Non-uniform Sampling Scheme Research Articles

Integration of Production Planning, Maintenance Scheduling and Noncentral Chi-square Chart Parameters with Random Failures and Multiple Assignable Causes

This study presents an integrated model of three dependent concepts including production planning, maintenance scheduling, and statistical process monitoring (SPM) in order to improve both economic and statistical features of the production systems. To bring the proposed model closer to real applications, the possibility of occurring several types of assignable causes during the production cycle is taken into account. Besides, a noncentral chi-square chart is used for simultaneous monitoring of the process mean and variability parameters. Moreover, it is assumed that both time-to-failure and time-to-shift are Weibull distributed random variables. In other words, the system may suddenly fail and goes to an out-of-control condition with two different increasing rates including the failure rate function and the shift occurrence rate function. Hence, to improve the system reliability, a nonuniform sampling scheme is developed in which a same integrated shift occurrence rate is obtained for all intervals. The goal of the model is to minimize the expected total cost per time unit, subject to some statistical constraints. Ultimately, three comparative studies are given to demonstrate the efficiency of the proposed model. The first one indicates that a nonuniform sampling scheme reduces the expected total cost and the length of out-of-control period. The second one confirms that considering the system failure not only increases the length of in-control period but also improves the economic feature of the production system. The third one shows that using chi-square chart decreases the quality loss cost which in turn decreases the expected total cost.

Integration of Multivariate Loss Function Approach in the Hotelling’s Charts under Banerjee-Rahim (1988) Weibull Shock Models

A proper monitoring of stochastic systems is the control charts of statistical process control and drift in characteristics of output may be due to one or several assignable causes. Although many research works have been done on the economic design of control charts with single assignable cause, the economic statistical design of T^2 control chart under Weibull shock model with multiple assignable causes and considering multivariate Taguchi loss function has not been presented yet. Using Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values ??of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with Taguchi loss function has a lower cost than single assignable cause model and integrated model with non-uniform sampling has a lower cost than that with uniform sampling.

Conditional Generative Adversarial Networks for Optimal Path Planning

Path planning plays an important role in autonomous robot systems. Effective understanding of the surrounding environment and efficient generation of an optimal collision-free path are both critical parts for solving path-planning problems. Although conventional sampling-based algorithms, such as the rapidly exploring random tree (RRT) and its improved optimal version (RRT*), have been widely used in path-planning problems because of their ability to find a feasible path in even complex environments, they fail to find an optimal path efficiently. To solve this problem and satisfy the two aforementioned requirements, we propose a novel learning-based path-planning algorithm which consists of a novel generative model based on the conditional generative adversarial networks (CGANs) and a modified RRT* algorithm (denoted by CGAN-RRT*). Given the map information, our CGAN model can generate an efficient probability distribution of feasible paths, which can be utilized by the CGAN-RRT* algorithm to find an optimal path with a nonuniform sampling strategy. The CGAN model is trained by learning from ground-truth maps, each of which is generated by putting all the results of executing the RRT algorithm 50 times on one raw map. We demonstrate the efficient performance of this CGAN model by testing it on two groups of maps and comparing the CGAN-RRT* algorithm with the Informed-RRT* algorithm and conventional RRT* algorithm.

Cognitive sampling: The power of harnessing sampling strategies with machine learning techniques for enhanced machine classification and machine interpretation of acoustic datasets

Machine learning has received increased popularity in the acoustical community for its ability to interpret, classify and predict information autonomously from large-scale datasets. Beyond traditional supervised and semi-supervised learning architectures such as deep learning, and ensemble approaches, unsupervised learning networks such as autoencoders are being used to discover efficient data codings that enable hitherto unforeseen feature spaces. Unrelated yet deeply significant to the success of these myriad approaches is the spectral resolution of the signal itself as it has implications on the richness of information used by the learning architecture. Furthermore, much remains to be done in interpreting machine-learnt feature representations by domain experts and linking the domain knowledge to the machine-learnt knowledge. This talk will introduce a new way of enabling this link, by harnessing the power of compressive sampling and more generally, non-uniform sampling strategies and information theory to popular machine learning techniques. Specific applications will include a variety of acoustical applications involving spectral feature generation and interpretation.

Non-Stationary Complementary Non-Uniform Sampling (NOSCO NUS) for Fast Acquisition of Serial 2D NMR Titration Data.

NMR spectroscopy offers unique benefits for ligand binding studies on isotopically labelled target proteins. These benefits include atomic resolution, direct distinction of binding sites and modes, a lowest detectable affinity limit, and function independent setup. Yet, retracing protein signal assignments from apo to holo states to derive exact dissociation constants and chemical shift perturbation amplitudes (for ligand docking and structure‐based optimization) requires lengthy titration series of 2D heteronuclear correlation spectra at variable ligand concentration that may exceed the protein's lifetime and available spectrometer time. We present a novel method to overcome this critical limitation, based on non‐stationary complementary non‐uniform sampling (NOSCO NUS) combined with a robust particle swarm optimization algorithm. We illustrate its potential in two challenging studies with very distinct protein sizes and binding affinities, showing that NOSCO NUS can reduce measurement times by an order of magnitude to make such highly informative NMR titration studies more broadly feasible.

Optimized non-uniform sampling of blood pressure time series from the operating room.

We investigate an optimized non-uniform sampling strategy for blood pressure time series from the operating room (OR). Our aim is to obtain an approximate bound on the achievable reconstruction fidelity given an average sampling rate constraint. Our data set consists of 117 hours of recordings of continuous invasive blood pressure from 28 surgery patients. We evaluate the root mean squared error (RMSE) of the zero-order hold sampling reconstruction of the blood pressure time series. We quantitatively compare the errors achieved by uniform versus optimized non-uniform sample placements for several average sample rates, ranging from 2 to 24 measurements per hour. An optimized non-uniform measurement schedule can lead to approximately 50% reduction of reconstruction RMSE for systolic, mean, and diastolic blood pressure time series with respect to uniform sampling, while maintaining the same average sampling rate.

MT-IVSN: a novel model for vehicle re-identification

Image re-identification is usually used to find specific images from image libraries or video sequences. In recent years, convolutional neural networks have gradually become the dominant method in this field. In this paper, a Multitask Identification-Verification Siamese Network for vehicles is proposed, which combines color feature vectors with the inherent structure, category and other attributes of the vehicle. A vehicle 2D structural model and a method of image viewpoint normalization are also presented to ensure the high consistency of features in the expression of images from different angles. In addition, based on the vehicle 2D structural model, a dynamic annular non-uniform partition color super-pixel sampling strategy for vehicle face is investigated to construct a color feature vector. In the experiments, the proposed model and method are evaluated on the public vehicles and VeRi datasets. The experimental results show that the proposed method and model have made great progress.

Developing nonuniform sampling strategies to improve sensitivity and resolution in 1,1-ADEQUATE experiments.

Nonuniform sampling (NUS) strategies are developed for acquiring highly resolved 1,1-ADEQUATE spectra, in both conventional and homodecoupled (HD) variants with improved sensitivity. Specifically, the quantile-directed and Poisson gap methods were critically compared for distributing the samples nonuniformly, and the quantile schedules were further optimized for weighting. Both maximum entropy and iterative soft thresholding spectral estimation algorithms were evaluated. All NUS approaches were robust when the degree of data reduction is moderate, on the order of a 50% reduction of sampling points. Further sampling reduction by NUS is facilitated by using weighted schedules designed by the quantile method, which also suppresses sampling noise well. Seed independence and the ability to specify the sample weighting in quantile scheduling are important in optimizing NUS for 1,1-ADEQUATE data acquisition. Using NUS yields an improvement in sensitivity, while also making longer evolution times accessible that would be difficult or impractical to attain by uniform sampling. Theoretical predictions for the sensitivity enhancements in these experiments are in the range of 5-20%; NUS is shown to disambiguate weak signals, reveal some n JCC correlations obscured by noise, and improve signal strength relative to uniform sampling in the same experimental time. This work presents sample schedule development for applying NUS to challenging experiments. The schedules developed here are made available for general use and should facilitate the broader utilization of ADEQUATE experiments (including 1,1-, 1,n-, and HD- variants) for challenging structure elucidation problems.

3D Displacement Field of Wenchuan Earthquake Based on Iterative Least Squares for Virtual Observation and GPS/InSAR Observations

The acquisition of a 3D displacement field can help to understand the crustal deformation pattern of seismogenic faults and deepen the understanding of the earthquake nucleation. The data for 3D displacement field extraction are usually from GPS/interferometric synthetic aperture radar (InSAR) observations, and the direct solution method is usually adopted. We proposed an iterative least squares for virtual observation (VOILS) based on the maximum a posteriori estimation criterion of Bayesian theorem to correct the errors caused by the GPS displacement interpolation process. Firstly, in the simulation examples, both uniform and non-uniform sampling schemes for GPS observation were used to extract 3D displacement. On the basis of the experimental results of the reverse fault, the normal fault with a strike-slip component, and the strike-slip fault with a reverse component, we found that the VOILS method is better than the direct solution method in both horizontal and vertical directions. When a uniform sampling scheme was adopted, the percentages of improvement for the reverse fault ranged from 3% to 9% and up to 70%, for the normal fault with a strike-slip component ranging from 4% to 8% and up to 68%, and for the strike-slip fault with a reverse component ranging from 1% to 8% and up to 22%. After this, the VOILS method was applied to extract the 3D displacement field of the 2008 Mw 7.9 Wenchuan earthquake. In the East–West (E) direction, the maximum displacement of the hanging wall was 1.69 m and 2.15 m in the footwall. As for the North–South (N) direction, the maximum displacement of the hanging wall was 0.82 m for the southwestern, 0.95 m for the northeastern, while that of the footwall was 0.77 m. In the vertical (U) direction, the maximum uplift was 1.19 m and 0.95 m for the subsidence, which was significantly different from the direct solution method. Finally, the derived vertical displacements were also compared with the ruptures from field investigations, indicating that the VOILS method can reduce the impact of the interpolated errors on parameter estimations to some extent. The simulation experiments and the case study of the 3D displacement field for the 2008 Wenchuan earthquake suggest that the VOILS method proposed in this study is feasible and effective, and the degree of improvement in the vertical direction is particularly significant.

Adaptive multistart Gauss–Newton approach for geodetic data inversion of earthquake source parameters

We present an adaptive multistart Gauss–Newton approach (AMGNA) to inverse earthquake source parameters with multiple geodetic data sets. The AMGNA can be combined with uniform and nonuniform sampling schemes to generate initial parameters. The AMGNA searches for the improved solution with an adaptively determined number of initial parameters based on a given stable level represented by a target probability; this process involves a first-order approximate uncertainty calculation and performs a joint inversion involved variance component estimation. We test the efficiency and reliability of the AMGNA with synthetic global positioning system and interferometric synthetic aperture radar data and apply the proposed approach to the 2009 Mw 6.3 L’Aquila earthquake and 2017 Mw 6.6 Bodrum–Kos earthquake. The results show that the AMGNA can retrieve well the designed source parameters by several simulated cases and estimate source parameters and uncertainties comparable to those of previous studies for real applications. The AMGNA can quickly estimate the source parameters and uncertainties within 0.5–25 min using six processes in parallel computing. Considering the easily implemented property of the nonuniform sampling scheme, our algorithm has potential applications in the fast and automatic inversion of earthquake source parameters.

$N$-Dimensional Tensor Completion for Nuclear Magnetic Resonance Relaxometry

This paper deals with tensor completion for the solution of multidimensional inverse problems arising in nuclear magnetic resonance (NMR) relaxometry. We study the problem of reconstructing an approximately low-rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, nonuniform sampling strategies, and parameter selection methods are developed in this context. In particular, we derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property-based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by nonuniform sampling from a Parseval tight frame. The proposed algorithm is then applied to the setting of nuclear magnetic resonance relaxometry, for both simulated and experimental data. We compare our results with basis pursuit as well as with the state-of-the-art nonsubsampled data acquisition and reconstruction approach. Our experiments indicate that tensor recovery promises to significantly accelerate $N$-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments to be performed. Our methods could also be applied to other similar inverse problems arising in machine learning, signal and image processing, and computer vision.

The influence of the probability density function on spectral quality in nonuniformly sampled multidimensional NMR

The goal of nonuniform sampling (NUS) is to select a subset of free induction decays (FIDs) from the conventional, uniform grid in a manner that sufficiently samples short evolution times needed for improved sensitivity and long evolution times needed for enhanced resolution. In addition to specifying the number of FIDs to be collected from a uniform grid, NUS schemes also specify the distribution of the selected FIDs, which directly impacts sampling-induced artifacts. Sampling schemes typically address these heuristic guidelines by utilizing a probability density function (PDF) to bias the distribution of sampled evolution times. Given this common approach, schemes differentiate themselves by how the evolution times are distributed within the envelope of the PDF. Here, we employ maximum entropy reconstruction and utilize in situ receiver operating characteristic (IROC) to conduct a critical comparison of the sensitivity and resolution that can be achieved by three types of biased sampling schemes: exponential (PDF is exponentially decaying), Poisson-gap (PDF derived from a sine function), and quantile-directed (PDF defined by simple polynomial decay). This methodology reveals practical insights and trends regarding how the sampling schemes and bias can provide the highest sensitivity and resolution for two nonuniformly sampled dimensions in a three-dimensional biomolecular NMR experiment. The IROC analysis circumvents the limitations of common metrics when used with nonlinear spectral estimation (a characteristic of all methods used with NUS) by quantifying the spectral quality via synthetic signals that are added to the empirical dataset. Recovery of these synthetic signals provides a proxy for the quality of the empirical portion of the spectrum. The central finding is that differences in spectral quality are primarily driven by the strength of bias in the PDF. In addition, a sampling coverage threshold is observed that appears to be connected to the dependence of each NUS method on its random seed. The differences between sampling schemes and biases are most relevant below 20% coverage where seed-dependence is high, whereas at higher coverages, the performance metrics for all of the sampling schemes begin to converge and approach a seed-independent regime. The results presented here show that aggressive sampling at low coverage can produce high-quality spectra by employing a sampling scheme that adheres to a decaying PDF with a bias to a broad range of short evolution times and includes relatively few FIDs at long evolution times.

Joins on samples

Despite decades of research on AQP (approximate query processing), our understanding of sample-based joins has remained limited and, to some extent, even superficial. The common belief in the community is that joining random samples is futile. This belief is largely based on an early result showing that the join of two uniform samples is not an independent sample of the original join, and that it leads to quadratically fewer output tuples. Unfortunately, this early result has little applicability to the key questions practitioners face. For example, the success metric is often the final approximation's accuracy, rather than output cardinality. Moreover, there are many non-uniform sampling strategies that one can employ. Is sampling for joins still futile in all of these settings? If not, what is the best sampling strategy in each case? To the best of our knowledge, there is no formal study answering these questions. This paper aims to improve our understanding of sample-based joins and offer a guideline for practitioners building and using real-world AQP systems. We study limitations of offline samples in approximating join queries: given an offline sampling budget, how well can one approximate the join of two tables? We answer this question for two success metrics: output size and estimator variance. We show that maximizing output size is easy, while there is an information-theoretical lower bound on the lowest variance achievable by any sampling strategy. We then define a hybrid sampling scheme that captures all combinations of stratified, universe, and Bernoulli sampling, and show that this scheme with our optimal parameters achieves the theoretical lower bound within a constant factor. Since computing these optimal parameters requires shuffling statistics across the network, we also propose a decentralized variant in which each node acts autonomously using minimal statistics. We also empirically validate our findings on popular SQL and AQP engines.

A Method Exploiting Compressive Sampling for Localization of Radio Frequency Emitters

This article presents a novel method for radio frequency (RF) emitter localization by using wideband spectrum sensors (WSSs) exploiting compressive sampling (CS). The method assumes that $R$ receivers with known Cartesian coordinates in the plane are deployed in the area, where the transmitters are expected to be. By using a nonuniform sampling (NUS) scheme, each WSS allows one to relax the throughput requirements for the data acquisition and transmission tasks. The mathematical description followed by numerical analysis is presented. Then, hardware implementation for the receiver was realized, by using commercial off-the-shelf components. The obtained results from simulation tests are reported, and an experimental assessment of the proposed method is provided. The experimental results are compared with those obtained by applying the maximum likelihood (ML) algorithm on the samples acquired according to the Nyquist criteria. As a figure-of-merit, the compression ratio (CR) of the proposed NUS scheme was evaluated and it was experimentally obtained that even for CR = 64 the spectrum reconstruction is acceptable for being used in the ML algorithm.

Comparing analytical and machine-learning techniques for predicting acoustic fields in ideal single- and multi-path environments

Neural-network-based machine learning provides a modern solution paradigm for a wide variety of problems. Trained neural networks can provide answers quickly because the primary computational effort is front-loaded into network training. This presentation provides the results of an investigation into the neural-network-development effort necessary to replace point-source Helmholtz-equation solutions in axisymmetric single-path, two-path, and multi-path environments having constant sound speed. Here, the acoustic and environmental input parameters are provided to the neural network as they would be to a propagation simulation. The single-path (free space) environment involves four parameters (sound speed, frequency, receiver range, and receiver depth). The two-path (Lloyd’s mirror) environment adds a reflecting surface and a fifth parameter, source depth. The multipath (ideal waveguide) environment further adds a second (deeper) reflecting surface and a sixth parameter, waveguide depth. In all cases, neural network training data and performance comparisons are developed from well-known analytical Helmholtz-equation solutions. Uniform and non-uniform sampling strategies for neural-netwok training are considered for frequencies in the 100s of Hz, depths up to 200 m, and ranges up to 2 km for sound speeds near 1500 m/s. Comparisons emphasize acoustic-field amplitude. Extensions of these results to acoustic-field phase and more than three propagation paths are considered.

Extreme Nonuniform Sampling for Protein NMR Dynamics Studies in Minimal Time.

NMR spectroscopy is an extraordinarily rich source of quantitative dynamics of proteins in solution using spin relaxation or chemical exchange saturation transfer (CEST) experiments. However, 15N-CEST measurements require prolonged multidimensional, so-called pseudo-3D HSQC experiments where the pseudo dimension is a radio frequency offset Δω of a weak 15N saturation field. Nonuniform sampling (NUS) approaches have the potential to significantly speed up these measurements, but they also carry the risk of introducing serious artifacts and the systematic optimization of nonuniform sampling schedules has remained elusive. It is demonstrated here how this challenge can be addressed by using fitted cross-peaks of a reference 2D HSQC experiment as footprints, which are subsequently used to reconstruct cross-peak amplitudes of a pseudo-3D data set as a function of Δω by a linear least-squares fit. It is shown for protein Im7 how the approach can yield highly accurate CEST profiles based on an absolutely minimally sampled (AMS) data set allowing a speed-up of a factor 20-30. Spectrum-specific optimized nonuniform sampling (SONUS) schemes based on the Cramer-Rao lower bound metric were critical to achieve such a performance, revealing also more general properties of optimal sampling schedules. This is the first systematic exploration and optimization of NUS schedules for the dramatic speed-up of quantitative multidimensional NMR measurements that minimize unwanted errors.

Constrained optimal design of Control Chart for correlated data under Weibull Shock Model with multiple assignable causes

An appropriate technique for monitoring a stochastic system is to utilize the control charts. In statistical process, control a drift in characteristics of output may be due to one or several assignable causes. In the establishment of charts in statistical process control, an assumption is made that there is no correlation within the samples. However, in practice there are many cases where the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. Although some research works have been done on the economic design of control charts with single assignable cause with correlated data, the economic statistical design of control chart under Weibull shock model with multiple assignable causes and correlated samples have not been presented yet. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values of sample size, sampling interval, and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with correlated samples with non-uniform sampling has a lower cost than that with uniform sampling.

Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE

We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The main result gives explicit bounds on the number of measurements in order to achieve stable recovery, which depends on the mutual coherence of the two systems. As a simple corollary, we prove the efficiency of nonuniform sampling strategies in cases when the two systems are not incoherent, but only asymptotically incoherent, as with the recovery of wavelet coefficients from Fourier samples. This general framework finds applications to inverse problems in partial differential equations, where the standard assumptions of compressed sensing are often not satisfied. Several examples are discussed, with a special focus on electrical impedance tomography.

Learning sampling distribution for motion planning with local reconstruction-based self-organizing incremental neural network

For sampling-based motion planners (e.g., PRM and RRT*), collision detection dominates the asymptotic running time and reduces the execution efficiency. The reason of this problem is that obtaining a high-dimensional implicit representation (i.e., configuration space distribution) of the state space is not easy, especially in the complicated environment with various obstacles. Though sampling-based planning algorithms and their variants perform well, most of these algorithms have strict restrictions and narrow applications. A possible ideal solution is to design a non-uniform sampling strategy to ensure the sampling process only occurs in collision-free region $$\chi _{free}$$ but not in collision region $$\chi _{col}$$ . Therefore, we propose a new methodology to learn the sampling distribution for non-uniform sampling. The sampling distribution is learned through a local reconstruction-based self-organizing incremental neural network and allows to generate samples from the learned latent distribution. Besides, our method can adapt well to environmental non-vigorous changes and adjust the learned distribution quickly. The method can effectively exploit the underlying structure of the planning problem and be spread for general use in combination with any sampling-based planning algorithms. Specifically, we use two typical planning problems to show that the proposed method can effectively learn and update the sampling distribution from the high-dimensional configuration space in the changed environment, resulting in a dominant performance in terms of the cost, running time and success rate.

Triplet NOAH supersequences optimised for small molecule structure characterisation.

A series of NMR supersequences are presented for the time-efficient structure characterisation of small molecules in the solution state. These triplet sequences provide HMBC, HSQC, and one homonuclear correlation experiment of choice according to the NMR by Ordered Acquisition using 1 H detection principle. The experiments are demonstrated to be compatible with non-uniform sampling schemes and may be acquired and processed under full automation.