Showing papers on "Parametric statistics published in 2021"

An Aligned Rank Transform Procedure for Multifactor Contrast Tests

Abstract: Data from multifactor HCI experiments often violates the assumptions of parametric tests (i.e., nonconforming data). The Aligned Rank Transform (ART) has become a popular nonparametric analysis in HCI that can find main and interaction effects in nonconforming data, but leads to incorrect results when used to conduct post hoc contrast tests. We created a new algorithm called ART-C for conducting contrast tests within the ART paradigm and validated it on 72,000 synthetic data sets. Our results indicate that ART-C does not inflate Type I error rates, unlike contrasts based on ART, and that ART-C has more statistical power than a t-test, Mann-Whitney U test, Wilcoxon signed-rank test, and ART. We also extended an open-source tool called ARTool with our ART-C algorithm for both Windows and R. Our validation had some limitations (e.g., only six distribution types, no mixed factorial designs, no random slopes), and data drawn from Cauchy distributions should not be analyzed with ART-C.

A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

Abstract: We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent low dimensionality of the solution manifold to obtain approximation rates which are significantly superior to those provided by classical neural network approximation results. Concretely, we use the existence of a small reduced basis to construct, for a large variety of parametric partial differential equations, neural networks that yield approximations of the parametric solution maps in such a way that the sizes of these networks essentially only depend on the size of the reduced basis.

Adaptive Finite-Time Stabilization of Stochastic Nonlinear Systems Subject to Full-State Constraints and Input Saturation

Abstract: In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved. To alleviate the serious uncertainties and state constraints, the adaptive backstepping control and barrier Lyapunov function are combined in a unified framework. Then, by applying a function approximation method and the auxiliary system method to deal with input saturation respectively, two adaptive state-feedback controllers are constructed. Based on the proposed stochastic Lyapunov theorem, each constructed controller can guarantee the closed-loop system achieves SGFSP, the system states remain in the defined compact sets and the output tracks the reference signal very well. Finally, a stochastic single-link robot system is established and used to demonstrate the effectiveness of the proposed schemes.

Deep Residual Networks With Adaptively Parametric Rectifier Linear Units for Fault Diagnosis

Abstract: Vibration signals under the same health state often have large differences due to changes in operating conditions. Likewise, the differences among vibration signals under different health states can be small under some operating conditions. Traditional deep learning methods apply fixed nonlinear transformations to all the input signals, which have a negative impact on the discriminative feature learning ability, i.e., projecting the intraclass signals into the same region and the interclass signals into distant regions. Aiming at this issue, this article develops a new activation function, i.e., adaptively parametric rectifier linear units, and inserts the activation function into deep residual networks to improve the feature learning ability, so that each input signal is trained to have its own set of nonlinear transformations. To be specific, a subnetwork is inserted as an embedded module to learn slopes to be used in the nonlinear transformation. The slopes are dependent on the input signal, and thereby the developed method has more flexible nonlinear transformations than the traditional deep learning methods. Finally, the improved performance of the developed method in learning discriminative features has been validated through fault diagnosis applications.

Robust Adaptive Control Barrier Functions: An Adaptive and Data-Driven Approach to Safety

Abstract: A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainty. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive controller for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as contraction does not require the system be invertible or in a particular form. The method is tested on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.

Shortcuts to Adiabaticity for the Quantum Rabi Model: Efficient Generation of Giant Entangled Cat States via Parametric Amplification.

Abstract: We propose a method for the fast generation of nonclassical ground states of the Rabi model in the ultrastrong and deep-strong coupling regimes via the shortcuts-to-adiabatic (STA) dynamics. The time-dependent quantum Rabi model is simulated by applying parametric amplification to the Jaynes-Cummings model. Using experimentally feasible parametric drive, this STA protocol can generate large-size Schrodinger cat states, through a process that is ∼10 times faster compared to adiabatic protocols. Such fast evolution increases the robustness of our protocol against dissipation. Our method enables one to freely design the parametric drive, so that the target state can be generated in the lab frame. A largely detuned light-matter coupling makes the protocol robust against imperfections of the operation times in experiments.

Deep Parametric Continuous Convolutional Neural Networks

Abstract: Standard convolutional neural networks assume a grid structured input is available and exploit discrete convolutions as their fundamental building blocks. This limits their applicability to many real-world applications. In this paper we propose Parametric Continuous Convolution, a new learnable operator that operates over non-grid structured data. The key idea is to exploit parameterized kernel functions that span the full continuous vector space. This generalization allows us to learn over arbitrary data structures as long as their support relationship is computable. Our experiments show significant improvement over the state-of-the-art in point cloud segmentation of indoor and outdoor scenes, and lidar motion estimation of driving scenes.

Model-Predictive-Control-Based Path Tracking Controller of Autonomous Vehicle Considering Parametric Uncertainties and Velocity-Varying

Abstract: The automated steering control technology is crucial for an autonomous vehicle, but due to parametric uncertainties and time varying, the performance of automated steering control can be degraded. Therefore, a vehicle automated steering controller based on a model predictive control (MPC) approach is proposed in this article. First, considering tire nonlinear characteristics, the state and control matrices are modified, then the time-varying vehicle speed is considered and a linear parameter varying lateral model is established through utilizing a polytope with finite vertices to describe vehicle longitudinal velocity. Then, the MPC-based vehicle path tracking controller, which is robust against parameter uncertainties, is designed; the proposed controller can be solved via a set of linear matrix inequalities (LMI), which are derived from Lyapunov asymptotic stability and the minimization of the worst case infinite horizon quadratic objective function. The proposed control system is evaluated by both cosimulations of MATLAB/Simulink & CarSim and real-bus tests. Results show the effectiveness of the proposed controller, and it can ensure the control accuracy and strong robustness.

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.

Abstract: Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.

Model Reduction and Neural Networks for Parametric PDEs

Abstract: We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model reduction. This combination results in a neural network approximation which, in principle, is defined on infinite-dimensional spaces and, in practice, is robust to the dimension of finite-dimensional approximations of these spaces required for computation. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology. Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems, showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature.

Likelihood-free inference by ratio estimation

Abstract: We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference in the absence of a likelihood function. The popular synthetic likelihood approach infers the parameters by modelling summary statistics of the data by a Gaussian probability distribution. In another popular approach called approximate Bayesian computation, the inference is performed by identifying parameter values for which the summary statistics of the simulated data are close to those of the observed data. Synthetic likelihood is easier to use as no measure of “closeness” is required but the Gaussianity assumption is often limiting. Moreover, both approaches require judiciously chosen summary statistics. We here present an alternative inference approach that is as easy to use as synthetic likelihood but not as restricted in its assumptions, and that, in a natural way, enables automatic selection of relevant summary statistic from a large set of candidates. The basic idea is to frame the problem of estimating the posterior as a problem of estimating the ratio between the data generating distribution and the marginal distribution. This problem can be solved by logistic regression, and including regularising penalty terms enables automatic selection of the summary statistics relevant to the inference task. We illustrate the general theory on canonical examples and employ it to perform inference for challenging stochastic nonlinear dynamical systems and high-dimensional summary statistics.

Fast and Accurate Motion Tracking of a Linear Motor System Under Kinematic and Dynamic Constraints: An Integrated Planning and Control Approach

Abstract: Achieving a fast transient response and high steady-state tracking accuracy simultaneously has been a challenging issue for the linear motor system in the presence of kinematic and dynamic constraints, various parametric uncertainties, and uncertain nonlinearities. To this end, a two-loop control structure is developed to maximize the converging speed of the transient response and achieve high steady-state accuracy. Specifically, in the outer loop, an online trajectory replanning algorithm is devised to force the replanned trajectory to merge into the desired trajectory in minimum time under the system’s kinematic and dynamic constraints. In the inner loop, an adaptive robust controller is synthesized to handle the parametric uncertainties and uncertain nonlinearities effectively so that high steady-state tracking accuracy is guaranteed. Particularly, the interaction between the two loops is intuitive since a feedforward term is optimized in the outer loop and then fed into the inner loop to make the model compensation. Comparative experiments are carried out on a linear-motor-driven system. Experimental results confirm that the proposed control structure can achieve a minimum-time transient response without violating the kinematic and dynamic constraints and also guarantee the excellent steady-state tracking accuracy.

High-order fully actuated system approaches: Part IV. Adaptive control and high-order backstepping

Abstract: Three types of high-order system models with parametric uncertainties are introduced, namely, the high-order fully actuated (HOFA) models, and the second- and high-order strict-feedback system (SFS...

Probabilistic physics-guided machine learning for fatigue data analysis

Abstract: A Probabilistic Physics-guided Neural Network (PPgNN) is proposed in this paper for probabilistic fatigue S-N curve estimation. The proposed model overcomes the limitations in existing parametric regression models and classical machine learning models for fatigue data analysis. Compared with explicit regression-type models (such as power law fitting), the PPgNN is flexible and does not impose restrictions on function types at different stress levels, mean stresses, or other factors. One unique benefit is that the proposed method includes the known physics/knowledge constraints in the machine learning model; the method can produce both accurate and physically consistent results compared with the classical machine learning model, such as neural network models. In addition, the PPgNN uses both failure and runout data in the training process, which encodes the runout data using a new proposed loss function, and is beneficial when compared with some existing models using only numerical point value data. A mathematical formulation is derived to include different types of physics constraints, which can deal with mean value, variance, and derivative/curvature constraints. Several data sets from open literature for fatigue S-N curve testing are used for model demonstration and model validation. Next, the proposed network architecture is extended to include multi-factor (e.g., mean stress, corrosion, frequency effect, etc.) fatigue data analysis. It is shown that the proposed PPgNN can serve as a flexible and robust model for general fitting and uncertainty quantification of fatigue data. This paper provides a feasible way to incorporate known physics/knowledge in neural network-based machine learning. This is achieved by properly designing the network topology and constraining the neural network’s biases and weights. The benefits for the proposed physics-guided learning for fatigue data analysis are illustrated by comparing results from neural network models with and without physics guidance. The neural network model, without physics guidance, produces results contradictory to the common knowledge, such as a monotonic decrease of S-N curve slope and a monotonic increase of fatigue life variance as the stress level decreases. This problem can be avoided using the physics-guided learning model with encoded prior physics knowledge.

GRU-Type LARC Strategy for Precision Motion Control With Accurate Tracking Error Prediction

Abstract: To simultaneously achieve accurate tracking error prediction, rigorous motion accuracy, and certain robustness to parameter variations and unknown disturbances, this article proposes a data-based learning adaptive robust control (LARC) strategy based on gated recurrent unit (GRU) neural network. Firstly, parameter adaptive control and robust control are utilized to guarantee the robustness against parametric uncertainties and unknown disturbances. A GRU neural network is then constructed and capable of precisely predicting the tracking error after training with data collected from a linear-motor-driven stage. Essentially, the GRU network can be viewed as a data-based model, which captures the tracking error dynamic characteristics and provides a prediction even before implementing the real trajectory. Consequently, a reference modification and a feedforward compensation part can be formed, which is the significant part of the whole LARC control structure. Comparative experimental investigation not only validates the effectiveness of the tracking error prediction ability, but also demonstrates the practically satisfactory transient/steady-state tracking performance of the proposed control strategy.

Parametric UMAP Embeddings for Representation and Semisupervised Learning.

Abstract: UMAP is a nonparametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) computing a graphical representation of a data set (fuzzy simplicial complex) and (2) through stochastic gradient descent, optimizing a low-dimensional embedding of the graph. Here, we extend the second step of UMAP to a parametric optimization over neural network weights, learning a parametric relationship between data and embedding. We first demonstrate that parametric UMAP performs comparably to its nonparametric counterpart while conferring the benefit of a learned parametric mapping (e.g., fast online embeddings for new data). We then explore UMAP as a regularization, constraining the latent distribution of autoencoders, parametrically varying global structure preservation, and improving classifier accuracy for semisupervised learning by capturing structure in unlabeled data.1.

High-order fully actuated system approaches: part VII. Controllability, stabilisability and parametric designs

Abstract: In this paper, high-order fully actuated (HOFA) models with multiple orders for general dynamical control systems are firstly proposed, for which controllers can be easily designed such that the cl...

Optimizing Performance Characteristics of Blower for Combustion Process Using Taguchi Based Grey Relational Analysis

Abstract: Complete combustion in a furnace must be achieved to reduce the emissions. In order to achieve the same, this work focuses on the optimization of performance parameters of centrifugal blower for complete combustion in the furnace with the aid of one the optimization techniques, i.e., Taguchi-based grey relational analysis. The type of blade and percentage of the opening of the blower duct is selected as input parametric characteristics. For experimental design, tests are planned based on Taguchi’s L12 orthogonal array and by conducting experiments as design, the output process parameters i.e. velocity, discharge, input power, output power, and mechanical efficiency are calculated and found the operating settings of the blower by manipulating grey relational grade with Taguchi optimization technique. The test results propose that the type of blade has the most noteworthy impact on the multiple performance qualities rather than the percentage of the opening of duct and blower with a backward blade and 50% opening of duct shows the best-operating conditions.

The box-cox transformation: review and extensions

Abstract: The Box-Cox power transformation family for non-negative responses in linear models has a long and interesting history in both statistical practice and theory, which we summarize. The relationship between generalized linear models and log transformed data is illustrated. Extensions investigated include the transform both sides model and the Yeo-Johnson transformation for observations that can be positive or negative. The paper also describes an extended Yeo-Johnson transformation that allows positive and negative responses to have different power transformations. Analyses of data show this to be necessary. Robustness enters in the fan plot for which the forward search provides an ordering of the data. Plausible transformations are checked with an extended fan plot. These procedures are used to compare parametric power transformations with nonparametric transformations produced by smoothing.

Photonic Crystal Optical Parametric Oscillator.

Abstract: We report a new class of optical parametric oscillators, based on a 20-μm-long semiconductor photonic crystal cavity and operating at telecom wavelengths. Because the confinement results from Bragg scattering, the optical cavity contains a few modes, approximately equispaced in frequency. Parametric oscillation is reached when these high-quality-factor modes are thermally tuned into a triply resonant configuration, whereas any other parametric interaction is strongly suppressed. The lowest pump power threshold is estimated to be 50–70 μW. This source behaves as an ideal degenerate optical parametric oscillator, addressing the needs in the field of quantum optical circuits and paving the way towards the dense integration of highly efficient nonlinear sources of squeezed light or entangled photons pairs. Photonic crystal-based optical parametric oscillators have remained elusive but have finally been demonstrated. Operating at telecom wavelengths, the source may prove particularly useful in quantum optics applications.

The impact of uncertainty on predictions of the CovidSim epidemiological code

Abstract: Epidemiological modelling has assisted in identifying interventions that reduce the impact of COVID-19. The UK government relied, in part, on the CovidSim model to guide its policy to contain the rapid spread of the COVID-19 pandemic during March and April 2020; however, CovidSim contains several sources of uncertainty that affect the quality of its predictions: parametric uncertainty, model structure uncertainty and scenario uncertainty. Here we report on parametric sensitivity analysis and uncertainty quantification of the code. From the 940 parameters used as input into CovidSim, we find a subset of 19 to which the code output is most sensitive—imperfect knowledge of these inputs is magnified in the outputs by up to 300%. The model displays substantial bias with respect to observed data, failing to describe validation data well. Quantifying parametric input uncertainty is therefore not sufficient: the effect of model structure and scenario uncertainty must also be properly understood. Through parametric sensitivity analysis and uncertainty quantification of the CovidSim model, a subset of this model’s parameters is identified to which the code output is most sensitive. Using these allows better and more informed decisions about proposed policies.

Analysing point patterns on networks — A review

Abstract: We review recent research on statistical methods for analysing spatial patterns of points on a network of lines, such as road accident locations along a road network. Due to geometrical complexities, the analysis of such data is extremely challenging, and we describe several common methodological errors. The intrinsic lack of homogeneity in a network militates against the traditional methods of spatial statistics based on stationary processes. Topics include kernel density estimation, relative risk estimation, parametric and non-parametric modelling of intensity, second-order analysis using the K-function and pair correlation function, and point process model construction. An important message is that the choice of distance metric on the network is pivotal in the theoretical development and in the analysis of real data. Challenges for statistical computation are discussed and open-source software is provided.

Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels

Abstract: High-resolution (HR) information of fluid flows, although preferable, is usually less accessible due to limited computational or experimental resources. In many cases, fluid data are generally sparse, incomplete, and possibly noisy. How to enhance spatial resolution and decrease the noise level of flow data is essential and practically useful. Deep learning (DL) techniques have been demonstrated to be effective for super-resolution (SR) tasks, which, however, primarily rely on sufficient HR labels for training. In this work, we present a novel physics-informed DL-based SR solution using convolutional neural networks (CNNs), which is able to produce HR flow fields from low-resolution (LR) inputs in high-dimensional parameter space. By leveraging the conservation laws and boundary conditions of fluid flows, the CNN-SR model is trained without any HR labels. Moreover, the proposed CNN-SR solution unifies the forward SR and inverse data assimilation for the scenarios where the physics is partially known, e.g., unknown boundary conditions. A new network structure is designed to enable not only the parametric SR but also the parametric inference for the first time. Several flow SR problems relevant to cardiovascular applications have been studied to demonstrate the proposed method's effectiveness and merit. A series of different LR scenarios, including LR input with Gaussian noises, non-Gaussian magnetic resonance imaging noises, and downsampled measurements given either well-posed or ill-posed physics, are investigated to illustrate the SR, denoising, and inference capabilities of the proposed method.

Predictor-Based Neural Network Finite-Set Predictive Control for Modular Multilevel Converter

Abstract: This letter investigates the possibility of deploying a novel finite control-set model predictive control solution for solving the ongoing research challenges in predictive control regulated modular multilevel converter, i.e., model parameter sensitiveness and excessive computational burden as well as weighting factors selection. Specifically, it is realized by cascading a predictor-based neural network design, which enables a smooth and fast identification of system dynamics, and a computationally efficient finite-set predictive control, which is responsible for simplifying the rolling optimization and reducing the computational complexity. The main contribution of the proposed methodology relies on the fact that no knowledge of any model parameters and weighting factors in whole control process are required, which leads to a significant enhancement in the robustness and reliability of the control system in the presence of parametric uncertainties, while remaining computationally feasible. Finally, the stability analysis is given, and the proposed methodology is experimentally assessed for modular multilevel converter, where steady-state and transient-state performance tests confirm the interest of the proposal.