Where do uncertainties reside within environmental risk assessments? Expert opinion on uncertainty distributions for pesticide risks to surface water organisms

A reliable characterisation of uncertainties can aid uncertainty identification during environmental risk assessments (ERAs). However, typologies can be implemented inconsistently, causing uncertainties to go unidentified. We present an approach based on nine structured elicitations, in which subject-matter experts, for pesticide risks to surface water organisms, validate and assess three dimensions of uncertainty: its level (the severity of uncertainty, ranging from determinism to ignorance); nature (whether the uncertainty is epistemic or aleatory); and location (the data source or area in which the uncertainty arises). Risk characterisation contains the highest median levels of uncertainty, associated with estimating, aggregating and evaluating the magnitude of risks. Regarding the locations in which uncertainty is manifest, data uncertainty is dominant in problem formulation, exposure assessment and effects assessment. The comprehensive description of uncertainty described will enable risk analysts to prioritise the required phases, groups of tasks, or individual tasks within a risk analysis according to the highest levels of uncertainty, the potential for uncertainty to be reduced or quantified, or the types of location-based uncertainty, thus aiding uncertainty prioritisation during environmental risk assessments. In turn, it is expected to inform investment in uncertainty reduction or targeted risk management action

A Dynamic System Model of Biogeography-Based Optimization

We derive a dynamic system model for biogeography-based optimization (BBO) that is asymptotically exact as the population size approaches infinity. The states of the dynamic system are equal to the proportion of each individual in the population; therefore, the dimension of the dynamic system is equal to the search space cardinality of the optimization problem. The dynamic system model allows us to derive the proportion of each individual in the population for a given optimization problem using theory rather than simulation. The results of the dynamic system model are more precise than simulation, especially for individuals that are very unlikely to occur in the population. Since BBO is a generalization of a certain type of genetic algorithm with global uniform recombination (GAGUR), an additional contribution of our work is a dynamic system model for GAGUR. We verify our dynamic system models with simulation results. We also use the models to compare BBO, GAGUR, and a GA with single-point crossover (GASP) for some simple problems. We see that with small mutation rates, as are typically used in real-world problems, BBO generally results in better optimization results than GAs for the problems that we investigate

Design and Rule Base Reduction of a Fuzzy Filter for the Estimation of Motor Currents

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 a fuzzy system with correlation-product inference and centroid defuzzification for motor winding current estimation, With the assumption that the membership functions are triangular (but not necessarily symmetric), we then optimize the membership functions using gradient descent. Next we use singular value decomposition to reduce the rule base for the fuzzy filter. Rule base reduction can be important for fuzzy systems in those cases where the fuzzy system needs to be implemented in real time. This is especially true with regard to fuzzy filtering in a real time motor controller. The methods discussed in this paper are demonstrated on real motor winding currents that were collected with a digital oscilloscope. It is demonstrated that fuzzy techniques provide a feasible approach to motor current estimation, that gradient descent optimization improves the performance of the filter, and that rule base reduction results in a relatively small degradation of filter performance. (C) 2000 Elsevier Science Inc. All rights reserved

Globally Optimal Periodic Robot Joint Trajectories

This paper presents a new method for the planning of robot trajectories. The method presented assumes that joint-space knots have been generated from Cartesian knots by an inverse kinematics algorithm. The method is based on the globally optimal periodic interpolation scheme derived by Schoenberg, and thus is particularly suited for periodic robot motions. Of all possible periodic joint trajectories which pass through a specified set of knots, the trajectory derived in this paper is the ‘best’. The performance criterion used is the integral (over one period) of a combination of the square of the joint velocity and the square of the joint jerk

Sum Normal Optimization of Fuzzy Membership Functions

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 optimization approach is modified in this paper so that the resulting membership functions are sum normal. Sum normality is desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The sum normal constraint is applied in this paper to both gradient descent optimization and Kalman filter optimization of fuzzy membership functions. The methods are illustrated on a fuzzy automotive cruise controller

Distributed Fault Tolerance in Optimal Interpolative Nets

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 rather than small weight perturbations). Realistic fault tolerance can be achieved through a smooth distribution of weights, resulting in low weight salience and distributed computation. Results of trained OI Nets on the Iris classification problem show that fault tolerance can be increased with the algorithm presented in this paper

Design and Rule Base Reduction of a Fuzzy Filter for the Estimation of Motor Currents

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 a fuzzy system with correlation-product inference and centroid defuzzification for motor winding current estimation, With the assumption that the membership functions are triangular (but not necessarily symmetric), we then optimize the membership functions using gradient descent. Next we use singular value decomposition to reduce the rule base for the fuzzy filter. Rule base reduction can be important for fuzzy systems in those cases where the fuzzy system needs to be implemented in real time. This is especially true with regard to fuzzy filtering in a real time motor controller. The methods discussed in this paper are demonstrated on real motor winding currents that were collected with a digital oscilloscope. It is demonstrated that fuzzy techniques provide a feasible approach to motor current estimation, that gradient descent optimization improves the performance of the filter, and that rule base reduction results in a relatively small degradation of filter performance. (C) 2000 Elsevier Science Inc. All rights reserved

H-infinity Estimation for Fuzzy Membership Function Optimization

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 specific shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a few variables and the membership optimization problem can be reduced to a parameter optimization problem. The parameter optimization problem can then be formulated as a nonlinear filtering problem. In this paper we solve the nonlinear filtering problem using H∞ state estimation theory. However, the membership functions that result from this approach are not (in general) sum normal. That is, the membership function values do not add up to one at each point in the domain. We therefore modify the H∞ filter with the addition of state constraints so that the resulting membership functions are sum normal. Sum normality may be desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The methods proposed in this paper are illustrated on a fuzzy automotive cruise controller and compared to Kalman filtering based optimization

Kalman Filtering With State Constraints: A Survey of Linear and Nonlinear Algorithms

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 does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results