Nonlinear Estimation Research Articles

Cross validation based transfer learning for cross-sectional non-linear shrinkage: A data-driven approach in portfolio optimization

Enhanced covariance estimation approaches, such as (non-)linear shrinkage, are well established in the literature. Non-linear shrinkage estimators generally minimize a certain loss function regarding statistical assumptions about the future covariance matrix. At the same time, the problem of covariance estimation is traditionally considered from a rather restrictive view since the only available data to determine the estimation parameters is given by the return history of the actual portfolio constituents. In this study, we propose a novel and purely data-driven perspective on covariance estimation. We present a non-linear shrinkage estimator that determines the estimation parameters using cross validation to be historically optimal on a disjoint dataset of assets according to the given objective, such as minimum variance or maximum risk-adjusted return. We then transfer the historically optimal estimation parameters learned on the disjoint dataset to the actual covariance estimation problem. Thereby, the sample eigenvalues are corrected in a purely data-driven way, agnostic to theoretically derived parameters. Another benefit of focusing on disjoint data is that we address the problem of limited data availability in high-dimensional estimation problems when the number of assets exceeds the history length. Our empirical evaluation, based on a total of six stock market indices and various problem dimensions, shows that our approach outperforms existing cross-sectional estimators in minimizing variance and maximizing risk-adjusted return. While our study is limited to the cross-section, the method of parameter selection using cross validation and transfer learning can also be combined with other estimators, such as time-series methods.

Research on adaptive feedforward control method for Tiltrotor Aircraft/Turboshaft engine system based on radial basis function neural network

The paper proposes an adaptive feedforward control approach based on a radial basis function neural network to address the issue of poor disturbance rejection capability in conventional integrated control methods for tiltrotor aircraft propulsion systems. Firstly, a comprehensive simulation model of the tiltrotor aircraft and turboshaft engine is established, and its accuracy is validated against the results of the General Tiltrotor Integrated Simulation Code. Building upon this, a cascade Proportional-integral control parameter design method based on separation principles is proposed to tackle the problem of designing control parameters for the Proportional Integral main loop structure. Subsequently, an adaptive feedforward control method that takes into account both aircraft-induced disturbances and model uncertainties for turboshaft engines is presented using a Radial Basis Function neural network. This approach includes a nonlinear estimator capable of estimating load disturbances and a Radial Basis Function adaptive feedforward controller. Furthermore, stability proof of the closed-loop system is provided based on Lyapunov function analysis. Finally, digital simulations and hardware-in-the-loop experiments are conducted based on a typical tiltrotor flight mission. The results demonstrate that the proposed method effectively mitigates the power turbine drop compared to the conventional Proportional Integral controller with collective pitch feedforward.

Smoking Intensity is Associated With Progressive Optic Nerve Head Vessel Density Loss in Glaucoma.

A lifetime history of greater smoking consumption was associated with faster vessel density loss over time. Smoking intensity should be considered when assessing the risk of glaucoma progression, as well as its management. To investigate the relationship of smoking and smoking intensity, with the rate of optic nerve head (ONH) whole image capillary density (wiCD) loss in primary open angle glaucoma (POAG) and glaucoma suspect patients. In this longitudinal study, patients with POAG who had at least 2 years of follow-up and optical coherence tomography angiography (OCTA) performed at a minimum of 4 visits were selected for study. The smoking intensity was calculated as the pack-year at the baseline OCTA. Univariable and multivariable linear mixed models were used to determine the effect of each parameter on the rates of wiCD loss over time. Nonlinear least-squares estimation with piecewise regression model was used to investigate the cutoff point for the relationship between wiCD loss and smoking intensity. One hundred sixty-four eyes (69 glaucoma suspect and 95 POAG) of 110 patients were included with a mean (95% CI) follow-up of 4.0 (3.9 to 4.1) years. Of the 110 patients, 50 (45.5%) had a reported history of smoking. Greater smoking intensity was associated with faster wiCD loss [-0.11 (-0.23 to 0.00)] %/year per 10 pack-year higher; P =0.048) after adjusting for covariates. The wiCD thinning became significantly faster when smoking intensity was greater than 22.2 pack-years. Smoking had no effect on the rate of wiCD thinning in patients who smoked <22.2 pack-years during their lifetime. A history of greater smoking consumption was associated with faster vessel density loss, suggesting smoking intensity as a potential risk factor for glaucoma.

A Multistage Nonlinear Method for Aeroengine Health Parameter Estimation Based on Adjacent Operating Points

Abstract Health parameter estimation is the core of engine gas path analysis (GPA), which is widely adopted for engine safety improvement, as well as for operation and maintenance cost reduction. The major challenge of GPA lies in the contradiction between the high dimensions of parameters under estimation, e.g., health parameters, and the limited measurements obtainable from a small number of sensors. Existent GPA methods for health parameters commonly apply dimension reduction before estimation, leading to information loss and hence inaccurate estimation. To tackle the challenge of limited sensor measurements and to have more system outputs than parameters under estimation, we proposed to augment the output vector of the system model by combining the measurements from multiple adjacent operating points. But the engine model can face the problem of homogenization if using data from adjacent operating points. This can, in turn, lead to a low identifiability of parameters. We analyze the internal mechanism of such large deviation of the parameter estimation results based on linear models and argue for the need of nonlinear method. Hence, we propose a multistage nonlinear parameter estimation method for health parameters, combining biased and unbiased estimation. In our extensive simulations based on 10 output measurements of a JT9D engine, our method can estimate 130% more parameters than the widely used GPA method, while reducing the maximum estimation error of health parameters from 2.2% to 0.1%.

New Equations for the Estimation of the Age of the Formation of the Harris Lines.

Harris Lines (HLs) are transverse, sclerotic lines that can be visualized by X-ray imaging and that occur in long bones, most commonly in the tibia and femur. HLs are associated with disrupted bone mineralization during endochondral ossification, affecting the normal growth process. The etiology of HLs is debated, with some claims linking their presence to detrimental factors such as inflammation, malnutrition, alcohol abuse, and diseases. The age at which HLs form can be estimated based on their location, which allows for a retrospective assessment of the individual's health status during childhood or youth. The current study is concerned with providing new equations to estimate the age of Harris Line occurrences using a simple calculating tool. Bone growth curves were derived based on a dataset provided by Byers in 1991 using non-linear estimation. The best model was chosen with the Akaike Information Criterion. New and old methods were compared through Bland-Altman plots. As a result, we managed to produce reliable, well-fitted growth curves, concordant with previous methods.

New Weibull Log-Logistic grey forecasting model for a hard disk drive failures

Forecasting the failure of hard disk drives is important in server operation and has attracted increasing attention. However, current disk drive warning systems suffer from high false positive rates and high resource consumption when dealing with hard disk drive overall failure. Therefore, to accurately and stably predict hard disk drive overall failure, this paper develops a new Weibull Log-Logistic grey forecasting model with multiple interaction effects. Firstly, to capture and fit the trend of hard disk failure data flexibly and reduce the volatility, a new accumulation generation operator is established by introducing the Weibull Log-Logistic mixture distribution. Secondly, the proposed model constructs a multiple interaction term to describe the nonlinear relationship of the dependent variables on the system behavior series and the multiple interaction effects between the independent variables. Then, the parameter estimation method is designed to improve the fitting accuracy of the new model, in which linear estimation method, nonlinear estimation method, and meta-heuristic optimization algorithm are used to calculate the parameter values according to their categories. Finally, four varieties of hard disk drive data sets from BackBlaze are selected as study cases to validate the effectiveness of the proposed model. The results show that the mean MAPE of the proposed method is 2.1181 %, 2.2306 %, 8.1712 %, and 4.3417 %, respectively, corresponding to (hard disk drives ST8000NM0055, ST12000NM0007, ST10000NM0086, and ST14000NM0138), and the average value of the evaluation metrics are optimal in all competing models. Furthermore, it is observed that the number of reallocated sectors has the greatest influence in causing the failure of hard disk drives.

On critical levels of ecological status for macrozoobenthic communities in Peter the Great Bay of the Japan Sea: field studies

Relationship between the environmental stress index (PES) and the mean total explained variance of biotic parameters (MEV, as a measure of the environmental factors influence on macrozoobenthic communities) is determined using the methods of multiple linear stepwise regression analysis and non-linear estimation. The relationship is S-shaped, with the points of beginning and end of linear growth confined to the PES ≈ 15–16 % and 30 %. These levels should be considered as boundary criteria for the status of macrozoobenthic communities. Under favorable environmental conditions, PES does not exceed 15 % (the first critical level), that is close to a «biologically balanced» state of the communities. The PES values in the range of 15–30 % indicate an increased influence of limiting factors, but this influence is not destructive. The PES values &gt; 30 % (the second critical level) indicate extreme deterioration of habitat conditions and transition to a «physically controlled» state of the communities.

Nonlinear kinetic estimate of Raman reflectivity in a hohlraum plasma with a radiation hydrodynamics code.

In this Letter, we introduce an inline model for stimulated Raman scattering (SRS), which runs on our radiation hydrodynamics code troll. This model accounts for nonlinear kinetic effects and for the SRS feedback on the plasma hydrodynamics. We dubbed it PIEM because it is a fully "PredIctivE Model," because no free parameter is to be adjusted a posteriori in order to match the experimental results. PIEM predictions are compared against experimental measurements performed at the Ligne d'Intégration Laser. From these comparisons, we discuss the PIEM ability to correctly catch the impact of nonlinear kinetic effects on SRS.

The impact of eco-preneurship and green technology on greenhouse gas emissions - An analysis of East Asian economies

The pressing need to address the effects of rising greenhouse gas emissions on the environment has become a global concern. Policymakers, governments, and stakeholders advocate a sustainable clean environment. Therefore, green technology and eco-entrepreneurship initiatives are being implemented to reduce these emissions. Despite their efforts in sustainable environments, there is insufficient research on how these initiatives impact economies. This study explores the impact of eco-entrepreneurship and green technology on reducing greenhouse gas emissions in East Asia. Using China and Japan, ranked the first and fifth highest greenhouse gas emitters globally, as case studies, the study employed ARDL and NARDL models for empirical analysis. The findings show that short-run linear estimates of eco-entrepreneurship are significant only in China, while nonlinear short-run estimates are significant for both China and Japan. Comparably, short-run linear estimates of green technology are significant for both China and Japan, while nonlinear coefficient estimates are significant only in Japan. The linear estimate of eco-entrepreneurship was significant and negative in both countries. The coefficient estimates for green technology are significant and negative for both countries. In the nonlinear model, the positive shock coefficient estimates for eco-entrepreneurship are negative and significant in China and Japan. These initiatives are vital for reducing greenhouse gas emissions and improving East Asian economies.

From Complexity to Clarity: M2KCSVA's Nonlinear Temporal Correlation Analysis and Stationary Estimation Pave the Way for Fault Diagnosis in Ironmaking Processes

From Complexity to Clarity: M2KCSVA's Nonlinear Temporal Correlation Analysis and Stationary Estimation Pave the Way for Fault Diagnosis in Ironmaking Processes

Nonlinear Gradient Field Estimation in Diffusion MRI Tensor Simulation.

Gradient nonlinearities not only induce spatial distortion in magnetic resonance imaging (MRI), but also introduce discrepancies between intended and acquired diffusion sensitization in diffusion weighted (DW) MRI. Advances in scanner performance have increased the importance of correcting gradient nonlinearities. The most common approaches for gradient nonlinear field estimations rely on phantom calibration field maps which are not always feasible, especially on retrospective data. Here, we derive a quadratic minimization problem for the complete gradient nonlinear field (L(r)). This approach starts with corrupt diffusion signal and estimates the L(r) in two scenarios: (1) the true diffusion tensor known and (2) the true diffusion tensor unknown (i.e., diffusion tensor is estimated). We show the validity of this mathematical approach, both theoretically and through tensor simulation. The estimated field is assessed through diffusion tensor metrics: mean diffusivity (MD), fractional anisotropy (FA), and principal eigenvector (V1). In simulation with 300 diffusion tensors, the study shows the mathematical model is not ill-posed and remains stable. We find when the true diffusion tensor is known (1) the change in determinant of the estimated L(r) field and the true field is near zero and (2) the median difference in estimated L(r) corrected diffusion metrics to true values is near zero. We find the results of L(r) estimation are dependent on the level of L(r) corruption. This work provides an approach to estimate gradient field without the need for additional calibration scans. To the best of our knowledge, the mathematical derivation presented here is novel.

Prediction of Production-Inflow Profile of a Well Producing Single-Phase Flow of Slightly Compressible Fluid from Multilayer Systems by Temperature and/or Pressure Transient Data

Summary This study focuses on the prediction of the production-inflow profile of a well producing a single-phase flow of slightly compressible fluid (water or oil flow) in a multilayered system using the layer permeability and skin values estimated by history matching spatial and temporal temperature and/or pressure data sets along the completion interval. Such data may be acquired by wireline formation testing, production-logging-tool (PLT), or distributed temperature sensing (DTS) fiber-optic cables. We use an in-house thermal, transient coupled reservoir/wellbore simulator developed during this study. It solves transient mass, momentum, and energy conservation equations simultaneously for both reservoir and wellbore. The effects of the Joule-Thomson (J-T), adiabatic expansion, conduction, and convection are all included for predicting the flow profiles across the wellbore. The results from our in-house simulator are verified with the results from a commercial simulator for the single-phase fluid flow of a vertical well producing geothermal brine and oil in a two-zone multilayer system. We also compare the results from our rigorous transient coupled wellbore/reservoir model with the results from a model assuming steady-state thermal wellbore model used in the previous studies. We find that the steady-state thermal wellbore model used in the previous studies that ignore accumulation terms in mass, momentum, and thermal energy balances is a reasonably accurate model for predicting wellbore pressures and temperatures when it is coupled with a nonisothermal reservoir model for slightly compressible fluid because the transient effect in the wellbore is less important with the slightly compressible fluid. We investigate the nonlinear parameter estimation problem based on the use of single or multiple observed temperature and/or pressure (if available) profiles recorded spatially inside the wellbore and at the sandface. The purpose is to identify if the wellbore or sandface data profiles are more useful to accurately estimate the permeability and skin information and predict a production-inflow profile of the well depending on the representation of an actual multilayer system by a reduced-layered or fine-layered model. We show that using an upscaled-layered model (e.g., representing each heterogeneous layer with a lumped single layer with uniform permeability and skin) provides estimates that are more toward the thickness-average permeability and skin factors of the layers and may not provide a good prediction of the well’s production-inflow profile. We show that including the sandface temperature data in regression worsens, while the use of wellbore temperature data sets improves the quality of parameter estimation if an upscaled multilayered model is used. We also show that regressing on multiple temperature profiles, preferably at the sandface, alone could be used to predict the production-inflow profile accurately if a “fine” multilayered heterogeneous model is used. We also investigate if including or excluding the temperature and/or pressure measurements at the nonperforated sections along the completion interval could help enhance the parameter estimation problem. The results show that when multiple profiles of temperatures including the data at nonperforated zones at different production rates are regressed, reliable estimates of the individual layer properties that predict the production-inflow profile accurately can be obtained, though layer permeability and skin factors may often exhibit wide 95% confidence intervals and high correlations among them. Adding sandface or wellbore pressure data, if available, into observed data sets in history matching always improves the quality of parameter estimation.

Particle Filter based on Jaya optimisation for Bayesian updating of nonlinear models

Particle filter (PF) is a powerful and commonly used filtering technique based on Sequential Monte Carlo framework. The main challenge in using PF for nonlinear state and parameter estimation is the degeneracy of particles. Although resampling techniques can solve this to some extent, it would still result in particle impoverishment when a limited number of particles are used thereby affecting the accuracy. Hence, a hybrid metaheuristic optimisation algorithm that combines the PF with Jaya optimisation, (PF-JAYA) has been proposed and implemented for joint state and parameter estimation for geotechnical engineering problems. The performance of PF-JAYA has been compared against the traditional Particle Filter with Sampling Importance Resampling (PF-SIR) technique. The synthetic examples show that PF-JAYA outperforms PF-SIR in terms of accuracy, rate of convergence, parameter identification and particle diversity. Furthermore, the performance of PF-JAYA is independent of the choice of prior distribution and due to its superior convergence proves to be efficient when working with sparse monitoring information. The performance of PF-JAYA on Bayesian updating of state and parameters of an elastoplastic model for a synthetic embankment case has also been evaluated where, along with PF-SIR, the Ensemble Kalman Filter (EnKF) is also chosen for comparison. Finally a further evaluation using the Lorenz ‘63 model, shows the superior performance of PF-JAYA in terms of accuracy and precision over the classical Data Assimilation techniques.

Comprehensive evaluation measures of nonlinear estimation algorithm performance

Although many scholars say that their algorithms are better than others in the state estimation problem, only a fewer convincing algorithms were applied to engineering practices. The reason is that their algorithms outperform others only in some aspects such as the estimation accuracy or the computation load. To solve the problem of performance evaluation of state estimation algorithms, in this paper, the comprehensive evaluation measures (CEM) for evaluating the nonlinear estimation algorithm (NEA) is proposed, which can comprehensively reflect the performance of the NEAs. First, we introduce three types of the NEAs. Second, the CEM combining the flatness, estimation accuracy and computation time of the NEAs, is designed to evaluate the above NEAs. Finally, the superiority of the CEM is verified by a numerical example, which helps decision makers of nonlinear estimation algorithms theoretically and technically.

Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth

Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth

A temperature control method of hot-bar soldering based on extended Kalman filter

PurposeThis study aims to introduce a novel technique for nonlinear sensor time constant estimation and sensor dynamic compensation in hot-bar soldering using an extended Kalman filter (EKF) to estimate the temperature of the thermocouple.Design/methodology/approachTemperature optimal control is combined with a closed-loop proportional integral differential (PID) control method based on an EKF. Different control methods for measuring the temperature of the thermode in terms of temperature control, error and antidisturbance are studied. A soldering process in a semi-industrial environment is performed. The proposed control method was applied to the soldering of flexible printed circuits and circuit boards. An infrared camera was used to measure the top-surface temperature.FindingsThe proposed method can not only estimate the soldering temperature but also eliminate the noise of the system. The performance of this methodology was exemplary, characterized by rapid convergence and negligible error margins. Compared with the conventional control, the temperature variability of the proposed control is significantly attenuated.Originality/valueAn EKF was designed to estimate the temperature of the thermocouple during hot-bar soldering. Using the EKF and PID controller, the nonlinear properties of the system could be effectively overcome and the effects of disturbances and system noise could be decreased. The proposed method significantly enhanced the temperature control performance of hot-bar soldering, effectively suppressing overshoot and shortening the adjustment time, thereby achieving precise temperature control of the controlled object.

Actuator and sensor fault isolation in a class of nonlinear dynamical systems

Fault isolation in dynamical systems is a challenging task due to modeling uncertainty and measurement noise, interactive effects of multiple faults and fault propagation. This paper proposes a unified approach for isolation of multiple actuator or sensor faults in a class of nonlinear uncertain dynamical systems. Actuator and sensor fault isolation are accomplished in two independent modules, that monitor the system and are able to isolate the potential faulty actuator(s) or sensor(s). For the sensor fault isolation (SFI) case, a module is designed which monitors the system and utilizes an adaptive isolation threshold on the output residuals computed via a nonlinear estimation scheme that allows the isolation of single/multiple faulty sensor(s). For the actuator fault isolation (AFI) case, a second module is designed, which utilizes a learning-based scheme for adaptive approximation of faulty actuator(s) and, based on a reasoning decision logic and suitably designed AFI thresholds, the faulty actuator(s) set can be determined. The effectiveness of the proposed fault isolation approach developed in this paper is demonstrated through a simulation example.

Полуэмпирическое моделирование температуры резания и шероховатости поверхности при точении конструкционных материалов твердосплавным инструментом с покрытием TiAlN

Introduction. In manufacturing, obtaining a specified surface roughness of the machined components is of great importance to fulfill functional requirements. However, this is significantly affected by the heat generated during processing, potentially causing variations in dimensional accuracy. The surface roughness significantly affects the fatigue performance of the component, while the cutting tool's lifespan is dictated by the generation of cutting temperatures. The purpose of the study is to create semi-empirical models for predicting surface roughness and temperature of different work materials. Improved cutting performance is achieved by precisely determining the cutting temperature in the zone being machined. However, calculating the cutting temperature for each specific case is fraught with difficulties in terms of labor resources and financial investments. This paper presents a comprehensive empirical formula designed to predict both theoretical temperature and surface roughness. The methodology. The surface roughness and temperature values were evaluated for EN 8, Al 380, SS 316 and SAE 8620 materials using TiAlN coated carbide tool. The TiAlN coating was formed using Physical Vapor Deposition (PVD) Technique. The response surface methodology was used to prepare predictive models. Cutting speed (140 to 340 m/min), feed (0.08 to 0.24 mm/rev) and depth of cut (0.6 to 1.0 mm) was used as input parameters for measuring the performance of all material in terms of surface roughness and cutting temperature. The tool-work thermocouple principle was used to measure the temperature at the chip-tool interface. A Novel Calibration Setup was developed to establish a connection between the electromotive force (EMF) generated during machining and the cutting temperature. Results and Discussion. It is observed that the power required for machining was largely transformed into heat. The highest cutting temperature is recorded when machining of SS 316 followed by SAE 8620, EN 8. However, low temperature is reported during machining of Al 380 and it is mainly governed by the thermal conductivity of the material. The lowest surface roughness is observed in SAE 8620, EN 8 material followed by SS 316 and Al 380. Semi-empirical method and regression model equations show a good agreement with each other. Statistical analysis of nonlinear estimation reveals that the cutting speed, feed, and density of the material have a greater effect on surface roughness, whereas the depth of cut has a greater effect on temperature generation. The study will be very useful for predicting industrial productivity when machining of EN 8, Al 380, SS 316 and SAE 8620 materials with TiAlN-coated carbide tool.

Estimating hidden relationships in dynamical systems: Discovering drivers of infection rates of COVID-19.

Discovering causal influences among internal variables is a fundamental goal of complex systems research. This paper presents a framework for uncovering hidden relationships from limited time-series data by combining methods from nonlinear estimation and information theory. The approach is based on two sequential steps: first, we reconstruct a more complete state of the underlying dynamical system, and second, we calculate mutual information between pairs of internal state variables to detail causal dependencies. Equipped with time-series data related to the spread of COVID-19 from the past three years, we apply this approach to identify the drivers of falling and rising infections during the three main waves of infection in the Chicago metropolitan region. The unscented Kalman filter nonlinear estimation algorithm is implemented on an established epidemiological model of COVID-19, which we refine to include isolation, masking, loss of immunity, and stochastic transition rates. Through the systematic study of mutual information between infection rate and various stochastic parameters, we find that increased mobility, decreased mask use, and loss of immunity post sickness played a key role in rising infections, while falling infections were controlled by masking and isolation.

Nonlinear imaging-based bubble cloud size estimates compared with histotripsy treatment zone: An in vitro study

Volterra filtering combined with subharmonic imaging was previously reported to enhance the visualization of the histotripsy bubble cloud. In this study, we compared the bubble cloud size obtained by imaging to the histotripsy ablation region using receiver operating characteristic (ROC) analysis. Histotripsy was performed in a red blood cell (RBC)-doped agarose phantom using a 1 MHz transducer. Ultrasound imaging data was acquired using a C5-2V probe and chirp-coded excitation (bandwidth: 2–5 MHz). These ultrasound acquisitions were then processed by subharmonic (SH) matched filtering alone, SH with quadratic Volterra filtering, and SH with cubic Volterra filtering. The therapy pulse and imaging sequence were interleaved (N = 100 frames), and a video camera was used to visualize the damaged region. A mean bubble cloud image was generated across all treatment sequences and co-registered with the camera image. A ROC curve was formed using binary classification of the mean bubble cloud versus the ablation zone, and the area under the ROC curve was determined. Filtering by quadratic and cubic Volterra filters reduced artifacts significantly [over 20 and 30 dB contrast-to-tissue enhancement (p &amp;lt; 0.01), respectively], along with achieving a high area under the ROC curve (0.97). These findings highlight the potential of Volterra filtering for histotripsy guidance.