Nonlinear Estimation Research Articles

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 Neural Phillips Curve and a Deep Output Gap

Many problems plague empirical Phillips curves (PCs). Among them is the hurdle that the two key components, inflation expectations and the output gap, are both unobserved. Traditional remedies include proxying for the absentees or extracting them via assumptions-heavy filtering procedures. I propose an alternative route: a Hemisphere Neural Network (HNN) whose architecture yields a final layer where components can be interpreted as latent states within a Neural PC. First, HNN conducts the supervised estimation of nonlinearities that arise when translating a high-dimensional set of observed regressors into latent states. Second, forecasts are economically interpretable. Among other findings, the contribution of real activity to inflation appears understated in traditional PCs. In contrast, HNN captures the 2021 upswing in inflation and attributes it to a large positive output gap starting from late 2020. The unique path of HNN’s gap comes from dispensing with unemployment and GDP in favor of an amalgam of nonlinearly processed alternative tightness indicators.

An ADCP Attitude Dynamic Errors Correction Method Based on Angular Velocity Tensor and Radius Vector Estimation

An acoustic Doppler current profiler (ADCP) installed on a platform produces rotational tangential velocity as a result of variations in the platform’s attitude, with both the tangential velocity and radial orientation varying between each pulse’s transmission and reception by the transducer. These factors introduce errors into the measurements of vessel velocity and flow velocity. In this study, we address the errors induced by dynamic factors related to variations in attitude and propose an ADCP attitude dynamic error correction method based on angular velocity tensor and radius vector estimation. This method utilizes a low-sampling-rate inclinometer and compass data and estimates the angular velocity tensor based on a physical model of vessel motion combined with nonlinear least-squares estimation. The angular velocity tensor is then used to estimate the transducers’ radius vectors. Finally, the radius vectors are employed to correct the instantaneous tangential velocity within the measured velocities of the vessel and flow. To verify the effectiveness of the proposed method, field tests were conducted in a water pool. The results demonstrate that the proposed method surpasses the attitude static correction approach. In comparison with the ASC method, the average relative error in vessel velocity during free-swaying movement decreased by 20.94%, while the relative standard deviation of the error was reduced by 17.38%.

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.

Event-triggered nonlinear state estimation with quantized innovations

This paper proposes an event-triggered (ET) estimator with quantization mechanism to relieve the bandwidth and energy limitations of wireless sensors, where the ET strategy reduces the overall communication rate of the system, and the quantization mechanism mitigates the instantaneous bit rate constraint. Then, Gaussian approximation is applied to derive the analytical form of the minimum mean squared error (MMSE) estimator under the event-triggered strategy and quantization mechanism. Furthermore, the relationship between the event-triggered parameter and the communication rate is explicitly established. Finally, theoretical results are validated through some simulations on a target tracking system.

GHZ protocols enhance frequency metrology despite spontaneous decay.

The use of correlated states and measurements promises improvements in the accuracy of frequency metrology and the stability of atomic clocks. However, developing strategies robust against dominant noise processes remains challenging. We address the issue of decoherence due to spontaneous decay and show that Greenberger-Horne-Zeilinger (GHZ) states, in conjunction with a correlated measurement and nonlinear estimation strategy, achieve gains of up to 2.25 decibel, comparable to fundamental bounds for up to about 80 atoms in the presence of decoherence. This result is unexpected because GHZ states do not provide any enhancement under dephasing due to white frequency noise compared to the standard quantum limit of uncorrelated states. The gain arises from a veto signal, which allows for the detection and mitigation of errors caused by spontaneous emission events. Through comprehensive Monte Carlo simulations of atomic clocks, we demonstrate the robustness of the GHZ protocol.

Deep learning based control of DSTATCOM for harmonic mitigation in hybrid distributed generation system with non-linear loads

The rising energy demand from the growing population has been historically met by conventional sources, but their availability is diminishing. To counter this, renewable energy sources are emerging as global alternatives to fossil fuels, with solar and wind power leading the way. Solar and wind energy, known for their reliability, are combined to enhance energy system stability and reduce generation costs. Implementing such hybrid systems enhances reliability and cost efficiency for load demands, especially for power electronics-based loads introducing harmonics. Various mitigation strategies have been developed, including active power filters like Distribution Static Compensators (DSTATCOM) that regulate power quality. However, conventional methods such as Synchronous Reference Frame (SRF) & Instantaneous Reactive Power (IRP) have limitations with non-linear loads and filter parameter estimation. To address these challenges, the paper proposes a Deep Learning (DL) control algorithm, using backpropagation (BP) for hybrid solar-wind systems, providing consistent and cost-effective energy solutions. The proposed technique's effectiveness is demonstrated through MATLAB/Simulink and real-time hardware setups.

Adaptive neural network backstepping control for the magnetorheological semi-active air suspension system with uncertain mass and time-varying input delay

Aiming at rejecting external disturbance induced by the random road profile, this paper proposes an adaptive robust control strategy to address the control problem of semi-active air suspension system installed with magnetorheological dampers (MRD) for enhancing ride comfort and handling performance. To effectively depict the inherent nonlinear dynamics of the adjustable air spring, a radial basis function neural network (RBFNN) model is trained by the experimental data offline, and an adaptive learning algorithm is introduced to maintain the modeling accuracy. Moreover, to handle the prevalent sensitive parameter variation (such as sprung mass), a nonlinear estimator is designed to estimate the uncertain sprung mass. Furthermore, a delay compensator is integrated into the control law to mitigate the impact of the time-varying input delay caused by the actuator of MRD to restrain the chattering phenomena. Additionally, the stability of the closed-loop system is rigorously proven by employing a Lyapunov–Krasovskii functional, guaranteeing the boundedness of both tracking error and estimation error. Simulation results are displayed and analyzed, illustrating the feasibility and efficiency of the proposed control strategy in depressing the sprung mass acceleration and tire deflection, showing its significance in both control performance enhancement and chattering elimination.

Adaptive nonlinear filtering algorithms for removal of non-stationary noise in electronystagmographic signals

Non-stationary physiological noise poses significant difficulties due to its time-varying and previously unknown characteristics. When processing electronystagmographic signals, linear filtering can distort diagnostically significant rapid changes caused by saccadic eye movements. In such cases, nonlinear filters based on robust estimators are more appropriate, whereas linear filtering effectively reduces white noise in parts of a signal with linear behaviour. Therefore, an adaptive signal processing approach that varies in nonlinearity from highly nonlinear robust estimation to linear averaging and combines their benefits appears promising. We have proposed a low-complexity adaptive method for switching filter sets and relevant filter parameter settings based on the estimated noise level and local signal behaviour. This method does not require time for filter parameter modification and does not need prior information on the signal model and noise variance. Based on this method, we have designed adaptive nonlinear filtering algorithms to exploit the advantages of both the nonlinear robust and linear averaging estimators. We have evaluated the filtering quality statistically using the minimum mean square error criteria and the maximum signal-to-noise ratio for a model signal with different levels of additive Gaussian noise. The proposed real-time adaptive filtering algorithms demonstrate a significant efficiency improvement compared to the commonly used filters. The proposed adaptive myriad algorithm achieves the highest efficiency by adjusting a sample myriad linearity parameter depending on the local estimate of a signal scale and changing the sliding window length and the coefficient affecting the linearity parameter.

Efficient Estimation of Synthetic Indicators for the Assessment of Nonlinear Systems Quality

The availability of synthetic indicators of the degree and type of nonlinearity in systems is used in various fields to assess system quality or to highlight possible malfunctions. Different distortion or damage indexes are synthetic measures designed (and standardized) to evaluate the frequency trend of specific aspects resulting from the nonlinear behavior of the system under consideration. The different measures of deviation from linear behavior quantitatively consider the system and its nonlinearity characteristics; they were defined according to practically feasible measurement methodologies and the various aspects of the system’s nonlinearity that needed to be highlighted. In parallel, techniques for representing and modeling nonlinear systems have been defined, capable of describing the system in a more general way, attempting to capture its input–output characteristics by varying the level of stress to which the system is subjected. Numerous modeling techniques have been proposed, aimed at representing the nonlinear behavior of physical devices. In this paper, after an extensive description of the Hammerstein model identification technique based on swept sinusoidal signals, we show how the nonlinear model of the system can be used to obtain accurate estimates of the parameter aimed at describing the nonlinearity characteristics of the system. This extensive description makes it possible to point out that the same Hammerstein model can be obtained not only from a single type of excitation, but it is shown that the identification technique can be extended to input signals of different types. The description of the method also makes clear the motivation behind the introduction of the proposed original technique for estimating, from a single measurement, the model parameters of the nonlinear system—and from these the synthetic estimators—relative to multiple values of the input signal amplitude, thus enabling a considerable increase in the estimation efficiency of these parameters. The proposed technique is verified with both synthetic and laboratory experiments, demonstrating the effectiveness of the method in evaluating nonlinear system parameters, distortion estimates, and parameters defined for an early detection of defects of the structure.

NON-HOMOGENEOUS POISSON PROCESS OF A QUADRATIC TRANSMUTED LOG-LOGISTIC MODEL

In recent years, software reliability engineering has become a major topic due to rapid technological advancements, as researchers work to interpret and analyze software reliability data. Therefore, establishing new software reliability models is essential to possess reliable tools for diagnosing software systems. This paper proposes a new NHPP model based on the quadratic transmuted log-logistic (QTLL) distribution. The characteristics of the model were obtained and graphically illustrated. Three real software data sets were applied to evaluate the proposed model based on different criteria. The parameters of the NHPP QTLL were estimated using maximum likelihood estimation (MLE), and nonlinear least squares estimation (NLSE), and a comparative analysis of the two estimation methods has been performed to estimate the model parameters. Additionally, a study was carried out to compare the suggested model with other well-known NHPP models. The results indicate that NLSE outperforms MLE in parameter estimation. Furthermore, the NHPP QTLL model demonstrated superior performance across all evaluation assessments compared to other models. The graphical representation also shows that the proposed model is more effective in fitting fault data than existing models.

Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects

Interstellar objects (ISOs) are likely representatives of primitive materials invaluable in understanding exoplanetary star systems. Due to their poorly constrained orbits with generally high inclinations and relative velocities, however, exploring ISOs with conventional human-in-the-loop approaches is significantly challenging. This paper presents Neural-Rendezvous—a deep-learning-based guidance and control framework for encountering fast-moving objects, including ISOs, robustly, accurately, and autonomously in real time. It uses pointwise minimum norm tracking control on top of a guidance policy modeled by a spectrally normalized deep neural network, where its hyperparameters are tuned with a loss function directly penalizing the model predictive control state trajectory tracking error. We show that Neural-Rendezvous provides a high probability exponential bound on the expected spacecraft delivery error, the proof of which leverages stochastic incremental stability analysis. In particular, it is used to construct a non-negative function with a supermartingale property, explicitly accounting for the ISO state uncertainty and the local nature of nonlinear state estimation guarantees. In numerical simulations, Neural-Rendezvous is demonstrated to satisfy the expected error bound for 100 ISO candidates. This performance is also empirically validated using our spacecraft simulator and in high-conflict and distributed unmanned aerial vehicle swarm reconfiguration with up to 20 unmanned aerial vehicles.

Control Based on Nonlinear Estimators of Parametric Uncertainties Applied to an Agricultural Tractor Equipped with a Towed Implement System

This article presents a nonlinear control strategy designed to address parametric uncertainties in an agricultural tractor system coupled to a towed implement. The controller ensures accurate tracking of lateral and yaw velocities relative to desired reference trajectories, even under the presence of parametric variations and external disturbances. The reference trajectories are derived from an “ideal” tractor model, excluding the effects of the towed implement. A High-Order Sliding Mode (HOSM) estimator is employed to provide an estimation of disturbances, which are subsequently mitigated by the controller to maintain system stability and precision. The effectiveness of the proposed control strategy is validated through Matlab-Simulink simulations, which include a double-step steer maneuver. This maneuver tests the system’s ability to handle abrupt steering changes, providing insight into the controller’s robustness and its capacity to ensure accurate trajectory tracking in demanding conditions.

Nonlinear effect of body mass index on postoperative survival following isolated heart transplantation

BackgroundGuidelines regarding recipient's Body Mass Index (BMI) for heart transplant are evolving with variable cutoffs depending on the country and institution. It is imperative to provide updated nonlinear estimates of postoperative risk attributable to a recipient’s BMI to evaluate relevance of existing cutoffs. MethodsA total of 30,787 patients were analyzed from the UNOS database. Patients receiving an isolated heart transplant ages 18 and older since 2010 were included. Overall survival was the primary outcome. A multivariate Cox proportional hazards model was applied and included a penalized smoothing spline term for recipient BMI and risk factors such as diabetes. We assessed the overall significance of the nonlinear penalized spline terms using an asymptotic Wald test. ResultsThe cohort consisted of 662 (2.2%) BMI<18.5, 9359 (30%) BMI 18.5-24.9, 10997 (36%) BMI 25-29.9, 9550 (31%) BMI 30-39.9, and 206 (0.7%) BMI≥40 patients. The nonlinear spline terms for recipient BMI were statistically significant (p<0.01). The Hazard Ratio appeared to grow linearly in BMI at an inflection point of BMI=26. No inflection point was observed at either of the ISHLT recommended cutoffs of BMI=30 (HR 1.11, CI 1.07-1.15) or BMI=35 (HR 1.29, CI 1.24-1.37). ConclusionsAfter multivariable adjustment, there is no sharp cutoff in survival risk at either BMI=30 or BMI=35. Unlike previously reported, postoperative survival risk grows approximately linearly in the BMI range from BMI=26 to BMI=40.

Retraction notice: Nonlinear function estimation fuzzy system (NFEFS) as a novel statistical approach to estimate nanofluids’ thermal conductivity according to empirical data

Retraction notice: Nonlinear function estimation fuzzy system (NFEFS) as a novel statistical approach to estimate nanofluids’ thermal conductivity according to empirical data

Nonexistence for a system of time‐fractional diffusion equations in an exterior domain

A system of time‐fractional diffusion equations posed in an exterior domain of ( ) under homogeneous Dirichlet boundary conditions is investigated in this paper. The time‐fractional derivatives are considered in the Caputo sense. Using nonlinear capacity estimates specifically adapted to the nonlocal properties of the Caputo fractional derivative, the geometry of the domain, and the boundary conditions, we obtain sufficient conditions for the nonexistence of a weak solution to the considered system.

A Robust Tri-Electromagnet-Based 6-DoF Pose Tracking System Using an Error-State Kalman Filter.

Magnetic pose tracking is a non-contact, accurate, and occlusion-free method that has been increasingly employed to track intra-corporeal medical devices such as endoscopes in computer-assisted medical interventions. In magnetic pose-tracking systems, a nonlinear estimation algorithm is needed to recover the pose information from magnetic measurements. In existing pose estimation algorithms such as the extended Kalman filter (EKF), the 3-DoF orientation in the S3 manifold is normally parametrized as unit quaternions and simply treated as a vector in the Euclidean space, which causes a violation of the unity constraint of quaternions and reduces pose tracking accuracy. In this paper, a pose estimation algorithm based on the error-state Kalman filter (ESKF) is proposed to improve the accuracy and robustness of electromagnetic tracking systems. The proposed system consists of three electromagnetic coils for magnetic field generation and a tri-axial magnetic sensor attached to the target object for field measurement. A strategy of sequential coil excitation is developed to separate the magnetic fields from different coils and reject magnetic disturbances. Simulation and experiments are conducted to evaluate the pose tracking performance of the proposed ESKF algorithm, which is also compared with standard EKF and constrained EKF. It is shown that the ESKF can effectively maintain the quaternion unity and thus achieve a better tracking accuracy, i.e., a Euclidean position error of 2.23 mm and an average orientation angle error of 0.45°. The disturbance rejection performance of the electromagnetic tracking system is also experimentally validated.

Intelligent Monitoring and Optimization of Wind Turbine Operation Status on Basis of Vibration Signals

In response to the large monitoring errors and incomplete consideration of fault locations in the operation status of wind turbines, this paper combined vibration signals and used a model constructed using nonlinear state estimation technology (NSET) to monitor and optimize the operation status of wind turbines. Firstly, it collected relevant SCADA (supervisory control and data acquisition) and vibration sensor data of Unit 5 of Guangdong Yangjiang Shaba Offshore Wind Farm on site, and used wavelet transform to denoise the vibration signal. Then, full consideration can be given to the faulty parts such as wind blades and gearboxes, and a model constructed by NSET using Markov distance to construct a process memory matrix can be used to monitor the status of the wind turbine equipment. Finally, the multi-level fuzzy comprehensive evaluation method can be used to optimize the comprehensive evaluation of the operating status of wind turbines, reducing monitoring errors.

Diffusion random Fourier adaptive filtering algorithm based on logistic distance metric for distributed estimation

Distributed adaptive filtering over networks can improve filtering performance by fusing information from nodes within the same neighbor. In nonlinear estimation, adaptive filters derived from a linear framework usually suffer from large misalignment. To solve the above problem, this work develops a diffusion kernel filtering algorithm based on the random Fourier approximation method. To promote robustness to impulsive noise, the minimum logistic distance metric (LDM) is employed as a loss function. Compared to traditional kernel algorithms, the presented algorithm uses a fixed-length filter and is suitable for online distributed adaptive filtering tasks. In addition, this work also conducts a performance analysis based on Isserlis' and Price's theorems with several statistical assumptions. Simulations are conducted to exhibit the robustness of the proposed method to impulsive noise and to examine the accuracy of the theory on performance analysis.

Iterative UKF under generalized maximum correntropy criterion for intermittent observation systems with complex non-Gaussian noise

The traditional unscented Kalman filters (UKFs) under the maximum correntropy criterion provide a powerful tool for nonlinear state estimation with heavy-tailed non-Gaussian noise. Nevertheless, the above-mentioned filters may yield biased estimates because the Gaussian kernel function can only handle certain types of non-Gaussian noise. Additionally, the use of statistical linearization methods can result in approximation errors when solving linear observation equations, while the system may also experience observation data loss. Therefore, a new iterative UKF with intermittent observations under the generalized maximum correntropy criterion is proposed for systems with complex non-Gaussian noise, called GMCC-IO-IUKF. Firstly, the connection between the UKF with and without intermittent observations is established by designing a coefficient matrix including intermittent observation variables, so as to derive the UKF with intermittent observations under the maximum correntropy criterion. Secondly, for the measurement update of GMCC-IO-IUKF, a nonlinear regression augmented model that can deal with both prediction and observation errors is established using the coefficient matrix and the nonlinear function. To better adapt to different types of non-Gaussian noise, the generalized Gaussian kernel function is substituted for the traditional Gaussian kernel function. Theoretically, GMCC-IO-IUKF can achieve better estimation performance by directly employing the nonlinear function and the latest iteration value. Finally, a classical target tracking model is used to evaluate the estimation performance and feasibility of our proposed GMCC-IO-IUKF algorithm. It appears from the experiment results that our proposed GMCC-IO-IUKF can not only promote estimation precision but also handle complex non-Gaussian noise flexibly.