Optimal Sampling Interval Research Articles

Optimal design on digital filter algorithm of Hankel transform

This study investigates the influence of the parameter c of Hankel transform pairs and sampling interval s on the digital filter of Hankel transform based on the idea of Hankel digital filtering algorithm proposed by Kong. The results show that the selection of the parameter c highly influence the precision of digital filter algorithm, i.e., an inappropriate c can induce algorithm errors. Upon the optimal selection of the parameter c and the constant length of the digital filter, it is found that an optimal sampling interval s also exists to achieve the best precision of digital filter algorithm. Finally, this study proposes six groups of 0-, 1-order Hankel transform digital filters with different length and promote its application.

Ultrafast photonic reinforcement learning based on laser chaos

Reinforcement learning involves decision making in dynamic and uncertain environments and constitutes an important element of artificial intelligence (AI). In this work, we experimentally demonstrate that the ultrafast chaotic oscillatory dynamics of lasers efficiently solve the multi-armed bandit problem (MAB), which requires decision making concerning a class of difficult trade-offs called the exploration–exploitation dilemma. To solve the MAB, a certain degree of randomness is required for exploration purposes. However, pseudorandom numbers generated using conventional electronic circuitry encounter severe limitations in terms of their data rate and the quality of randomness due to their algorithmic foundations. We generate laser chaos signals using a semiconductor laser sampled at a maximum rate of 100 GSample/s, and combine it with a simple decision-making principle called tug of war with a variable threshold, to ensure ultrafast, adaptive, and accurate decision making at a maximum adaptation speed of 1 GHz. We found that decision-making performance was maximized with an optimal sampling interval, and we highlight the exact coincidence between the negative autocorrelation inherent in laser chaos and decision-making performance. This study paves the way for a new realm of ultrafast photonics in the age of AI, where the ultrahigh bandwidth of light wave can provide new value.

Application of the information approach to the analysis of two-year microwave observations of the atmosphere by the RPG-HATPRO radiometer at St. Petersburg University

ABSTRACTSince June 2012 the ground-based microwave (MW) radiometer RPG-HATPRO (Radiometer Physics GmbH – Humidity and Temperature Profiler) G3 (generation 3) has been operating at the Faculty of Physics of St. Petersburg State University in constant mode with sampling interval of 1–2 s. The results of MW radiation brightness temperature measurements in 14 spectral channels of the RPG-HATPRO radiometer have been analysed for the time period December 2012 to November 2014. Within this time period, different data ensembles are compiled that have different duration and describe the variety of atmospheric situations at the observational site. Two different approaches are used for the assessment of the information characteristics of MW measurements. The first one is based on calculation of Shannon’s information content that characterizes the number of atmospheric states distinguishable by measurements. We use the modification proposed by Kozlov – the ‘information volume’ approach. The second approach is based on calculation of the information quantity that characterizes the degree of correlation between measurements and atmospheric state parameter variations. The information quantities are calculated and analysed for the complete set of spectral channels and for two subsets that comprised seven so-called ‘temperature’ and seven so-called ‘humidity’ channels separately. Kozlov’s ‘information volume’ approach is also applied to the problem of estimation of the optimal sampling interval of MW measurements. It is shown that for St. Petersburg University observation site that represents subarctic region with maritime climate: (1) the information volume of MW measurements for a cold and dry season is significantly less than for a warm and humid season due to lack of information from ‘humidity channels’; (2) for stable atmospheric conditions the sampling interval of MW measurements should not be greater than 100–200 s; (3) the degree of correlation between MW measurements and atmospheric temperature and humidity does not considerably depend on season of observations.

Cost comparisons of modifiedX̅chart for autocorrelated observations

This paper presents the economic design of modified X chart for autocorrelated data and comparison with the economic design of Shewhart’s X chart. An attempt has been made to counter autocorrelation by designing the modified X chart; as the cost of operating a process control system is an important element in the economic design of control charts. The economic designs of both modified and Shewhart X charts for autocorrelated observations are presented; using Lorenzen-Vance [1] cost model. The modified X chart is based upon sum of chi-squares and has simplicity like Shewhart X chart but more efficient than standard chart. Two sets of parameters suggested by Montgomery [2] are used to determine the optimal sampling intervals (h) and expected costs per hour. It shows that sampling interval (h) and expected cost/hour (C) depend upon various parameters of chart, used in this model. The expected costs/hour (C) for both the charts are computed for sample sizes of 2 and 4 at the various levels of correlation and process shifts in mean. It is concluded that at each level of correlation and shift in the process mean, the expected costs/hour of the modified X chart are lower than the Shewhart chart.

Determining soil salinity and plant biomass response for a farmed coastal cropland using the electromagnetic induction method

Apparent electrical conductivity (ECa) measured by electromagnetic induction (EM) instruments has been successfully used as an ancillary variable to estimate soil salinity from field to watershed scales. It is particularly useful in the case of coastal farming area where reliable estimates of soil salinity aid farmers and researchers in understanding the development of salinization and establishing appropriate management practices. The objectives of this research were to estimate soil salinity (ECe) using intensive EM survey data and prediction equations relating soil salinity to ECa, to determine the optimal data interval in EM survey and to validate the prediction reliability using plant biomass response to soil salinity. This study was conducted in a typical coastal rain-fed farmland in north Jiangsu Province, China. The results indicated that apparent electrical conductivity showed significant correlation with ECe and EM readings from the horizontal coil orientation can be used as the sole predictor in a linear mixed model. Field EM survey data exhibited directional trend resulting from the impact of anthropogenic activities on soil salinity. An optimal sampling interval of 16m in the survey transect essentially meets the need of spatial prediction when field EM survey is performed. Soil salinity increased with depth and higher soil salinity mainly occurs in areas where rice was previously planted, particularly in lower-lying regions and areas adjacent to the aquaculture plant. Plant biomass is negatively related to both, measured and estimated soil salinity. The relation to measured soil salinity was closer than to estimated soil salinity. Boundary line analysis shows that root zone salinity (ECe) causes a 4.4% and 6.4% plant biomass reduction per dS/m for rice and cotton, respectively. Such results allowed us to conclude that a larger data interval of EM survey than the present could produce satisfactory estimation accuracy of field soil salinity, and the relationship between soil salinity (or ECa data) and plant biomass could help to derive site specific yield goals and management practices in the farmed coastal cropland.

Optimal criteria and sampling interval to detect a V̇O2 plateau at V̇O2max in patients with metabolic syndrome

This study sought to determine the optimal criteria and sampling interval to detect a V̇O2 plateau at V̇O2max in patients with metabolic syndrome. Twenty-three participants with criteria-defined metabolic syndrome underwent a maximal graded exercise test. Four different sampling intervals and three different V̇O2 plateau criteria were analysed to determine the effect of each parameter on the incidence of V̇O2 plateau at V̇O2max. Seventeen tests were classified as maximal based on attainment of at least two out of three criteria. There was a significant (p < 0.05) effect of 15-breath (b) sampling interval on the incidence of V̇O2 plateau at V̇O2max across the ≤50 and ≤80 mL∙min−1 conditions. Strength of association was established by the Cramer’s V statistic (φc); (≤50 mL∙min−1 [φc = 0.592, p < 0.05], ≤80 mL∙min−1 [φc = 0.383, p < 0.05], ≤150 mL∙min−1 [φc = 0.246, p > 0.05]). When conducting maximal stress tests on patients with metabolic syndrome, a 15-b sampling interval and ≤50 mL∙min−1 criteria should be implemented to increase the likelihood of detecting V̇O2 plateau at V̇O2max.

Non-destructive strain determination based on phase measurement and radial basis function

A method of non-destructive strain field determination based on the combination of the temporal phase measurement interferometry (TPMI) with radial basis function (RBF) was proposed in this paper. The quality of unwrapped phase obtained by TPMI was improved after RBF interpolation. Then accurate displacements can be obtained, followed by the strain components calculated by employing point-wise local least-squares fitting technique. Optimal sampling intervals of images with different sizes were given based on numerical experiments. For validation, the normal strain distributions in y direction of an aluminum plate subjected to uniform tensile loading were determined by the proposed technique and compared with values measured by strain gauge. The results are in good agreement with each other. Besides, strain distribution of a three-point bending beam with pre-notch was evaluated by the proposed method and the strain gauge technique. Comparison of the results reveals the effectiveness and feasibility of the proposed method.

Economic-Statistical Design of EWMA Control Charts Based on Taguchi's Loss Function

This paper proposes an economic-statistical design of the EWMA chart with time-varying control limits in which the Taguchi's quadratic loss function is incorporated into the economic-statistical design based on Lorenzen and Vance's economical model. A nonlinear programming with statistical performance constraints is developed and solved to minimize the expected total quality cost per unit time. This model, which is divided into three parts, depends on whether production continues during the period when the assignable cause is being searched for and/or repaired. Through a computational procedure, the optimal decision variables, including the sample size, the sampling interval, the control limit width, and the smoothing constant, can be solved for by each model. It is showed that the optimal economic-statistical design solution can be found from the set of optimal solutions obtained from the statistical design, and both the optimal sample size and sampling interval always decrease as the magnitude of shift increases.

Monitoring and Diagnosing Process Loss Using a Weighted‐Loss Control Chart

Product and service quality and productivity loss are all crucial competitive factors of companies in numerous industries. The loss function is a popular method for measuring the loss caused by variations in product or service quality. This study proposes a weighted‐loss (WL) control chart to monitor the loss variation among manufacturing or service processes. Because loss is caused by a quality variable deviating from its target value, we set up two corresponding control charts to diagnose the sources of out‐of‐control loss and implement processes to correct these losses. We further present a WL chart using optimal variable sampling intervals (VSIs) in order to detect out‐of‐control losses faster compared with a WL chart using a fixed sampling interval (FSI). An example then demonstrates and evaluates the ability of the proposed VSI WL control chart to monitor and diagnose out‐of‐control process loss. Numerical analyses indicate that the optimal VSI WL chart outperforms the FSI WL chart, the joint and S2 charts and the VSI Average Loss chart in detecting out‐of‐control process loss. Thus, the proposed VSI WL chart is recommended. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Considering Taguchi loss function on statistically constrained economic sum of squares exponentially weighted moving average charts

In this paper, Duncan's cost model combined Taguchi's quadratic loss function is applied to develop the economic-statistical design of the sum of squares exponentially weighted moving average (SS-EWMA) chart. The genetic algorithm is applied to search for the optimal decision variables of SS-EWMA chart such that the expected cost is minimized. Sensitivity analysis reveals that the optimal sample size and sampling interval decrease; optimal smoothing constant and control limit increase as the mean and/or variance increases. Moreover, the combination of optimal parameter levels in orthogonal array experiment plays an important guideline for monitoring the process mean and/or variance.

Split dynamic MRI: Single bolus high spatial–temporal resolution and multi contrast evaluation of breast lesions

To test the feasibility of a novel "split dynamic" method in which high temporal and high spatial resolution dynamic MR images are acquired during a single bolus injection. High temporal resolution images were acquired using a three-dimensional (3D) dual-echo EPI sequence. The high spatial resolution images were acquired using a 3D T1 -weighted turbo field echo sequence. Simulations were performed to test the split dynamic method in terms of accuracy relative to a continuous acquisition and for temporal sampling requirements for accurate estimation of kinetic parameters. The method was tested in four patients where pharmacokinetic parameters were extracted from the high temporal resolution data. The split dynamic method enabled quantitative evaluation of both T1- and T2*-weighted characteristics. Simulations showed that splitting the dynamic acquisition does not significantly influence the reliability of parameter estimations. Simulation showed a required temporal resolution of 13, 16, and 8 s for accurate estimates of Ktrans, ve, and vp, respectively, and an optimal sampling interval between 2 and 6 s for peak R2*. The split dynamic sequence enabled detailed assessment of dynamic T1- and T2*-weighted contrast kinetics without compromising guidelines concerning spatial resolution.

Optimal representation of non-stationary random fields with finite numbers of samples: A linear MMSE framework

In this article we consider the representation of a finite-energy non-stationary random field with a finite number of samples. We pose the problem as an optimal sampling problem where we seek the optimal sampling interval under the mean-square error criterion, for a given number of samples. We investigate the optimum sampling rates and the resulting trade-offs between the number of samples and the representation error. In our numerical experiments, we consider a parametric non-stationary field model, the Gaussian–Schell model, and present sampling schemes for varying noise levels and for sources with varying numbers of degrees of freedom. We discuss the dependence of the optimum sampling interval on the problem parameters. We also study the sensitivity of the error to the chosen sampling interval.

Optimal variable sample size and sampling interval ‘mean squared error’ chart

The deployment of statistical process control in the service process is a prominent global phenomenon in recent years. In this paper, we proposed the optimal variable sample size and sampling interval (VSSI) mean square error (MSE) control chart to monitor the difference between the process mean and the target value and the process variation shifts, and its performance is measured by the average time to signal. From data analyses, we found the optimal VSSI MSE chart that performs better than the specific VSSI and the optimal variable sampling interval and the fixed parameters MSE charts. An example was given to illustrate this new proposed approach.

Using a new VSI EWMA average loss control chart to monitor changes in the difference between the process mean and target and/or the process variability

A single chart, instead of X¯ and R charts or X¯ and S charts, to simultaneously monitor the process mean and variability would reduce the required time and effort. A number of studies have attempted to find such charts. Moreover, a number of studies demonstrated that the adaptive control charts may detect process shifts faster than the fixed control charts. This paper proposes an easier EWMA average loss chart with variable sampling intervals to effectively monitor the process and diagnose whether the out-of-control process is caused by the changes in the difference of process mean and target or the increase in process variability, or both. Furthermore, an optimal variable sampling interval EWMA average loss chart is also proposed. An example is used to illustrate the application and evaluate the performance of the proposed control chart in detecting and diagnosing the increases in the difference of the process mean and target and/or the process variability. Numerical analyses demonstrated that the optimal VSI EWMA average loss chart outperforms the average loss chart with fixed design parameters and the Shewhart joint X¯ and S charts. Therefore, the (optimal) VSI EWMA average loss chart is recommended.

Optimal Variable Sample Size and Sampling Interval MSE Chart Based on Improved Square Root Transformation

In the field of statistical process control (SPC), control charts for attributes are widely used to detect the out-of-control condition by checking the number of nondefective units or nondefective in a sample. In this article, we use the average time to signal (ATS) and the average number of observations to signal (ANOS) to evaluate the performance of the optimal variable sample size and sampling interval (VSSI) improved square root transformation (ISRT) mean square error (MSE) (VSSI_ ISRT_ MSE) control chart for attribute data. In addition, this control chart will be used to monitor: (1) the difference between the process mean and the target value, and (2) the process variance shifts. We found that the optimal VSSI_ ISRT_ MSE chart performs better than the specific VSSI, the optimal variable sampling interval (VSI), and the fixed parameters (FP) ISRT_MSE charts. An example is given to illustrate this new proposed approach.

Economic–statistical Design of Maximum Exponentially Weighted Moving Average Control Charts

The maximum exponentially weighted moving average (MaxEWMA) control chart effectively combines the two EWMA charts into one chart and monitors both increases and decreases in the mean and/or variability. In this paper, we develop the economic–statistical design of the MaxEWMA control chart in which the Taguchi's quadratic loss function is incorporated into the Duncan's economical model. Numerical simulations are executed to minimize the expected total cost model and determine the optimal decision variables, including the sample size, sampling interval, control limit width, and the smoothing constant of the MaxEWMA control chart. It is shown that the optimal control limit width and smoothing constant increase as the optimal cost value increases and that both the optimal sample size and sampling interval always decrease as the magnitudes of mean and/or variance shifts increase. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Different V˙O2max Time-Averaging Intervals in Swimming

We aimed to determine the effect of sampling interval strategy on VO(2max) assessment to establish a standard time averaging method that allows a better identification of the VO(2) plateau incidence in swimming. To this end, 3 incremental protocols utilizing different step lengths for each sampling interval were used to compare VO(2max)measurements. 11 trained male swimmers performed 3 repetitions of a front crawl intermittent incremental protocol until exhaustion (increments of 0.05 m.s(-1), with 30 s and 24-48 h intervals between steps and tests, respectively) with 200, 300 and 400-m step lengths. VO(2) was directly measured, and 6 sampling intervals were compared: bxb and averages of 5, 10, 15, 20 and 30 s. Shorter sampling intervals (≤ 15 s) allowed the highest incidence of the VO(2) plateau, independent of the step lengths used; the 200 and 300-m step protocols accounted for higher percentage of VO(2) plateau incidence, and higher VO(2max) values, compared to the 400-m step protocol. As an optimal sampling interval should be used for the validation of the research findings, and considering that swimmers and coaches prefer less time-consuming protocols, the use of the 10 s time-average interval (once bxb and 5 s samplings present high variability) in a 200-m step incremental protocol for VO(2max) assessment in swimming is suggested.

Three-Dimensional Wheel Topography Measurement with Laser Triangulation

Laser triangulation was used to measure the topography of vitrified CBN wheels and optimum sampling interval was obtained by comparing measuring results with different sampling intervals. Four evaluation indexes including the mean protrusion height of abrasive grains Hm, the standard deviation of grain protrusion height Hv, the standard deviation of the distance between two adjacent grains Dv and the number of micro cutting edges per square millimeter Nm were put forward to assess wheel topography and grinding performance. These indexes were verified to be effective by comparing 3D topography of newly manufactured wheel and dressed wheel.

Novel approach to adaptive statistical process control optimisation with variable sampling interval and minimum expected loss

We investigate the properties of an adaptive control chart with a variable sampling interval, intended to be the function of an observed standard score, optimising a control performance (minimum expected loss) versus a fixed sampling interval chart scheme. In order to solve this problem its transforming to an optimal control problem is proposed. The latter is then analysed by application of Pontryagin’s maximum principle. The advantage of the optimal variable sampling interval in comparison with a fixed sampling interval is demonstrated.

The importance of sampling interval for rough contact mechanics

The contact of random surfaces is discussed in this paper. Commonly used elastic and elastic–plastic microcontact models were applied to modeled and measured isotropic surface topographies of a Gaussian ordinate distribution, assuming a constant and a distributed radius of surface summits, respectively. The calculation procedures allowed the mean surface separation and the real area of contact to be calculated as a function of contact load and sampling intervals. Results are presented for a wide range of contact load and sampling intervals, showing the difference obtained after using various models. The applicability of the profile spectral moment approach to areal random surface specification was checked. This technique relates geometrical properties of a surface important for rough contact mechanics to those of its constituent profiles. Suggestions for choosing the optimum sampling interval are provided.