A framework to use crop models for multi-objective constrained optimization of irrigation strategies

This paper discusses an innovative framework to use crop models which combines sensitivity analysis, uncertainty analysis and constrained optimisation runs for irrigation optimisation purposes, facing competing constraints on several agricultural variables (e.g. crop yield, total irrigation amount, financial expectations). For simplicity, this ex-post optimisation relies on direct calculations only, exploiting the dispersions on the target variables. The screening of the parameter space for sensitivity analysis yields a reference dispersion which is expectedly reduced by reducing the uncertainties in the sensitive parameters and/or climatic forcings. Additional dispersions are calculated to evaluate if the management controls on irrigation strategies (amounts, triggers, periods) are more influential on model predictions than the remaining uncertainties on the soil, plant, irrigation and climatic inputs, eventually allowing optimisation. As a case study, the Optirrig model is used. A discussion proposes future ways to convert diagnostics into real-time near-optimal decision rules, for example through learning algorithms.     

Sensitivity and uncertainty propagation in coupled models for assessing smallholder farmer food security in the Olifants River Basin,South Africa

Using family balance (i.e., combined net farm and non-farm incomes less family expenses), an output from an integrated model, which couples water resource, agronomic and socio-economic models, its sensitivity and uncertainty are evaluated for five smallholder farming groups (A–E) in the Olifants Basin. The crop management practiced included conventional rainfed, untied ridges, planting basins and supplemental irrigation. Scatter plots inferred the most sensitive variables affecting family balance, while the Monte Carlo method, using random sampling, was used to propagate the uncertainty in the model inputs to produce family balance probability distributions. A non-linear correlation between in-season rainfall and family balance arises from several factors that affect crop yield, indicating the complexity of farm family finance resource-base in relation to climate, crop management practices and environmental resources of soil and water. Stronger relationships between family balance and evapotranspiration than with in-season rainfall were obtained. Sensitivity analysis results suggest more targeted investment effort in data monitoring of yield, in-season rainfall, supplemental irrigation and maize price to reduce family balance uncertainty that varied from 42% to 54% at 90% confidence level. While supplemental irrigation offers the most marginal increase in yields, its wide adoption is limited by availability of water and infrastructure cost.     

How sensitive is a vineyard crop model to the uncertainty of its runoff module?

Many crop models use the NRCS Curve Number method to estimate runoff, but the simplified assumptions of this method are rarely considered in model uncertainty assessments. The associated uncertainty may be high for cropping systems with a significant part of bare soil like vineyards, specifically under a Mediterranean climate. In this work, we evaluate for a vineyard crop model the structure uncertainty coming from its uncertain runoff module. We introduce a new method based on additional knowledge about the runoff process and on a mathematical property of the model structure. Situations characterized in terms of soil water content and mean runoff conditions are studied for two applications of the vineyard model and guidelines for model users are derived. This work shows that uncertainty quantification can benefit from the knowledge of mathematical properties of a model and provide clear guidelines to model users.     

Adaptive model predictive control of nonlinear systems with state‐dependent uncertainties

This paper studies adaptive model predictive control (AMPC) of systems with time‐varying and potentially state‐dependent uncertainties. We propose an estimation and prediction architecture within the min‐max MPC framework. An adaptive estimator is presented to estimate the set‐valued measures of the uncertainty using piecewise constant adaptive law, which can be arbitrarily accurate if the sampling period in adaptation is small enough. Based on such measures, a prediction scheme is provided that predicts the time‐varying feasible set of the uncertainty over the prediction horizon. We show that if the uncertainty and its first derivatives are locally Lipschitz, the stability of the system with AMPC can always be guaranteed under the standard assumptions for traditional min‐max MPC approaches, while the AMPC algorithm enhances the control performance by efficiently reducing the size of the feasible set of the uncertainty in min‐max MPC setting. Copyright © 2017 John Wiley & Sons, Ltd.     

草酸钴合成过程批次间自适应优化

本文以钴湿法冶金过程草酸钴合成为背景,研究基于多向偏最小二乘回归(MPLS)模型的草酸钴平均粒度批次间自适应优化策略.本文首先利用MPLS方法建立草酸钴平均粒度的数据模型;针对模型不确定性情况下难以获得最优操作变量的问题,提出利用批次间修正项自适应优化方法,使迭代优化结果逐渐趋向于实际最优值;本文还通过引入T2统计量软约束将优化结果限制在数据模型的有效区间之内.数值仿真表明该方法可以有效解决草酸钴合成过程的批次间自适应优化问题,且与传统两步方法和迭代学习控制相比具有更好的优化效果.     

基于参数区间不确定性分析的无人机辅助物联网鲁棒优化

无人机辅助物联网技术被广泛应用于灾害应急通信中,但物联网设备的通信中存在多种不确定因素。针对位置参数区间存在不确定性的问题,提出了无人机辅助物联网通信的鲁棒优化方法。使用椭球不确定集对地面物联网设备位置参数区间不确定性进行描述,建立了包含不确定性的物联网设备通信鲁棒优化模型,并对模型进行了求解。为提高模型求解的准确性,提出一个有关位置参数区间不确定和椭球误差域之间的相关分析方法,分析了两类不确定因素对物联网设备通信模型的影响程度。以地面物联网设备最优部署和通信最小功率为目的,设计了仿真实验。结果表明,在不确定因素存在时,所提优化模型能有效实现地面物联网设备间的最优部署和通信功率最小化。     

基于光伏预测的微电网能源随机优化调度

可再生能源的间歇性和负荷的随机性对微电网能源管理系统（ EMS）产生了巨大的挑战。在随机环境下的能源优化调度问题在微电网的研究中具有重要意义。以微电网中光伏发电系统的功率预测为基础,将光伏预测误差当做随机变量,建立了一种基于期望模型的能源随机优化调度模型。用Monte Carlo模拟方法生成了光伏发电预测误差的情景集,应用粒子群优化算法来解决随机优化调度模型。通过与确定性模型产生的调度方案相对比,证明了随机优化调度模型更加有效。     

Economic performance analysis in the design of on-line batch optimization systems

In this paper, the on-line optimization of batch reactors under parametric uncertainty is considered. A method is presented that estimates the likely economic performance of the on-line optimizer. The method of orthogonal collocation is employed to convert the differential algebraic optimization problem (DAOP) of the dynamic optimization into a nonlinear program (NLP) and determine the nominal optimum. Based on the resulting NLP, the optimization steps are approximated by neighbouring extremal problems and the average deviation from the true process optimum is estimated dependent on the measurement error and the parametric uncertainty. The true process optimum is assumed to be represented by the optimum of the process model with the true parameter values. A back off from the active path and endpoint inequality constraints is determined at each optimization step which ensures the feasible operation of the process. Based on the analysis results the optimal structure of the optimizer in terms of measured variables and estimated parameters can be determined. The method of the average deviation from optimum is developed for the fixed terminal time case and for time optimal problems. In both cases, the theory is demonstrated on an example.     

Robustness analysis of genetic regulatory networks affected by model uncertainty

A fundamental problem in systems biology consists of investigating robustness properties of genetic regulatory networks (GRNs) with respect to model uncertainty. This paper addresses this problem for GRNs where the coefficients are rationally affected by polytopic uncertainty, and where the saturation functions are not exactly known. First, it is shown that a condition for ensuring that the GRN has a globally asymptotically stable equilibrium point for all admissible uncertainties can be obtained in terms of a convex optimization problem with linear matrix inequalities (LMIs), hence generalizing existing results that mainly consider only the case of GRNs where the coefficients are linearly affected by the uncertainty and the regulatory functions are in SUM form. Second, the problem of estimating the worst-case convergence rate of the trajectories to the equilibrium point over all admissible uncertainties is considered, and it is shown that a lower bound of this rate can be computed by solving a quasi-convex optimization problem with LMIs. Third, the paper considers the problem of estimating the set of uncertainties for which the GRN has a globally asymptotically stable equilibrium point. This problem is addressed, first, by showing how one can compute estimates with fixed shape by solving a quasi-convex optimization problem with LMIs, and second, by deriving a procedure for computing estimates with variable shape. Numerical examples illustrate the use of the proposed techniques.     

具有可参数化不确定性系统的对偶自适应模型预测控制

控制系统中存在的不确定性为其性能优化带来诸多问题.自适应控制和鲁棒控制是针对系统存在的不确定性而采取的不同设计策略;前者没有充分考虑系统的未建模动态,而后者往往是针对不确定的最大界而设计,具有较强的保守性.本文试图将自适应控制和鲁棒控制的策略相结合,提出了一种在模型预测控制中利用未来不确定信息的对偶自适应模型预测控制策略.该策略将系统中由未建模动态引起的不确定性参数化表达,并为其设定边界约束,作为优化问题中新的约束,在优化控制目标的同时减小系统不确定性对控制的影响.仿真结果表明,本文提出的算法较传统自适应模型预测控制算法,对于系统存在的不确定性由于在迭代过程中采用参数化描述,得到了更好的系统性能,且具有更好的收敛性.     

Supply Chain Management in Food Chains: Improving Performance by Reducing Uncertainty

This paper investigates the impact of Supply Chain Management on logistical performance indicators in food supply chains. From a review of quantitative and more qualitative managerial literature, we believe that Supply Chain Management should be concerned with the reduction or even elimination of uncertainties to improve the performance of the chain. The following clusters of sources of uncertainty are identified: order forecast horizon, input data, administrative and decision processes and inherent uncertainties. For each source of uncertainty, several improvement principles are identified. A case study was conducted in a food chain in which a simulation model helped quantify the effects of alternative configurations and operational management concepts. By comparing this simulation study with a pilot study, the model is validated against real data, and organisational consequences are identified. The results of the case study suggest that reduction of uncertainties can improve service levels significantly, although current supply chain configurations restrict possible benefits. The availability of real-time information systems is found to be a requirement for obtaining efficient and effective Supply Chain Management concepts.     

Reliability-based design optimization for crashworthiness of vehicle side impact

With the advent of powerful computers, vehicle safety issues have recently been addressed using computational methods of vehicle crashworthiness, resulting in reductions in cost and time for new vehicle development. Vehicle design demands multidisciplinary optimization coupled with a computational crashworthiness analysis. However, simulation-based optimization generates deterministic optimum designs, which are frequently pushed to the limits of design constraint boundaries, leaving little or no room for tolerances (uncertainty) in modeling, simulation uncertainties, and/or manufacturing imperfections. Consequently, deterministic optimum designs that are obtained without consideration of uncertainty may result in unreliable designs, indicating the need for Reliability-Based Design Optimization (RBDO).Recent development in RBDO allows evaluations of probabilistic constraints in two alternative ways: using the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). The PMA using the Hybrid Mean Value (HMV) method is shown to be robust and efficient in the RBDO process, whereas RIA yields instability for some problems. This paper presents an application of PMA and HMV for RBDO for the crashworthiness of a large-scale vehicle side impact. It is shown that the proposed RBDO approach is very effective in obtaining a reliability-based optimum design.     

Structural optimization under uncertain loads and nodal locations

This paper presents algorithms for solving structural topology optimization problems with uncertainty in the magnitude and location of the applied loads and with small uncertainty in the location of the structural nodes. The second type of uncertainty would typically arise from fabrication errors where the tolerances for the node locations are small in relation to the length scale of the structural elements. We first review the discrete form of the uncertain loads problem, which has been previously solved using a weighted average of multiple load patterns. With minor modifications, we extend this solution to include loads described by continuous joint probability density functions. We then proceed to the main contribution of this paper: structural optimization under uncertainty in the nodal locations. This optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix. It is shown, however, that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads. By expressing these equivalent loads in terms of continuous random variables, we are able to make use of the extended form of the uncertain loads problem presented in the first part of this paper. The optimization algorithms are developed in the context of minimum compliance (maximum stiffness) design. Simple examples are presented. The results demonstrate that load and nodal uncertainties can have dramatic impact on optimal design. For structures containing thin substructures under axial loads, it is shown that these uncertainties (a) are of first-order significance, influencing the linear elastic response quantities, and (b) can affect designs by avoiding unrealistically optimistic and potentially unstable structures. The additional computational cost associated with the uncertainties scales linearly with the number of uncertainties and is insignificant compared to the cost associated with solving the deterministic structural optimization problem.     

Two-Stage Robust Optimization Under Decision Dependent Uncertainty

In the conventional robust optimization(RO)context, the uncertainty is regarded as residing in a predetermined and fixed uncertainty set. In many applications, however,uncertainties are affected by decisions, making the current RO framework inapplicable. This paper investigates a class of twostage RO problems that involve decision-dependent uncertainties.We introduce a class of polyhedral uncertainty sets whose righthand-side vector has a dependency on the here-and-now decisions and seek to deri...     

Assessment of the different sources of uncertainty in a SWAT model of the River Senne (Belgium)

Although rainfall input uncertainties are widely identified as being a key factor in hydrological models, the rainfall uncertainty is typically not included in the parameter identification and model output uncertainty analysis of complex distributed models such as SWAT and in maritime climate zones. This paper presents a methodology to assess the uncertainty of semi-distributed hydrological models by including, in addition to a list of model parameters, additional unknown factors in the calibration algorithm to account for the rainfall uncertainty (using multiplication factors for each separately identified rainfall event) and for the heteroscedastic nature of the errors of the stream flow. We used the Differential Evolution Adaptive Metropolis algorithm (DREAM_(zs)) to infer the parameter posterior distributions and the output uncertainties of a SWAT model of the River Senne (Belgium). Explicitly considering heteroscedasticity and rainfall uncertainty leads to more realistic parameter values, better representation of water balance components and prediction uncertainty intervals.     

基于作物生长模型和多源数据的融合技术研究进展

精确的区域作物产量估计在社会食品安全生产中起着重要作用。首先讨论了常用的2种区域作物产量估计方法,包括产量监测和产量模拟。其中,作物生长模型能够反映作物的整个生长演变过程,并能最终预报作物产量,因此在区域作物产量预报中起着重要作用,但是由于作物生长模型在输入数据、模型参数和模型结构等方面存在较大的不确定性,导致最终的模拟结果也存在较大的不确定性,尤其是应用到区域尺度时,这种不确定性使得模拟结果同真实的作物产量空间分布图存在较大的不一致性。而产量监测,尤其是利用先进的多源遥感信息,可捕捉真实的区域尺度的地面作物生长信息,但是仅为瞬时信息。因此利用数据融合算法,融合模型和数据的优点,得到更为可靠的区域产量估计结果是十分有意义的。所以在详述了当前主要的作物生长模型的基础上,重点讨论了常用的2种数据融合技术,即优化方法和顺序数据同化方法,以及目前利用这两种方法在作物生长模型中融合观测信息的部分案例。     

Estimating model prediction error: Should you treat predictions as fixed or random?

Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEP_fixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEP_uncertain(X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEP_uncertain (X) can be estimated using a random effects ANOVA. It is argued that MSEP_uncertain (X) is the more informative uncertainty criterion, because it is specific to each prediction situation.     

金氰化浸出过程建模及实时优化自适应策略

以金氰化浸出过程为背景,基于物料守恒方程建立动态机理模型,用Tikhonov正则化方法估计动力学反应速度,进而辨识模型未知参数,有效降低了测量噪声对估计及辨识结果的影响;采用实时优化约束自适应方法减小模型参数失配对优化结果的影响.仿真结果表明,在模型参数失配时,所提出的方法仍能收敛到实际过程的最优设定点,不必求实际数据梯度,且受噪声影响小,便于实际应用,为湿法冶金全流程优化控制的顺利实施奠定了基础.     

Confidence in soil carbon predictions undermined by the uncertainties in observations and model parameterisation

Soil carbon (C) responds quickly and feedbacks significantly to environmental changes such as climate warming and agricultural management. Soil C modelling is the only reasonable approach available for predicting soil C dynamics under future conditions of environmental changes, and soil C models are usually constrained by the average of observations. However, model constraining is sensitive to the observed data, and the consequence of using observed averages on C predictions has rarely been studied. Using long-term soil organic C datasets from an agricultural field experiment, we constrained a process-based model using the average of observations or by taking into account the variation in observations to predict soil C dynamics. We found that uncertainties in soil C predictions were masked if ignoring the uncertainties in observations (i.e., using the average of observations to constrain model), if uncertainties in model parameterisation were not explicitly quantified. However, if uncertainties in model parameterisation had been considered, further considering uncertainties in observations had negligible effect on uncertainties in SOC predictions. The results suggest that uncertainties induced by model parameterisation are larger than that induced by observations. Precise observations representing the real spatial pattern of SOC at the studied domain, and model structure improvement and constrained space of parameters will benefit reducing uncertainties in soil C predictions. The results also highlight some areas on which future C model development and software implementations should focus to reliably infer soil C dynamics.     

Predicting Enhanced Vegetation Index (EVI) curves for ecosystem modeling applications

Vegetation indices derived from remote sensing data provide information about the variability in stature, growth and vigor of the vegetation across a region, and have been used to model plant processes. For example, the Enhanced Vegetation Index (EVI) provides a measure of greenness of the vegetation that can be used to predict net primary production. However, ecosystem models relying on remote sensing data for EVI or other vegetation indices are limited by the time series of the satellite data record. Our objective was to develop a statistical model to predict EVI in order to extend the time series for modeling applications. To explain the functional behavior of the seasonal EVI curves, a two-stage multiple regression fitting procedure within a semi-parametric mixed effect (SPME) model framework was used. First, a linear mixed effect (LME) model was fitted to the EVI with climate indexes, crop and irrigation information as predictor variables. Second, Penalized B-splines were used to explain the behavior of the smooth residuals, which result from a smooth model fit to the smooth EVI data curve, in order to describe the uncertainty of the EVI curve. Individual models were fit within individual Major Land Resources Areas (MLRAs). Predicted seasonal EVI, derived from our regression equations, showed a strong agreement with the observed EVI and was able to capture the site by site and year by year variation in the EVI curve. Out-of-sample prediction produced excellent results for a majority of the sites, except for sites without clear seasonal patterns, which may have resulted from cloud contamination and/or snow cover. Therefore, given the appropriate climate, crop, and irrigation information, the proposed approach can be used to predict seasonal EVI curves for extending the time series into the past and future.