Model Structure Identification: Development and Assessment of a Recursive Prediction Error Algorithm

The paper aims to develop a more systematic approach to the problem of model structure identification for continuous time (physically based) mathematical models with discrete observations. An introduction to the model structure identification problem is first presented. The approach to this problem is the application of a modified version of the extended Kalman filter, originally defined in [23]. This filter is tested using artificial data. The results obtained lead to a further discussion of the filter's stability properties and also to a metaphor for model structures. Further study of the numerical properties of the algorithm reveal that its stability can be improved. An alternative algorithm, the so called recursive prediction error algorithm, is modified to a Kalman-like algorithm in continuous-discrete formulation. This algorithm is also tested using artificial data. The RPE-type of filter has better stability properties and appears to be very robust to initial conditions. Its applicability to environmental case studies is set out through the application of the filter to a familiar case study. Applications of this type of filter is valuable for validation/verification of environmental and/or economical models that include a set of ordinary differential equations

Network inference via adaptive optimal design

Background Current research in network reverse engineering for genetic or metabolic networks very often does not include a proper experimental and/or input design. In this paper we address this issue in more detail and suggest a method that includes an iterative design of experiments based, on the most recent data that become available. The presented approach allows a reliable reconstruction of the network and addresses an important issue, i.e., the analysis and the propagation of uncertainties as they exist in both the data and in our own knowledge. These two types of uncertainties have their immediate ramifications for the uncertainties in the parameter estimates and, hence, are taken into account from the very beginning of our experimental design. Findings The method is demonstrated for two small networks that include a genetic network for mRNA synthesis and degradation and an oscillatory network describing a molecular network underlying adenosine 3'-5' cyclic monophosphate (cAMP) as observed in populations of Dyctyostelium cells. In both cases a substantial reduction in parameter uncertainty was observed. Extension to larger scale networks is possible but needs a more rigorous parameter estimation algorithm that includes sparsity as a constraint in the optimization procedure. Conclusion We conclude that a careful experiment design very often (but not always) pays off in terms of reliability in the inferred network topology. For large scale networks a better parameter estimation algorithm is required that includes sparsity as an additional constraint. These algorithms are available in the literature and can also be used in an adaptive optimal design setting as demonstrated in this pape

On a geometric approach to the structural identifiability problem and its application in a water quality case study

Abstract¿We present and apply an alternative method for the investigation of the well-known parameter identifiability question for non-linear system models. The method is based on a geometric analysis of the parametric output sensitivities and is, in fact, an application of the tools that are available in non-linear control theory to an augmented system, including the parametric output sensitivities. Accessibility Lie algebras are calculated that yield insight (through a simple rank test) in the controllability of this augmented system. The method is demonstrated in an example that is due to Dochain et al [4]. Results are confirmed by the method that has certain advantages in comparison to, for example, the Taylor series approach that seeks for identifiable combinations of parameters through inspection of the individual terms in a Taylor series expansion of the output signal, i.e. application of the well-known method of Pohjanpalo [15]. Parametric output sensitivities (as already noted by D¨otsch and Van den Hof [5] and Peeters and Hanzon [13]) play a crucial role in identifiability analysis and we further elaborate on this insight in the current paper. Our goals are (i) to present an interesting method for addressing the (local) identifiability question for non-linear systems and (ii) to gain better understanding in the role of parametric state- and output sensitivities in the identifiability question that stems from an alternative perspective, and that has not been presented in the identification literature. Of course, we are aware of other algorithms and software that establishes an answer to the identifiability question, albeit from a different perspective, e.g. [19], but seek in the current paper mainly for another interpretation and computational framework to address the question of local identifiability, shedding some new light on the problem

Sensitivity analysis of a mechanistic model for the ammonia emission of dairy cow houses

Emission of ammonia (NH3) from animal husbandry, and specially from the dairy sector, contributes significantly to acidification and eutrophication, and affects sensitive natural areas. In the nineties Monteny (1998) introduced a mechanistic model to understand and predict the NH3 emissions from cubicle dairy cow houses. Although a limited sensitivity analysis was carried out, we still lack information that essential for further development of the model. Our aim is that the model can predict and assess the NH3 emission from dairy cow houses under practical circumstance. The objective of this research was 1) to determine the relevance and irrelevance of a limited set of input factors, and 2) assess options for further development of the model for use in practice. A full factorial sensitivity analysis was carried out for eight variables related to NH3 emission from a urine puddle on the floor. Relative importance and R2 of the regression model factors were determined. The NH3 emission varied strongly with both high and low emissions. Strongly contributing process variables were puddle pH, initial urea concentration, urination frequency, puddle depth and puddle area. We conclude that deviations in these influencing variables lead to large fluctuations in the NH3 emission, which means that precise quantification of these variables in practice is essential for accurate predictions. Moreover, the results also show that the model may be over-parameterized, having several inputs that seem hardly relevant for the level of NH3 emission

A model for the climate of an innovative closed greenhouse for model based control

A new greenhouse type is designed to study ways of decreasing horticultural water use in semi-arid regions. To control the greenhouse a model based control design will be applied. Hereto a model is needed to predict the systems behavior (1 day ahead), without much computational effort. A physics-based model for this new type of greenhouse is developed, based on enthalpy and mass balances. The greenhouse is divided in four compartments; the plant area, the roof area, the heat exchanger and the soil. For all compartments only the main energy and mass fluxes are modeled, in order to keep the model simple. Since the model describes only the main characteristics of the system with physical equations, careful calibration and validation (systems identification) is needed. Real data gained from the experimental greenhouse are used in a controlled random search to find the optimal parameter value

Prediction uncertainty assessment of a systems biology model requires a sample of the full probability distribution of its parameters

Multi-parameter models in systems biology are typically ‘sloppy’: some parameters or combinations of parameters may be hard to estimate from data, whereas others are not. One might expect that parameter uncertainty automatically leads to uncertain predictions, but this is not the case. We illustrate this by showing that the prediction uncertainty of each of six sloppy models varies enormously among different predictions. Statistical approximations of parameter uncertainty may lead to dramatic errors in prediction uncertainty estimation. We argue that prediction uncertainty assessment must therefore be performed on a per-prediction basis using a full computational uncertainty analysis. In practice this is feasible by providing a model with a sample or ensemble representing the distribution of its parameters. Within a Bayesian framework, such a sample may be generated by a Markov Chain Monte Carlo (MCMC) algorithm that infers the parameter distribution based on experimental data. Matlab code for generating the sample (with the Differential Evolution Markov Chain sampler) and the subsequent uncertainty analysis using such a sample, is supplied as Supplemental Information

Watergy: Infrastructure for Process Control in a Closed Greenhouse in Semi-arid Regions

Abstract A novel solar humid-air-collector system for combined water treatment, space-cooling and ¿heating has been designed in an EU framework-5 financed project called Watergy. The design consists of a construction of two prototypes for applications in architecture and greenhouse horticulture: a South European variant (for arid climate and emphasis on agricultural use) and a Central-/North European variant (for temperate climate and emphasis on integral building design). The core is the development of a collector system, following the principle of a closed, two phase thermo siphon. It achieves combined evaporation and ¿condensation, efficient heat transfer to a central heat exchanger as well as increased heat conduction from (humid) air to water. Main improvements are cost reduction in space heating and -cooling of buildings and greenhouses. Furthermore, viability increases by additional integration of greenhouse irrigation water recycling, desalination and building grey-water recycling. Sensors and actuators, connected to low-level controllers, activate a model-based control system to manage these processes. The paper describes the different appendages, sensor systems, network connections, databases, alarming systems, user interfaces and remote management from the Netherlands to Spain through the Internet