Uncertain Domains Research Articles

Studies in the PuO2 – ZrO2 Pseudo-binary Phase Diagram

The phase relationship between ZrO2 and PuO2 was examined in the ZrO2-rich region by high temperature X-ray diffractometry. At 1273 K, for the studied range of compositions, the samples exhibited two stable phases: monoclinic and cubic. At higher temperatures, several configurations were observed depending on the temperature and the composition. It was concluded that there should be a eutectoid line at 1463 K and that the composition of the eutectoid point was in between 2.3 and 3.1 mol% PuO2.Then, the pseudo-binary phase diagram was calculated by minimisation of Gibbs energies, on the whole range of concentrations and up to 3200 K. A good fitting of experimental data was obtained. The resulting diagram shows three solid solution domains. A large fee domain allows complete solubility at high temperature. On the ZrO2 rich side, small amounts of PuO2 can be in solution either under monoclinic or tetragonal form depending on the temperature. These solid solution domains are separated by two-phase ones.This experimental and computational study provides a re-evaluation of the pseudo-binary diagram PuO2 – ZrO2. It gives a clearer view of the previously uncertain domains and it provides a good starting point for studying more complex phase relationships both in the frame of rock-like fuels and minor actinide transmutation.

A quality index for decision tree pruning

Abstract Decision tree is a divide and conquer classification method used in machine learning. Most pruning methods for decision trees minimize a classification error rate. In uncertain domains, some sub-trees that do not decrease the error rate can be relevant in pointing out some populations of specific interest or to give a representation of a large data file. A new pruning method (called DI pruning) is presented here. It takes into account the complexity of sub-trees and is able to keep sub-trees with leaves yielding to determine relevant decision rules, although they do not increase the classification efficiency. DI pruning allows to assess the quality of the data used for the knowledge discovery task. In practice, this method is implemented in the UnDeT software.

Soft Computing for diagnostics in equipment service

We present methods and tools from the Soft Computing (SC) domain, which is used within the diagnostics and prognostics framework to accommodate imprecision of real systems. SC is an association of computing methodologies that includes as its principal members fuzzy, neural, evolutionary, and probabilistic computing. These methodologies enable us to deal with imprecise, uncertain data and incomplete domain knowledge typically encountered in real-world applications. We outline the advantages and disadvantages of these methodologies and show how they can be combined to create synergistic hybrid SC systems. We conclude the paper with a description of successful SC case study applications to equipment diagnostics.

Using soft computing to build real world intelligent decision support systems in uncertain domains

Whilst the builders of traditional decision support systems have regularly used game theory and operations research, they have rarely used statistical techniques to build intelligent support systems for fields that have weak domain models. Further, the principle tools in the artificial intelligence arsenal were centred on symbol manipulation and predicate logic, while the use of numerical techniques were looked upon with disfavour. We claim that soft computing techniques (such as fuzzy reasoning and neural networks) can be integrated with symbolic techniques to provide for efficient decision making in knowledge-based systems. We illustrate our claim through the discussion of two decision support systems that have been constructed using soft computing techniques. Split-Up uses rules and neural networks to advise on property distribution following divorce in Australia, whilst IFDSSEA uses fuzzy reasoning to assists teachers in New York State to grade essays. We focus on how both systems reason and how they have been evaluated.

Building large-scale Bayesian networks

Bayesian networks (BNs) model problems that involve uncertainty. A BN is a directed graph, whose nodes are the uncertain variables and whose edges are the causal or influential links between the variables. Associated with each node is a set of conditional probability functions that model the uncertain relationship between the node and its parents. The benefits of using BNs to model uncertain domains are well known, especially since the recent breakthroughs in algorithms and tools to implement them. However, there have been serious problems for practitioners trying to use BNs to solve realistic problems. This is because, although the tools make it possible to execute large-scale BNs efficiently, there have been no guidelines on building BNs. Specifically, practitioners face two significant barriers. The first barrier is that of specifying the graph structure such that it is a sensible model of the types of reasoning being applied. The second barrier is that of eliciting the conditional probability values. In this paper we concentrate on this first problem. Our solution is based on the notion of generally applicable “building blocks”, called idioms, which serve solution patterns. These can then in turn be combined into larger BNs, using simple combination rules and by exploiting recent ideas on modular and object oriented BNs (OOBNs). This approach, which has been implemented in a BN tool, can be applied in many problem domains. We use examples to illustrate how it has been applied to build large-scale BNs for predicting software safety. In the paper we review related research from the knowledge and software engineering literature. This provides some context to the work and supports our argument that BN knowledge engineers require the same types of processes, methods and strategies enjoyed by systems and software engineers if they are to succeed in producing timely, quality and cost-effective BN decision support solutions.

Anti-Optimization Versus Probability in an Applied Mechanics Problem: Vector Uncertainty

In this study probabilistic and nonprobabilistic anti-optimization approaches are contrasted to evaluate their relative advantages and disadvantages while solving a mechanical problem in presence of vector uncertainty. The different cases that are analyzed in probabilistic setting that deal with either uniform or generic probability density functions for the uncertain variables varying in a rectangular domain. This case has been compared with interval analysis, a particular case of anti-optimization. The presence of a convex, smooth boundary of the uncertain domain has been also considered for comparing results obtained with these two alternative methods. It is shown that in case of vector uncertainty the anti-optimization method yields the same solution for the design problem as is provided by means of more complex probabilistic considerations. [S0021-8936(00)03103-2]

The uncertain domain of resistance to change

The uncertain domain of resistance to change

Permissive planning: extending classical planning to uncertain task domains

Uncertainty, inherent in most real-world domains, can cause failure of apparently sound classical plans. On the other hand, reasoning with representations that explicitly reflect uncertainty can engender significant, even prohibitive, additional computational costs. This paper contributes a novel approach to planning in uncertain domains. The approach is an extension of classical planning. Machine learning is employed to adjust planner bias in response to execution failures. Thus, the classical planner is conditioned towards producing plans that tend to work when executed in the world. The planner's representations are simple and crisp; uncertainty is represented and reasoned about only during learning. The user-supplied domain theory is left intact. The operator definitions and the planner's projection ability remain as the domain expert intended them. Some structuring of the planner's bias space is required. But with suitable structuring the approach scales well. The learning converges using no more than a polynomial number of examples. The system then probabilistically guarantees that either the plans produced will achieve their goal when executed or that adequate planning is not possible with the domain theory provided. An implemented robotic system is described.

Five Useful Properties of Probabilistic Knowledge Representations From the Point of View of Intelligent Systems

Although probabilistic knowledge representations and probabilistic reasoning have by now secured their position in artificial intelligence, it is not uncommon to encounter misunderstanding of their foundations and lack of appreciation for their strengths. This paper describes five properties of probabilistic knowledge representations that are particularly useful in intelligent systems research. (1) Directed probabilistic graphs capture essential qualitative properties of a domain, along with its causal structure. (2) Concepts such as relevance and conflicting evidence have a natural, formally sound meaning in probabilistic models. (3) Probabilistic schemes support sound reasoning at a variety of levels ranging from purely quantitative to purely qualitative levels. (4) The role of probability theory in reasoning under uncertainty can be compared to the role of first order logic in reasoning under certainty. Probabilistic knowledge representations provide insight into the foundations of logic-based schemes, showing their difficulties in highly uncertain domains. Finally, (5) probabilistic knowledge representations support automatic generation of understandable explanations of inference for the sake of user interfaces to intelligent systems.

A Convex Approach to the Mixed ${{\mathcal{H}_2 } / {H_\infty }}$ Control Problem for Discrete-Time Uncertain Systems

This paper considers ${{\mathcal{H}_2 } / {\mathcal{H}_\infty }}$ control problems involving discrete-time uncertain linear systems. The uncertain domain is supposed to be convex bounded, which naturally covers, as a particular case, the important class of interval matrices. The $\mathcal{H}_\infty$, guaranteed-cost control problem, solved for this class of uncertain systems, under no matching conditions, can be stated as follows: determine a state feedback gain (if one exists) such that the $\mathcal{H}_\infty$ norm of a given transfer function remains bounded by a prespecified level for all possible models. In the same context, problems on the determination of the smallest $\mathcal{H}_\infty$ upper bound and the minimization of an $\mathcal{H}_2$ cost upper bound subject to $\mathcal{H}_\infty$ constraints are also addressed. The results follow from the fact that those problems are convex in the particular parametric space under consideration. Some examples illustrate the theory.

Robust linear regulator design for discrete-time systems under polyhedral constraints

The robust linear constrained regulation problem for uncertain linear discrete-time systems ( A, B) is investigated using the theory of positively invariant polyhedral sets. Closed and bounded polyhedral uncertain domains are considered, involving parameters of both A and B-matrices and polyhedral constraints on both state and control vectors. New sufficient conditions for the solvability of the regulation problem are presented. For computational solution of the regulation problem, a linear programming approach is proposed where the constraints are given by the solvability conditions and the performance index represents a guaranteed trade-off between the closed-loop stability margin and the level of control effort.

Planning in bridge with thematic actions

The task of planning in a dynamic and an uncertain domain is considerably more challenging than in domains traditionally adopted byai planning methods. Planning in real situations has to be a knowledge intensive process, particularly since it is not easy to predict all the effects of one’s actions. Contract bridge offers a domain in which many of the issues involved in real world problems can be addressed without having to make simplifications in representation. Planning in the game of bridge takes us away from the traditional search-based methods (like the alpha-beta procedure), which are applicable in complete-information games like chess. In this paper we look at how knowledge can be structured to plan for declarer play in bridge. This involves deploying known move combinations, triggered by patterns which are abstracted out of the input, and then assembling the structures into a workable plan. The results demonstrate the viability of the proposed concepts.

Distributed approach to dynamic resource management based on temporal influence

The paper describes an approach to resource management in uncertain domains, which is based on the concept of temporal influence. The Distributed Interactive Scheduling with Abstractions Project is aimed at building a scheduling system designed to address the uncertainties of real-world domains. The system has two main features; it is distributed, taking a multi-agent view, and it uses a solution method that employs temporal abstractions to aid decision-making. The multi-agent view is a novel architecture based on a hierarchical representation of time and a dynamic heterogenetic structure for problem-solving agents. Temporal abstractions in the form of summarisations and generalisations are used for problem reduction and conflict resolution, providing a second novel idea. An additional goal of this project is to provide the user with the environment and information necessary to allow useful and intelligent interaction with the problem-solving process. Temporal abstractions also play an important role in the satisfaction of this goal.

Formula omitted]∞ guaranteed cost control for uncertain continuous-time linear systems

This paper deals with the H ∞ guaranteed cost control problems for continuous-time uncertain systems. It consist of the determination of a stabilizing state feedback gain which imposes on all possible closed-loop models an H ∞ -norm upper bound γ > 0. Assuming that the uncertain domain is convex-bounded and the uncertain system is quadratic-stabilizable with γ disturbance attenuation, it is shown how to determine, by means of a convex programming problem, the global minimum of γ. As a particular and important case, for precisely known linear systems, the last problem reduces to the classical H ∞ optimal control problem. The results follow from the definition of a special parameter space on which the above-mentioned problems are convex.

Denken und Handeln in Unbestimmtheit und Komplexität

In this article two purposes should be fulfilled: First we shall analyze the error tendencies of humans when confronted with the challenges of coping with very complex and uncertain domains of reality. From the results of experimental and case studies we try to derive a coherent picture of the slips, lapses and mistakes in different phases (goal elaboration, hypothesis formation, planning, decision making, control of success, self-reflexion) of the organization of action in complex environments. Additionally we try to find the reasons for these error tendencies. Behind a lot of very different forms of behaviour exhibited by humans when confronted with uncertain and very complex environments we recognize a small number of basic conditions for the human cognitive “machinery”, namely the restricted capacity of human conscious thinking, the overweight of the actual motive, the tendency to guard one's own feeling of competence and – quite simple – forgetting, which makes it difficult for us to identify the laws of time series. Eventually we investigate what could be done for the augmentation of the capability to cope with complexity and uncertainty. We recommend the use of computer-simulations of complex realities as a “wind-tunnel” to develop and to try out strategies to cope with very complex problems.

Managing uncertainty in time-critical plan evaluation

In complex real-world domains, uncertainty in predicting the results of plan execution drives the evaluation component of the planning cycle to explore a combinatorial explosion of alternative futures. This evaluation component is critical in evaluating the feasibility, strengths and weaknesses of a proposed plan. In time critical situations the planner is thus faced with a trade-off between timeliness and evaluation completion. Furthermore, a human planner is faced with the additional problem of evaluation credibility when using fast automatic evaluation in a complex and uncertain domain. An approach to handling these problems of time-criticality, uncertainty, and credibility is explored using the wargaming component of the military operational planning cycle. The Semi-Automated Forces Wargamer has been developed using two techniques. The first technique integrates procedural representations of plans and intentions with heuristic representations of simulated probabilistic execution. This facilitates the simulated execution of plans with multiple worlds corresponding to the possible results of actions taken in the real and uncertain world. The second provides a what-if capability via a tree representation of the possible combat outcomes. This provides the user with a tool for intelligent and focussed exploration of the space of possible outcomes to the plan. These techniques combine to generate a manageable and useful subset of the space of simulated plan results from which the user can apply human expertize to guide plan exploration.

End-user inputs and the performance of uncertainty representation schemes

Abstract Most of the approaches to uncertain reasoning developed for expert systems require user judgements about the degree to which evidence is present or absent. These user inputs are incorporated directly into the uncertainty calculations and influence the advice a completed system offers. Although all the other system parameters are set by the developer when the system is built and “tuned,” user inputs are likely to vary according to individual opinions. This empirical study examines the effects of user inputs on system accuracy. Subjects used one of two uncertain reasoning models to build and tune a system that captured their knowledge of a hypothetical, inherently uncertain domain. In the course of doing so, each subject also provided personal judgments of how evidence values for a uniform set of test cases mapped onto the uncertainty parameter values input by users. Our analysis examines the error introduced by using each subject's inputs for the test cases in conjunction with each of the other subject's systems. We also discuss the practical implications of our findings for system builders.

Integrating logical and probabilistic reasoning for decision making : Jack Breese Rockwell International Science Center, Palo Alto Laboratory, 444 High Street, Suite 400, Palo Alto, California 94301 Edison Tse Department of Engineering—Economic Systems, Stanford University, Stanford, California 94305

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and solution of probabilistic and decision-theoretic models for complex and uncertain domains. Given a query, a logical proof is produced if possible; if not, an influence diagram based on the query and the knowledge of the decision domain is produced and subsequently solved. A uniform declarative, first-order, knowledge representation is combined with a set of integrated inference procedures for logical, probabilistic, and decision-theoretic reasoning.

A case-based system for process planning

Process planning is the phase of manufacturing that is concerned with the selection, and sequencing of manufacturing operations necessary to transform an initial stock material into a finished part. It is a tedious operation that requires highly skilled and experienced personnel of which there is currently great shortage. To disseminate the costly expertise and to reduce process planning times, which tend to add high costs to small batch production, many automated computer systems have been introduced and applied. All these systems, though, require the supervision of an experienced human being and fail to capture the knowledge and reasoning behind process planning decisions. The causes of the lack of an efficient automatic system for process planning are the unique characteristics of the domain. In contrast to other areas where knowledge-based and expert systems have been applied, process planning demands the solution of several different planning problems before a final solution is achieved. Every change introduced to the previous world model creates a completely new world model with its own, new constraints and preconditions that nedd to be satisfied. This, in turn, affects the applicability of the knowledge to the new model. To provide solutions to the above problems we have designed a prototypical knowledge-based system that uses the high level, dynamic memory structures of MOPs (Memory Organization Packages), meta-MOPs and TOPs (Thematic Organization Packets) to rearrange its knowledge according to its experiences and to predict and avoid errors. To model the dynamic, sharable knowledge and the constantly changing world model a knowledge-representation language named TOLTEC has been designed and used in the system. Furthermore, we propose a novel planning method based on abstract plans and constraints that can solve planning problems in uncertain domains given incomplete information.

Some Reasons for Distinguishing Between “Non-normative Response” and “Irrational Decision”

Abstract Three concerns that limit the implications of normative decision research were described in this study. First, because there is no unequivocal way to determine whether any particular base rate is appropriate in a particular instance, the significance of the apparent base rate underutilization reported by a number of investigators is unclear. Second, because there are discrepancies between natural language and formal logic, word problems are an uncertain domain within which to gauge human inferential skills. Third, because different people will have different strategies and preferences, no single solution may be correct or optimal for all persons. In light of these limitations, a more functional approach to decision interpretation is discussed.