Moment Uncertainty Research Articles

Control Methods of Active Front Wheel Steering for 4WD Electric Vehicle

Based on two freedom degrees of vehicle model, control method which takes yaw rate and sideslip angle as system state, and front wheel corner and direct yaw moment as control input is put forward. Considering uncertainty of velocity and direct yaw moment, feedforward-feedback controllers are designed. Four wheel drive force are allocated by using feedforward compensation and yaw moment which is formed by driving force difference value. It makes yaw rate and sideslip well of tracking the desirable model when the vehicle drive steering. Finally, vehicle handling stability is studied on conditions of step input and sine input by simulation.

Analysis and Attitude Control of Spacecraft with Input Uncertainty

A moving mass control of rotating spacecraft is a kind of new control mode, it differs from other control modes because it generates an angle of attack and an angle of sideslip directly from the mass motion.The nonlinear equations of motion for rotating Maneuverable Spacecraft are derived. the variable structure attitude controller is presented according to the nonlinear equations, It’s based on two-timescale separation and with two loops, faster loop and slower loop respectively. Inertial uncertainties and aerodynamic moment uncertainties are considered simultaneously, In order to track the command signals perfectly, the sliding surface is of integral form, results of the simulation shows that this kind of attitude control system is potentially practical and robust in the presence of inertial uncertainties of guided missile and uncertainties of aerodynamic moments. Compared with the common attitude control system, it has the following advantages:(1) non linear model is directly controlled,(2)it has robust. Because the non-linear factor is considered, it has the practical use for the engineering field.

Constraints on the long-period moment-dip tradeoff for the Tohoku earthquake

Since the work of Kanamori and Given (1981), it has been recognized that shallow, pure dip-slip earthquakes excite long-period surface waves such that it is difficult to independently constrain the moment (M_0) and the dip (δ) of the source mechanism, with only the product M_0 sin(2δ) being well constrained. Because of this, it is often assumed that the primary discrepancies between the moments of shallow, thrust earthquakes are due to this moment-dip tradeoff. In this work, we quantify how severe this moment-dip tradeoff is depending on the depth of the earthquake, the station distribution, the closeness of the mechanism to pure dip-slip, and the quality of the data. We find that both long-period Rayleigh and Love wave modes have moment-dip resolving power even for shallow events, especially when stations are close to certain azimuths with respect to mechanism strike and when source depth is well determined. We apply these results to USGS W phase inversions of the recent M9.0 Tohoku, Japan earthquake and estimate the likely uncertainties in dip and moment associated with the moment- dip tradeoff. After discussing some of the important sources of moment and dip error, we suggest two methods for potentially improving this uncertainty.

Verification and validation of CFD predictions for a manoeuvring tanker

This paper presents a study on the Verification and Validation (V&V) of CFD solutions for a tanker without appendages manoeuvring at varying drift angles and water depths. A steady state Reynolds-Averaged Navier-Stokes solver is applied to solve the viscous flow around the ship neglecting the free surface, sinkage and trim. Discretization errors and uncertainties in hydrodynamic forces and moments are estimated through grid convergence studies. Validation is performed by comparison with model test data.

Assessment of the Propagation of Uncertainty on Link Segment Model Results

Link segment models are usually used to calculate proximal net reaction forces (PRF), as well as, proximal net moments (PNM). The correlation between electromyographic data and PNM is usually used to verify the model's results. Nevertheless, this method permits only a qualitative verification of the obtained results. To assess model's results in a quantitative perspective, another approach is needed. The aim of the current study was to assess the propagation of uncertainty on a link segment model results and identify the main sources of error on the quantification of PRF and PNM. One male performed five repetitions of different upper limb movements. An inverse dynamics approach associate with 3D link segment model was used to quantify PRF and PNM. The results of the model were evaluated by the use of Kleine and McClintock's equation. The propagation of uncertainty for PRF reached, on average, 0.27 and for PNM, 0.97. The main cause of propagation of uncertainty was associated to the second time derivative calculations. Consequently, it is possible to suggest that the reduction of small distortions of center of mass acceleration will diminish the proximal net moment and proximal reaction force uncertainty values.

Moment tensor inversion of nine events in Iran using INSN data

In this research, moment tensor (MT) inversion procedure in frequency domain is applied to nine events in order to evaluate the data efficiencies in computing source parameters of earthquakes in Iran. The events are recorded by Iranian National Seismological Network (INSN) stations, currently comprising 22 broadband stations. For the purpose of this study, first, the inversion procedure is applied to obtain source parameters. Then, the results obtained here are compared with those of Harvard global centroid moment tensors (GCMT) in order to estimate their reliabilities. The results show reasonable consistencies with those of Harvard GCMT within 0.075 uncertainties in logarithmic scalar moment or 0.05 in moment magnitude and 20° in Kagan angle for focal angles. Furthermore, according to the present research, the calculated source parameters are not significantly sensitive to the azimuthal gap.

Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

Stochastic programming can effectively describe many decision-making problems in uncertain environments. Unfortunately, such programs are often computationally demanding to solve. In addition, their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix). We demonstrate that for a wide range of cost functions the associated distributionally robust (or min-max) stochastic program can be solved efficiently. Furthermore, by deriving a new confidence region for the mean and the covariance matrix of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. These arguments are confirmed in a practical example of portfolio selection, where our framework leads to better-performing policies on the “true” distribution underlying the daily returns of financial assets.

Earthquake size distribution: Power-law with exponent [formula omitted

We propose that the widely observed and universal Gutenberg–Richter relation is a mathematical consequence of the critical branching nature of earthquake process in a brittle fracture environment. These arguments, though preliminary, are confirmed by recent investigations of the seismic moment distribution in global earthquake catalogs and by the results on the distribution in crystals of dislocation avalanche sizes. We consider possible systematic and random errors in determining earthquake size, especially its seismic moment. These effects increase the estimate of the parameter β of the power-law distribution of earthquake sizes. In particular, we find that estimated β-values may be inflated by 1–3% because relative moment uncertainties decrease with increasing earthquake size. Moreover, earthquake clustering greatly influences the β-parameter. If clusters (aftershock sequences) are taken as the entity to be studied, then the exponent value for their size distribution would decrease by 5–10%. The complexity of any earthquake source also inflates the estimated β-value by at least 3–7%. The centroid depth distribution also should influence the β-value, and an approximate calculation suggests that the exponent value may be increased by 2–6%. Taking all these effects into account, we propose that the recently obtained β-value of 0.63 could be reduced to about 0.52–0.56: near the universal constant value (1/2) predicted by theoretical arguments. We also consider possible consequences of the universal β-value and its relevance for theoretical and practical understanding of earthquake occurrence in various tectonic and Earth structure environments. Using comparative crystal deformation results may help us understand the generation of seismic tremors and slow earthquakes and illuminate the transition from brittle fracture to plastic flow.

Robust oscillation control of wheeled mobile robots

In cases where a wheeled mobile robot runs fast on a rough surface, the sensors mounted on the robot’s body may be destroyed due to the body acceleration and oscillation. In this article, we propose a new scheme to reduce the body acceleration at any specified location for mobile robots with the actuators set on the wheel axes. To achieve this, a combined ideal robot model is designed. In the combined ideal robot model, the location where the acceleration performance is at its best can easily be moved by setting only two design parameters. Next, a robust model tracking controller is developed so that the behavior of an actual mobile robot can track the combined ideal robot model. The developed controller has the following useful properties. (1) The body acceleration at any specified location can easily be improved. (2) The developed controller has good robustness for uncertainties in robot mass, pitch and roll moment of inertia of the robot’s body, and the position of the center of gravity.

Determination of the Newtonian Gravitational ConstantGwith Time-of-Swing Method

We present a new value of the Newtonian gravitational constant G by using the time-of-swing method. Several improvements greatly reduce the uncertainties: (1) measuring the anelasticity of the fiber directly; (2) using spherical source masses minimizes the effects of density inhomogeneity and eccentricities; (3) using a quartz block pendulum simplifies its vibration modes and minimizes the uncertainty of inertial moment; (4) setting the pendulum and source masses both in a vacuum chamber reduces the error of measuring the relative positions. By two individual experiments, we obtain G = 6.673 49(18) x 10;{-11} m;{3} kg;{-1} s;{-2} with a standard uncertainty of about 2.6 parts in 10;{5}.

On the Determination of Partial Molar Polarizations and Dipole Moments of Solutes from Multicomponent Solutions Alone: Experimental and Model Development Using Deutero-Labeled Organic Compounds

A general inverse problem methodology is introduced to determine the partial molar polarizations and the dipole moments of individual solutes from multicomponent solutions alone. A model quaternary system consisting of three deuterated solutes, for example, acetone-d6, acetonitrile-d3, and dimethylformamide-d7 in cyclohexane at 298.15 K and 0.1013 MPa, was studied. Following an experimental design protocol, multicomponent solutions in the range of concentration 0.0006 < x(solute i) < 0.0085 were prepared using a semi-batch procedure by injecting one solute at a time. In situ FTIR spectroscopic measurements of these quaternary solutions were performed together with simultaneous condensed-phase bulk measurements of density, refractive index, and relative permittivity. Three different numerical approaches were used to determine the individual limiting solute molar polarizations from the multicomponent solutions. These limiting molar polarizations were then used to calculate the individual solute dipole moments using the Debye formula. In addition, direct dipole moment calculations were performed using the Guggenheim-Smith formula where individual solute parameters were obtained from multivariate analysis of the multicomponent solution data. Response surface models played a central role in many of the inverse problems. The results of the various methods are compared. In general, the dipole moments of all solutes from multicomponent solutions were in good agreement with those determined from independent binary experiments. Additionally, numerical sensitivity analysis was performed in order to identify the significant contributions to dipole moment uncertainty. The general approach introduced in the present contribution can be applied to a wide range of systems.

The Magnetometer Instrument on MESSENGER

The Magnetometer (MAG) on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission is a low-noise, tri-axial, fluxgate instrument with its sensor mounted on a 3.6-m-long boom. The boom was deployed on March 8, 2005. The primary MAG science objectives are to determine the structure of Mercury’s intrinsic magnetic field and infer its origin. Mariner 10 observations indicate a planetary moment in the range 170 to 350 nT R3 M (where RM is Mercury’s mean radius). The uncertainties in the dipole moment are associated with the Mariner 10 trajectory and variability of the measured field. By orbiting Mercury, MESSENGER will significantly improve the determination of dipole and higher-order moments. The latter are essential to understanding the thermal history of the planet. MAG has a coarse range, ±51,300 nT full scale (1.6-nT resolution), for pre-flight testing, and a fine range, ±1,530 nT full scale (0.047-nT resolution), for Mercury operation. A magnetic cleanliness program was followed to minimize variable and static spacecraft-generated fields at the sensor. Observations during and after boom deployment indicate that the fixed residual field is less than a few nT at the location of the sensor, and initial observations indicate that the variable field is below 0.05 nT at least above about 3 Hz. Analog signals from the three axes are low-pass filtered (10-Hz cut- off) and sampled simultaneously by three 20-bit analog-to-digital converters every 50 ms. To accommodate variable telemetry rates, MAG provides 11 output rates from 0.01 s“1 to 20 s-1. Continuous measurement of fluctuations is provided with a digital 1-10 Hz bandpass filter. This fluctuation level is used to trigger high-time-resolution sampling in eight-minute segments to record events of interest when continuous high-rate sampling is not possible. The MAG instrument will provide accurate characterization of the intrinsic planetary field, magnetospheric structure, and dynamics of Mercury’s solar wind interaction.

Sources of elastic deformations in steel frame and framed-tube structures: Part 2: Detailed subassemblage models

This paper examines the accuracy of a set of equations for computing Displacement Participation Factors (DPFs) for beam–column subassemblages of steel moment resisting frame buildings. These factors allow the analyst to determine how the entire subassemblage or individual components of a subassemblage contribute to a given structural displacement. Additionally, the component’s contribution to displacement may be evaluated in terms of sources of axial, flexural, or shear deformation. When applied to a set of 12 isolated subassemblages, it was shown in Part 1 of the paper that deformations in the beam–column joint are very significant, and that flexural deformation in the joint, which is often ignored, should be considered in all analyses. The total displacement predicted through the use of the DPFs correlates extremely well with the results of detailed three dimensional finite element analyses of the same subassemblages. However, it was also shown that there is considerable uncertainty in the bending moments and moments of inertia that are used to compute joint flexural deformations. The objective of this paper, which is the second part of a two-part paper, is to further investigate the accuracy of the DPF expressions developed in Part 1. This is done by computing DPFs from the results of detailed three dimensional finite element analysis, and comparing these to those computed through the use of the simple expressions. The results of the analysis show that the joint flexural deformations are accurately predicted by the simple DPF expressions, but that this accuracy arises from compensating “errors” in the simplified analysis. It is also shown that the use of beam flange continuity plates has a marginal effect on computed displacements. The paper ends with recommendations for using the simplified expressions for computing subassemblage deformations, and for including such deformations in structural analysis of steel frame and tube structures.

SU‐FF‐I‐87: Qualifying Magnetic Moments in Small Cylindrical Objects by Complex Sum Method

Purpose: Our ultimate goal is to quantify magnetic moments of small cylindrical objects in‐vivo from MR images, without any a priori information. We want to achieve this goal with the complex sum method [1,2]. Methods: Simulation procedures and the experimental setups were described in [1]. The magnetic moment is defined as . The magnetic moment of an object is proportional to the phase values around the object in MR phase images. Three concentric circles were chosen on a phase image with radii R1, R2 and R3. In the simulations, if the magnetic moment is known in advance, the phase values around the object can be used to determine the radii, using formulas in [3]. Each radius has to be larger than the size of the phase aliasing area[2]. Knowing the radii can be used to determine the magnetic moment of the object [2]. We also study the uncertainties of the magnetic moment with the presence of both systematic and thermal noises through error propagation methods. A gel image is also analyzed. Results: For the uncertainty studies, we found that the phase combination (φ1,φ2,φ3)=(3,2,1), in units of radians, leads to an uncertainty of the magnetic moment within 3% of the expected moment, which seems to be the lowest uncertainty. Using this phase combination and the known magnetic moment −5.78 ppm‐mm2 from gel data [1], we were able to determine those three radii and then solve the magnetic moment between the gel‐air interface. The result is −5.53 ppm‐mm2 which is within 5% uncertainty of the expected value.Conclusions: We have shown that the current method is feasible of extracting the magnetic moment of a small cylindrical object within good accuracy.

Quantifying uncertainty due to random errors for moment analyses of breakthrough curves

The uncertainty in moments calculated from breakthrough curves (BTCs) is investigated as a function of random measurement errors in the data used to define the BTCs. The method presented assumes moments are calculated by numerical integration using the trapezoidal rule, and is theoretically applicable to moments of any order. Moreover, the method is applicable to either temporal or volumetric moments, and in the latter case, explicitly accounts for errors in volume measurements. The complexity of the calculations for the zeroth moment is comparable to that associated with the typical propagation-of-errors formula based on a Taylor series expansion. However, the formulae for higher moments are substantially more complex than the typical propagation-of-errors formula. For the zeroth and normalized first moments, moment uncertainties are more sensitive to random errors in concentration measurements compared to random errors in volume measurements. The robust nature of moment calculations is exemplified by the fact that relative uncertainty in moments is less than the relative error in volume and concentration measurements. Furthermore, moment uncertainty decreases as more data points are collected to define the BTC. For a BTC (based upon the solution to the one-dimensional advective-dispersion equation with a Peclet number of 10) with 100 data points, the zeroth moment and normalized first moment coefficient of variations are approximately 6 and 2%, respectively, for concentration coefficient of variation equal to 25% over a range of volume errors.

Theoretical study of the rovibrationally resolved transitions of CaH

Comprehensive absorption line lists for CaH40 have been calculated for electronic transitions from the X 2Σ+ ground state to the A 2Π, B/B′ 2Σ+, and E 2Π low-lying excited states. The lists include transition energies and oscillator strengths for all possible allowed transitions and were computed using the most recent set of theoretical potential energy curves and dipole transition moment functions, with adjustments to account for experimental dissociation energies and asymptotic limits. Good agreement with previous calculations and available experimental data has been obtained. Oscillator strengths for the transition from the X 2Σ+ state to the D 2Σ+ state are also given, but due to the large uncertainty of the available dipole transition moment function the line list is highly uncertain. For the C 2Σ+←X 2Σ+ transition, a Franck–Condon approximation has been used.

Uncertainty in Second Moments: Implications for Portfolio Allocation

This paper investigates the uncertainty in second moments of asset returns. It is commonly believed that the second moments are accurately measured. However, time varying volatility and nonnormality of returns can lead to imprecise variance estimates. Using CRSP value weighted monthly returns from 1926 to 2001, the paper shows that the variance is less accurately estimated than the expected return. In addition, a mean variance investor will incur significant certainty equivalent loss due to the uncertainty in second moments. Applying the Fama French 3 factor model to 25 size, BE/ME sorted portfolios from 1963 to 2001, the loss due to the second moment estimation can be shown to be as large as the loss due to the first moment estimation. Moreover, as the number of assets in the portfolio increases, the loss due to the uncertainty in second moments becomes larger. This provides a possible explanation to the home bias puzzle.

Seismic moment distribution revisited: I. Statistical results

SUMMARY An accumulation of seismic moment data gathered over the previous decade justifies a new attempt at a comprehensive statistical analysis of these data: herein, more rigourous statistical techniques are introduced, their properties investigated, and these methods are employed for analysis of large modern data sets. Several theoretical distributions of earthquake size (seismic moment‐frequency relations) are described and compared. We discuss the requirements for such distributions and introduce an upper bound or a ‘corner moment’ for a distribution to have a finite energy or moment flux. We derive expressions for probability density functions and statistical moments of the distributions. We also describe parameter evaluation, in particular how to estimate the seismic moment distribution for the largest earthquakes. Simulating earthquake size distributions allows for a more rigourous evaluation of distribution parameters and points to the limitations of the classical statistical analysis of earthquake data. Simulations suggest that several earthquakes approaching or exceeding the corner magnitude (mc) limit need to be registered to evaluate mc with reasonable accuracy. Using the Harvard catalogue data, we compare moment distribution parameters for various temporal spans of the catalogue, for different tectonic provinces and depth ranges, and for earthquakes with various focal mechanisms. The statistical analysis suggests that the exponent b is universal (b=0.60‐0.65) for all moderate earthquakes. The corner moment (Mc) value, determined by the maximum-likelihood method, both in subduction zones and globally, is about 10 21 N m, corresponding to the corner moment magnitude mc#8.0. For midoceanic earthquakes, mc is apparently smaller for spreading ridges, it is about 5.8, and for strike-slip earthquakes on transform faults it decreases from 7.2 to 6.5 as the relative slip velocity of faults increases. We investigate the seismic moment errors, both random and systematic, and their dependence on earthquake size. The relative errors seem to decrease for larger events. The influence of moment uncertainties on the parameter estimates is studied. Whereas the b values do not appear to be significantly influenced by the errors, for the corner moment large errors can lead to substantially biased estimates. We compare the Harvard catalogue results with the earthquake data from instrumental catalogues in the first three-quarters of the 20th century. Several very large earthquakes (mi9) occurred around the middle of the century. Their magnitude values cannot be fitted by a modified Gutenberg‐Richter law with mc=8.0‐8.5. Among other factors, this discrepancy can be explained by either substantially higher errors in the earlier magnitude values, or by mc being higher for some subduction zones. It is unlikely that data available presently or soon will be sufficient to determine the corner magnitude of 9 and above, with reasonable precision, using purely statistical methods.

Uncertainty analysis of the BIPM susceptometer

A magnetic susceptometer developed at the Bureau International des Poids et Mesures (BIPM) is used by many national laboratories to determine the magnetic properties of stainless-steel mass standards. This device relies on a small, cylindrical magnet to simulate a magnetic point dipole. According to simple theoretical considerations, (a) the uncertainty in the magnetic moment contributes weakly to the combined uncertainty of any measured susceptibility provided that unknowns are measured relative to a standard of similar size; (b) a cylindrical magnet with a height-to-diameter ratio of 0.87 best approximates a point dipole; and (c) the magnetic moment of the cylindrical magnet used can be determined by the susceptometer itself. Experimental tests of these assertions are presented. The properties of the cylindrical magnet generally become more important when determining the susceptibility of "small"-sized samples relative to a "large" standard. Small samples provide additional challenges, which are discussed in the context of a more general uncertainty analysis.

Measurement of the gravitational constant G in space (SEE project): sensitivity to orbital parameters and space charge effect

We describe some new estimates concerning the recently proposed SEE (Satellite Energy Exchange) experiment for measuring the gravitational interaction parameters in space. The experiment entails precision tracking of the relative motion of two test bodies (a heavy ''Shepherd'', and a light ''Particle'') on board a drag-free space capsule. The new estimates include (i) the sensitivity of Particle trajectories and G measurement to the Shepherd quadrupole moment uncertainties; (ii) the measurement errors of G and the strength of putative Yukawa-type force whose range parameter λ may be either of the order of a few metres or close to the Earth radius; (iii) a possible effect of the Van Allen radiation belts on the SEE experiment due to test-body electric charging. The main conclusions are that (i) the SEE concept may allow G to be measured with an uncertainty of less tha 1 part in 107 and progress up to two orders of magnitude is possible in the assessment of possible Yukawa forces and (ii) Van Allen charging of test bodies is a significant problem but it may be solved by existing methods.