Minimum Variance Theory Research Articles

Stochastic performance evaluation method of wind power DC bus voltage control system

The stochastic fluctuation of DC bus voltage of wind power grid-connected system is related to the safe and stable of power system, and the stochastic performance evaluation is an important means for early warning system. In order to evaluate stochastic performance of control system, this paper proposes a stochastic performance evaluation method based on minimum variance theory. A dual closed loop control model of wind power grid-connected converter DC bus voltage is established, the stochastic performance evaluation indicator is derived by time-series analysis and Diophantine decomposition, and the method to solve the indicator through operation data is given. The effectiveness of the proposed method is verified by FAST-MATLAB co-simulation platform. And the results show that the stochastic performance of the system can be improved by optimizing the parameters of the controller and the DC bus voltage.

How do the consideration of non-normal return distributions and of higher moments influence the optimal asset allocation in Swiss pension funds?

The low interest rates that prevail on many capital markets impose great challenges for the asset management of financial organizations. They try to achieve target returns for their clients, a solid one-period funding ratio and a low one-period underfunding probability. In this summarizing contribution of Muller and Wagner (2018), we aim to study the impact of capital allocation strategies for pension funds in Switzerland. Thereby, we compare classic Markowitz theory with an extended Taylor series approach for the utility function. It is further analyzed how the assumption of normally distributed returns drives the optimal asset allocation when compared with using the distributions corresponding to the best fit of the historical data. Taking the extended utility function including the first four central moments and the alternative return distributions, we simulate the assets of a pension fund in a one-period model with the Monte Carlo method. A comparison of these results with those obtained from the classic minimum variance theory concludes that a considerable change of the portfolio weights takes place. Our research is relevant for theory and practice alike. Financial institutions can strongly profit from comparing different approaches when assessing their investment strategy.

Nonlinear control study on aircraft engine using a generalized minimum variance approach

With the requirements of the advanced propulsion systems for aircraft control performance increasing, it has attracted the attention to design more efficient controller that is based on the nonlinear model over the flight envelope directly. A nonlinear aircraft engine control method based on generalized minimum variance approach is studied. A nonlinear autoregressive with extra input aircraft engine model for a certain turbofan engine is built and is chosen as the control plant in this study. Then, a controller is designed for the identification model based on the nonlinear generalized minimum variance theory. And simulation results manifest the controller to satisfy the requirements of the tracking with the transient process and the regulation with the steady process.

Interacting Multiple Model LK Tracking

The nonlinear motion state of object seriously affects the object tracking characteristics in complex motion scene. In this paper, we propose an interacting multiple model LK (IMM-LK) tracking algorithm to enhance the performance of tracking nonlinear moving object. LK tracking approach is based on the localized gradient obtaining stable optical-flow feature, based on LK, we build several motion models of the tracked object that interact with each other in the tracking process. The method extracts different model's object features, estimates the object state and calculates the matching rate of each model with the current motion model using theory of minimum variance. Combining with the optimal transfer matrix then we can track the nonlinear moving object. The proposed IMM-LK algorithm performs favorably against conventional LK tracking on the performance of tracking nonlinear moving object.

An Improved Interacting Multiple Model Algorithm Used in Aircraft Tracking

There are some problems in traditional interacting multiple model algorithms (IMM) when used in target tracking systems. For instance, the mode transition matrix is inaccurate and cannot be determined when the sojourn times are not known. To solve these problems, an optimal mode transition matrix IMM (OMTM-IMM) algorithm is proposed in this paper. The linear minimum variance theory is used to calculate the mode transition matrix which depends on the continuous system state rather than the sojourn times in this algorithm. Moreover, the correlation of the subfilter is considered; hence the covariance matrices are utilized to compute mode transition matrix. In this algorithm, the model probability is defined as a diagonal matrix which is combined with the filters outputs; thus the effects produced by each state can be distinguished. Finally, to verify the superiority of the new algorithm, the theoretical proof and simulation results are given. They show that the OMTM-IMM algorithm can improve the tracking accuracy and can be utilized in the complex environment.

Movement trajectory smoothness is not associated with the endpoint accuracy of rapid multi-joint arm movements in young and older adults

The minimum variance theory proposes that motor commands are corrupted by signal-dependent noise and smooth trajectories with low noise levels are selected to minimize endpoint error and endpoint variability. The purpose of the study was to determine the contribution of trajectory smoothness to the endpoint accuracy and endpoint variability of rapid multi-joint arm movements. Young and older adults performed arm movements (4 blocks of 25 trials) as fast and as accurately as possible to a target with the right (dominant) arm. Endpoint accuracy and endpoint variability along with trajectory smoothness and error were quantified for each block of trials. Endpoint error and endpoint variance were greater in older adults compared with young adults, but decreased at a similar rate with practice for the two age groups. The greater endpoint error and endpoint variance exhibited by older adults were primarily due to impairments in movement extent control and not movement direction control. The normalized jerk was similar for the two age groups, but was not strongly associated with endpoint error or endpoint variance for either group. However, endpoint variance was strongly associated with endpoint error for both the young and older adults. Finally, trajectory error was similar for both groups and was weakly associated with endpoint error for the older adults. The findings are not consistent with the predictions of the minimum variance theory, but support and extend previous observations that movement trajectories and endpoints are planned independently.

Endpoint accuracy for a small and a large hand muscle in young and old adults during rapid, goal-directed isometric contractions

The minimum variance theory proposes that stronger (larger) muscles produce less variable trajectories compared with weaker (smaller) muscles and thus can accomplish more accurate contractions. The purpose of the study was to determine the influence of muscle size and trajectory variability on the endpoint accuracy of goal-directed isometric contractions. Twelve young (25 +/- 5 years) and 12 old adults (76 +/- 6 years) performed 100 trials with each of two muscles in both hands. Subjects were instructed to match the peak of a force trajectory to a target force by controlling either the abduction (first dorsal interosseus muscle; FDI) or adduction force (second palmar interosseus muscle; SPI) exerted by the index finger of each hand. The time to peak force was 150 ms and the peak force required was 25% of the maximal force that could be achieved in 150 ms. Endpoint accuracy and variability in force and time along with intramuscular EMG activity of the agonist muscle (FDI and SPI) involved in each task were quantified for each set of 100 trials. The MVC force was less for the SPI muscle, and the force endpoint error and variance were greater in the SPI muscle compared with the FDI muscle. Conversely, endpoint measures that included timing were similar for the two muscles. Trajectory variability was greater for the FDI muscle, but did not influence endpoint error for either muscle. The young and old adults had similar strength values, but the old adults were less accurate and more variable than the young subjects. Nonetheless, the accuracy and variability displayed by the old adults for the two muscles was the same as that observed for the young adults. The force accuracy and variability findings are consistent with the predictions of the minimum variance theory that motor-output variability is inversely related to muscle size, strength, and motor unit number.

Rapid Computation of Time-Optimal, Open-Loop Forearm Movement

Minimal movement time for open-loop rotation of the human forearm, along with the associated input signal to the forearm muscles, is calculated using matrix multiplication. This permits rapid evaluation of movement times across a four-dimensional mesh of initial conditions, each moving to a common terminal state. The described discrete-time solution is based on the continuous-time solution of Tanaka et al., and the minimum-variance theory of Harris and Wolpert. Underlying algorithm concepts are discussed, and proofs of solution existence are provided.

Fluctuations In Force Trajectory Predict End-point Accuracy During Rapid Isometric Contractions

The minimum-variance theory predicts that the central nervous system preferentially selects trajectories that comprise low levels of force fluctuations to minimize signal-dependent noise and maximize end-point accuracy. Purpose To determine the association between fluctuations in the force trajectory and end-point accuracy of rapid, goal-directed isometric contractions. Methods Eleven men and 11 women (23±5 yrs), performed 100 discrete isometric contractions with the first dorsal interosseus muscle. Each subject was instructed to match a force trajectory to a target by controlling the abduction force exerted by the index finger. Visual feedback of the force-time curve, the force-time trajectory, and target location was provided to each subject 1 s after each trial. The time to peak force was 150 ms and the peak force required was 25% of the maximal force that each subject could exert at 150 ms. End-point accuracy was quantified in two ways: (1) overall error — the average distance from the target based on the force and time coordinates; (2) ellipsoid — the product of the SD of the force and SD of time, as used previously by the proponents of the minimum-variance theory. Trajectory variability was quantified as the SD of the detrended force (SDF) from the initial rise in force to the peak force. Results Both the overall error and ellipsoid measures declined with trial number and indicated that ten trials were needed to reach a plateau in accuracy. The two measures of end-point accuracy, however, were not significantly associated (r2 = 0.10, P = 0.15). The SDF was strongly associated with the overall error (r2 = 0.80, P <0.001), but only weakly associated with the ellipsoid (r2 = 0.18, P = 0.049). The overall error was predicted (r2 = 0.80, P = 0.001) equally from the error in force (r = 0.56) and time (r = 0.53). Further, end-point accuracy was also predicted by the impulse to peak force, which was highly associated with overall error (r2 = 0.81, P <0.001). Conclusion As predicted from the minimum-variance theory, endpoint accuracy during open-loop isometric contractions appears to be strongly related to the fluctuations in the force trajectory. The measure of end-point accuracy that is most sensitive to the fluctuations in the force trajectory, however, appears to be the distance from the target (overall error) and not the total variability of the responses (ellipsoid). Supported by NIA R03 AG024662-01 to EAC.

Fluctuations In Force Trajectory Predict End-point Accuracy During Rapid Isometric Contractions

The minimum-variance theory predicts that the central nervous system preferentially selects trajectories that comprise low levels of force fluctuations to minimize signal-dependent noise and maximize end-point accuracy. Purpose To determine the association between fluctuations in the force trajectory and end-point accuracy of rapid, goal-directed isometric contractions. Methods Eleven men and 11 women (23±5 yrs), performed 100 discrete isometric contractions with the first dorsal interosseus muscle. Each subject was instructed to match a force trajectory to a target by controlling the abduction force exerted by the index finger. Visual feedback of the force-time curve, the force-time trajectory, and target location was provided to each subject 1 s after each trial. The time to peak force was 150 ms and the peak force required was 25% of the maximal force that each subject could exert at 150 ms. End-point accuracy was quantified in two ways: (1) overall error — the average distance from the target based on the force and time coordinates; (2) ellipsoid — the product of the SD of the force and SD of time, as used previously by the proponents of the minimum-variance theory. Trajectory variability was quantified as the SD of the detrended force (SDF) from the initial rise in force to the peak force. Results Both the overall error and ellipsoid measures declined with trial number and indicated that ten trials were needed to reach a plateau in accuracy. The two measures of end-point accuracy, however, were not significantly associated (r2 = 0.10, P = 0.15). The SDF was strongly associated with the overall error (r2 = 0.80, P <0.001), but only weakly associated with the ellipsoid (r2 = 0.18, P = 0.049). The overall error was predicted (r2 = 0.80, P = 0.001) equally from the error in force (r = 0.56) and time (r = 0.53). Further, end-point accuracy was also predicted by the impulse to peak force, which was highly associated with overall error (r2 = 0.81, P <0.001). Conclusion As predicted from the minimum-variance theory, endpoint accuracy during open-loop isometric contractions appears to be strongly related to the fluctuations in the force trajectory. The measure of end-point accuracy that is most sensitive to the fluctuations in the force trajectory, however, appears to be the distance from the target (overall error) and not the total variability of the responses (ellipsoid). Supported by NIA R03 AG024662-01 to EAC.

A note on minimum-variance theory and beyond

We revisit the minimum-variance theory proposed by Harris and Wolpert (1998 Nature 394 780–4), discuss the implications of the theory on modelling the firing patterns of single neurons and analytically find the optimal control signals, trajectories and velocities. Under the rate coding assumption, input control signals employed in the minimum-variance theory should be Fitts processes rather than Poisson processes. Only if information is coded by interspike intervals, Poisson processes are in agreement with the inputs employed in the minimum-variance theory. For the integrate-and-fire model with Fitts process inputs, interspike intervals of efferent spike trains are very irregular. We introduce diffusion approximations to approximate neural models with renewal process inputs and present theoretical results on calculating moments of interspike intervals of the integrate-and-fire model. Results in Feng, et al (2002 J. Phys. A: Math. Gen. 35 7287–304) are generalized. In conclusion, we present a complete picture on the minimum-variance theory ranging from input control signals, to model outputs, and to its implications on modelling firing patterns of single neurons.

Towards a mathematical foundation of minimum-variance theory

The minimum-variance theory which accounts for arm and eye movements with noise signal inputs was proposed by Harris and Wolpert (1998 Nature 394 780–4). Here we present a detailed theoretical analysis of the theory and analytical solutions of the theory are obtained. Furthermore, we propose a new version of the minimum-variance theory, which is more realistic for a biological system. For the new version we show numerically that the variance is considerably reduced.

The Brain-Like Sensorimotor Control System

In this paper, we propose brain-like (BL) sensorimotor control system that is assumed to be composed of its unconscious and conscious part. The conscious part of BL sensorimotor control system is emerged when Prefrontal Cortex (PFC) acts with respect to spatiotemporal selective attention mechanism in particular. In our framework, the selective attention can be induced by Baye's rule comprising of PFC-based neural network where both unsupervised and supervised learning schemes are employed. A preliminary experiment is manually carried out to analyse human control mechanism for the stability of RC-helicopter. As a result, we suggest the relationship between the selective attention and the minimum variance theory. BL sensorimotor control system is favorably considered to build subject to suffice the minimum variance theory that is the key for computing spatiotemporal selective attention mechanism, computed by the PFC-based neural network. In this paper, the network is also examined with respect to control the RC-helicopter and the result shows the soundness of BL sensorimotor control system.

Signal-dependent noise determines motor planning.

When we make saccadic eye movements or goal-directed arm movements, there is an infinite number of possible trajectories that the eye or arm could take to reach the target. However, humans show highly stereotyped trajectories in which velocity profiles of both the eye and hand are smooth and symmetric for brief movements. Here we present a unifying theory of eye and arm movements based on the single physiological assumption that the neural control signals are corrupted by noise whose variance increases with the size of the control signal. We propose that in the presence of such signal-dependent noise, the shape of a trajectory is selected to minimize the variance of the final eye or arm position. This minimum-variance theory accurately predicts the trajectories of both saccades and arm movements and the speed-accuracy trade-off described by Fitt's law. These profiles are robust to changes in the dynamics of the eye or arm, as found empirically. Moreover, the relation between path curvature and hand velocity during drawing movements reproduces the empirical 'two-thirds power law. This theory provides a simple and powerful unifying perspective for both eye and arm movement control.

Adaptive multi-layer self-tuning high performance tracking control for DC brushless motor

Adaptive control for high performance drive systems has become an important subject of research. In applications such as robotics, actuation, and manipulation, the rotor of the electric motor should follow a pre-selected track at all time. The tracking accuracy should not be affected by parameter uncertainties, unknown load variations, or sudden external disturbances. In this paper two schemes of adaptive control are developed and tested for a DC brushless motor. The first scheme is a single-layer self-tuning controller based on the generalized minimum variance theory. The second is a multi-layer adaptive controller consisting of a self-tuning control layer and a supervisory control layer. The supervisory controller continuously monitors the status of the system parameters, the structure of the controller, and the motor performance. A laboratory setup is constructed to test the proposed methods. Laboratory results show that the multi-layer controller is capable of achieving the tracking process with a high degree of accuracy, even in the presence of large and sudden disturbances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Heuristic Method for Measurement and Characterization of River Meander Wavelength

Historically, meander planform data have been analyzed by various statistical and geometrical techniques, but uncertainty persists about the wavelength, frequency, and reference geometry. Therefore meander wavelength was analyzed in the Fourier frequency domain by power spectral analysis in terms of hierarchical centerlines as a reference geometry, eliminating some of the subjective bias associated with wavelength measurements. Equally spaced sampling points were located along the talweg of meandering streams. Sample values were measured as the perpendicular distance to a reference line connecting meander belt midpoints. This line, itself meandering, constitutes a river's second‐order meander frequency, which is analyzed with respect to a still higher‐order reference line. Sampling along the talweg attenuates the spectral estimates of natural frequencies of meanders. Corrections are obtained by multiplying frequency peaks by the sinuosity of the study reach. Power spectra obtained from hierarchical reference lines of first‐ and second‐order meanders of the White River in southern Indiana indicate discrete frequencies in each order. First‐ and second‐order harmonics are observed at high and low frequencies. Complex meandering along the Dolores River in western Colorado is characterized by very low‐frequency energy in third‐order meanders and successively higher frequency energy in second‐ and first‐order meanders. A comparison of power spectra for hierarchical and arbitrary reference lines shows that arbitrary references condense spectral estimates of meander energy within artificially averaged frequency bands. Another comparison, using the theory of minimum variance for meander formation, confirms that hierarchical reference lines improve meander characterization.

The Inherent Asymmetry of River Meander Planform

Inspection of the planform of meandering rivers indicates that they are generally not symmetric but display at least two forms of asymmetry indicative of flow direction. One is downchannel delay in the inflection point of meanders, producing traverses (the part of the channel trace that crosses from one side of the valley to the other) which are dominantly convex facing down valley. The other is upvalley skew in the axis of gooseneck loops. An index of inflection asymmetry is presented and applied to 15 rivers: the data confirm the statistical preference for delayed inflection. An explanation of the phenomenon is offered based on the hydraulics of flow through bends. Of major importance appears to be the persistence downchannel of patterns of helical circulation and cross-sectional distribution of longitudinal velocity well past the bend that forms them. The upvalley skew of goosenecks is, in many cases, nothing more than an extreme form of convex-downvalley looping, maintained as meanders have increased their tortuosity. Some goosenecks, however, show no delayed inflection and appear to develop from differences in rates of downvalley migration between adjacent meander traverses. It is concluded that the minimum variance theory and sine-generated model of meanders should now be discarded.

Channel Geometry in the Riffle-Pool Sequence

Hypotheses developed to explain meandering in river channels often demand excess energy to initiate bank erosion, which is usually assumed to occur in the location of a pool. Field observations of variations of channel geometry in riffle-pool sequences on the River Fowey, Cornwall, England indicate that equilibrium channels can, however, be wider at riffles because of bank erosion at these locations. Further- more, the varying flow geometry suggests that the minimum variance theory of meandering may require reassessment.

THE ROLE OF MINIMUM VARIANCE THEORY IN DEFINING THE REGIME CHARACTERISTICS OF THE LOWER NAMOI‐GWYDIR DRAINAGE BASIN1

ABSTRACT: While minimum variance theory appears to offer an explanation for the hydraulic behaviour and regularity among channel systems it is not entirely successful in predicting the regime of a channel system. In the case of the Namoi‐Gwydir river system the hydraulic variables velocity, depth, width, slope, friction, and shear appear to govern the behaviour and, hence regime of the channels. The significance of sediment load in determining regime could not be assessed.