A chance-constrained multi-period model for a special multi-reservoir system

We develop a model for optimal multi-period operation of a multi-reservoir system for a basin operating under a conjunctive use of ground and surface water. The inflows to the main reservoir as well as the irrigation demands are stochastic. The ground stock suffers from severe overdrafts increasing the risk of the total depletion of the aquifer in addition to the quality degradation and the threat of seawater intrusion. We treat the uncertainties in the inflows through chance constraints and penalties of failure to release the planned amounts of surface water from the main reservoir. However, we reflect uncertainties in irrigation demands by opting for deficit irrigation and using adequate production functions to estimate the expected crop yields. We attempt in the model to avoid large deficits except perhaps for periods where crop yields are relatively insensitive to water shortage. The objective is to maximize the total expected profit of the entire region. We illustrate the model through an example partially based on some hypothetical data.     

Global sensitivity analysis measures the quality of parameter estimation: The case of soil parameters and a crop model

One common limitation of the use of crop models for decision making in precise crop management is the need for accurate values of soil parameters for a whole field. Estimating these parameters from data observed on the crop, using a crop model, is an interesting possibility. Nevertheless, the quality of the estimation depends on the sensitivity of model output variables to the parameters. The goal of this study is to explain the results for the quality of parameter estimation based on global sensitivity analysis (GSA). The case study consists of estimating the soil parameters by using the STICS-wheat crop model and various synthetic observations on wheat crops (LAI, absorbed nitrogen and grain yield). Suitable criteria summarizing the sensitivity indices of the observed variables were created in order to link GSA indices with the quality of parameter estimation. We illustrate this link on 16 different configurations of different soil, climatic and crop conditions. The GSA indices were computed by the Extended FAST method and a function of RMSE was computed with an importance sampling method based on Bayes theory (GLUE). The proposed GSA-based criteria are able to rank the parameters with respect to their quality of estimation and the different configurations (especially climate and observation set) with respect to their ability to estimate the whole parameter set. They may be used as a tool for predicting the performance of different observation datasets with regard to parameter estimation.     

Assessing the propagation of uncertainties in multi-objective optimization for agro-ecosystem adaptation to climate change

It is widely acknowledged that uncertainty needs to be accounted for in climate impact studies, be it in scenario analyses or optimization applications. In this study we investigate how climate and crop model uncertainties affect multi-objective optimization outputs aiming to identify optimum agricultural management adaptations for Western Switzerland. Results are visualized by ternary plots that map optimum management measures, crop yield, erosion and leaching with associated uncertainties for navigating through the optimum adaptation space. We find that the relevance of climate model vs. parameter uncertainty can differ substantially depending on the prioritization of objectives and local conditions. The optimum choice of irrigation level was found to be the decision variable subject to greatest uncertainty particularly on coarser soil. This finding suggests that for the long-term planning of irrigation infrastructure and management, a robust adaptation approach is required for approaching unavoidable uncertainty from a risk management perspective.     

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.     

An integrated crop and hydrologic modeling system to estimate hydrologic impacts of crop irrigation demands

The present paper discusses a coupled gridded crop modeling and hydrologic modeling system that can examine the benefits of irrigation and costs of irrigation and the coincident impact of the irrigation water withdrawals on surface water hydrology. The system is applied to the Southeastern U.S. The system tools to be discussed include a gridded version (GriDSSAT) of the crop modeling system DSSAT. The irrigation demand from GriDSSAT is coupled to a regional hydrologic model (WaSSI). GriDSSAT and WaSSI are coupled through the USDA NASS CropScape data to provide crop acreages in each watershed. The crop model provides the dynamic irrigation demand which is a function of the weather. The hydrologic model responds to the weather and includes all other anthropogenic competing uses of water. Examples of the system include an analysis of the hydrologic impact of future expansion of irrigation and the real-time impact of short-term drought.     

On the disturbance model in the robustification of explicit predictive control

This article deals with the predictive control for linear systems, described in a explicit form as piecewise affine (PWA) state feedback laws. The main goal is to reduce the sensitivity of these schemes with respect to the model uncertainties. This objective can be attained by considering worst-case (min–max) formulations, optimisation over the control policies or tube predictive control. Such comprehensive approaches may lead to fastidious on-line optimisation, thus reducing the range of application. In the present note, a two-stage predictive strategy is proposed, which in the first place synthesises an analytical (continuous and piecewise linear) control law based on the nominal model and secondly robustifies the control law in the neighbourhood of the equilibrium point (the feedback gain obtained for the unconstrained control problem – most often assimilated to the LQR gain). How the disturbance model corresponding to the unconstrained control robustification can be used to improve the robustness of the PWA control law is also shown.     

A set of software components for the simulation of plant airborne diseases

Models to evaluate the impact of plant diseases on crop production under current and future climatic conditions are increasingly requested by different stakeholders. This paper presents four software components – InoculumPressure, DiseaseProgress, ImpactsOnPlants, AgromanagementDisease – which implement models to simulate the dynamics of generic polycyclic fungal epidemics and interactions with crop physiological processes. The software architecture adopted allows extending the components with alternate approaches to reproduce specific pathosystems or compare predictive capabilities. As proofs of concept, (i) the components are coupled with two crop simulators to reproduce wheat brown rust and rice blast epidemics and their impacts on leaf area and yield formation; (ii) spatially distributed sensitivity analyses are performed for rice in China and wheat in Europe to investigate model behaviour; (iii) a preliminary evaluation against observations of rice blast severity is performed in Northern Italy. The components are explicitly targeted to the modelling of crop–pathogen interactions to perform scenario analysis.     

Variance-based sensitivity analysis of the probability of hydrologically induced slope instability

Analysis of the sensitivity of predictions of slope instability to input data and model uncertainties provides a rationale for targeted site investigation and iterative refinement of geotechnical models. However, sensitivity methods based on local derivatives do not reflect model behaviour over the whole range of input variables, whereas methods based on standardised regression or correlation coefficients cannot detect non-linear and non-monotonic relationships between model input and output. Variance-based sensitivity analysis (VBSA) provides a global, model-independent sensitivity measure. The approach is demonstrated using the Combined Hydrology and Stability Model (CHASM) and is applicable to a wide variety of computer models. The method of Sobol’, assuming independence between input variables, was used to identify interactions between model input variables, whilst replicated Latin Hypercube Sampling (LHS) is used to investigate the effects of statistical dependence between the input variables. The SIMLAB software was used, both to generate the input sample and to calculate the sensitivity indices. The analysis provided quantified evidence of well-known sensitivities as well demonstrating how uncertainty in slope failure during rainfall is, for the examples tested here, more attributable to uncertainty in the soil strength than to uncertainty in the rainfall.     

Stabilisation of large-scale nonlinear systems by modifying the interconnection network

In this article, we develop a new strategy for the robust stabilisation of large-scale singular systems. The models that we will be concerned with consist of a large number of nonlinear subsystems, which are linked through a linear interconnection network. This approach does not require the availability of control inputs, and focuses instead on variable parameters in the interconnection network. It is shown that the determination of appropriate parameter values reduces to a constrained static output feedback problem, which can be solved using linear matrix inequalities. The proposed method is designed to minimise the number of optimisation variables, and is therefore suitable for large-scale applications. It can also incorporate information structure constraints and uncertainties in the system model.     

A Fuzzy Decision Support System for irrigation and water conservation in agriculture

Since agriculture is the major water consumer, web services have been developed to provide the farmers with considerate irrigation suggestions. This study improves an existing irrigation web service, based on the IRRINET model, by describing a protocol for the field implementation of a fully automated irrigation system. We demonstrate a Fuzzy Decision Support System to improve the irrigation, given the information on the crop and site characteristics. It combines a predictive model of soil moisture and an inference system computing the most appropriate irrigation action to keep this above a prescribed “safe” level. Three crops were used for testing the system: corn, kiwi, and potato. This Fuzzy Decision Support System (FDSS) favourably compared with an existing agricultural model and data-base (IRRINET). The sensitivity of the FDSS was tested with random rainfall and also in this extended case the water saving was confirmed.     

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.     

Probabilistic sensitivity analysis methods for general decision models

Probabilistic sensitivity analysis has previously been described for the special case of dichotomous decision trees. We now generalize these techniques for a wider range of decision problems. These methods of sensitivity analysis allow the analyst to evaluate the impact of the multivariate uncertainty in the data used in the decision model and to gain insight into the probabilistic contribution of each of the variables to the decision outcome. The techniques are illustrated using Monte Carlo simulation on a trichotomous decision tree. Application of these powerful tools permits the decision analyst to investigate the structure and limitations of more complex decision problems with inherent uncertainties in the data upon which the decisions are based. Probabilistic sensitivity measures can provide guidance into the allocation of resources to resolve uncertainty about critical components of medical decisions.     

Partitioning total variance in risk assessment: Application to a municipal solid waste incinerator

Comprehensive health risk assessment based on aggregate exposure and cumulative risk calculations requires a better understanding of exposure variables and uncertainty associated with them. Although there are many sources of uncertainty in system models, two basic kinds of parametric uncertainty are fundamentally different from each other: natural/stochastic and epistemic uncertainties. However, conventional methods such as standard Monte Carlo Sampling (MCS), which assumes vagueness as random property, may not be suitable for this type of uncertainty analysis. An improved systematic uncertainty and variability analysis can provide insight into the level of confidence in model estimates, and it can aid in assessing how various possible model estimates should be weighed. The main goal of the present study was to introduce Fuzzy Latin Hypercube Sampling (FLHS), a hybrid approach for incorporating epistemic and stochastic uncertainties separately. An important property of this technique is its ability to merge inexact generated data of the LHS approach to increase the quality of information. The FLHS technique ensures that the entire range of each variable is sampled with proper incorporation of uncertainty and variability. A fuzzified statistical summary of the model results produces a detailed sensitivity analysis, which relates the effects of variability and uncertainty of input variables to model predictions. The feasibility of the method has been tested with a case study, analyzing total variance in the calculation of incremental lifetime risks due to polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) for the residents living in the surroundings of a municipal solid waste incinerator (MSWI) in the Basque Country, Spain.     

Free vibration analysis and optimisation of axisymmetric plates and shells—II. Shape optimisation

The second part of this paper is concerned with the structural shape optimisation of vibrating axisymmetric shells. Natural frequencies and mode shapes are determined using curved, variable thickness, Mindlin-Reissner FEs introduced and benchmarked in the first part of the paper. The whole shape optimisation process is carried out by integrating FE analysis, cubic spline shape and thickness definitions, sensitivity analysis and mathematical programming. The semi-analytical method is used to determine the sensitivities of the objective function and constraints to changes in the design variables. Several examples are considered to illustrate and highlight various features of the optimisation, including various plates, a conical shell, a branched shell, and a church bell.     

Robust optimization using a gradient index: MEMS applications

This paper discusses a simple and effective robust optimization formulation and illustrates its application to MicroElectroMechanical Systems (MEMS) devices. The proposed formulation improves robustness of the objective function by minimizing a gradient index (GI), defined as a function of gradients of performance functions with respect to uncertain variables. The level of constraint feasibility is also enhanced by adding a term determined by a constraint value and the gradient index. In the robust optimal design procedure, a deterministic optimization for performance improvement is followed by a sensitivity analysis with respect to uncertainties such as MEMS fabrication errors and changes of material properties. During the process of the deterministic optimization and sensitivity analysis, dominant performances and critical uncertain variables are identified to define the GI. Our approach for robust design requires no statistical information on the uncertainties and yet achieves robustness effectively. Two MEMS application examples including a micro accelerometer and a resonant-type micro probe are presented.     

Retrieval of canopy biophysical variables from bidirectional reflectance: Using prior information to solve the ill-posed inverse problem

Estimation of canopy biophysical variables from remote sensing data was investigated using radiative transfer model inversion. Measurement and model uncertainties make the inverse problem ill posed, inducing difficulties and inaccuracies in the search for the solution. This study focuses on the use of prior information to reduce the uncertainties associated to the estimation of canopy biophysical variables in the radiative transfer model inversion process. For this purpose, lookup table (LUT), quasi-Newton algorithm (QNT), and neural network (NNT) inversion techniques were adapted to account for prior information. Results were evaluated over simulated reflectance data sets that allow a detailed analysis of the effect of measurement and model uncertainties. Results demonstrate that the use of prior information significantly improves canopy biophysical variables estimation. LUT and QNT are sensitive to model uncertainties. Conversely, NNT techniques are generally less accurate. However, in our conditions, its accuracy is little dependent significantly on modeling or measurement error. We also observed that bias in the reflectance measurements due to miscalibration did not impact very much the accuracy of biophysical estimation.     

Evolutionary algorithms in control systems engineering: a survey

Challenging optimisation problems, which elude acceptable solution via conventional methods, arise regularly in control systems engineering. Evolutionary algorithms (EAs) permit flexible representation of decision variables and performance evaluation and are robust to difficult search environments, leading to their widespread uptake in the control community. Significant applications are discussed in parameter and structure optimisation for controller design and model identification, in addition to fault diagnosis, reliable systems, robustness analysis, and robot control. Hybrid neural and fuzzy control schemes are also described. The important role of EAs in multiobjective optimisation is highlighted. Evolutionary advances in adaptive control and multidisciplinary design are predicted.     

A robust optimisation model and cutting planes for the planning of energy-efficient wireless networks

In this paper, we present an optimisation model for the energy-efficient planning of future wireless networks. By applying robust optimisation, we extend this model to a robust formulation which considers demand uncertainties. The computability of the resulting model is moderate. Hence, we apply three different cutting plane approaches for an improvement. Furthermore, an extensive case study is performed to examine the price of robustness, to compare the robust solution to conventional planning, and to explore the performance of the cutting planes.     

CAD-based shape optimisation using adjoint sensitivities

Existing approaches to CAD-based design optimisation using adjoint sensitivities are reviewed and their shortcomings are recalled. An alternative approach is presented which uses the control points of the boundary representation (BRep) as design parameters. The sensitivity of the objective function with respect to the design variables is calculated using automatic differentiation (AD). Results for a 2-D aerofoil are presented.