Stability Error Research Articles

Nonlinear Stable Least Trimmed Squares for Regression Models with Stable Errors

The common method for estimating nonlinear regression coefficients with Gaussian errors is nonlinear least squares. It is not robust for regression with heavy-tailed errors. The nonlinear least trimmed squares method is an efficient procedure for regression with heavy-tailed errors. We are introducing nonlinear least trimmed squares for the nonlinear regression with non-Gaussian stable errors and estimate the parameters of the stable distributions based on the order statistics. The traditional least trimmed squares regression algorithm is adopted for errors with infinite variance by modifying the trimming procedure. This paper estimated the nonlinear regression coefficients with stable errors through the proposed nonlinear least trimmed squares algorithm based on a new trimming procedure based on the properties of stable order statistics moments. The proposed algorithm was applied to real and simulated datasets and evaluated using a bootstrap standard deviation estimator.

A-203 A Disconnect Between Detectable Patient Error Rates and QC Understanding

Abstract Background ISO 14971 defines “risk evaluation as the process of comparing the estimated risk against given risk criteria to determine the acceptability of the risk. Effective QC processes would detect if a stable acceptable error rate became unacceptable. Methods A survey was circulated through LinkedIn and Labvine. Forty respondents who included their credentials were included in the final analysis. Questions included: 1. What is the best choice for acceptable error rate when an analytical process is stable and in control, 2. If an analytical process “fails,” how many errors are you willing to report before the lab should stop reporting, and 3. “If an analytical process has a 5% stable error, how high would the error rate after failure need to become for a 1-2s rule to detect failure with one QC sample in a single QC run?” This interactive poster will allow viewers to cast their vote for Question 4 and then reveal an LJ chart depicting a stable error rate of 5% with a shift to show the number of 1-2s failures with their chosen acceptable post-failure error rate. Results During stable operation, only 8% wanted zero errors while 38% voted that they would allow up to 5% errors; After failure, 66% wanted to report zero errors and only 10% would allow 5% failure. 69% believed they would see a 1-2s failure in one run if the error rate rose to less than 50%; 19% believed it required a 100% error rate. Conclusions There is a strange disconnect where most believed it was acceptable to report more errors during stable operation than if the method failed. There is a widespread misunderstanding of the logic that connects management of acceptable patient risk with the capabilities of statistical QC.

Enhancing ultrasonic attenuation images through multi-frequency coupling with total nuclear variation.

Quantitative ultrasound is a non-invasive image modality that numerically characterizes tissues for medical diagnosis using acoustical parameters, such as the attenuation coefficient slope. A previous study introduced the total variation spectral log difference (TVSLD) method, which denoises spectral log ratios on a single-channel basis without inter-channel coupling. Therefore, this work proposes a multi-frequency joint framework by coupling information across frequency channels exploiting structural similarities among the spectral ratios to increase the quality of the attenuation images. A modification based on the total nuclear variation (TNV) was considered. Metrics were compared to the TVSLD method with simulated and experimental phantoms and two samples of fibroadenoma in vivo breast tissue. The TNV demonstrated superior performance, yielding enhanced attenuation coefficient slope maps with fewer artifacts at boundaries and a stable error. In terms of the contrast-to-noise ratio enhancement, the TNV approach obtained an average percentage improvement of 34% in simulation, 38% in the experimental phantom, and 89% in two in vivo breast tissue samples compared to TVSLD, showing potential to enhance visual clarity and depiction of attenuation images.

In Situ Measurement of Deep-Sea Salinity Using Optical Salinometer Based on Michelson Interferometer

Ocean salinity plays an important role in oceanographic research as one of the fundamental parameters. An optical salinometer based on the Michelson interferometer (MI) suitable for in situ measurement in deep-sea environments is proposed in this work, and it features real-time calibration and multichannel multiplexing using the frequency modulated continuous wave (FMCW) technique. The symmetrical sapphire structure used to withstand deep-sea pressure can not only achieve automatic temperature compensation, but also counteract the changes in optical path length under deep-sea pressure. A model formula suitable for optical salinity demodulation is proposed through the nonlinear least squares fitting method. In vertical profile testing, the optical salinometer demonstrated remarkable tracking performance, achieving an error of less than 0.001 psu. The sensor displays a stable salinity demodulation error within ±0.002 psu during a three-month long-term test at a depth of 4000 m. High stability and resolution make this optical salinometer have broad development prospects in ocean observation.

Convolutional Neural Network Processing of Radio Emission for Nuclear Composition Classification of Ultra-High-Energy Cosmic Rays

Ultra-high-energy cosmic rays (UHECRs) are extremely rare energetic particles of ordinary matter in the Universe, traveling astronomical distances before reaching the Earth’s atmosphere. When primary cosmic rays interact with atmospheric nuclei, cascading extensive air showers (EASs) of secondary elementary particles are developed. Radio detectors have proven to be a reliable method for reconstructing the properties of EASs, such as the shower’s axis, its energy, and its maximum (Xmax). This aids in understanding fundamental astrophysical phenomena, like active galactic nuclei and gamma-ray bursts. Concurrently, data science has become indispensable in UHECR research. By applying statistical, computational, and deep learning methods to both real-world and simulated radio data, researchers can extract insights and make predictions. We introduce a convolutional neural network (CNN) architecture designed to classify simulated air shower events as either being generated by protons or by iron nuclei. The classification achieved a stable test error of 10%, with Accuracy and F1 scores of 0.9 and an MCC of 0.8. These metrics indicate strong prediction capability for UHECR’s nuclear composition, based on data that can be gathered by detectors at the world’s largest cosmic rays experiment on Earth, the Pierre Auger Observatory, which includes radio antennas, water Cherenkov detectors, and fluorescence telescopes.

Reinvestigating Thomas Hardy’s Motives in The Characterisation of Alec D’urbervilles and Angel Clare in Tess of the D’urbervilles

One stable error of judgement by critics of Thomas Hardy’s Tess of the d’Urbervilles is regarding Alec D’Urbervilles as a villainous tool of fate instrumental to Tess Durbeyfield’s tragedy. This idea goes with the associated assumption that Tess has all the moral and ethical reasons to reject him and embrace Angel. This paper seeks to redeem the name of Alec in Thomas Hardy’s Tess of the d’Urbervilles by positing that all the odium placed on him result from gross misrepresentation and that he is a hero of love, whose tragedy results from bestowing his love on Tess unrequitedly. It will be proven by comparison that Angel Clare is ironically the evil in the set-up, and the embodiment of all the tragic contents of Victorian moral laws and patriarchal customs. This study is a product of a qualitative research approach, involving interpretive and content analysis aimed at deepening the argument that while Alec’s conduct is almost completely unimpeachable, Angel is the agent of distraction and destruction that single-handedly brings about the tragedy of both Tess and Alec. The key finding is that Tess’s tragedy happens as a result of her rejecting Alec’s love and bestowing her love on the wrong person.

Modeling of bonding pressure based on the plastic deformation mechanism of interfacial voids closure in solid-state diffusion bonding

The model of the diffusion bonding pressure was established using the analysis calculation method and further verified by the finite element analysis (FEA) and the experiments. The normalized temperature was defined as the ratio of temperature and the melting point of the base materials. And the normalized bonding pressure was defined as the ratio of the applied bonding pressure and the yield strength at the bonding temperature. The contribution of the plastic deformation to the void closure expressed a linear relationship with the normalized bonding pressure, of which the slope was 3. The relationship was appropriate in TiAl6V4, pure copper C11000, aluminium alloy AA6061, stainless steel SUS 304, and Ni-based alloy Inconel 617 using analysis calculation. The diffusion bonding pressure design range can be summarized as σn = 0.05–0.577. Subsequently, the analytic computational model was verified by FEA. The results showed that the maximum stress was concentrated in the position of the void neck. And the linear relationship between the normalized bonding pressure and the bonded ratio was also tenable. There was a stable static error existed between FEA and the analytic computational analysis. Furthermore, the experimental verification showed the verification and accuracy of the analytic computational analysis results.

State of Health Estimation of Lithium-Ion Battery for Electric Vehicle Based on VMD-DBO-SVR Model

State-of-health (SOH) of lithium-ion batteries is an important indicator for measuring performance and remaining life. We propose an innovative prediction model that integrates variational mode decomposition (VMD), Dung Beetle optimizer (DBO), and support vector regression (SVR) algorithms. We extracted relevant features from the discharge characteristic curve and incremental capacity curve. We used Pearson and Spearman correlation coefficient methods for correlation analysis on the extracted health factors (HFs), selecting those that significantly impact SOH as input features. A DBO-SVR model was constructed to establish a nonlinear correlation between HFs and SOH, and the DBO algorithm was used to globally search and optimize the hyperparameters of the SVR model to improve its prediction accuracy. To reduce the impact of noise in battery signals on model performance, VMD technology was introduced to decompose battery signals into multiple intrinsic mode components, to extract useful features and remove noise to further improve prediction accuracy. The proposed method was validated using the NASA battery dataset and compared with other algorithm models. Results showed that the prediction model was significantly better than other models, with a maximum RMSE value of 0.84%, a maximum MAE value of 0.71%, and a stable prediction error value within 1%.

Tracking Control for $(x,u)$-Flat Systems by Quasi-Static Feedback of Classical States

It is well known that for flat systems the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovský state are available, a linear, decoupled and asymptotically stable tracking error dynamics can be achieved. However, from a practical point of view, it is often desirable to achieve the same tracking error dynamics by feedback of a classical state instead of a generalized one. This is due to the fact that the components of a classical state typically correspond to measurable physical quantities, whereas a generalized Brunovský state often contains higher order time derivatives of the (fictitious) flat output which are not directly accessible by measurements. In this paper, a systematic solution for the tracking control problem based on quasi-static feedback and measurements of classical states only is derived for the subclass of $(x,u)$-flat systems.

Monitoring and Reconstruction of Actuator and Sensor Attacks for Lipschitz Nonlinear Dynamic Systems Using Two Types of Augmented Descriptor Observers

Fault data injection attacks may lead to a decrease in system performance and even a malfunction in system operation for an automatic feedback control system, which has motive to develop an effective method for rapidly detecting such attacks so that appropriate measures can be taken correspondingly. In this study, a secure descriptor estimation technique is proposed for continuous-time Lipschitz nonlinear cyber physical systems affected by actuator attacks, sensor attacks, and unknown process uncertainties. Specifically, by forming a new state vector composed of original system states and sensor faults, an equivalent descriptor dynamic system is built. A proportional and derivate sliding-mode observer is presented so that the system states, sensor attack, and actuator attack can be reconstructed successfully. The observer gains are obtained by using linear matrix inequality to secure robustly stable estimation error dynamics. Moreover, a robust descriptor fast adaptive observer estimator is presented as a complement. Finally, the efficacy levels of the proposed design approaches are validated using a vertical take-off and landing aircraft system. Comparison studies are also carried out to assess the tracking performances of the proposed algorithms.

Optimization of machining path for integral impeller side milling based on SA-PSO fusion algorithm in CNC machine tools

The five axis linkage Computer Numerical Control machine tool for integral impeller can achieve blade machining through side milling, which is of great significance for improving the machining accuracy, production efficiency, and long-term stability of integral impeller blades. This study is based on non-uniform rational B-spline curves and aims to reduce the surface over cutting or under cutting of integral turbine blades. The path planning of non deployable ruled surfaces was analyzed in depth through side milling, and the path planning model of the side milling cutter axis was solved through a fusion algorithm of simulated annealing algorithm and particle swarm optimization algorithm, in order to find the optimal path through iterative process. As the number of iterations increased, the error values of particle swarm optimization algorithm and simulated annealing particle swarm optimization fusion algorithm gradually decreased, with convergence times of about 7 and 6, respectively. The stable error value of the fusion algorithm was 0.253, which is 30.45% lower than that of the particle swarm optimization algorithm. The optimal number of iterations for solving the model using particle swarm optimization algorithm and fusion algorithm was the 7th, with range values of 0.0213 and 0.0165 mm, respectively. The tool axis trajectory surface optimized by the fusion algorithm was closer to the tool axis motion state compared to the initial tool axis trajectory surface. The range of the sum of mean squared deviations for single and global cutting was 0.0011–0.0198 and 0.046–0.0341, but the overall error value was relatively small. This study effectively reduces the envelope error of machining tools and improves machining accuracy, thereby solving the principle error of non expandable ruled surfaces in the motion trajectory of the blade axis of the integral turbine. This provides new research ideas for the intelligent development of Computer Numerical Control machining technology.

New control scheme for a dynamic voltage restorer based on selective harmonic injection technique with repetitive controller

Repetitive controller and selective harmonic injection technique (SHI) in medium and low voltage distribution networks improve dynamic voltage restorer (DVR) DC bus voltages as well as nullify power quality (PQ) problems. DVRs use sinusoidal pulse width modulation (SPWM) firing control, but DC bus use seems to be limited, affecting density, cost, and power packaging. By adding 1/6th of the 3rd harmonic waveform to the basic waveform, SPWM yields the developed model. According to the findings, 15% of DC bus usage improves and produces high voltage AC. Nevertheless, just control systems perturb PQ. The proposed controller uses feed forward and feedback to enhance transient response and justify stable zero error. 3rd third harmonic injection pulse width modulation (THIPWM) improves total harmonic distortion (THD) in the proposed scheme. Power system computer aided design (PSCAD) simulation produced high accuracy for THIPWM and repetitive controllers.

Adaptive Neural Network Finite-Time Prescribed Performance Consensus Control for a Class of Second-Order Multi-Agent Systems

This research investigates the semi-global practical finite-time prescribed performance consensus control issue for a class of second-order multi-agent systems with unknown nonlinear functions. Unlike the previous finite-time control set by a finite-time performance function, we give finite-time control by constraining the terminal sliding manifold in a performance function. In addition, an adaptive neural network control scheme is designed, which simplifies the controller and avoids the chattering issue existing in traditional sliding mode control. Eventually, a novel adaptive finite-time prescribed performance consensus control strategy is designed, which ensures that all system variables are semi-globally practical finite-time stable and consensus errors of the multi-agent systems converge within the prescribed region in finite time. The effectiveness and practicality of the presented control strategy are evaluated by conducting simulation cases.

Estimating the productivity of US agriculture: The Fisher total factor productivity index for time series data with unknown prices

AbstractIn this paper, we propose a straightforward way to estimate the Fisher ideal total factor productivity (TFP) index (FI) in cases where price information is unavailable, using ‘shadow prices’ derived from data envelopment analysis (DEA). A Monte Carlo experiment shows that the shadow price Fisher ideal TFP index (SPFI) can effectively estimate the ‘true’ FI with relatively small (and stable) errors. The empirical application to the US agriculture sector (1948–2017) further suggests that the SPFI is a (superior) alternative to the traditional Malmquist DEA, especially in dealing with unbalanced panel or time series data when price data are unknown.

Assessment of Roughness Characterization Methods for Data-Driven Predictions

A comparative analysis is undertaken to explore the impact of various roughness characterization methods as input variables on the performance of data-driven predictive models for estimating the roughness equivalent sand-grain size ks\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_s$$\\end{document}. The first type of model, denoted as ENNPS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {ENN}_\ ext {PS}$$\\end{document}, incorporates the roughness height probability density function (p.d.f.) and power spectrum (PS), while the second type of model, ENNPA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {ENN}_\ ext {PA}$$\\end{document}, utilizes a finite set of 17 roughness statistical parameters as input variables. Furthermore, a simplified parameter-based model, denoted as ENNPAM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {ENN}_\ ext {PAM}$$\\end{document}, is considered, which features only 6 input roughness parameters. The models are trained based on identical databases and evaluated using roughness samples similar to the training databases as well as an external testing database based on literature. While the predictions based on p.d.f. and PS achieves a stable error level of around 10% among all considered testing samples, a notable deterioration in performance is observed for the parameter-based models for the external testing database, indicating a lower extrapolating capability to diverse roughness types. Finally, the sensitivity analysis on different types of roughness confirms an effective identification of distinct roughness effects by ENNPAM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {ENN}_\ ext {PAM}$$\\end{document}, which is not observed for ENNPA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {ENN}_\ ext {PA}$$\\end{document}. We hypothesize that the successful training of ENNPAM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {ENN}_\ ext {PAM}$$\\end{document} is attributed to the enhanced training efficiency linked to the lower input dimensionality.

Scalar auxiliary variable pressure-correction method for natural convection problems⋆

In this article, we present first-order standard pressure-correction and second-order rotational pressure-correction algorithms using an exponential scalar auxiliary variable (SAV) approach for the natural convection problems. The SAV pressure-correction method is linear and decoupled with explicit treatment of nonlinear terms, so it only needs to solve a sequence of Poisson equations for velocity and pressure at each time step. Furthermore, we proved the first- and second-order algorithms are unconditionally stable and established error estimates of the velocity, temperature and pressure approximation for the first-order algorithms without any restriction on the time step. Finally, some numerical experiments are provided to support the theoretical analysis and to show the performances of our proposed algorithms.

Adaptive Weighted Error-Correction Method Based on the Error Distribution Characteristics of Multi-Channel Alignment.

As process nodes of advanced integrated circuits continue to decrease below 10 nm, the requirement for overlay accuracy is becoming stricter. The alignment sensor measures the position of the alignment mark relative to the wafer; thus, sub-nanometer alignment position accuracy is vital. The Phase Grating Alignment (PGA) method is widely used due to its high precision and stability. However, the alignment error caused by the mark asymmetry is the key obstacle preventing PGA technology from achieving sub-nanometer alignment accuracy. This error can be corrected using many methods, such as process verification and multi-channel weighted methods based on multi-diffraction, multi-wavelength and multi-polarization state alignment sensors. However, the mark asymmetry is unpredictable, complex and difficult to obtain in advance. In this case, the fixed-weight method cannot effectively reduce the alignment error. Therefore, an adaptive weighted method based on the error distribution characteristic of a multi-channel is proposed. Firstly, the simulation result proves that the error distribution characteristic of the multi-alignment result has a strong correlation with the mark asymmetry. Secondly, a concrete method of constructing weight values based on error distribution is described. We assume that the relationship between the weight value of each channel and the deviations of all channels' results is second-order linear. Finally, without other prior process correction in the simulation experiment, the residual error's Root Mean Square (RMS) of fixed weighted method is 14.0 nm, while the RMS of the adaptive weighted method is 0.01 nm, when dealing with five typical types of mark asymmetry. The adaptive weighted method exhibits a more stable error correction effect under unpredictable and complicated mark asymmetry.

Matrix recovery from nonconvex regularized least absolute deviations

In this paper, we consider the low-rank matrix recovery problem. We propose the nonconvex regularized least absolute deviations model via ℓ1−αℓ2 (0<α<1) minimization. We establish the theoretical analysis of the proposed model and obtain a stable error estimation. Our result is a nontrivial extension of some previous work. Different from most of the state-of-the-art methods, our method does not need any knowledge of standard deviation or any moment assumption of the noise. Numerical experiments show that our method is effective for many types of noise distributions.

Event‐triggered H∞ and reduced‐order asynchronous filtering for fuzzy Markov jump systems with time‐varying delays

AbstractThe challenge of and asynchronous reduced‐order design for Takagi‐Sugeno (T‐S) fuzzy Markovian jump systems (MJSs) with time‐varying delays under the event‐triggered scheme (ETS) is investigated in this dissertation. A distributed event‐triggered strategy is provided on the basis of the specified triggering function to ensure consensus in the system, so effectively reducing data transmission. The existence conditions for a class of Markovian jump discrete‐time systems are determined. Unlike previous results, we present a novel membership function‐dependent fuzzy Lyapunov‐Krasovsikii (L‐K) functional with mode‐dependent integral terms, resulting in a stochastically stable filtering error system with the desired performance. By solving linear matrix inequality (LMIs), the recommended filter parameters are achieved. The proposed reduced‐order filter is demonstrated in numerical examples as effective as it is advantageous.

The residual life prediction of power grid transformers based on GA-ELM computational model and digital twin data

As one of the core equipment of the power grid, the operation status of transformers directly affects the stability and reliability of the power system. To accurately evaluate the remaining life of power grid transformers, a genetic algorithm is applied to optimize the Extreme Learning Machine based on digital twin technology. Then, considering changes in load rate, a residual life prediction model for power grid transformers is constructed. From the results, the error of the research method was within 2℃, with a maximum error of only 1.76℃. The research model converged with a fitness value of 0.04 at 150 iterations. It showed good predictive performance for hot spot temperatures under different load rates, with an average accuracy of 99.97%. Compared with backpropagation models and extreme learning machine models, the research method improved accuracy by 2.85% and 1.01%, respectively, with small and stable prediction errors. It verified the superiority of the research model, indicating that the research method can improve the accuracy of predicting the remaining life for power grid transformers. By monitoring the operation status of transformers in real-time, potential faults can be detected in a timely manner. The maintenance and replacement can be carried out in advance to avoid power outages caused by equipment damage. In addition, the research can provide reference for the planning and design of power systems, and support the stability and reliability of power systems.