Effect Of Modeling Errors Research Articles

A new adaptive deep neural network controller based on sparse auto‐encoder for the antilock bracking system systems subject to high constraints

AbstractWe contribute in the current paper to extend the universal function approximation property of deep learning hybrid strategy to design both : (a) adaptive deep neural network observer to estimate derivatives of the tracking error dynamics (b) and robust deep neural network (DNN) output feedback control scheme (OFCS) that will overcome successfully effects of both parametric variations and modeling errors. First, the designed controller employs OFCS to linearize the partially known antilock bracking (ABS) dynamics, and then, the dynamic compensator is involved to stabilize the linearized system. However, conventional controllers suffer from limitations due to the presence of these high uncertainties. Therefore, we aim to demonstrate for the first time in the control area the feasibility of applying deep learning algorithm based on sparse auto‐encoder as an approximator for neglected dynamics and uncertain parameters of the ABS. The estimated states are used as inputs to the neural network (NN) and in the adaptation laws as an error signal. Simulations of the proposed control algorithm based adaptive DNN observer are conducted then compared to bang–bang controller, PI controller, and adaptive controller‐based single hidden layer‐neural network with only one‐neuron in hidden layers (SHL(1N)NN) to demonstrate its practical potential. Furthermore, both feasibility and efficiency of involving deep learning algorithm (DLA) in the control area have been successfully confirmed through robustness test.

Ultra-Low-Cost Tightly Coupled Triple-Constellation GNSS PPP/MEMS-Based INS Integration for Land Vehicular Applications

The rapid rise of ultra-low-cost dual-frequency GNSS chipsets and micro-electronic-mechanical-system (MEMS) inertial sensors makes it possible to develop low-cost navigation systems, which meet the requirements for many applications, including self-driving cars. This study proposes the use of a dual-frequency u-blox F9P GNSS receiver with xsens MTi670 industrial-grade MEMS IMU to develop an ultra-low-cost tightly coupled (TC) triple-constellation GNSS PPP/INS integrated system for precise land vehicular applications. The performance of the proposed system is assessed through comparison with three different TC GNSS PPP/INS integrated systems. The first system uses the Trimble R9s geodetic-grade receiver with the tactical-grade Stim300 IMU, the second system uses the u-blox F9P receiver with the Stim300 IMU, while the third system uses the Trimble R9s receiver with the xsens MTi670 IMU. An improved robust adaptive Kalman filter is adopted and used in this study due to its ability to reduce the effect of measurement outliers and dynamic model errors on the obtained positioning and attitude accuracy. Real-time precise ephemeris and clock products from the Centre National d’Etudes Spatials (CNES) are used to mitigate the effects of orbital and satellite clock errors. Three land vehicular field trials were carried out to assess the performance of the proposed system under both open-sky and challenging environments. It is shown that the tracking capability of the GNSS receiver is the dominant factor that limits the positioning accuracy, while the IMU grade represents the dominant factor for the attitude accuracy. The proposed TC triple-constellation GNSS PPP/INS integrated system achieves sub-meter-level positioning accuracy in both of the north and up directions, while it achieves meter-level positioning accuracy in the east direction. Sub-meter-level positioning accuracy is achieved when the Stim300 IMU is used with the u-blox F9P GNSS receiver. In contrast, decimeter-level positioning accuracy is consistently achieved through TC GNSS PPP/INS integration when a geodetic-grade GNSS receiver is used, regardless of whether a tactical- or an industrial-grade IMU is used. The root mean square (RMS) errors of the proposed system’s attitude are about 0.878°, 0.804°, and 2.905° for the pitch, roll, and azimuth angles, respectively. The RMS errors of the attitude are significantly improved to reach about 0.034°, 0.038°, and 0.280° for the pitch, roll, and azimuth angles, respectively, when a tactical-grade IMU is used, regardless of whether a geodetic- or low-cost GNSS receiver is used.

Optimal Sensor Placement for Reliable Virtual Sensing Using Modal Expansion and Information Theory.

A framework for optimal sensor placement (OSP) for virtual sensing using the modal expansion technique and taking into account uncertainties is presented based on information and utility theory. The framework is developed to handle virtual sensing under output-only vibration measurements. The OSP maximizes a utility function that quantifies the expected information gained from the data for reducing the uncertainty of quantities of interest (QoI) predicted at the virtual sensing locations. The utility function is extended to make the OSP design robust to uncertainties in structural model and modeling error parameters, resulting in a multidimensional integral of the expected information gain over all possible values of the uncertain parameters and weighted by their assigned probability distributions. Approximate methods are used to compute the multidimensional integral and solve the optimization problem that arises. The Gaussian nature of the response QoI is exploited to derive useful and informative analytical expressions for the utility function. A thorough study of the effect of model, prediction and measurement errors and their uncertainties, as well as the prior uncertainties in the modal coordinates on the selection of the optimal sensor configuration is presented, highlighting the importance of accounting for robustness to errors and other uncertainties.

Feedback Gains modulate with Motor Memory Uncertainty

A sudden change in dynamics produces large errors leading to increases in muscle co-contraction and feedback gains during early adaptation. We previously proposed that internal model uncertainty drives these changes, whereby the sensorimotor system reacts to the change in dynamics by upregulating stiffness and feedback gains to reduce the effect of model errors. However, these feedback gain increases have also been suggested to represent part of the adaptation mechanism. Here, we investigate this by examining changes in visuomotor feedback gains during gradual or abrupt force field adaptation. Participants grasped a robotic manipulandum and reached while a curl force field was introduced gradually or abruptly. Abrupt introduction of dynamics elicited large initial increases in kinematic error, muscle co-contraction and visuomotor feedback gains, while gradual introduction showed little initial change in these measures despite evidence of adaptation. After adaptation had plateaued, there was a change in the co-contraction and visuomotor feedback gains relative to null field movements, but no differences between the abrupt and gradual introduction of dynamics. This suggests that the initial increase in feedback gains is not part of the adaptation process, but instead an automatic reactive response to internal model uncertainty. In contrast, the final level of feedback gains is a predictive tuning of the feedback gains to the external dynamics as part of the internal model adaptation. Together, the reactive and predictive feedback gains explain the wide variety of previous experimental results of feedback changes during adaptation.

Detection and quantification of damage in bridges using a hybrid algorithm with spatial filters under environmental and operational variability

It is essential to isolate the environmental effects on the structure from the incipient damage during structural health monitoring, failing which, may mislead the diagnostic process in a way, either, by giving false positive alarms or masking the existing real damage. The modal filter is popularly used to handle environmental variability, while detecting the current state of the structure, during structural health monitoring. However, this technique is a qualitative one and it cannot identify the spatial location and the extent of the damage. In this paper, the modal filter is combined with an inverse algorithm to localize and quantify the extent of damage, while handling environmental variability. The inverse damage detection problem is formulated as a constrained optimization problem and solved using a Multi cluster hybrid adaptive differential search algorithm (MCHADSA). A new damage index is proposed, to detect the exact time instant of damage, alleviating the effecting confounding factors like environmental and operational variability (EoV) and measurement noise. Numerical experiments are conducted to evaluate the performance of the proposed inverse damage diagnostic MCHADS algorithm and the results are presented in this paper. A beam girder is taken as the first example followed by a more realistic example of a live bridge across river Amaravati near Dharapuram, Tamil Nadu, India. The studies presented in this paper indicate that the proposed Modal filter-based hybrid inverse algorithm is effective in localizing as well as quantifying the damage. The effect of modeling errors is also investigated in the proposed algorithm.

Data-driven active flutter control of airfoil with input constraints based on adaptive dynamic programming method

The stable flight region can be extended by adding control flap at the wing trailing edge and combined with active control technology. We studied the active flutter control by considering the input constraints. By designing the data-driven optimal controller, the limit cycle oscillations of a typical two-dimensional airfoil wing can be suppressed with single trailing edge control surface. The traditional control methods always need a precise mathematical model of the system, which put high requirements on system modeling. In this study, a novel data-driven optimal controller is proposed by using the input–output data and without depending on the nonlinear system dynamic model. This model-free approach avoids the effects of modeling errors and system uncertainty. When the data-driven controller is applied, the limit cycle oscillation phenomenon of the airfoil wing is eliminated within several seconds. It can be seen from the numerical simulation result that the data-driven adaptive dynamic programming control method possess superiority and feasibility.

Effects of Dynamic Model Errors in Task-Priority Operational Space Control

SUMMARYControl algorithms of many Degrees-of-Freedom (DOFs) systems based on Inverse Kinematics (IK) or Inverse Dynamics (ID) approaches are two well-known topics of research in robotics. The large number of DOFs allows the design of many concurrent tasks arranged in priorities, that can be solved either at kinematic or dynamic level. This paper investigates the effects of modeling errors in operational space control algorithms with respect to uncertainties affecting knowledge of the dynamic parameters. The effects on the null-space projections and the sources of steady-state errors are investigated. Numerical simulations with on-purpose injected errors are used to validate the thoughts.

Indirect health monitoring of bridges using Tikhonov regularization scheme and signal averaging technique

This paper presents a novel damage identification technique for bridges based on the dynamic response of a moving vehicle. A quarter car vehicle model instrumented with two accelerometers and an inertial profilometer is used for this purpose. The method involves the coupling of Tikhonov regularization scheme with signal averaging technique to handle the problem of measurement noise and road roughness. In the first stage, a damage-dependent road roughness profile is estimated from measured acceleration response by minimizing a Tikhonov regularized least squares cost function. The second stage involves the minimization of the profile roughness residual function that depends on the location and magnitude of damage. This objective function compares the roughness profile computed from the first stage and that measured by the inertial profilometer. It is proved that efficient damage detection ensues from considering multiple runs of the vehicle and choosing the appropriate regularization parameter. The present study considers various aspects, such as the uniqueness of results, robustness of results to measurement noise, effect of modelling error, effect of vehicle speed, and uncertainty in estimation. Numerical results show that the approach is capable of detecting the magnitude as well as the location of damage. In addition, the problem of road roughness and measurement noise is handled competently.

Effect of Stochastic Model Errors on Significance Test for Velocities in Analysis of GPS Position Time Series

AbstractThis study investigates the effect of stochastic model errors on the significance test for velocities in the analysis of a global positioning system (GPS) position time series. This effect ...

Multi-sensor fusion approach based on nonlinear H∞ filter with interval type 2 fuzzy adaptive parameters tuning for unmanned vehicle localization

In most applications of autonomous navigation, the state of a system must be estimated from noisy sensors. Accurate estimation of the true system state can be achieved using data fusion algorithms. Furthermore, the fusion scheme can be affected by many factors such as modeling errors and parameters uncertainties. The gaps and inconsistencies due to the sensors noise and modeling errors can be reached with robust nonlinear filtering. In this article, a new framework has been developed for data fusion algorithms based on nonlinear NH∞ filter with fuzzy adaptive bound and adaptive disturbances attenuations. Type-1 Fuzzy Adaptive NH∞ algorithm has been proposed and compared with the Interval Type 2 Fuzzy Adaptive NH∞, for unmanned vehicle localization. The proposed algorithms fuse data from low-cost sensors using inertial navigation system, Global Positioning System and monocular vision. Type-1 Fuzzy Adaptive NH∞ and Interval Type 2 Fuzzy Adaptive NH∞ algorithms, adaptively, handle the effects of noisy sensors, parameters uncertainties and modeling errors. Both algorithms use adaptive bounds [Formula: see text] and adaptive disturbance attenuation [Formula: see text] for higher-order terms of the Taylor development. The adaptive bounds consider issues associated to Gyro drift, image distortion and Global Positioning System dilution of precision which make the proposed algorithms more accurate than the classical NH∞. The validating experiment and the efficiency of Type-1 Fuzzy Adaptive NH∞ and Interval Type 2 Fuzzy Adaptive NH∞ have been conducted in real scenario and in unstructured outdoor environment without any a priori knowledge of the evolution of the vehicle. The experimental results have demonstrated the robustness and efficiency of these two filtering strategies against uncertainties and their online sensor switching capability. The Interval Type 2 Fuzzy Adaptive NH∞ algorithm provides more accuracy and robustness compared to the Type-1 Fuzzy Adaptive NH∞.

Modified frequency and spatial domain decomposition method based on maximum likelihood estimation

In this study, a Modified Frequency and Spatial Domain Decomposition (MFSDD) technique is developed for modal parameter identification, using output-only response measurements. According to the presented procedure, the most probable power spectral density matrix of the measured response (output PSD) is updated by a maximum likelihood estimation based on the observed data. Different from the available Frequency Domain Decomposition (FDD) techniques, a prediction error term which is associated with the measurement noise and modelling errors is included in the proposed methodology. In this context, a detailed discussion is provided from various aspects for the effect of measurement noise and modelling errors on the parameter estimation quality. Two numerical and two experimental analysis are conducted in order to demonstrate the effectiveness and accuracy of the proposed methodology under some extreme effects. The obtained results indicate that the proposed method shows very good performance in modal parameter estimation in case of noisy measurements.

Damage detection of steel moment frames under earthquake excitation

This paper investigates the effects of uncertainties and modeling errors on the performance of nonlinear updating process through an experimental study on two 1/8-scale four-story steel moment-resisting frames. To examine the accuracyo of the models calibrated using different data features and modeling assumptions, the actual structural responses obtained from shaking table tests and the response of the models have been compared. The modeling uncertainties are investigated by applying frames with different modeling assumptions, including concentrated and distributed plasticity, and different hysteretic material behaviors. To calibrate the models, four data features are considered and combined: (1) acceleration time history, (2) displacement time history, (3) instantaneous characteristics of the decomposed monocomponent of the response, and (4) dissipated energy. In this paper, a sensitivity analysis has been performed to investigate the effect of various parameters of hysteretic materials on the response of reference steel moment-resisting frames. To this end, the optimum values of the unknown parameters are determined through minimizing the objective function defined based on the residuals of data features for the actual structure and finite element (FE) model. By comparing the structural responses of the model with concentrated plasticity calibrated by instantaneous characteristics with those of the other models, it can be concluded that the concentrated plasticity model predicts a more accurate response compared to the other models. Consequently, the aleatory uncertainty was taken into account by evaluating the performance of the system with concentrated plasticity under 40 seismic ground motions, and the structural response has been obtained through the calibrated model.

Dynamic behaviour analysis of coupled rotor active magnetic bearing system in the supercritical frequency range

In this article, an attempt has been made to model and estimate speed-dependent characteristic parameters of coupling misalignment and AMB, in an AMB integrated coupled flexible rotor system running in the supercritical frequency range. For estimation algorithm, desired current and displacement responses in time series are acquired from Simulink. The practical limitation of FEM modelling is the number of sensors and availability of measurement locations that have been overcome by applying a novel gyroscopic high-frequency condensation (GHFC) scheme. The transformation matrix obtained from standard high-frequency condensation (SHFC) is modified by adding a gyroscopic effect into the transformation matrix to achieve the novel GHFC. The numerical analysis has been performed on a coupled rotor train system along with AMB. The estimations are presented and compared for SHFC and GHFC. The GHFC is found effective over SHFC techniques. The effect of noisy response and modelling error on the estimation algorithm is analysed and found competent. The experimental responses obtained for a different level of misalignment conditions have been compared with the numerically simulated response and found that the application of AMB suppresses the excessive vibration.

Design on Type-2 Fuzzy-Based Distributed Supervisory Control With Backlash-Like Hysteresis

In this article, the distributed synchronization control problem is investigated for a class of uncertain nonlinear leader-following systems on directed graph, where unknown backlash-like hysteresis exists in the actuator of each follower and the topology of the graph is fixed. Based on basic graph theory, the principle of variable structure control and Lyapunov theory, by using the unknown smooth function approximation capability of type-2 fuzzy logic systems, a new distributed adaptive supervisory control design method is proposed such that all followers asymptotically synchronize to the leader and each synchronizing error is bounded. In the control method, with the help of supervisor control strategy, it is guaranteed that the resulting closed-loop signals including system states, respectively, belong to the corresponding compact sets, which is necessary for fuzzy approximation theory because it is on a compact set that an unknown smooth function can be approximated by fuzzy logic system. Furthermore, the adaptive compensation terms of the optimal approximation errors are adopted to reduce the effects of modeling errors. Finally, simulation results demonstrate the effectiveness of the proposed new design method.

Stress-based topology optimization under uncertainty via simulation-based Gaussian process

Gaussian processes (GP) form a well-established predictive tool which provides a natural platform for tackling high-dimensional random input data in challenging simulations. This paper introduces a generic framework for integrating Gaussian Processes with risk-based structural optimization. We solve robust and reliability-based design problems in the context of stress-based topology optimization under imperfections in geometry and material properties, and loading variability. We construct independent GPs for primal and adjoint quantities, namely the global maximum von Mises stress and its sensitivity where we enhance the computational efficiency by leveraging the information from multiresolution finite element simulations. The GP framework naturally lends itself to modeling noise in data. We investigate the effect of numerical modeling error in high-fidelity simulations via a noisy GP emulator and provide a pareto curve that shows the robustness of optimal design with respect to the noise level. We provide a posteriori error estimates that quantify the discrepancy between the noisy emulator and true simulations, and verify them with a numerical study. We demonstrate our approach on a benchmark L-shape structure which exhibits stress concentration, a compliant mechanism design and a heat sink design. We also provide practical guidelines for estimation of failure probability and its sensitivity to facilitate reliability-based topology optimization.

Adaptive Shape Control for Antenna Reflectors Based on Feedback Error Learning Algorithm

To achieve high-precision shape control of antenna reflectors in the presence of model errors, an adaptive shape control method based on the feedback error learning algorithm is proposed. First, the finite element model of a planar hexagonal reflector with 30 piezoelectric actuators is established, by which the influence coefficient matrix is derived. Second, the feedback error learning method is developed, and it can iteratively modify the inverse model of the reflector system through online learning, thus avoiding the effect of model errors on shape control precision. An adaptive step size adjustment strategy for the method is proposed to improve the convergence precision and speed. Then, the effectiveness of the proposed method is intensively studied in comparison with the traditional influence coefficient matrix method by numerical simulations. Numerical results demonstrate that the proposed method can achieve a fairly high precision for all kinds of model errors, whereas the model errors will greatly reduce the precision of the influence coefficient matrix method. The adaptive step size adjustment strategy can greatly improve the convergence precision and speed. Finally, experimental results further verified the above conclusions, which prove the effectiveness and practicability of the proposed method for the high-precision shape control.

Fast and robust volumetric refractive index measurement by unified background-oriented schlieren tomography

We propose a novel approach to background-oriented schlieren (BOS) tomography (BOST) that unifies the deflection sensing and reconstruction algorithms. BOS is a 2D flow visualization technique that renders light deflections due to refraction in the fluid. Simultaneous BOS measurements from unique views can be reconstructed by tomography to estimate the fluid’s 3D refractive index field. The cameras are focused through the fluid on textured background patterns. Deflections between an undistorted reference image and distorted image are typically determined by gradient-based optical flow (OF), which is a complex inverse problem and potential source of error in BOST. This paper presents an alternative approach to BOST that unifies the OF equations and deflection model. Our new operator simultaneously calculates the image distortions seen by each camera for a discrete refractive index distribution. Unified BOST (UBOST) thus reconstructs observed image distortions instead of inferred deflections, which are influenced by user-selected OF parameters. The UBOST operator has one third as many equations as the classical BOST operator. We show that our formulation reduces the effects of model error and the computational cost of reconstruction. These advantages are demonstrated with a numerical experiment using phantoms of varied complexity. Best practice UBOST reconstructions were more accurate than classical reconstructions of the exact deflections for each phantom. Moreover, UBOST estimates converged substantially faster, resulting in a $$\ge $$ 62.5% speedup with our solver.

Solving inverse bioheat problems of skin tumour identification by dynamic thermography

Dynamic thermography is a promising new non-invasive diagnostic technique for skin cancer, not just to identify the skin tumour in its early stage but also to evaluate some of tumour parameters showing the stage and invasiveness. This paper covers the solution of inverse bioheat problems of simultaneous identification of tumour diameter, thickness, blood perfusion rate and thermoregulation coefficient based on the surface temperature difference between healthy skin and lesion during the rewarming period of dynamic thermography. The problem has been treated using numerically generated measurement data for Clark II and Clark IV tumours by adding noise to mimic real measurement data. The solution is based on a more realistic 3D numerical model, composed of different layers including the thermoregulation response of the skin, tumour and surrounding tissue using a deterministic Levenberg–Marquardt optimisation algorithm that is robust and fast. The paper covers the analysis of the starting point of the solution, randomness and level of added noise, as well as the effect of numerical model error on the inverse solution. Tumour diameter and thermoregulation response can be estimated accurately regardless of noise and stage, while blood perfusion and tumour thickness can only be estimated accurately for low noise level or later tumour stage. The solution sensitivity to metabolic heat generation, thickness, blood perfusion rate and thermoregulation coefficient of skin and fat was low, while heat capacity and thermal conductivity of skin and tumour should be determined precisely in the numerical model to be able to evaluate all four tumour parameters as accurately as possible.

Reply to “Comments on ‘What Is the Predictability Limit of Midlatitude Weather?’”

Abstract In their comment, Žagar and Szunyogh raised concerns about a recent study by Zhang et al. that examined the predictability limit of midlatitude weather using two up-to-date global models. Zhang et al. showed that deterministic weather forecast may, at best, be extended by 5 days, assuming we could achieve minimal initial-condition uncertainty (e.g., 10% of current operational value) with a nearly perfect model. Žagar and Szunyogh questioned the methodology and the experiments of Zhang et al. Specifically, Žagar and Szunyogh raised issues regarding the effects of model error on the growth of the forecast uncertainty. They also suggested that estimates of the predictability limit could be obtained using a simple parametric model. This reply clarifies the misunderstandings in Žagar and Szunyogh and demonstrates that experiments conducted by Zhang et al. are reasonable. In our view, the model error concern in Žagar and Szunyogh does not apply to the intrinsic predictability limit, which is the key focus of Zhang et al. and the simple parametric model described in Žagar and Szunyogh does not serve the purpose of Zhang et al.

Data Adaptable Sparse Reconstruction for Hyperspectral Image Recovery from Compressed Measurements

Hyperspectral image compression using compressive sensing technique is very much important in the area of satellite image compression because it can greatly en hance the compression rate. The research work proposes a novel data adaptable sparse reconstruction algorithm for the reconstruction of hyperspectral images from compressive sensing measurements. In the proposed algorithm, compressive sensing technique is used for the compression of HSIs, where Gaussian i.i.d. matrix is used to generate compressive sensing measurements. The algorithm solves the optimization problem containing total variation regularization and data adaptable parameter terms. The regularization terms are added to provide hyperspectral data characteristics as priors into the objective function. The addition of priors helps in convergence of the algorithm into the desired solution. The algorithm alternatively reconstructs the end member matrix and abundance matrix instead of reconstructing the entire HSI at once, thereby reducing the computational complexity at the reconstruction process. To nullify the effect of modelling errors, debiasing is performed.