A Non-Gaussian Bayesian Filter Using Power and Generalized Logarithmic Moments

In our previous paper, we proposed a non-Gaussian Bayesian filter using power moments of the system state. A density surrogate parameterized as an analytic function is proposed to approximate the true system state, of which the distribution is only assumed Lebesgue integrable. To our knowledge, it is the first Bayesian filter where there is no prior constraints on the true density of the state and the state estimate has a continuous form of function. In this very preliminary version of paper, we propose a new type of statistics, which is called the generalized logarithmic moments. They are used to parameterize the state distribution together with the power moments. The map from the parameters of the proposed density surrogate to the power moments is proved to be a diffeomorphism, which allows to use gradient methods to treat the optimization problem determining the parameters. The simulation results reveal the advantage of using both moments for estimating mixtures of complicated types of functions.Comment: 20 pages, 3 figure

Density Steering by Power Moments

This paper considers the problem of steering an arbitrary initial probability density function to an arbitrary terminal one, where the system dynamics is governed by a first-order linear stochastic difference equation. It is a generalization of the conventional stochastic control problem where the uncertainty of the system state is usually characterized by a Gaussian distribution. We propose to use the power moments to turn the infinite-dimensional problem into a finite-dimensional one and to present an empirical control scheme. By the designed control law, the moment sequence of the controls at each time step is positive, which ensures the existence of the control for the moment system. We then realize the control at each time step as a function in analytic form by a convex optimization scheme, for which the existence and uniqueness of the solution have been proved in our previous paper. Two numerical examples are given to validate our proposed algorithm.Comment: 6 pages, 6 figure

Group Steering: Approaches Based on Power Moments

This paper considers the problem of steering a colossal group of agents of which the dynamics are governed by a discrete-time first-order linear system, which is a very preliminary version. The group of agents are characterized as a probability density function and an occupation measure respectively in the paper and two corresponding treatments are given. We propose to use the power moments to characterize the density function/occupation measure of the agents. A moment system representation of the original system is put forward for control and an empirical control scheme corresponding to it is proposed. By the designed control law, the moment sequence of the control at each time step is positive, which ensures the existence of the control for the moment system. We then realize the control as an analytic form of function by a convex optimization scheme of which the existence and uniqueness of the solution have been proved in our previous paper. An error analysis of the terminal density from the specified one is also provided. For the problem where the group of agents is characterized as an occupation measure, the control for each agent is determined by drawing independent and identically-distributed(i.i.d) samples from the realized analytic function. Finally we simulate both unconstrained and constrained controls of a colossal group of agents, which validate our proposed algorithms.Comment: 15 pages, 16 figures. Portions of this work were submitted to the IFAC World Congress 2023. arXiv admin note: substantial text overlap with arXiv:2211.0232

A Multivariate Non-Gaussian Bayesian Filter Using Power Moments

In this paper, which is a very preliminary version, we extend our results on the univariate non-Gaussian Bayesian filter using power moments to the multivariate systems, which can be either linear or nonlinear. Doing this introduces several challenging problems, for example a positive parametrization of the density surrogate, which is not only a problem of filter design, but also one of the multiple dimensional Hamburger moment problem. We propose a parametrization of the density surrogate with the proofs to its existence, Positivstellensatze and uniqueness. Based on it, we analyze the error of moments of the density estimates through the filtering process with the proposed density surrogate. An error upper bound in the sense of total variation distance is also given. A discussion on continuous and discrete treatments to the non-Gaussian Bayesian filtering problem is proposed to explain why our proposed filter shall also be a mainstream of the non-Gaussian Bayesian filtering research and motivate the research on continuous parametrization of the system state. Last but not the least, simulation results on estimating different types of multivariate density functions are given to validate our proposed filter. To the best of our knowledge, the proposed filter is the first one implementing the multivariate Bayesian filter with the system state parameterized as a continuous function, which only requires the true states being Lebesgue integrable.Comment: 16 pages, 2 figures. arXiv admin note: text overlap with arXiv:2207.0851

Friction surface structure of a Cf/C-SiC composite brake disc after bedding testing on a full-scale dynamometer

We have examined friction surface structure of a carbon ceramic brake disc tested on a full-scale dynamometer with microscopy techniques. The bedded friction surface is composed of two types of regions: transferred materials (TM) and SiC. The TM regions were formed through the deposition of wear debris into surface voids, followed by compaction and crystallite refinement during braking. A thin friction layer (FL) was developed on top of TM and SiC regions with nano-sized copper/iron oxide crystallites as the primary constituent. Analysis shows that debris generated from pad is the main source of TM and FL. No evidence shows chemical diffusion bonding between TM and composite constituent. On silicon carbide surface, dislocations were activated as the sources of surface fracture

BAYHENN: Combining Bayesian Deep Learning and Homomorphic Encryption for Secure DNN Inference

Recently, deep learning as a service (DLaaS) has emerged as a promising way to facilitate the employment of deep neural networks (DNNs) for various purposes. However, using DLaaS also causes potential privacy leakage from both clients and cloud servers. This privacy issue has fueled the research interests on the privacy-preserving inference of DNN models in the cloud service. In this paper, we present a practical solution named BAYHENN for secure DNN inference. It can protect both the client's privacy and server's privacy at the same time. The key strategy of our solution is to combine homomorphic encryption and Bayesian neural networks. Specifically, we use homomorphic encryption to protect a client's raw data and use Bayesian neural networks to protect the DNN weights in a cloud server. To verify the effectiveness of our solution, we conduct experiments on MNIST and a real-life clinical dataset. Our solution achieves consistent latency decreases on both tasks. In particular, our method can outperform the best existing method (GAZELLE) by about 5x, in terms of end-to-end latency.Comment: accepted by IJCAI 2019; camera read

Friction and surface fracture of a silicon carbide ceramic brake disc tested against a steel pad

Friction coefficients of a SiC ceramic disc were measured on a laboratory-scale dynamometer by testing against a mild steel pad under different initial braking speeds, and its friction surface was investigated with microscopy techniques. At bedding, averaged friction coefficient for a braking stop varied significantly with the initial braking speed; after bedding, it converged to ~0.6, regardless of braking speed. Surface fracture on the SiC disc was responsible for the transformation from a flat surface into a rough one, making ploughing a dominant friction mechanism at bedded stage. It was found that fracture surface and non-contact regions directly contributed friction coefficient variation at bedding stage. Friction layer composed of iron oxides and plastic deformation with partial dislocations activated appeared on SiC surface, but were unsustainable owing to surface fracture. A quantitative analysis is provided to understand friction coefficient variation and SiC surface fracture during braking