Random variability and imprecision are two distinct facets of the uncertainty affecting parameters that influence the assessment of risk. While random variability can be represented by probability ...distribution functions, imprecision (or partial ignorance) is better accounted for by possibility distributions (or families of probability distributions). Because practical situations of risk computation often involve both types of uncertainty, methods are needed to combine these two modes of uncertainty representation in the propagation step. A hybrid method is presented here, which jointly propagates probabilistic and possibilistic uncertainty. It produces results in the form of a random fuzzy interval. This paper focuses on how to properly summarize this kind of information; and how to address questions pertaining to the potential violation of some tolerance threshold. While exploitation procedures proposed previously entertain a confusion between variability and imprecision, thus yielding overly conservative results, a new approach is proposed, based on the theory of evidence, and is illustrated using synthetic examples
The compact representation of incomplete probabilistic knowledge which can be encountered in risk evaluation problems, for instance in environmental studies is considered. Various kinds of knowledge ...are considered such as expert opinions about characteristics of distributions or poor statistical information. The approach is based on probability families encoded by possibility distributions and belief functions. In each case, a technique for representing the available imprecise probabilistic information faithfully is proposed, using different uncertainty frameworks, such as possibility theory, probability theory, and belief functions, etc. Moreover the use of probability–possibility transformations enables confidence intervals to be encompassed by cuts of possibility distributions, thus making the representation stronger. The respective appropriateness of pairs of cumulative distributions, continuous possibility distributions or discrete random sets for representing information about the mean value, the mode, the median and other fractiles of ill-known probability distributions is discussed in detail.
The aim of this review is twofold. Firstly, we present the state of the art in dynamic modelling and model-based design, optimisation and control of food systems. The need for nonlinear, dynamic, ...multi-physics and multi-scale representations of food systems is established. Current difficulties in building such models are reviewed: incomplete, piecewise available knowledge, spread out among different disciplines (physics, chemistry, biology and consumer science) and contributors (scientists, experts, process operators, process managers), scarcity, uncertainty and high cost of measured data, complexity of phenomena and intricacy of time and space scales. Secondly, we concentrate on the opportunities offered by the complex systems science to cope with the difficulties faced by food science and engineering. Newly developed techniques such as model-based viability analysis, optimisation, dynamic Bayesian networks etc. are shown to be relevant and promising for design and optimisation of foods and food processes based on consumer needs and expectations.
•Knowledge regarding complex systems are heterogeneous and fragmented.•modelling dynamic complex systems in the framework of dynamic credal networks.•practical methodology coupling Dirichlet ...distributions with interval probabilities to incrementally build and update model parameters whatever source and format of knowledge.•enables to take into account (1) stochastic and epistemic uncertainties pertaining to the system; (2) the confidence level on the different sources of information.•illustrate the application of the methodology to the modelling of a simplified industrial case study.
Modeling complex dynamical systems from heterogeneous pieces of knowledge varying in precision and reliability is a challenging task. We propose the combination of dynamical Bayesian networks and of imprecise probabilities to solve it. In order to limit the computational burden and to make interpretation easier, we also propose to encode pieces of (numerical) knowledge as probability intervals, which are then used in an imprecise Dirichlet model to update our knowledge. The idea is to obtain a model flexible enough so that it can easily cope with different uncertainties (i.e., stochastic and epistemic), integrate new pieces of knowledge as they arrive and be of limited computational complexity.
►Modelling the cheese ripening complex system is a challenge. ► It needs tools to integrate expert and scientific knowledge. ► Expert’s knowledge about cheese ripening is elicited. ► Numeric ...collected data and expertise are unified in a Dynamic Bayesian Network. The adequacy of the model is about 85% with experimental data.
Modelling the cheese ripening process continues to remain a challenge because this process is a complex system. There is still lack of knowledge to understand the interactions taking place at different level of scale during the process. However, knowledge may be gathered from scientific and operational experts’ skills. Integrating this knowledge with knowledge extracted from experimental databases may allow a better understanding of the whole ripening process. This study presents an approach adapted from cognitive science to elicit and formalise experts’ knowledge about the camembert-type cheese ripening process. Next, the collected data were unified in a mathematical model based on a dynamic Bayesian network. This formalism makes it possible to integrate this heterogeneous data. The established model presents an average adequacy rate of about 85% with experimental data.
This paper presents a digital learning tool, MESTRAL (“Modélisation Et Simulation des TRansformations ALimentaires”, “Modelling and Simulating Food Processing” in English), that can provide educators ...with a tool to teach food processing using simulators and a broad range of models derived from research in food science & engineering. It was built using electronic knowledge books (eK-book). The eK-book represents knowledge in the form of concept maps and knowledge sheets, connected via a network of hypertext links. MESTRAL encompasses 15 modules, that cover approximately 150 h of teaching and a broad range of real systems, from a single unit operation (e.g., frying a banana) to a logistic chain (e.g., ham cold chain). Each module conveys information on a food product or a food process, and includes a simulator based on a published scientific model. Altogether, the models address various scale of systems and are based on different theoretical frameworks. For each simulator, the model inputs and outputs are stored in a database. Outputs are visualized through abacuses, which can be used for virtual practice. MESTRAL modules also include training exercises and tests to help students to assess the knowledge they have acquired during consultation of the modules. Finally, MESTRAL has already been successfully tested by different audiences according to various learning forms.
•A digital learning tool, Mestral, was built to train people in food processes.•Knowledge is presented in an electronic book with concept maps.•Mestral covers 15 real (food and process) systems and is based on published models.•Each module contains a simulator which represents graphically the model results.•Mestral has been tested satisfactorily and opens up prospects for blended learning.
► The unified framework of dynamic Bayesian network to model complex system. ► Using of Dirichlet distributions to enrich model whatever the nature of knowledge. ► Taking into account uncertainty and ...confidence level regarding information. ► Feasibility and the practical use of our hybrid parameter learning in food science.
Faced with the fragmented and heterogeneous character of knowledge regarding complex food systems, we have developed a practical methodology, in the framework of the dynamic Bayesian networks associated with Dirichlet distributions, able to incrementally build and update model parameters each time new information is available whatever its source and format. From a given network structure, the method consists in using a priori Dirichlet distributions that may be assessed from literature, empirical observations, experts opinions, existing models, etc. Next, they are successively updated by using Bayesian inference and the expected a posteriori each time new or additional information is available and can be formulated into a frequentist form. This method also enables to take (1) uncertainties pertaining to the system; (2) the confidence level on the different sources of information into account. The aim is to be able to enrich the model each time a new piece of information is available whatever its source and format in order to improve the representation and thus provide a better understanding of systems. We have illustrated the feasibility and practical using of our approach in a real case namely the modelling of the Camembert-type cheese ripening.
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