Nonlinear Estimation Method Research Articles

Application of Nonlinear Optimization in Flight Path Reconstruction of a Sub-scale Aircraft

One key challenge in working with free-flight test data is ensuring its compatibility with the dynamic systems of sub-scale unmanned aircraft. This is crucial to avoid errors in measurements, bias, or scaling issues that could compromise the integrity of the estimated results. We refer to this initial processing step as data compatibility checking, a rigorous process that forms the foundation of our research.Typically, this verification process involves flight path data reconstruction (FPR) predicated on estimating the aircraft’s flight kinematics. The predominant methodologies encompass the stochastic approach, the Extended Kalman Filter (EKF), and the deterministic approach, employing the Output Error Method (OEM). In this research, we propose to approach the problem from the perspective of a nonlinear optimizer to estimate the reconstruction of data derived from free-flight tests of a sub-scale aircraft.The nonlinear optimizer we employ in this research was designed to verify the authenticity of the data representing the aircraft's actual flight. It does this by comparing the measurements of attitude angles, accelerations, and velocities with the expected kinematic behavior of the aircraft. This rigorous evaluation process ensures that the reconstructed data is as close to the actual flight as possible, enhancing the reliability of our results.The sub-scale model deployed in these tests was engineered to emulate the dynamic characteristics of a full-scale aircraft, utilizing the Froude number criterion for appropriate scaling. The chosen aircraft for this project was a Cessna 177B, and the sub-scale aircraft was developed by the Aeronautical Systems Laboratory (LSA) at the Aeronautics Institute of Technology (ITA).This study will delineate the outcomes achieved through FPA employing OEM techniques and compare these results with the studies derived from the proposed nonlinear estimation method.

Modeling and Measurement of Tool Wear During Angular Positioning of a Round Cutting Insert of a Toroidal Milling Tool for Multi-Axis Milling

The aim of this study was to develop a concept for an angular positioning method for a round cutting insert in a torus cutter body dedicated to the multi-axis milling process under high-speed machining cutting conditions. The method concept is based on a developed wear model using a non-linear estimation method adopting a quasi-linear function. In addition, a tool life model was developed, taking into account the cutting blade work angle parameter, the laser marking method for the round cutting insert, and a wear measurement methodology. The developed tool wear model provides an accuracy of 90% in predicting the flank wear of the cutting blade. The developed procedure for angular positioning of the round cutting insert enables the entire cutting edge to be fully utilized, extending the total tool life. In addition, the measured largest defect values between the worn cutting edge and the nominal outline of the round cutting insert indicate the location of notching-type wear.

A convolutional neural network based method for fork type wing fuselage docking

The fork-ear connection attachment method is a widely used technique for attaching the fuselage to the wing. During the fork-ear wing-fuselage docking process, it is essential to ensure that the fork-ear holes in the fuselage and wing are precisely aligned before inserting the mounting pins to complete the final connection. Thus, the alignment accuracy of the fork-ear holes is crucial during the assembly process. When employing conventional visual servo methods to determine the pose adjustment for fork-type wing-fuselage docking, it is necessary to establish a conversion relationship between the image, camera, and posture adjustment mechanism. However, this process can introduce various nonlinear errors that are challenging to compensate for through mathematical modeling. To address this issue, this paper proposes a method for nonlinear mapping estimation of the pose adjustment amounts and develops a pose adjustment estimation convolutional neural network (PAAECNN) with superior performance validated through experiments and discussions. PAAECNN achieves end-to-end mapping from the fork-ear intersection hole images to the pose adjustment amounts for fork-ear wing-fuselage docking. The experimental results demonstrate that the proposed method for estimating the pose adjustment amounts in fork-ear wing-fuselage docking is highly accurate and suitable for visually guided docking tasks.

Examining the impact of ecological deficit on life expectancy in GCC countries: a nonlinear panel data investigation

AbstractThe Gulf Cooperation Council (GCC) countries have witnessed remarkable economic growth over recent decades. Arguably, this progress of these major oil and natural gas producers has come to the detriment of the environment in terms of increased CO2 emissions and associated ecological degradation. The effects of these high emissions and environmental challenges on human health, specifically life expectancy (LE), have not been thoroughly explored in the literature. We aim to fill this research gap by assessing the relationship between Ecological footprint deficiency and the diverse and context-specific factors affecting LE in the GCC, highlighting the critical roles of urbanization, economic indicators, and digitization in shaping health outcomes. The study employs panel data for the 2000–2020 period. It utilizes linear and non-linear panel estimation methods to analyze these variables’ long-term and short-term effects. Specifically, we run unit root tests, cointegration analysis to validate our datasets, and OLS, ARDL, and panel threshold regressions to examine said relationships. Our findings reveal a significant relationship between ecological footprint and LE across the GCC countries. The results indicate that a higher ecological deficit is associated with lower LE in our sampled nations. Meanwhile, our panel threshold results highlight more nuanced impacts of our variables of interest, revealing significant threshold effects and intricate dynamics influencing LE. Our results are robust when substituting CO2 emissions for the ecological footprint suggesting and supporting our evidence for a more complex, potentially nonlinear relationship. Our study emphasizes the urgent need for sustainable environmental policies to mitigate health risks and promote long-term well-being in the GCC region. Nuanced approaches are needed to address each GCC country's health and environmental challenges.

Observer-based consensus control for a class of nonlinear singular multi-agent systems

This paper studies the bounded consensus control problem for nonlinear singular multi-intelligence systems (NSMASs) based on observers, where the structure of nonlinear dynamics is completely unknown. Firstly, the unknown nonlinear terms are estimated by the linear parameterization method. However, since the system state is not directly available, the observers are used for state estimations, which leads to a double estimation problem in the parameterization process. Moreover, the distributed adaptive control protocols and the adaptive laws of unknown parameter estimations are developed in the leader-following and leaderless frameworks. Furthermore, the proposed control protocols achieve bounded consensus for the NSMASs. And the proposed nonlinear estimation methods guarantee bounded estimation performance of the unknown nonlinear terms in the double estimation problem. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

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 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 > 30 % (the second critical level) indicate extreme deterioration of habitat conditions and transition to a «physically controlled» state of the communities.

A Dynamic Event-Triggered Saturation Method for Nonlinear Estimation with Application to Drag-free Control Systems

A Dynamic Event-Triggered Saturation Method for Nonlinear Estimation with Application to Drag-free Control Systems

Nonlinear solutions applied to parameter estimation of overhead transmission lines and submarine cables in offshore facilities

AbstractThis paper proposes a nonlinear analysis of the parameter estimation problem in overhead and submarine power cable applications. The proposed methodology is able to estimate both positive and zero sequence parameters. Also, the measurement model incorporates random uncertainty in a rigorous manner, addressing the issue of noise propagation after applying symmetrical components. Three nonlinear estimation methods were studied to address the nonlinear least squares problems. Several noise levels and sample sizes were considered to demonstrate the robustness of the proposed approach. Finally, the methods were validated using both a simplified 2‐bus system and the IEEE 14‐bus system. The results obtained demonstrated significantly better performance compared to similar results found in the technical literature.

Fault estimation for nonlinear parameter-varying time-delayed systems

A fault estimation method for a class of nonlinear parameter-varying systems subject to time-varying delay and unmeasured nonlinearities is presented. The unmeasured time-varying parameters are effectively handled using a sector-based condition approach. A gain-scheduling intermediate estimator is proposed to simultaneously estimate the system state and the unknown faults. Design conditions are derived based on Lyapunov–Krasovskii functional and integral inequality techniques. These conditions, expressed as linear matrix inequalities, ensure that the estimation error dynamics are input-to-state stable with respect to the time-derivative of the faults. Moreover, it is demonstrated that for the case of piecewise constant faults, the estimation error dynamics are exponentially stable. As a corollary result, conditions are also presented to design gain-scheduling intermediate estimators for nonlinear parameter-varying systems without time-varying delays. Three physically motivated examples are provided to demonstrate the effectiveness and practical interests of the proposed nonlinear estimation method.

A novel nonlinear spectrum estimation method and its application in on-line condition assessment of bearing-rotor system

In this paper, a novel approach for nonlinear spectrum estimation is proposed and combined with Support Vector Machine (SVM) classifier to assess the condition of bearing-rotor systems, including fault types and severity. The proposed approach involves extraction and reconstruction of target harmonics, dynamic process modeling of the reconstructed signal based on a data-driven method, and extraction of nonlinear spectrum features in the form of nonlinear output frequency response functions (NOFRFs). The focus is on the influence of model stability and accuracy evaluation on the robustness of NOFRFs. Then the robustness of the NOFRFs based on the proposed estimation approach is compared with the conventional estimation approach using simulation cases and experiments. SVM is used to classify the extracted nonlinear spectrum features. Finally, the classification accuracy of NOFRFs evaluated by the proposed approach is compared with time-domain and frequency-domain features. Neighborhood Component Analysis (NCA) is used to select sensitive features and improve classification accuracy. The proposed condition assessment strategy does not require the selection of sensitive features, ensuring the stability of assessment results, which is also a significant advantage of the proposed strategy.

Parallel Kalman filter group integrated particle filter method for the train nonlinear operational status high-precision estimation under non-Gaussian environment

For the problem of multi-mode state estimation in actual train operation, this paper proposes a nonlinear non-gaussian high-precision parallel Kalman filter group (NN-HEKFG) integrated Particle Filter. A multi-model Gaussian decomposition of the probability density function for state equations and measurement equations is performed, and each local state model is represented by a multi-dimensional high-order polynomial to establish the expanded dimensional state model. Then, by updating the mean and variance of the local state expanded dimensional model and in turn solving the particle filtering posterior probability density distribution function, the global estimation results are obtained. In reducing the number of Gaussian terms, a new parameter reduction criterion is established, which can effectively carry out the re-identification of parameters such as weights and means, so as to avoid the problem of parameter explosion. The superiority of NN-HEKFG over particle filters and Gaussian sum filters and its effectiveness for train running state estimation are verified by simulating the multi-model running state of trains.

Image-Like Situational Difference Mapping (ILSDM)-Based Method for Detecting Anomalies in Electromagnetic Environment

Electromagnetic environment anomaly radiation source detection (EMEARD) can provide a basis for electromagnetic (EM) equipment behavior cognition and battlefield threat assessment. Existing methods mainly focus on generating EM space situations but ignore the research on anomaly signal detection. In this paper, the connections between information geometry and performance of sensor networks for anomaly detection are explored. Nonlinear estimation methods based on information geometry can be directly used for anomaly detection. However, Riemann distance as a metric function faces the disadvantages of extensive computation and high complexity. To tackle this issue here, we propose a method based on image-like situation difference mapping, namely ILSDM. which takes the data-driven strategy to obtain the analytic expression of situation difference mapping distance function (DMDF), and anomaly detection is equivalent to the mapping reconstruction of information geometry. Firstly, the EM space situation is acquired through the distributed sensor network. In addition, to solve the perceptual blind area problem, the sensors’ data is estimated by spatial autocovariance optimal interpolation algorithm (Kriging). Secondly, we apply the Gaussian mixture model (GMM) to fit the statistical features of each sensing node into probability density function (PDF), and adjacent sensors with similar PDF are fused by the neighbor average fusion method (NAF). Then, based on the information geometry, the fused PDFs are mapped to the Riemannian manifold space as a series of coordinates, and we further propose to use image-like situation (ILS) to represented the EM space situation. Finally, DMDF measures the information distance between different ILSs to achieve anomaly detection. Numerical simulations and real experiments were conducted to prove the superiority and feasibility of our method for anomaly detection in EM space.

Trade Infrastructure and Export Competitiveness in the East African Community

The purpose of this paper is to examine the influence of trade infrastructure components: port infrastructure, telephone usage and electricity on the export competitiveness of firms in the East African Community (EAC). The study adopted the structural gravity model and the Poisson Pseudo Maximum Likelihood (PPML), a nonlinear estimation method that was applied in STATA on balanced panel data for the period of 2007 to 2018. Data was obtained from World Bank International Trade Centre (ITC) and World Bank development indicators. Results show that telephone usage, electricity and port infrastructure are positive and significant predictors of export competitiveness in East African Community partner states. The results of this study show that electricity usage, telephone usage and port infrastructure are important contributors to improving export competitiveness in the EAC. There is a need to examine the intricate nature of the EAC economy in order to further this study’s findings. The EAC partner states need to embrace deep integration by removing the behind-the-border trade barriers, in addition to other trade restrictions, to create a common economic space among member states. This will further shrink the delivery time and the tracking and tracing of exports hence improving the competitiveness of EAC exports within the region and outside. Also, common and harmonized economic policies and regulations can be implemented through mutual recognition agreements where countries agree to recognize one another’s conformity assessments.

Convolutional neural network-based pose mapping estimation as an alternative to traditional hand-eye calibration.

The vision system is a crucial technology for realizing the automation and intelligence of industrial robots, and the accuracy of hand-eye calibration is crucial in determining the relationship between the camera and robot end. Parallel robots are widely used in automated assembly due to their high positioning accuracy and large carrying capacity, but traditional hand-eye calibration methods may not be applicable due to their limited motion range and resulting accuracy problems. To address this issue, we propose using a pose, nonlinear mapping estimation method to solve the hand-eye calibration problem and have constructed a 1-D pose estimation convolutional neural network (PECNN) with excellent performance, through experiments and discussions. The PECNN achieves an end-to-end mapping of the variation of the target object pose to the variation of the robot end pose. Our experiments have shown that the proposed hand-eye calibration method has high accuracy and can be applied to the automated assembly tasks of vision-guided parallel robots. Moreover, the method is also applicable to most parallel robots and tandem robots.

A Precise Zenith Hydrostatic Delay Calibration Model in China Based on the Nonlinear Least Square Method

Abstract Zenith hydrostatic delay (ZHD) is a crucial parameter in Global Navigation Satellite System (GNSS) navigation and positioning and GNSS meteorology. Since the Saastamoinen ZHD model has a larger error in China, it is significant to improve the Saastamoinen ZHD model. This work first estimated the Saastamoinen model using the integrated ZHD as reference values obtained from radiosonde data collected at 73 stations in China from 2012 to 2016. Then, the residuals between the reference values and the Saastamoinen modeled ZHDs were calculated, and the correlations between the residuals and meteorological parameters were explored. The continuous wavelet transform method was used to recognize the annual and semiannual characteristics of the residuals. Because of the nonlinear variation characteristics of residuals, the nonlinear least squares estimation method was introduced to establish an improved ZHD model—China Revised Zenith Hydrostatic Delay (CRZHD)—adapted for China. The accuracy of the CRZHD model was assessed using radiosonde data and International GNSS Service (IGS) data in 2017; the radiosonde data results show that the CRZHD model is superior to the Saastamoinen model with a 69.6% improvement. The three IGS stations with continuous meteorological data present that the BIAS and RMSE are decreased by 2.7 and 1.5 (URUM), 5.9 and 5.3 (BJFS), and 9.6 and 8.8 mm (TCMS), respectively. The performance of the CRZHD model retrieving PWV was discussed using radiosonde data in 2017. It is shown that the CRZHD model retrieving PWV (CRZHD-PWV) outperforms the Saastamoinen model (SAAS-PWV), in which the precision is improved by 44.4%. The BIAS ranged from −1 to 1 mm and RMSE ranged from 0 to 2 mm in CRZHD-PWV account for 89.0% and 95.9%, while SAAS-PWV account for 46.6% and 58.9%. Significance Statement Zenith hydrostatic delay (ZHD) is one of the most important parameters in Global Navigation Satellite System (GNSS) navigation and positioning and GNSS meteorology, which can be derived from a precise ZHD model due to its stability. This research established an improved ZHD model for China to obtain accurate ZHD, which is a prerequisite for pinpoint precipitable water vapor (PWV) retrieval. And the PWV value is beneficial to analyze the change in precipitation in some regions, forecast the short-term rainfall, and monitor the climate.

Modeling the competitive transmission of the Omicron strain and Delta strain of COVID-19

Since November 2021, there have been cases of COVID-19's Omicron strain spreading in competition with Delta strains in many parts of the world. To explore how these two strains developed in this competitive spread, a new compartmentalized model was established. First, we analyzed the fundamental properties of the model, obtained the expression of the basic reproduction number, proved the local and global asymptotic stability of the disease-free equilibrium. Then by means of the cubic spline interpolation method, we obtained the data of new Omicron and Delta cases in the United States of new cases starting from December 8, 2021, to February 12, 2022. Using the weighted nonlinear least squares estimation method, we fitted six time series (cumulative confirmed cases, cumulative deaths, new cases, new deaths, new Omicron cases, and new Delta cases), got estimates of the unknown parameters, and obtained an approximation of the basic reproduction number in the United States during this time period as R0≈1.5165. Finally, each control strategy was evaluated by cost-effectiveness analysis to obtain the optimal control strategy under different perspectives. The results not only show the competitive transmission characteristics of the new strain and existing strain, but also provide scientific suggestions for effectively controlling the spread of these strains.

The increase in the elasticity of substitution between capital and labour: a repeated cross-country investigation

ABSTRACT The economics literature emphasizes the importance of the elasticity of substitution between capital and labour in several economic contexts. However, analyses of the effect of the elasticity of substitution on the direction of technological change are often overlooked. Most assessments of the direction of technological change rely on a Constant Elasticity of Substitution (CES) production framework. This strand of empirical work considers the elasticity of substitution between capital and labour as a deep and fixed parameter. In this article, we show that the change in the elasticity of substitution that has occurred in recent decades might be an alternative source of change of factor income shares in addition to changes in factor-augmenting technological change. We construct a theoretical environment in which the elasticity of substitution is determined endogenously by the capital share and capital intensity. Rolling window estimates and non-linear estimation methods show that the elasticity of substitution in nine OECD economies observed between 1950 and 2017 was not constant and that, in fact, in the latter half of the 1970s, the elasticity of substitution increased, in the presence of labour-augmenting technical change.

The Simple Solution for Nonlinear State Estimation of Ill-Conditioned Systems: The Normalized Unscented Kalman Filter

An easy-to-implement method for nonlinear state estimation for ill-conditioned systems is proposed. By propagating standard deviations and correlations instead of the covariance in the unscented Kalman filter (UKF), the condition numbers of relevant matrices are reduced. The reduction in the condition number is related to the scaling of the problem. Hence, what we propose is a normalization method that acts as an “auto-scaler”. Compared to other methods in state estimation for ill-conditioned systems, our proposed method factors the covariance matrix into physically meaningful statistics which can be used to check for filter divergence online. The method is compared to a standard UKF in a case study and shows a significant reduction in the condition number.