Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

Effective handling of dialogue state in the hidden information state POMDP-based dialogue manager

Effective dialogue management is critically dependent on the information that is encoded in the dialogue state. In order to deploy reinforcement learning for policy optimization, dialogue must be modeled as a Markov Decision Process. This requires that the dialogue statemust encode all relevent information obtained during the dialogue prior to that state. This can be achieved by combining the user goal, the dialogue history, and the last user action to form the dialogue state. In addition, to gain robustness to input errors, dialogue must be modeled as a Partially Observable Markov Decision Process (POMDP) and hence, a distribution over all possible states must be maintained at every dialogue turn. This poses a potential computational limitation since there can be a very large number of dialogue states. The Hidden Information State model provides a principled way of ensuring tractability in a POMDP-based dialogue model. The key feature of this model is the grouping of user goals into partitions that are dynamically built during the dialogue. In this article, we extend this model further to incorporate the notion of complements. This allows for a more complex user goal to be represented, and it enables an effective pruning technique to be implemented that preserves the overall system performance within a limited computational resource more effectively than existing approaches. © 2011 ACM.

A single-rate context-dependent learning process underlies rapid adaptation to familiar object dynamics.

Motor learning has been extensively studied using dynamic (force-field) perturbations. These induce movement errors that result in adaptive changes to the motor commands. Several state-space models have been developed to explain how trial-by-trial errors drive the progressive adaptation observed in such studies. These models have been applied to adaptation involving novel dynamics, which typically occurs over tens to hundreds of trials, and which appears to be mediated by a dual-rate adaptation process. In contrast, when manipulating objects with familiar dynamics, subjects adapt rapidly within a few trials. Here, we apply state-space models to familiar dynamics, asking whether adaptation is mediated by a single-rate or dual-rate process. Previously, we reported a task in which subjects rotate an object with known dynamics. By presenting the object at different visual orientations, adaptation was shown to be context-specific, with limited generalization to novel orientations. Here we show that a multiple-context state-space model, with a generalization function tuned to visual object orientation, can reproduce the time-course of adaptation and de-adaptation as well as the observed context-dependent behavior. In contrast to the dual-rate process associated with novel dynamics, we show that a single-rate process mediates adaptation to familiar object dynamics. The model predicts that during exposure to the object across multiple orientations, there will be a degree of independence for adaptation and de-adaptation within each context, and that the states associated with all contexts will slowly de-adapt during exposure in one particular context. We confirm these predictions in two new experiments. Results of the current study thus highlight similarities and differences in the processes engaged during exposure to novel versus familiar dynamics. In both cases, adaptation is mediated by multiple context-specific representations. In the case of familiar object dynamics, however, the representations can be engaged based on visual context, and are updated by a single-rate process.

Syllable language models for Mandarin speech recognition: exploiting character language models.

Mandarin Chinese is based on characters which are syllabic in nature and morphological in meaning. All spoken languages have syllabiotactic rules which govern the construction of syllables and their allowed sequences. These constraints are not as restrictive as those learned from word sequences, but they can provide additional useful linguistic information. Hence, it is possible to improve speech recognition performance by appropriately combining these two types of constraints. For the Chinese language considered in this paper, character level language models (LMs) can be used as a first level approximation to allowed syllable sequences. To test this idea, word and character level n-gram LMs were trained on 2.8 billion words (equivalent to 4.3 billion characters) of texts from a wide collection of text sources. Both hypothesis and model based combination techniques were investigated to combine word and character level LMs. Significant character error rate reductions up to 7.3% relative were obtained on a state-of-the-art Mandarin Chinese broadcast audio recognition task using an adapted history dependent multi-level LM that performs a log-linearly combination of character and word level LMs. This supports the hypothesis that character or syllable sequence models are useful for improving Mandarin speech recognition performance.

Development of realistic liquid equations of state for multi-phase CFD modelling

Several equations of state (EOS) have been incorporated into a novel algorithm to solve a system of multi-phase equations in which all phases are assumed to be compressible to varying degrees. The EOSs are used to both supply functional relationships to couple the conservative variables to the primitive variables and to calculate accurately thermodynamic quantities of interest, such as the speed of sound. Each EOS has a defined balance of accuracy, robustness and computational speed; selection of an appropriate EOS is generally problem-dependent. This work employs an AUSM+-up method for accurate discretisation of the convective flux terms with modified low-Mach number dissipation for added robustness of the solver. In this paper we show a newly-developed time-marching formulation for temporal discretisation of the governing equations with incorporated time-dependent source terms, as well as considering the system of eigenvalues that render the governing equations hyperbolic.

State estimation schemes for independent component coupled hidden Markov models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results. © Taylor & Francis Group, LLC.

Functional requirements for reward-modulated spike-timing-dependent plasticity.

Recent experiments have shown that spike-timing-dependent plasticity is influenced by neuromodulation. We derive theoretical conditions for successful learning of reward-related behavior for a large class of learning rules where Hebbian synaptic plasticity is conditioned on a global modulatory factor signaling reward. We show that all learning rules in this class can be separated into a term that captures the covariance of neuronal firing and reward and a second term that presents the influence of unsupervised learning. The unsupervised term, which is, in general, detrimental for reward-based learning, can be suppressed if the neuromodulatory signal encodes the difference between the reward and the expected reward-but only if the expected reward is calculated for each task and stimulus separately. If several tasks are to be learned simultaneously, the nervous system needs an internal critic that is able to predict the expected reward for arbitrary stimuli. We show that, with a critic, reward-modulated spike-timing-dependent plasticity is capable of learning motor trajectories with a temporal resolution of tens of milliseconds. The relation to temporal difference learning, the relevance of block-based learning paradigms, and the limitations of learning with a critic are discussed.

Slowness: an objective for spike-timing-dependent plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this "temporal stability" or "slowness" approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing-dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the "trace rule." The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.