137 research outputs found
Variational message passing for online polynomial NARMAX identification
We propose a variational Bayesian inference procedure for online nonlinear
system identification. For each output observation, a set of parameter
posterior distributions is updated, which is then used to form a posterior
predictive distribution for future outputs. We focus on the class of polynomial
NARMAX models, which we cast into probabilistic form and represent in terms of
a Forney-style factor graph. Inference in this graph is efficiently performed
by a variational message passing algorithm. We show empirically that our
variational Bayesian estimator outperforms an online recursive least-squares
estimator, most notably in small sample size settings and low noise regimes,
and performs on par with an iterative least-squares estimator trained offline.Comment: 6 pages, 4 figures. Accepted to the American Control Conference 202
Learning Deep Input-Output Stable Dynamics
Learning stable dynamics from observed time-series data is an essential
problem in robotics, physical modeling, and systems biology. Many of these
dynamics are represented as an inputs-output system to communicate with the
external environment. In this study, we focus on input-output stable systems,
exhibiting robustness against unexpected stimuli and noise. We propose a method
to learn nonlinear systems guaranteeing the input-output stability. Our
proposed method utilizes the differentiable projection onto the space
satisfying the Hamilton-Jacobi inequality to realize the input-output
stability. The problem of finding this projection can be formulated as a
quadratic constraint quadratic programming problem, and we derive the
particular solution analytically. Also, we apply our method to a toy bistable
model and the task of training a benchmark generated from a glucose-insulin
simulator. The results show that the nonlinear system with neural networks by
our method achieves the input-output stability, unlike naive neural networks.
Our code is available at https://github.com/clinfo/DeepIOStability.Comment: Accepted in NeurIPS 202
Gradient-based particle filter algorithm for an ARX model with nonlinear communication output
A stochastic gradient (SG)-based particle filter (SG-PF) algorithm is developed for an ARX model with nonlinear communication output in this paper. This ARX model consists of two submodels, one is a linear ARX model and the other is a nonlinear output model. The process outputs (outputs of the linear submodel) transmitted over a communication channel are unmeasurable, while the communication outputs (outputs of the nonlinear submodel) are available, and both of the twotype outputs are contaminated by white noises. Based on the rich input data and the available communication output data, a SG-PF algorithm is proposed to estimate the unknown process outputs and parameters of the ARX model. Furthermore, a direct weight optimization method and the Epanechnikov kernel method are extended to modify the particle filter when the measurement noise is a Gaussian noise with unknown variance and the measurement noise distribution is unknown. The simulation results demonstrate that the SG-PF algorithm is effective
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Novel methods for biological network inference: an application to circadian Ca2+ signaling network
Biological processes involve complex biochemical interactions among a large number of species like cells, RNA, proteins and metabolites. Learning these interactions is essential to interfering artificially with biological processes in order to, for example, improve crop yield, develop new therapies, and predict new cell or organism behaviors to genetic or environmental perturbations. For a biological process, two pieces of information are of most interest. For a particular species, the first step is to learn which other species are regulating it. This reveals topology and causality. The second step involves learning the precise mechanisms of how this regulation occurs. This step reveals the dynamics of the system. Applying this process to all species leads to the complete dynamical network. Systems biology is making considerable efforts to learn biological networks at low experimental costs. The main goal of this thesis is to develop advanced methods to build models for biological networks, taking the circadian system of Arabidopsis thaliana as a case study. A variety of network inference approaches have been proposed in the literature to study dynamic biological networks. However, many successful methods either require prior knowledge of the system or focus more on topology. This thesis presents novel methods that identify both network topology and dynamics, and do not depend on prior knowledge. Hence, the proposed methods are applicable to general biological networks. These methods are initially developed for linear systems, and, at the cost of higher computational complexity, can also be applied to nonlinear systems. Overall, we propose four methods with increasing computational complexity: one-to-one, combined group and element sparse Bayesian learning (GESBL), the kernel method and reversible jump Markov chain Monte Carlo method (RJMCMC). All methods are tested with challenging dynamical network simulations (including feedback, random networks, different levels of noise and number of samples), and realistic models of circadian system of Arabidopsis thaliana. These simulations show that, while the one-to-one method scales to the whole genome, the kernel method and RJMCMC method are superior for smaller networks. They are robust to tuning variables and able to provide stable performance. The simulations also imply the advantage of GESBL and RJMCMC over the state-of-the-art method. We envision that the estimated models can benefit a wide range of research. For example, they can locate biological compounds responsible for human disease through mathematical analysis and help predict the effectiveness of new treatments
A comprehensive expectation identification framework for multirate time-delayed systems
The expectation maximization (EM) algorithm has been extensively used to solve system identification problems with hidden variables. It needs to calculate a derivative equation and perform a matrix inversion in the EM-M step. The equations related to the EM algorithm may be unsolvable for some complex nonlinear systems, and the matrix inversion has heavy computational costs for large-scale systems. This article provides two expectation-based algorithms with the aim of constructing a comprehensive expectation framework concerning different kinds of time-delayed systems: 1) for a small-scale linear system, the classical EM algorithm can quickly obtain the parameter and time-delay estimates; 2) for a complex nonlinear system with low order, the proposed expectation gradient descent algorithm can avoid derivative function calculation; 3) for a large-scale system, the proposed expectation multidirection algorithm does not require eigenvalue calculation and has less computational costs. These two algorithms are developed based on the gradient descent and multidirection methods. Under such an expectation framework, different kinds of models are identified on a case-by-case basis. The convergence analysis and simulation examples show the effectiveness of the algorithms
Data driven discovery of cyber physical systems
Cyber-physical systems embed software into the physical world. They appear in a wide range of applications such as smart grids, robotics, and intelligent manufacturing. Cyber-physical systems have proved resistant to modeling due to their intrinsic complexity arising from the combination of physical and cyber components and the interaction between them. This study proposes a general framework for discovering cyber-physical systems directly from data. The framework involves the identification of physical systems as well as the inference of transition logics. It has been applied successfully to a number of real-world examples. The novel framework seeks to understand the underlying mechanism of cyber-physical systems as well as make predictions concerning their state trajectories based on the discovered models. Such information has been proven essential for the assessment of the performance of cyber- physical systems; it can potentially help debug in the implementation procedure and guide the redesign to achieve the required performance
Increasing the robustness of autonomous systems to hardware degradation using machine learning
Autonomous systems perform predetermined tasks (missions) with minimum supervision. In most applications, the state of the world changes with time. Sensors are employed to measure part or whole of the world’s state. However, sensors often fail amidst operation; feeding as such decision-making with wrong information about the world. Moreover, hardware degradation may alter dynamic behaviour, and subsequently the capabilities, of an autonomous system; rendering the original mission infeasible. This thesis applies machine learning to yield powerful and robust tools that can facilitate autonomy in modern systems. Incremental kernel regression is used for dynamic modelling. Algorithms of this sort are easy to train and are highly adaptive. Adaptivity allows for model adjustments, whenever the environment of operation changes. Bayesian reasoning provides a rigorous framework for addressing uncertainty. Moreover, using Bayesian Networks, complex inference regarding hardware degradation can be answered. Specifically, adaptive modelling is combined with Bayesian reasoning to yield recursive estimation algorithms that are robust to sensor failures. Two solutions are presented by extending existing recursive estimation algorithms from the robotics literature. The algorithms are deployed on an underwater vehicle and the performance is assessed in real-world experiments. A comparison against standard filters is also provided. Next, the previous algorithms are extended to consider sensor and actuator failures jointly. An algorithm that can detect thruster failures in an Autonomous Underwater Vehicle has been developed. Moreover, the algorithm adapts the dynamic model online to compensate for the detected fault. The performance of this algorithm was also tested in a real-world application. One step further than hardware fault detection, prognostics predict how much longer can a particular hardware component operate normally. Ubiquitous sensors in modern systems render data-driven prognostics a viable solution. However, training is based on skewed datasets; datasets where the samples from the faulty region of operation are much fewer than the ones from the healthy region of operation. This thesis presents a prognostic algorithm that tackles the problem of imbalanced (skewed) datasets
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