Number Of Necessary Components Research Articles

MaglevMotor: Design and optimisation of a novel hybrid linear actuator for 6 degrees of freedom rail‐passive Maglev carrier

AbstractA novel levitating hybrid linear actuator is proposed for magnetically levitated carrier systems. This hybrid linear actuator, “MaglevMotor”, is capable to levitate itself under the passive rail and thrusts itself in a single longitudinal direction. The proposed structure aims to reduce complexity by minimising the necessary number of components, resulting in simplified geometry, improved assembly convenience, and decreased manufacturing tolerances. The MaglevMotor is optimised in multi‐physics aspect. Optimisation objectives are maximising thrust force, minimising total mass and minimising mechanical deformation of yoke with constraints of a user defined magnetic flux density (B) in yoke and zero power condition for specific air gap value. The authors present pre‐optimisation studies, optimisation results and final MaglevMotor designs step by step. By utilising three of the MaglevMotors units, the carrier is able to achieve motion in six degrees of freedom. The carrier's performance targets, including a 0.2 G acceleration, a total mass of less than 10 kg, and a 5 mm levitation air gap, have been both attained and validated through corresponding experiments.

Orbital Uncertainty Propagation Based on Adaptive Gaussian Mixture Model under Generalized Equinoctial Orbital Elements

The number of resident space objects (RSOs) has been steadily increasing over time, posing significant risks to the safe operation of on-orbit assets. The accurate prediction of potential collision events and implementation of effective and nonredundant avoidance maneuvers require the precise estimation of the orbit positions of objects of interest and propagation of their associated uncertainties. Previous research mainly focuses on striking a balance between accurate propagation and efficient computation. A recently proposed approach that integrates uncertainty propagation with different coordinate representations has the potential to achieve such a balance. This paper proposes combining the generalized equinoctial orbital elements (GEqOE) representation with an adaptive Gaussian mixture model (GMM) for uncertainty propagation. Specifically, we implement a reformulation for the orbital dynamics so that the underlying state and the moment feature of the GMM are propagated under the GEqOE coordinates. Starting from an initial Gaussian probability distribution function (PDF), the algorithm iteratively propagates the uncertainty distribution using a detection-splitting module. A differential entropy-based nonlinear detector and a splitting library are utilized to adjust the number of GMM components dynamically. Component splitting is triggered when a predefined threshold of differential entropy is violated, generating several GMM components. The final probability density function (PDF) is obtained by a weighted summation of the component distributions at the target time. Benefiting from the nonlinearity reduction caused by the GEqOE representation, the number of triggered events largely decreases, causing the necessary number of components to maintain uncertainty realism also to decrease, which enables the proposed approach to achieve good performance with much more efficiency. As demonstrated by the results of propagation in three scenarios with different degrees of complexity, compared with the Cartesian-based approach, the proposed approach achieves comparable accuracy to the Monte Carlo method while largely reducing the number of components generated during propagation. Our results confirm that a judicious choice of coordinate representation can significantly improve the performance of uncertainty propagation methods in terms of accuracy and computational efficiency.

Adaptive denoising for chemical exchange saturation transfer MR imaging.

High image signal-to-noise ratio (SNR) is required to reliably detect the inherently small chemical exchange saturation transfer (CEST) effects in vivo. In this study, it was demonstrated that identifying spectral redundancies of CEST data by principal component analysis (PCA) in combination with an appropriate data-driven extraction of relevant information can be used for an effective and robust denoising of CEST spectra. The relationship between the number of relevant principal components and SNR was studied on fitted in vivo Z-spectra with artificially introduced noise. Three different data-driven criteria to automatically determine the optimal number of necessary components were investigated. In addition, these criteria facilitate straightforward assessment of data quality that could provide guidance for CEST MR protocols in terms of SNR. Insights were applied to achieve a robust denoising of highly sampled low power Z-spectra of the human brain at 3 and 7T. The median criterion provided the best estimation for the optimal number of components consistently for all three investigated artificial noise levels. Application of the denoising technique to in vivo data revealed a considerable increase in image quality for the amide and rNOE contrast with a considerable SNR gain. At 7T the denoising capability was quantified to be comparable or even superior to an averaging of six measurements. The proposed denoising algorithm enables an efficient and robust denoising of CEST data by combining PCA with appropriate data-driven truncation criteria. With this generally applicable technique at hand, small CEST effects can be reliably detected without the need for repeated measurements.

Aging Management in the Design of Nuclear Power Plants

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Dirichlet process Gaussian mixture models: choice of the base distribution

In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the "correct" number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture (DPM) models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model (DPGMM). We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.

Dirichlet Process Gaussian Mixture Models: Choice of the Base Distribution

In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the “correct” number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture (DPM) models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model (DPGMM). We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.

Dirichlet process Gaussian mixture models

In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of componen...

Human vertical jump at resonance

A mechanical model is proposed which quantitatively describes the dynamics of the centre of gravity (c.g.) during the take-off phase of the long jump. The model entails a minimal but necessary number of components: a linear leg spring with the ability of lengthening to describe the active peak of the force time curve and a distal mass coupled with nonlinear visco-elastic elements to describe the passive peak. The influence of the positions and velocities of the supported body and the jumper's leg as well as of systemic parameters such as leg stiffness and mass distribution on the jumping distance were investigated. Techniques for optimum operation are identified: (1) There is a minimum stiffness for optimum performance. Further increase of the stiffness does not lead to longer jumps. (2) For any given stiffness there is always an optimum angle of attack. (3) The same distance can be achieved by different techniques. (4) The losses due to deceleration of the supporting leg do not result in reduced jumping distance as this deceleration results in a higher vertical momentum. (5) Thus, increasing the touch-down velocity of the jumper's supporting leg increases jumping distance.

Dynamics of the long jump

A mechanical model is proposed which quantitatively describes the dynamics of the centre of gravity (c.g.) during the take-off phase of the long jump. The model entails a minimal but necessary number of components: a linear leg spring with the ability of lengthening to describe the active peak of the force time curve and a distal mass coupled with nonlinear visco-elastic elements to describe the passive peak. The influence of the positions and velocities of the supported body and the jumper's leg as well as of systemic parameters such as leg stiffness and mass distribution on the jumping distance were investigated. Techniques for optimum operation are identified: (1) There is a minimum stiffness for optimum performance. Further increase of the stiffness does not lead to longer jumps. (2) For any given stiffness there is always an optimum angle of attack. (3) The same distance can be achieved by different techniques. (4) The losses due to deceleration of the supporting leg do not result in reduced jumping distance as this deceleration results in a higher vertical momentum. (5) Thus, increasing the touch-down velocity of the jumper's supporting leg increases jumping distance.

Theoretical studies on the necessary number of components in mixtures

Theoretical studies on the necessary numbers of components in mixtures (for example multiclonal varieties or mixtures of lines) have been performed according to the relations between the juvenile-mature correlations of mixtures and their number of components. For the juvenile-mature correlation rE based upon the values of the single components (= component means at juvenile and mature ages) and the juvenile-mature correlation rM based upon the means of mixtures of different components we usually will have rM>rE. Furthermore, rM will increase with an increasing number of components in the mixtures. The effectiveness of an early selection will be mainly determined by the magnitude of the juvenile-mature correlation. If we have rM>rE an improvement of early testing can be realized by using mixtures instead of single components. But, what are the necessary numbers of components so that rM will be sufficiently high to enable an effective early selection of mixtures? Some relations between rE and rM can be obtained and conclusions have been derived.The statistical approach 'significant difference between rE and rM for a given numerical value of rM' leads to estimates for the necessary number n of components dependent on rM, α, rE and N where: N = total number of components, which are available for the composition of mixtures and α = error probability. For different tree species rE can be estimated by an appropriate formula which depends on T with T = time (in years) from planting date until the mature age.Lambeth's formula, for example, has been developed for height growth in pines. For this situation numerical calculations are performed using rM=0.90 and α=0.05. The necessary numbers n for T=5, T=10, T=20 and T=50 are: 6, 9, 10 and 12 (for N=50); 13, 17, 20 and 23 (for N=100); 26, 34, 40 and 46 (for N=200); 38, 51, 60 and 69 (for N=300); 64, 85, 100 and 114 (for N=500) and 128, 171, 199 and 228 (for N=1,000). The dependence of these necessary numbers n of components on different type I errors α and different levels of rM have been investigated numerically.

Theoretical studies on the necessary number of components in mixtures

Theoretical studies on the necessary numbers of components in mixtures (for example multiclonal varieties or mixtures of lines) have been performed according to risk considerations - using the binomial distribution and the Polya-distribution. The 'risk' r of a mixture has been defined as the probability of 'catastrophic' losses (catastrophe = decrease of productivity of q% or more by 'susceptibilities' of the components). Using 1) the binomial distribution and 2) its generalization, the Polya-distribution, and several simplifying assumptions, the risks r = r (x, a, q, n) have been calculated numerically (n = number of components in the mixture, a = parameter for the intensity of contagion and dispersion of 'susceptibilities' (for example: diseases and epidemics), x = probability of 'susceptibility'). The Polya-model reduces to the binomial case if a = 0. The main results are: 1. For each number n of components the risk r decreases markedly with decreasing x (for each q and for each a). 2. For x < = q the risk r decreases with an increasing number n of components (for each a). 3. For each number n of components and x and q with x < q the risk r increases with increasing a. 4. For given q, x and a the functions r = r(n) are asymptotic for larger numbers n of components with n > n(*). In spite of further increasing numbers of components in the mixture the risk remains almost constant. For all situations, where the risk decreases with increasing n these numbers n(*), therefore, can be considered as necessary numbers of components in mixtures, n(*) depends on q, x and a. Nevertheless, a global and rough conclusion can be formulated: In many situations one obtains necessary numbers of 30-40 components for a≠0 and 20-30 components for a = 0.

Theoretical studies on the necessary number of components in mixtures

Theoretical studies on the necessary number of components in mixtures (for example multiclonal varieties or mixtures of lines) have been performed according to yielding ability. All theoretical investigations are based upon a Gram-Charlier frequency distribution of the component means with skewness γ1 and kurtosis γ2. The selected fraction p of the best components constitutes the mixture under consideration. The same selection differential S = S (p, γ1, γ2) can be realized by different parameter values of p, γ1 and γ2. Therefore, equal yield levels of the mixture can be achieved by different selected fractions p which implies different numbers of components in the mixture. Numerical results of S = S(p) for different values of γ1 and γ2 are presented and discussed. Of particular interest are the selected fractions p which lead to a maximal selection differential S. These results on S for 'large populations' must be reduced in the case of finite population size. For this correction term we used an approximation B = B (p, n, γ1, γ2) given by Burrows (1972) where n = number of selected components. For given parameter values of γ1, γ2 and p, the necessary number n of components can be calculated by using the condition: Burrows-correction less than a certain percentage g of S - for example with g = 0.05 or g = 0.01. For given γ1 and γ2, the number n leading to a maximal selection differential S can be regarded as necessary number of components (necessary = maximum gain of selection under the given conditions). Numerical results are given for γ2 = 0 and for eight situations which are defined by linear relations γ2 = c γ1 between skewness and kurtosis. These cases will contain all possible numerical situations for γ1 and γ2, which may be relevant for practical applications. The necessary number of components turns out to be nearly independent of the numerical value of the kurtosis γ2. The n-intervals leading to selected fractions p from 0.01 to 0.20 approximately are: 2 ≤ n ≤ 4 for g = 0.05, 6 ≤ n ≤ 20 for g = 0.01 and 11 ≤ n ≤ 40 for g = 0.005, respectively. However, percentages g less than 0.01 would be unrealistically excessive. Therefore, following the assumptions and restrictions given in this paper one may conclude that n = 20 seems to be an appropriate upper bound for the necessary number of components in mixtures.

Theoretical studies on the necessary number of components in mixtures

Theoretical studies on the optimal numbers of components in mixtures (for example multiclonal varieties or mixtures of lines) have been performed according to phenotypic yield stability (measured by the parameter 'variance'). For each component i, i = 1, 2,..., n, a parameter ui with 0 ≦ ui ≦ 1 has been introduced reflecting the different survival and yielding ability of the components. For the stochastic analysis the mean of each ui is denoted by u 1 and its variance by σ i (2) For the character 'total yield' the phenotypic variance V can be explicitly expressed dependent on 1) the number n of components in the mixture, 2) the mean [Formula: see text] of the σ i (2) 3) the variance of the σ i (2) 4) the ratio [Formula: see text] and 5) the ratio σ i (2) /χ(2) where χ denotes the mean of the u i and σ u (2) is the variance of the u j. According to the dependence of the phenotypic stability on these factors some conclusions can be easily derived from this V-formula. Furthermore, two different approaches for a calculation of necessary or optimal numbers of components using the phenotypic variance V are discussed: A. Determination of 'optimal' numbers in the sense that a continued increase of the number of components brings about no further significant effect according to stability. B. A reduction of b % of the number of components but nevertheless an unchanged stability can be realized by an increase of the mean χ of the u i by 1% (with [Formula: see text] and σ u (2) assumed to be unchanged). Numerical results on n (from A) and 1 (from B) are given. Computing the coefficient of variation v for the character 'total yield' and solving for the number n of components one obtains an explicit expression for n dependent on v and the factors 2.-5. mentioned above. In the special case of equal variances, σ i (2) = σ o (2) for each i, the number n depends on v, x = (σ0/χ)(2) and y = (σu/χ)(2). Detailed numerical results for n = n (v, x, y) are given. For x ≦ 1 and y ≦ 1 one obtains n = 9, 20 and 79 for v = 0.30, 0.20 and 0.10, respectively while for x ≦ 1 and arbitrary y-values the results are n = 11, 24 and 95.