Short-term ocean wave forecasting using an autoregressive moving average model

In order to predict future observations of a noisedriven system, we have to find a model that exactly or at least approximately describes the behavior of the system so that the current system state can be recovered from past observations. However, sometimes it is very difficult to model a system accurately, such as real ocean waves. It is therefore particularly interesting to analyze ocean wave properties in the time-domain using autoregressive moving average (ARMA) models. Two ARMA/AR based models and their equivalent state space representations will be used for predicting future ocean wave elevations, where unknown parameters will be determined using linear least squares and auto-covariance least squares algorithms. Compared to existing wave prediction methods, in this paper (i) an ARMA model is used to enhance the prediction performance, (ii) noise covariances in the ARMA/AR model are computed rather than guessed and (iii) we show that, in practice, low pass filtering of historical wave data does not improve the forecasting results

Relations between Full Information and Kalman-Based Estimation

For nonlinear state space systems with additive noises, sometimes the number of process noise signals could be less than the dimension of the state space. In order to improve the accuracy and stability of nonlinear state estimation, this paper provides for the first time the derivation of the full information estimator (FIE) for such nonlinear systems. We verify our derivation of the FIE by firstly proving the unbiasedness and minimum-variance of the FIE for linear time varying (LTV) systems, then showing the equivalence between the Kalman filter/smoother and the FIE for LTV systems. Finally, we prove that the FIE will provide more accurate state estimates than the extended Kalman filter (EKF) and smoother (EKS) for nonlinear systems

Energy-efficient scheduling for homogeneous multiprocessor systems

We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a discrete speed set, we propose solving a tractable linear program. Our formulations are based on a fluid model and a global scheduling scheme, i.e. tasks are allowed to migrate between processors. The new methods are compared with three global energy/feasibility optimal workload allocation formulations. Simulation results illustrate that our methods achieve both feasibility and energy optimality and outperform existing methods for constrained deadline tasksets. Specifically, the results provided by our algorithm can achieve up to an 80% saving compared to an algorithm without a frequency scaling scheme and up to 70% saving compared to a constant frequency scaling scheme for some simulated tasksets. Another benefit is that our algorithms can solve the scheduling problem in one step instead of using a recursive scheme. Moreover, our formulations can solve a more general class of scheduling problems, i.e. any periodic real-time taskset with arbitrary deadline. Lastly, our algorithms can be applied to both online and offline scheduling schemes

Noise Covariance Identification for Time-varying and Nonlinear Systems

Kalman-based state estimators assume a priori knowledge of the covariance matrices of the process and observation noise. However, in most practical situations, noise statistics and initial conditions are often unknown and need to be estimated from measurement data. This paper presents an auto-covariance least-squares-based algorithm for noise and initial state error covariance estimation of large-scale linear time-varying (LTV) and nonlinear systems. Compared to existing auto-covariance least-squares based-algorithms, our method does not involve any approximations for LTV systems, has fewer parameters to determine and is more memory/computationally efficient for large-scale systems. For nonlinear systems, our algorithm uses full information estimation/moving horizon estimation instead of the extended Kalman filter, so that the stability and accuracy of noise covariance estimation for nonlinear systems can be guaranteed or improved, respectively

Implementing a model and processes for mapping digital literacy in the curriculum (online badges)

Digital literacy has been identified as an essential part of a number of other skills and competences that should be developed and are collectively known as 21st Century Skills (The Partnership for 21st Century Learning, 2015; United Nations Education Scientific and Cultural Organisation, 2008). The increasing demand for the workforce to become digitally competent compels educational institutions to review their programmes and ensure that digital skills become embedded as a graduate attribute (Figel’, 2007; Quality Assurance Agency, 2014). In the UK and at a national level, the ambition to enhance the digital capability of the workforce and the population in general has been articulated in numerous occasions by a variety of stakeholders. Examples within Higher Education include national initiatives such as the Developing Digital Literacies programme (Joint Information Systems Committee, 2013), the Digital Literacies in the Disciplines programme (Higher Education Academy, 2014) and the Changing the Learning Landscape programme (Higher Education Funding Council England, 2015). A unique perspective was gained whilst working within a faculty and supporting their learning-technology developmental needs as a professional practitioner. The need for a new approach to academic professional development of digital capabilities was identified

Automatic Scenario Generation for Robust Optimal Control Problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 2 14+3×192 boundary scenarios are considered. A validation with randomly-drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used

Automatic scenario generation for efficient solution of robust optimal control problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2¹⁴⁺³×¹⁹² extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive

Tightly Bounded Polynomials via Flexible Discretizations for Dynamic Optimization Problems

Polynomials are widely used to represent the trajectories of states and/or inputs. It has been shown that a polynomial can be bounded by its coefficients, when expressed in the Bernstein basis. However, in general, the bounds provided by the Bernstein coefficients are not tight. We propose a method for obtaining numerical solutions to dynamic optimization problems, where a flexible discretization is used to achieve tight polynomial bounds. The proposed method is used to solve a constrained cart-pole swing-up optimal control problem. The flexible discretization eliminates the conservatism of the Bernstein bounds and enables a lower cost, in comparison with non-flexible discretizations. A theoretical result on obtaining tight polynomial bounds with a finite discretization is presented. In some applications with linear dynamics, the non-convexity introduced by the flexible discretization may be a drawback

Capstone Assessment as Faculty Development

Portland State University (PSU) is a public institution in Portland, Oregon, serving 28,000 students, including 23,000 undergraduates. PSU implemented Capstone courses in 1995 as the culminating experience in the revised general education program, University Studies (UNST). Capstones at PSU are community‐based courses composed of interdisciplinary teams of students actively engaged with community partners, designed to address the UNST learning goals (inquiry and critical thinking; communication; ethics and social responsibility; and diversity, equity, and social justice). Each Capstone course creates one or more collaboratively developed final products intended to serve the community partner. In this article, we describe the evolution of our Capstone assessment practice and highlight the current process we designed to assess these courses. Through this process—which is the latest and most successful iteration of an assessment protocol for these highly contextual courses—we recognized that conceptualizing an assessment process as simultaneously a forum for peer‐driven faculty support increases faculty ownership over assessment and investment in using assessment results to make change in their own courses

Automatic scenario generation for efficient solution of robust optimal control problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2¹⁴+³ₓ¹⁹² extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive