looking for the best course of management decisions to efficiently conserve metapopulation systems, a classic approach in the ecology literature is to model the optimisation problem as a Markov decision process and find an optimal control policy using exact stochastic dynamic programming techniques. Stochastic dynamic programming is an iterative procedure that seeks to optimise a value function at each timestep by evaluating the benefits of each of the actions in each state of the system defined in the Markov decision process.Although stochastic dynamic programming methods provide an optimal solution to conservation management questions in a stochastic world, their applicability in metapopulation problems has always been limited by the so-called curse of dimensionality. The curse of dimensionality is the problem that adding new state variables inevitably results in much larger (often exponential) increases in the size of the state space, which can make solving superficially small problems impossible. The high computational requirements of stochastic dynamic programming methods mean that only simple metapopulation management problems can be analysed. In this paper we overcome the complexity burden of exact stochastic dynamic programming methods and present the benefits of an on-line sparse sampling algorithm proposed by Kearns, Mansour and Ng (2002). The algorithm is particularly attractive for problems with large state spaces as the running time is independent of the size of the state space of the problem. This appealing improvement is achieved at a cost: the solutions found are no longer guaranteed to be optimal.We apply the algorithm of Kearns et al. (2002) to a hypothetical fish metapopulation problem where the management objective is to maximise the number of occupied patches over the management time horizon. Our model has multiple management options to combat the threats of water abstraction and waterhole sedimentation. We compare the performance of the optimal solution to the results of the on-line sparse sampling algorithm for a simple 3-waterhole case. We find that three look-ahead steps minimises the error between the optimal solution and the approximation algorithm. This paper introduces a new algorithm to conservation management that provides a way to avoid the effects of the curse of dimensionality. The work has the potential to allow us to approximate solutions to much more complex metapopulation management problems in the future.     

Imposed and inherent scales in cellular automata models of habitat

Both observational and modelling studies of the natural environment are characterised by their ‘grain’ and ‘extent’, the smallest and largest scales represented in time and space. These are imposed scales that should be chosen to ensure that the natural scales of the system are captured in the study. A simple cellular automata model of habitat represents only the presence or absence of vegetation, with global and local interactions described by four empirical parameters. Such a model can be formulated as a nonlinear Markov equation for the habitat probability. The equation produces inherent space and time scales that may be considered as transition scales or the scales for recovery from disturbance. However, if the resolution of the model is changed, the empirical parameters must be changed to preserve the properties of the system. Further, changes in the spatial resolution lead to different interpretations of the spatial structure. In particular, as the resolution is reduced, the apparent dominance of one habitat type over the other increases. The model provides an ability to compare both field and model investigations conducted at different resolutions in time and space.