First-order Taylor Series Research Articles

Non-probabilistic wear reliability analysis of swash-plate/slipper of water hydraulic piston motor based on convex model

Water hydraulic piston motor is one of the important transmission components in a water hydraulic system. For lack of enough experimental information to analyze the reliability in water hydraulic motor design, the convex model is chosen as wear reliability model for hydraulic friction pairs, which is more economical and reasonable than the interval model. The non-probabilistic reliability index based on the convex model is established using first-order Taylor series expansion, and the non-probabilistic reliability model of wear reliability analysis for the friction pair of swash-plate/slipper in water hydraulic piston motor is introduced based on the convex model. For the non-probabilistic reliability model, only the bounds on uncertain parameters are needed, instead of probabilistic density distribution or statistical quantities. Numerical examples are used to illustrate the validity and feasibility of the presented method.

Interval analysis of acoustic field with uncertain-but-bounded parameters

This paper presents an interval perturbation finite element method (IPFEM) and a modified interval perturbation finite element method (MIPFEM) for the uncertain acoustic field prediction with uncertain-but-bounded parameters. The interval matrix and vector in both methods are expanded by the first-order Taylor series. The interval matrix inverse in IPFEM is approximated by the first-order Neumann series; however, the interval matrix inverse in MIPFEM is approximated by a modified Neumann expansion in which the higher order terms of Neumann series are considered. Numerical results demonstrate the accuracy of MIPFEM to evaluate the intervals of sound pressure response in acoustic field.

기준신호원을 이용한 배열센서의 위치, 이득, 위상 보정기법

The geometrical and electrical errors of array sensors can severely degrade the performance of array sensor system. Various calibration techniques are developed to alleviate this problem. In this paper, two different calibration methods with respect to location, gain and phase of array sensors are presented. One method applies the first-order Taylor series expansion to approximate the true steering vector from the nominal values of array sensors. Then a set of equations is formed by using the null characteristics of the MUSIC spectrum to estimate errors of location, gain and phase of array sensors. Another method estimates these errors based on the data covariance matrix of pilot sources. From the simulations, it is demonstrated that two calibration algorithms calibrated an array system successfully. In addition to that, Fistas and Manikas's algorithm is more robust against noise than Ng and Lie's one when SNR is from 10dB to 50dB.

Modified particle swarm optimization structure approach to direction of arrival estimation

This study considers the problem of estimating the direction-of-arrival (DOA) for code-division multiple access (CDMA) signals. In this type of problem, the associated cost function of the DOA estimation is generally a computationally-expensive and highly-nonlinear optimization problem. A fast convergence of the global optimization algorithm is therefore required to attain results within a short amount of time. In this paper, we propose a new application of the modify particle swarm optimization (MPSO) structure to achieve a global optimal solution with a fast convergence rate for this type of DOA estimation problem.The MPSO uses a first-order Taylor series expansion of the objective function to address the issue of enhanced PSO search capacity for finding the global optimum leads to increased performance. The first-order Taylor series approximates the spatial scanning vector in terms of estimating deviation results in and reducing to a simple one-dimensional optimization problem and the estimating deviation has the tendency to fly toward a better search area. Thus, the estimating deviation can be used to update the velocity of the PSO. Finally, several numerical examples are presented to illustrate the design procedure and to confirm the performance of the proposed method.

Improved Position Estimation Using Hybrid TW-TOA and TDOA in Cooperative Networks

This paper addresses the problem of positioning multiple target nodes in a cooperative wireless sensor network in the presence of unknown turn-around times. In this type of cooperative networks, two different reference sensors, namely, primary and secondary nodes, measure two-way time-of-arrival (TW-TOA) and time-difference-of-arrival (TDOA), respectively. Motivated by the role of secondary nodes, we extend the role of target nodes such that they can be considered as pseudo secondary nodes. By modeling turn-around times as nuisance parameters, we derive a maximum likelihood estimator (MLE) that poses a difficult global optimization problem due to its nonconvex objective function. To avoid drawbacks in solving the MLE, we linearize the measurements using two different techniques, namely, nonlinear processing and first-order Taylor series, and obtain linear models based on unknown parameters. The proposed linear estimator is implemented in three steps. In the first step, a coarse position estimate is obtained for each target node, and it is refined through steps two and three. To evaluate the performance of different methods, we derive the Cramer-Rao lower bound (CRLB). Simulation results show that the cooperation technique provides considerable improvements in positioning accuracy compared to the noncooperative scenario, especially for low signal-to-noise-ratios.

Interval Analysis Method for Structural Damage Identification Based on Multiple Load Cases

Based on the measured static displacements, an improved interval analysis technique was proposed for the structural damage identification. Due to the scarcity of uncertain information, the uncertainties were considered as interval numbers in this paper. Via the first-order Taylor series expansion, the interval bounds of the elemental stiffness parameters of undamaged and damaged structures are respectively obtained. The structural damage was detected by the quantitative measure of the possibility of damage existence in elements, which was more reasonable than the probability of damage existence in the condition of less sample points for the measurement data. Furthermore, the classic interval analysis method was improved by adopting the membership-set identification and two-step model updating procedure to make identification results more accurate. An uncertain truss structure was employed for damage identification, the damage identification results obtained by interval analysis method and probabilistic method, respectively, were compared. Moreover, the effects on the detection results of the damage level and uncertainty level subjected to single or multiple load cases were studied as well. The numerical example shows that the wide intervals resulting from the interval operation can be narrowed by the improved nonprobabilistic approach, and the feasibility and effectiveness of the present method were validated.

Disaggregation of SMOS Soil Moisture in Southeastern Australia

Disaggregation based on Physical And Theoretical scale Change (DisPATCh) is an algorithm dedicated to the disaggregation of soil moisture observations using high-resolution soil temperature data. DisPATCh converts soil temperature fields into soil moisture fields given a semi-empirical soil evaporative efficiency model and a first-order Taylor series expansion around the field-mean soil moisture. In this study, the disaggregation approach is applied to Soil Moisture and Ocean Salinity (SMOS) satellite data over the 500 km by 100 km Australian Airborne Calibration/validation Experiments for SMOS (AACES) area. The 40-km resolution SMOS surface soil moisture pixels are disaggregated at 1-km resolution using the soil skin temperature derived from Moderate Resolution Imaging Spectroradiometer (MODIS) data, and subsequently compared with the AACES intensive ground measurements aggregated at 1-km resolution. The objective is to test DisPATCh under various surface and atmospheric conditions. It is found that the accuracy of disaggregation products varies greatly according to season: while the correlation coefficient between disaggregated and in situ soil moisture is about 0.7 during the summer AACES, it is approximately zero during the winter AACES, consistent with a weaker coupling between evaporation and surface soil moisture in temperate than in semi-arid climate. Moreover, during the summer AACES, the correlation coefficient between disaggregated and in situ soil moisture is increased from 0.70 to 0.85, by separating the 1-km pixels where MODIS temperature is mainly controlled by soil evaporation, from those where MODIS temperature is controlled by both soil evaporation and vegetation transpiration. It is also found that the 5-km resolution atmospheric correction of the official MODIS temperature data has a significant impact on DisPATCh output. An alternative atmospheric correction at 40-km resolution increases the correlation coefficient between disaggregated and in situ soil moisture from 0.72 to 0.82 during the summer AACES. Results indicate that DisPATCh has a strong potential in low-vegetated semi-arid areas where it can be used as a tool to evaluate SMOS data (by reducing the mismatch in spatial extent between SMOS observations and localized in situ measurements), and as a further step, to derive a 1-km resolution soil moisture product adapted for large-scale hydrological studies.

An Improved Array-Error Estimation Method for Constellation SAR Systems

In this letter, we consider the problem of estimating gain-phase and position errors for constellation synthetic aperture radar (SAR) systems. In the conventional method, the position error estimation is based on the first-order Taylor series expansion of the position-error exponential function. However, the first-order Taylor series expansion causes an approximation error, resulting in the inaccuracy of the estimation by the conventional method. In this letter, an improved method is developed to overcome this problem, based on the fact that the aforementioned approximation error decreases with the reduction in position errors. In the improved method, we first compensate the position error estimates obtained at the kth iteration in order to reduce the remaining position errors at the (k + 1) th iteration. Then, the position error estimates obtained at all iterations are summed as the estimates of the true position errors. In this way, the improved method removes the aforementioned approximation error, leading to estimates with high accuracy. Simulation results verify that the estimates by the improved method are closer to the true array errors than those by the conventional method. In addition, simulation results show that the improved method is more robust to position errors than the conventional method. Furthermore, the increase in the computational load of the improved method is negligible.

Robust Capon beamformer based on direction search

In the presence of pointing errors, a direction search based robust Capon beamformer is proposed. The direction of the desired signal is first estimated by searching for the local maximum of the array output power using the first-order Taylor series expansion of the array steering vector, and then the robust Capon beamformer is developed with the estimated direction as the presumed one.

Efficient Propagation of Error Through System Models for Functions Common in Engineering

System modeling can help designers make and verify design decisions early in the design process if the model’s accuracy can be determined. The formula typically used to analytically propagate error is based on a first-order Taylor series expansion. Consequently, this formula can be wrong by one or more orders of magnitude for nonlinear systems. Clearly, adding higher-order terms increases the accuracy of the approximation but it also requires higher computational cost. This paper shows that truncation error can be reduced and accuracy increased without additional computational cost by applying a predictable correction factor to lower-order approximations. The efficiency of this method is demonstrated in the kinematic model of a flapping wing. While Taylor series error propagation is typically applicable only to closed-form equations, the procedure followed in this paper may be used with other types of models, provided that model outputs can be determined from model inputs, derivatives can be calculated, and truncation error is predictable.

Calibration-free wavelength modulated TDLAS under high absorbance conditions

Currently, the method that uses a first-order Taylor series to approximate laser transmission has seriously affected the gas concentration measurement accuracy of tunable diode laser-absorption spectroscopy (TDLAS). This paper employs a second-order Taylor series to approximate laser transmission, and a high-precision second-order algorithm has been established that can determine the gas concentration directly. Then, this algorithm is used to test the NH₃ mole fraction in a cell with NH₃-Air mixtures. Experimental results show that the second-order algorithm not only effectively improves the measurement accuracy of gas concentration but also greatly broadens the scope of TDLAS.

Reliability-Based Underseepage Analysis in Levees Using a Response Surface–Monte Carlo Simulation Method

Present methods for assessing the potential for unsatisfactory levee performance because of underseepage consist of deterministic seepage analyses and simplified reliability methods. Deterministic methods consist of calculating factors of safety based on the ratio of the critical gradients of the soil and hydraulic exit gradients without taking into account high levels of uncertainty in soil properties and subsur- face geometry that are inherent to many levee analyses. The most common simplified reliability approaches currently being used to analyze levees against underseepage apply the first-order second-moment Taylor series method, using the U.S. Army Corps of Engineers blanket theory equations as the performance functions. In many cases, these methods do not realistically reflect the geometry of the levee's foundation soils and the uncertainty associated with their performance. This study proposes a new application for the response surface method that allows modeling the initiation of erosion process with more accurate failure mechanisms and more complex subsurface geometry. The response surface-Monte Carlo (RSMC) simulation method uses finite-element analyses to develop a series of equations that define the relationship between the variables and the factor of safety (F). Using these equations, probability density functions (PDF) for variables, and the computer program @Risk, a Monte Carlo simulation is performed to calculate the conditional probability of unsatisfactory performance because of underseepage for a given river flood level. Two examples are presented to illustrate the proposed procedure. Multiple regression analyses are performed to assess the relative effect that changes in the input variables have on the F for the various analyses. The results suggest that uncertainty in the levee geometry has the greatest effect on the variation of the F for the cases studied. DOI: 10.1061/(ASCE)GT.1943-5606 .0000650. © 2012 American Society of Civil Engineers.

RESPONSE STATISTICS OF LINEAR STRUCTURES WITH UNCERTAIN-BUT-BOUNDED PARAMETERS UNDER GAUSSIAN STOCHASTIC INPUT

Uncertainty plays a fundamental role in structural engineering since it may affect both external excitations and structural parameters. In this study, the analysis of linear structures with slight variations of the structural parameters subjected to stochastic excitation is addressed. It is realistically assumed that sufficient data are available to model the external excitation as a Gaussian random process, while only fragmentary or incomplete information about the structural parameters are known. Under this assumption, a nonprobabilistic approach is pursued and the fluctuating properties are modeled as uncertain-but-bounded parameters via interval analysis. A method for evaluating the lower and upper bounds of the second-order statistics of the response is presented. The proposed procedure basically consists in combining random vibration theory with first-order interval Taylor series expansion of the mean-value and covariance vectors of the response. After some algebra, the sets of first-order ordinary differential equations ruling the nominal and first-order sensitivity vectors of response statistics are derived. Once such equations are solved, the bounds of the mean-value and covariance vectors of the response can be evaluated by handy formulas. To validate the procedure, numerical results concerning two different structures with uncertain-but-bounded stiffness properties under seismic excitation are presented.

IMC-PID tuning method based on sensitivity specification for process with time-delay

To overcome the deficiencies addressed in the conventional PID control and improve the dynamic performance and robustness of the system, a simple design and parameters tuning approach of internal model control-PID (IMC-PID) controller was proposed for the first order plus time-delay (FOPTD) process and the second order plus time-delay (SOPTD) process. By approximating the time-delay term of the process model with the first-order Taylor series, the expressions for IMC-PID controller parameters were derived, and they had only one adjustable parameter λ which was directly related to the dynamic performance and robustness of the system. Moreover, an analytical approach of selecting λ was given based on the maximum sensitivity Ms. Then, the robust tuning of the system could be achieved according to the value of Ms. In addition, the proposed method could be extended to the integrator plus time-delay (IPTD) process and the first order delay integrating (FODI) process. Simulation studies were carried out on various processes with time-delay, and the results show that the proposed method could provide a better dynamic performance of both the set-point tracking and disturbance rejection and robustness against parameters perturbation.

Generalized expressions of second and third order for the evaluation of standard measurement uncertainty

The Guide to the Expression of Uncertainty in Measurement (GUM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the measurement function is strongly non-linear the use of this linear approximation may be inadequate and therefore higher order terms from the Taylor series cannot be neglected. The present paper aims to derive generalized expressions of second and third order for the evaluation of the estimate of a measurand and its associated standard uncertainty. A case study is given to illustrate an application of the proposed methods and the results obtained with the GUM method are compared to the corresponding ones when applying the method proposed in GUM Supplement 1.

Accurate phase expansion on reference planes in grating projection profilometry

A novel phase expansion technology based on a binary quadratic rational polynomial model is proposed. Firstly, the unwrapped phase distribution on reference planes parallel with a zero reference plane in a different grating project profilometry measurement system is analyzed and synthesized. Then a binary quadratic rational polynomial model is proposed to express the uneven phase distribution on every reference plane. The least-squares iterative estimation method based on a first-order Taylor series expansion is employed to obtain the polynomial coefficients. Finally, accurate phase expansion of reference planes is implemented according to the rational polynomial model. The results of the experiments proved that the method proposed in this paper can recover the phase distribution on the full field from parts reference planes, and the measurement errors such as the geometrical parameter error, system structure error, real reference plane profile error and random error can be decreased.

Analysis of Interventions Influencing or Reducing Patient Waiting While Stratifying by Surgical Procedure

Facilitation of the coordination of presurgical care is desirable not only from the patients' perspective, but also for increasing operating room productivity of surgeons and anesthesiologists. Times from each patient's first referral to a surgeon until surgery will be available on a vast scale from regional health information exchanges. Treatments (interventions) can include, for example, case management and use of health system networks with common electronic medical records. We developed a method to compare waiting times between treatment (intervention) groups, while stratifying by procedure, despite (1) highly skewed but non-lognormally distributed data, (2) highly heterogeneous sample sizes among groups and procedures, and (3) many combinations of groups and procedures with small sample sizes, resulting in estimated means and variances having substantial uncertainty. Corresponding results obtained by analyzing data from a health system were as follows. (1) The method uses a random-effects model to accommodate procedure heterogeneity and is otherwise distribution free. Log transformation reduced the skewness in waiting time data, making the distribution-free first-order Taylor series approximation analysis of proportional changes between treatments (interventions) reasonable. However, when instead of the random-effects distribution-free analysis, the assumption was made of lognormal distributions, the estimate of treatment effect was biased. (2) Repeating the analysis without stratification by procedure also resulted in biased estimates. (3) There are nearly an unlimited number of different procedures, most rare, so that considering procedure as a random effect was appropriate. Over the ranges of estimated parameter values, prior Monte-Carlo simulation studies showed that meta-analysis using the simple method of moments was appropriate. However, because many treatment/procedure combinations have small sample sizes, confidence interval coverage for the treatment effect was too narrow other than when the degrees of freedom were corrected. Nevertheless, the resulting statistical methodology is straightforward to apply because the data needed are just the summary statistics and the method involves just a series of equations to be followed in a stepwise manner (e.g., in a spreadsheet program such as Microsoft Office Excel).

Nonlinear fixed and random generalized height–diameter models for Portuguese cork oak stands

The objective of the research was to develop a generalized height–diameter model for Quercus suber L. in Portugal, which can be applied both to undebarked and debarked trees, with diameter at breast height over cork larger than 2.5 cm. A nonlinear fixed effects model (NLFEM) and a nonlinear mixed effects model (NLMEM) approaches were used. Parameters estimates were obtained using the SAS macro NLINMIX, which uses a linear approximation to the marginal likelihood function by expanding it with a first-order Taylor series on the random effects. The option of expanding on the random effects at their current empirical best linear unbiased predictors (EBLUP) was used. The fitted models were evaluated using an independent data set, together with an existing model specific for undebarked trees. To obtain subject specific predictions with the NLMEM, a conventional and an improved calibration procedures were applied, considering four different tree sub-sampling designs. Both proposed models included dominant height and stand density as covariates to explain plot variability. Validation indicated that, even in the situations where the NLMEM calibration is not possible, this model should be preferred. The differences between the validated models, which were more evident for young stands, were considered. No large differences in predictive accuracy were found between the calibrated NLMEM using the conventional or the improved calibration procedures, for all the considered sub-sampling designs.

Adjusted intraclass correlation coefficients for binary data: methods and estimates from a cluster-randomized trial in primary care

Accurate estimates of the intraclass correlation coefficient (ICC) are important for calculating appropriate sample sizes for cluster-randomized trials. The ICC and hence the sample size may be reduced through adjustment for baseline covariates. A method exists for calculating adjusted ICCs for binary outcomes based on the logit link, used to calculate odds ratios. Recent interest in presenting relative risks rather than odds ratios indicates that a method based on the log link is needed. To determine and evaluate a method for calculating adjusted ICCs based on the log link, and to provide and compare unadjusted and adjusted ICCs from a cluster-randomized trial in primary care based on the logit and log link. Two methods are proposed for calculating adjusted ICCs for the log link based on a first-order Taylor series expansion and properties of the lognormal distribution. The methods are evaluated by simulation. Unadjusted and adjusted ICCs are calculated for binary outcomes from the Point of Care Testing (PoCT) Trial using the logit and log link. The methods for calculating adjusted ICCs for the log link produced similar results unless the between cluster variance was large. Unadjusted ICCs for the PoCT Trial ranged from 0.001 to 0.048. The impact of adjustment on the ICC varied between outcomes and link functions, ranging from a 59% reduction to an 89% increase. The true ICC was unknown for the simulation study. Adjustment was made for age and gender only for the PoCT Trial. The method for calculating adjusted ICCs for binary outcomes depends on the link function. For the log link, the method based on the lognormal distribution is recommended. This method will be useful for cluster-randomized trials where the relative risk, rather than the odds ratio, is the effect measure of interest.

Grand canonical ensemble molecular dynamics simulation of water solubility in polyamide-6,6

Grand canonical ensemble molecular dynamics simulation is employed to calculate the solubility of water in polyamide-6,6. It is shown that performing two separate simulations, one in the polymeric phase and one in the gaseous phase, is sufficient to find the phase coexistence point. In this method, the chemical potential of water in the polymer phase is expanded as a first-order Taylor series in terms of pressure. Knowing the chemical potential of water in the polymer phase in terms of pressure, another simulation for water in the gaseous phase, in the grand canonical ensemble, is done in which the target chemical potential is set in terms of pressure in the gas phase. The phase coexistence point can easily be calculated from the results of these two independent simulations. Our calculated sorption isotherms and solubility coefficients of water in polyamide-6,6, over a wide range of temperatures and pressures, agree with experimental data.