Error Formulation Research Articles

Bilateral photoplethysmography for arterial steal detection in arteriovenous fistula using a fractional-order decision-making quantizer.

As inflow and outflow stenoses worsen, both flow resistance and pressure increase in the stenotic vascular access. During dialysis, when blood flow decreases, it may retrograde from the peripheral artery through the palmar arch to the arterial anastomosis site. Arterial steal syndrome (ASS) causes distal hypoperfusion, resulting in hand ischemia or extremity pain and edema. Hence, this study proposes the bilateral photoplethysmography (PPG) for ASS detection in arteriovenous fistulas. The decision-making quantizer utilizes the fractional-order feature extraction method and a non-cooperative game (NCG) framework to evaluate the ASS risk level. Bilateral asynchronous PPG signals have significant differences in the rise time and amplitude in relation to the degree of stenosis. The fractional-order self-synchronization error formulation is a feature extraction method used to quantify bilateral differences in blood flow changes between the dexter and sinister PPG signals. The NCG model as a method of decision-making is then employed to evaluate the ASS risk level. Using an acoustic Doppler measurement, the resistive (Res) index is also used to evaluate the vascular access stenosis at the arterial anastomosis site. In contrast with alternative methods including the high-sensitivity C-reactive protein level or Res index, our experimental results indicate that the proposed decision-making quantizer is more efficient in preventing ASS during hemodialysis treatment.

A novel integrated dynamic acceleration/deceleration interpolation algorithm for a CNC controller

In this paper, an integrated dynamic acceleration/deceleration (IDAD) interpolation algorithm which combines the acceleration/deceleration before interpolation (ADBI) and acceleration/deceleration after interpolation (ADAI) is proposed. The IDAD scheme could confine the maximum contour error at the junction of a linear line (G01) block under consideration of the command and servo dynamic errors. The contour error formulation for the IDAD is derived analytically and then utilized for interpolation design. Because the error formulation could predict the command and dynamic errors analytically, the IDAD could adjust the connecting velocity of two blocks such that the overall contour errors are bounded within the given tolerance. The simulation results validate the proposed algorithm that can reduce the contour errors by 50 % but only an increase of 10 % machining time as compared to the integrated acceleration/deceleration (IAD) interpolation technique.

An Event-Driven Stereo System for Real-Time 3-D 360° Panoramic Vision

A new multiperspective stereo concept for real-time 3-D panoramic vision is presented in this paper. The main contribution is a novel event-driven stereo approach enabling 3-D 360° high-dynamic-range panoramic vision for real-time application in a natural environment. This approach makes use of a sparse visual code generated by a rotating pair of dynamic vision line sensors. The use of this system allows panoramic images to be generated by the transformation of events, eliminating the need to capture a large set of images. It thereby increases the acquisition speed, which improves accuracy in dynamic scenes. This paper focuses on its 3-D reconstruction and performance analysis using such a rotating multiperspective vision system. First, a theoretical analysis of the stereo matching accuracy is performed. Second, a depth error formulation is developed, which takes motion into consideration and reveals the leverage of scene dynamics on depth estimation. In this paper, disparity is measured in time units, which allows accurate depth maps to be estimated from a moving sensor system. Third, a stereo matching workflow is presented using standard stereo image matching to assess the 3-D reconstruction accuracy. Finally, experimental results are reported on real-world sensor data, showing that the system allows for the 3-D reconstruction of high-resolution round views even under challenging illumination conditions.

Identification of a Parameter in Fourth-Order Partial Differential Equations by an Equation Error Approach

Abstract The objective of this short note is to employ an equation error approach to identify a variable parameter in fourth-order partial differential equations. Existence and convergence results are given for the optimization problem emerging from the equation error formulation. Finite element based numerical experiments show the effectiveness of the proposed framework.

Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces

We prove that the covering radius of an N-point subset XN of the unit sphere Sd⊂Rd+1 is bounded above by a power of the worst-case error for equal weight cubature 1N∑x∈XNf(x)≈∫Sdfdσd for functions in the Sobolev space Wps(Sd), where σd denotes normalized area measure on Sd. These bounds are close to optimal when s is close to d/p. Our study of the worst-case error along with results of Brandolini et al. motivate the definition of Quasi-Monte Carlo (QMC) design sequences for Wps(Sd), which have previously been introduced only in the Hilbert space setting p=2. We say that a sequence (XN) of N-point configurations is a QMC-design sequence for Wps(Sd) with s>d/p provided the worst-case equal weight cubature error for XN has order N−s/d as N→∞, a property that holds, in particular, for a sequence of spherical t-designs in which each design has order td points. For the case p=1, we deduce that any QMC-design sequence (XN) for W1s(Sd) with s>d has the optimal covering property; i.e., the covering radius of XN has order N−1/d as N→∞. A significant portion of our effort is devoted to the formulation of the worst-case error in terms of a Bessel kernel, and showing that this kernel satisfies a Bernstein type inequality involving the mesh ratio of XN. As a consequence we prove that any QMC-design sequence for Wps(Sd) is also a QMC-design sequence for Wp′s(Sd) for all 1≤p<p′≤∞ and, furthermore, if (XN) is a quasi-uniform QMC-design sequence for Wps(Sd), then it is also a QMC-design sequence for Wps′(Sd) for all s>s′>d/p.

Bilateral photoplethysmography analysis for arteriovenous fistula dysfunction screening with fractional-order feature and cooperative game-based embedded detector.

The bilateral photoplethysmography (PPG) analysis for arteriovenous fistula (AVF) dysfunction screening with a fractional-order feature and a cooperative game (CG)-based embedded detector is proposed. The proposed detector uses a feature extraction method and a CG to evaluate the risk level for AVF dysfunction for patients undergoing haemodialysis treatment. A Sprott system is used to design a self-synchronisation error formulation to quantify the differences in the changes of blood volume for the sinister and dexter thumbs' PPG signals. Bilateral PPGs exhibit a significant difference in rise time and amplitude, which is proportional to the degree of stenosis. A less parameterised CG model is then used to evaluate the risk level. The proposed detector is also studied using an embedded system and bilateral optical measurements. The experimental results show that the risk of AVF stenosis during haemodialysis treatment is detected earlier.

UAV Flyable Trajectory Generation and Its Tracking Control

For the complex combat environment, considering the flyable performance constrains and the safety constrains, an online trajectory planning algorithm of UAVs(Unmanned Aerial Vehicles) based on Pythagorean Hodograph (PH) curve is put forward, which is easy to traced. When the unexpected obstacles are detected, based on the velocity obstacles avoidance method, the collision avoidance trajectory is planned online. The position of the interrupt point and the direction of the UAV turn are calculated. To fully use the PH trajectories performance that the curvature of the curve is continuous and precisely known, the location and crossing heading error equations were established within the Serret-Frenet coordinates. The corresponding asymptotically stable convergence backstepping trajectory tracking control law was designed based on the error formulations. The autonomous collision avoidance trajectory simulation result and its tracking control result show that the proposed trajectory generation method and the corresponding adaptive tracking control method are effective and can improve the tracking accuracy.

Hemodialysis Arteriovenous Shunts Dysfunction Screening with a Fractional-order Feature and Non-cooperative Game Based Decision-making Model

s Early clots and thrombosis to the progress of stenosis leading to arteriovenous shunt dysfunction occurs at the venous anastomsis site or the outflow vein. To prevent vascular access complications, such as inflow or outflow stenosis, this study proposes a computerized decision support system combining feature extraction methods and a non-cooperative game (NCG)-based decision-making model to evaluate arteriovenous shunt stenosis in clinical usages. Feature extraction methods, including the Burg autoregressive (AR) method and the fractional-order self-synchronization error formulation, are used to estimate the characteristic frequencies and to quantify the differences between the reference data and the routine examination data, in terms of the degree of stenosis (DOS). For 42 long-term follow-up patients, a less parameterized NCG model is then used to identify the possible level of stenosis. A novel screening model might be further built on an embedded system, for portable medical screening applications.

Flow-Based and Density-Based Time-Dependent Demand Estimation for Congested Urban Transportation Networks

This paper compares the estimation quality of two time-dependent origin–destination demand estimation methods in congested networks. The first method uses time-dependent link flow rate observations, whereas the second uses time-dependent link density observations. The developed methods adopt a bilevel formulation framework in which the lower-level problem solves for the time-dependent link proportions by using a simulation-based dynamic traffic assignment model. The upper-level problem is in the form of a least squares error minimization program that minimizes the difference between the observations and their corresponding estimated values. The solution algorithm integrates a simulation-based dynamic traffic assignment model and a linear approximation of the least squares error formulation by using a separable programming approach. An iterative solution algorithm is developed to achieve consistency between the estimated demand and the link proportions. A set of experiments conducted with hypothetical and real-world networks examines the performance of the two methods in replicating the observed congestion pattern in these networks. Results show that the density-based demand estimation method is more suitable for demand estimation in congested networks in that the former method captures the flow breakdown and spillback phenomena associated with high congestion.

Accounting for model error due to unresolved scales within ensemble Kalman filtering

We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently explored for variational schemes and extended Kalman filter. The model error statistic required in the analysis update is estimated using historical reanalysis increments and a suitable model error evolution law. Two different versions of the method are described; a time‐constant model error treatment where the same model error statistical description is time‐invariant, and a time‐varying treatment where the assumed model error statistics is randomly sampled at each analysis step. We compare both methods with the standard method of dealing with model error through inflation and localization, and illustrate our results with numerical simulations on a low‐order nonlinear system exhibiting chaotic dynamics. The results show that the filter skill is significantly improved through the proposed model error treatments, and that both methods require far less parameter tuning than the standard approach. Furthermore, the proposed approach is simple to implement within a pre‐existing ensemble‐based scheme. The general implications for the use of the proposed approach in the framework of square‐root filters such as the ETKF are also discussed.

Volumetric error formulation and mismatch test for five-axis CNC machine compensation using differential kinematics and ephemeral G-code

Machine tool kinematic errors directly impact on the accuracy of machined parts. A general volumetric error formulation effectively implementing ISO230-1:2012 definition and an off-line compensation scheme are proposed and partly tested to improve part accuracy on a five-axis CNC machine. Using rigid body kinematics and estimated machine error parameters, the machine position commands contained in a standard G-code are used to calculate the tool erroneous location. The Jacobian, expressing the differential joint space to Cartesian space relationship, is also developed and used to calculate minute joint command modifications so that the effect of inter-axis link errors and intra-axis error motions, for example, can be canceled by making small changes directly to the G-code. Finally, a simple case of a machining sequence producing a surface mismatch in the presence of particular machine deviations is used to illustrate the usefulness of the analytical tools presented. A graphical representation of the volumetric errors assists in understanding the impact of each error source for this particular application. The measurement results are compatible with the predicted volumetric error values and show an accuracy improvement of about 90 % after compensation.

Output feedback robust MPC with one free control move for the linear polytopic uncertain system with bounded disturbance

In this paper a previous approach, for the robust model predictive control (MPC) for a linear polytopic uncertain system, is extended to the case with bounded disturbance and unmeasurable state. The controller on-line optimizes a free control move followed by an output feedback control law based on the pre-specified state estimator. A key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem. The quadratic boundedness (QB) of the augmented state is guaranteed by the proposed approach. A numerical example is given to illustrate the effectiveness of the proposed controller.

Estimating Residual Stenosis for an Arteriovenous Shunt Using a Flexible Fuzzy Classifier

This article determines whether the diameter of a vascular lumen is clinically valuable for hemodialysis therapy. A novel method is proposed that uses a flexible fuzzy classifier (FFC) implementing a curve approximation function to estimate residual stenosis in an arteriovenous shunt (AVS). The auscultation method provides a noninvasive technique for monitoring the degree of AVS stenoses. The Burg autoregressive method is used to identify the characteristic spectra for changes in frequency and amplitude between frequencies of 25 and 800 Hz. Fractional order self-synchronization error formulation is then used to quantify the degree of stenosis between normal access and AVS stenosis in the frequency spectra. To estimate the diameter of a vascular lumen, the FFC is used to create a nonlinear prediction model. For the 42 long-term patients studied, the results of this examination show that the proposed prediction model estimates residual stenosis efficiently.

Design and implementation of an improved linear quadratic regulation control for oxygen content in a coke furnace

In view of the performance deterioration of conventional model predictive control strategies under model/plant mismatches, this study first proposes an improved linear quadratic regulation control (LQR) strategy and then tests it on the oxygen content in an industrial coke furnace. The control system design consists of two steps. Based on the direct use of the measured input and output variables and the formulation of output error, a state space model is first developed. Then, by incorporating the dynamics of process states into the cost function of the controller design, a new LQR is proposed to obtain an improved performance for closed-loop control systems. Comparisons with conventional state space model predictive control are also given in terms of both regulatory and servo performance. The case study on the oxygen content in the coke furnace shows that the proposed improves control performance under model/plant mismatches.

Non-Cooperative Game Model Applied to an Advanced Metering Infrastructure for Non-Technical Loss Screening in Micro-Distribution Systems

This paper proposes a non-cooperative game (NCG) model for non-technical loss (NTL) screening in micro-distribution systems. This model can compound an infra-structure with smart electric meters and fractional-order self-synchronization error formulation to distinguish illegal activities between profiled usages and non-technical usages. Then a NCG-based decision-making model is used to locate the abnormalities. Experimental results are presented to demonstrate the effectiveness of the proposed method.

Bayesian Expected Shortfall Forecasting Incorporating the Intraday Range

Intraday sources of data have proved to be effective for dynamic volatility and tail risk estimation. Expected shortfall (ES) is a tail risk measure, which is now recommended by the Basel Committee, involving a conditional expectation that can be semi-parametrically estimated via an asymmetric sum of squares function. The conditional autoregressive expectile class of model, used to implicitly model ES, is generalized to incorporate information on the intraday range. An asymmetric Gaussian density model error formulation allows a likelihood to be developed that leads to direct estimation and one-step-ahead forecasts of expectiles and, subsequently, of ES. Adaptive Markov chain Monte Carlo sampling schemes are employed for estimation, while their performance is assessed via a simulation study. The proposed models compare favorably with a large range of competitors in an empirical study forecasting seven financial return series over a 10-year period.

Residual stenosis estimation of arteriovenous grafts using a dual-channel phonoangiography with fractional-order features.

The residual stenosis estimation of an arteriovenous shunt is a valuable for evaluating outcomes of percutaneous transluminal angioplasty (PTA) treatment and surgical revision. This paper proposes a dual-channel phonoangiography (PCG) with fractional-order features to estimate the residual of stenosis estimation of arteriovenous shunt. The auscultation technique provides a noninvasive tool to monitor the degrees of arteriovenous grafts (AVGs). Then, support methods, such as the Burg autoregressive (AR) method and self-synchronization error formulation (SSEF), are used to extract fractional-order features between the loop site (L-site) and venous anastomosis site (V-site). Using 2-D patterns (nonlinear mapping), a generalized regression neural network (GRNN) is designed as a nonlinear estimate model to indicate the outcome of surgical revision or AVG stenosis upon routine monthly examinations. For 42 long-term follow-up patients, the results of examination show the proposed GRNN-based screening model efficiently estimates residual stenosis.

Excitation prediction by dynamic transmission error under sliding friction in helical gear system

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

Asymptotically efficient estimators for the fittings of coupled circles and ellipses

Fitting a pair of coupled geometric objects to a number of coordinate points is a challenging and important problem in many applications including coordinate metrology, petroleum engineering and image processing. This paper derives two asymptotically efficient estimators, one for concentric circles fitting and the other for concentric ellipses fitting, based on the weighted equation error formulation and non-linear parameter transformation. The Kanatani–Cramér–Rao (KCR) lower bounds for the parameter estimates of the concentric circles and concentric ellipses under zero-mean Gaussian noise are provided to serve as the performance benchmark. Small-noise analysis shows that the proposed estimators reach the KCR lower bound performance asymptotically. The accuracy of the proposed estimators is corroborated by experiments with synthetic data and realistic images.

An Alternative Formulation of the Dynamic Transmission Error to Study the Oscillations of Automotive Hypoid Gears

A new modeling approach on the torsional dynamics of hypoid gear pairs is presented in this work. The current formulation is characterized by an alternative expression of the dynamic transmission error (DTE), accounting for the variation of the effective mesh position. Speed dependent resistive torque is introduced on the gear wheel, enabling the system to reach dynamic equilibrium based on realistic vehicle operating conditions. The above are supplementing past research studies, where simplifications were introduced in the calculation of DTE, while the operating angular velocity was defined a priori. The analysis is accompanied by numerical results, indicating the rich dynamic behavior captured by the new formulation. The dynamic complexity of the system necessitates the identification of the various response regimes. A solution continuation method (software AUTO) is employed to follow the stable/unstable periodic response branches over the operating range of the differential under examination.