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Systems Engineering and Multidisciplinary Design Optimization Commons™
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- Optimization (4)
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Articles 1 - 8 of 8
Full-Text Articles in Systems Engineering and Multidisciplinary Design Optimization
Kalman Filtering With State Constraints: A Survey Of Linear And Nonlinear Algorithms, Daniel J. Simon
Kalman Filtering With State Constraints: A Survey Of Linear And Nonlinear Algorithms, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter …
Biogeography-Based Optimization, Daniel J. Simon
Biogeography-Based Optimization, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
Biogeography is the study of the geographical distribution of biological organisms. Mathematical equations that govern the distribution of organisms were first discovered and developed during the 1960s. The mindset of the engineer is that we can learn from nature. This motivates the application of biogeography to optimization problems. Just as the mathematics of biological genetics inspired the development of genetic algorithms (GAs), and the mathematics of biological neurons inspired the development of artificial neural networks, this paper considers the mathematics of biogeography as the basis for the development of a new field: biogeography-based optimization (BBO). We discuss natural biogeography and …
A Comparison Of Filtering Approaches For Aircraft Engine Health Estimation, Daniel J. Simon
A Comparison Of Filtering Approaches For Aircraft Engine Health Estimation, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
Different approaches for the estimation of the states of linear dynamic systems are commonly used, the most common being the Kalman filter. For nonlinear systems, variants of the Kalman filter are used. Some of these variants include the LKF (linearized Kalman filter), the EKF (extended Kalman filter), and the UKF (unscented Kalman filter). With the LKF and EKF, performance varies depending on how often Jacobians (partial derivative matrices) are updated. In other words, we see a tradeoff between computational effort and filtering performance. With the unscented Kalman filter, Jacobians are not calculated but computational effort is typically high due to …
A Game Theory Approach To Constrained Minimax State Estimation, Daniel J. Simon
A Game Theory Approach To Constrained Minimax State Estimation, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
This paper presents a game theory approach to the constrained state estimation of linear discrete time dynamic systems. In the application of state estimators, there is often known model or signal information that is either ignored or dealt with heuristically. For example, constraints on the state values (which may be based on physical considerations) are often neglected because they do not easily fit into the structure of the state estimator. This paper develops a method for incorporating state equality constraints into a minimax state estimator. The algorithm is demonstrated on a simple vehicle tracking simulation.
Data Smoothing And Interpolation Using Eighth-Order Algebraic Splines, Daniel J. Simon
Data Smoothing And Interpolation Using Eighth-Order Algebraic Splines, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
A new type of algebraic spline is used to derive a filter for smoothing or interpolating discrete data points. The spline is dependent on control parameters that specify the relative importance of data fitting and the derivatives of the spline. A general spline of arbitrary order is first formulated using matrix equations. We then focus on eighth-order splines because of the continuity of their first three derivatives (desirable for motor and robotics applications). The spline's matrix equations are rewritten to give a recursive filter that can be implemented in real time for lengthy data sequences. The filter is lowpass with …
Sum Normal Optimization Of Fuzzy Membership Functions, Daniel J. Simon
Sum Normal Optimization Of Fuzzy Membership Functions, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This …
Distributed Fault Tolerance In Optimal Interpolative Nets, Daniel J. Simon
Distributed Fault Tolerance In Optimal Interpolative Nets, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
The recursive training algorithm for the optimal interpolative (OI) classification network is extended to include distributed fault tolerance. The conventional OI Net learning algorithm leads to network weights that are nonoptimally distributed (in the sense of fault tolerance). Fault tolerance is becoming an increasingly important factor in hardware implementations of neural networks. But fault tolerance is often taken for granted in neural networks rather than being explicitly accounted for in the architecture or learning algorithm. In addition, when fault tolerance is considered, it is often accounted for using an unrealistic fault model (e.g., neurons that are stuck on or off …
Design And Rule Base Reduction Of A Fuzzy Filter For The Estimation Of Motor Currents, Daniel J. Simon
Design And Rule Base Reduction Of A Fuzzy Filter For The Estimation Of Motor Currents, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
Fuzzy systems have been used extensively and successfully in control systems over the past few decades, but have been applied much less often to filtering problems. This is somewhat surprising in view of the dual relationship between control and estimation. This paper discusses and demonstrates the application of fuzzy filtering to motor winding current estimation in permanent magnet synchronous motors. Motor winding current estimation is an important problem because in order to implement effective closed-loop control, a good estimation of the current is needed. Motor winding currents are notoriously noisy because of electrical noise in the motor drive. We use …