This work develops a measurement-driven and model-based formal verification approach, applicable to systems with partly unknown dynamics. We provide a principled method, grounded on reachability analysis and on Bayesian inference, to compute the confidence that a physical system driven by external inputs and accessed under noisy measurements, verifies a temporal logic property. A case study is discussed, where we investigate the bounded- and unbounded-time safety of a partly unknown linear time invariant system.
As control systems become increasingly more complex, there exists a pressing need to find systematic ways of verifying them. To address this concern, there has been significant work in developing test generation schemes for black-box control architectures. These schemes test a black-box control architecture's ability to satisfy its control objectives, when these objectives are expressed as operational specifications through temporal logic formulae. Our work extends these prior, model based results by lower bounding the probability by which the black-box system will satisfy its operational spec…
This paper introduces for the first time, to the best of our knowledge, the Bayesian Physics-Informed Neural Networks for applications in power systems. Bayesian Physics-Informed Neural Networks (BPINNs) combine the advantages of Physics-Informed Neural Networks (PINNs), being robust to noise and missing data, with Bayesian modeling, delivering a confidence measure for their output. Such a confidence measure can be very valuable for the operation of safety critical systems, such as power systems, as it offers a degree of trustworthiness for the neural network output. This paper applies the BPI…
Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of large models or of a limited sample size. Common solutions to reduce the effect of variance are regularized estimators, shrinkage estimators and Bayesian estimation. In the current work we investigate the latter two solutions, which have not yet been applied to subspace identification. Our experimental results show that our proposed estimators may reduce the estimation risk up to $40\%$ of that of traditional subspace methods.
Technische Universität Chemnitz（开姆尼茨工业大学）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）
Traction parameters, that characterize the ground-wheel contact dynamics, are the central factor in the energy efficiency of vehicles. To optimize fuel consumption, reduce wear of tires, increase productivity etc., knowledge of current traction parameters is unavoidable. Unfortunately, these parameters are difficult to measure and require expensive force and torque sensors. An alternative way is to use system identification to determine them. In this work, we validate such a method in field experiments with a mobile robot. The method is based on an adaptive Kalman filter. We show how it estima…
This paper presents a Bayesian method for identification of jump Markov linear system parameters. A primary motivation is to provide accurate quantification of parameter uncertainty without relying on asymptotic in data-length arguments. To achieve this, the paper details a particle-Gibbs sampling approach that provides samples from the desired posterior distribution. These samples are produced by utilising a modified discrete particle filter and carefully chosen conjugate priors.
Delft University of Technology（代尔夫特理工大学）；Western Sydney University（西悉尼大学）；The University of Manchester（曼彻斯特大学）
This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification problems. First, DNNs are known to be too complex that they can easily overfit the training data. Second, the selection of the input regressors for system identification is nontrivial. Third, uncertainty quantification of the model parameters and predictions are necessary. The proposed Bayesian approach offers a principled way to alleviate the above challenges by …
This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their data-driven construction. Our starting point is the sparse-identification of nonlinear dynamics (SINDy) framework, which reformulates system identification as a regression problem, where unknown functions are approximated from a sparse subset of an underlying library. In this manuscript, we formulate this system identification method in a Bayesian framework to handle …
The recent advances in power plants and energy resources have extended the applications of DC-DC converters in the power systems (especially in the context of DC micro-grids). Parameter identification can extract the parameters of the converters and generate accurate discrete simulation models. In this paper, we propose a measurement-based converter parameter calibration method by an adaptive Approximate Bayesian Computation with sequential Monte Carlo sampler (ABC SMC), which estimates the parameters related to passive and parasitic components. At first, we propose to find suitable prior dist…
The increasing integration of intermittent renewable generation, especially at the distribution level,necessitates advanced planning and optimisation methodologies contingent on the knowledge of thegrid, specifically the admittance matrix capturing the topology and line parameters of an electricnetwork. However, a reliable estimate of the admittance matrix may either be missing or quicklybecome obsolete for temporally varying grids. In this work, we propose a data-driven identificationmethod utilising voltage and current measurements collected from micro-PMUs. More precisely,we first present a…
Nonlinear system identification is important with a wide range of applications. The typical approaches for nonlinear system identification include Volterra series models, nonlinear autoregressive with exogenous inputs models, block-structured models, state-space models and neural network models. Among them, neural networks (NN) is an important black-box method thanks to its universal approximation capability and less dependency on prior information. However, there are several challenges associated with NN. The first one lies in the design of a proper neural network structure. A relatively simp…
This paper considers Bayesian parameter estimation of dynamic systems using a Markov Chain Monte Carlo (MCMC) approach. The Metroplis-Hastings (MH) algorithm is employed, and the main contribution of the paper is to examine and illustrate the efficacy of a particular proposal density based on energy preserving Hamiltonian dynamics, which results in what is known in the statistics literature as ``Hamiltonian Monte--Carlo'' (HMC). The very significant utility of this approach is that, as will be illustrated, it greatly reduces (almost to the point of elimination) the typically very high correlat…
Massachusetts Institute of Technology（麻省理工学院）；ExxonMobil Research and Engineering（埃克森美孚研究与工程公司）
In processing and manufacturing industries, there has been a large push to produce higher quality products and ensure maximum efficiency of processes. This requires approaches to effectively detect and resolve disturbances to ensure optimal operations. While the control system can compensate for many types of disturbances, there are changes to the process which it still cannot handle adequately. It is therefore important to further develop monitoring systems to effectively detect and identify those faults such that they can be quickly resolved by operators. In this paper, a novel probabilistic…
University of California San Diego（加州大学圣地亚哥分校）；University of Michigan（密歇根大学）
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse science and engineering applications such as astrophysics, robotics, vortex dynamics, charged particle dynamics, and quantum mechanics. The numerical experiments demonstrate that the proposed method recovers dynamical systems with higher accuracy and reduced predictive uncertainty compared to state-of-the-art approaches. The results further show that accurate pred…
Massachusetts Institute of Technology（麻省理工学院）；Broad Institute of MIT and Harvard（MIT和哈佛大学Broad研究所）；Basis Research Institute（Basis研究机构）；Eric and Wendy Schmidt Center（埃里克和温迪·施密特中心）；BCAM (Basque Center for Applied Mathematics)（BCAM（巴斯克应用数学中心））；Ikerbasque (Basque Foundation for Science)（Ikerbasque（巴斯克科学基金会））
We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising when modeling complex physical systems given by the interconnection of many sub-units where feedback and algebraic loops can be encountered. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. The stable spline covariance is used to include information on smooth expone…
