Inverse Scheme Research Articles

Robust optical flow integration.

We analyze the problem of how to correctly construct dense point trajectories from optical flow fields. First, we show that simple Euler integration is unavoidably inaccurate, no matter how good is the optical flow estimator. Then, an inverse integration scheme is analyzed which is more robust to bias and input noise and shows better stability properties. Our contribution is threefold: 1) a theoretical analysis that demonstrates why and in what sense inverse integration is more accurate; 2) a rich experimental validation both on synthetic and real (image) data; and 3) an algorithm for approximate online inverse integration. This new technique is precious whether one is trying to propagate information densely available on a reference frame to the other frames in the sequence or, conversely, to assign information densely over each frame by pulling it from the reference.

Inverse determination of convective heat transfer between an impinging jet and a continuously moving flat surface

In this study an inverse method is developed to determine the heat flux distribution on a moving plane wall. The method uses a thin layer of material (the measurement medium) glued on the conveyor belt. The heat flux distribution on the moving wall is then determined by an inverse method based on the temperature measurement by infrared thermography on the upper surface of the measurement medium. A finite element based inverse algorithm of a steady state heat conduction advection in the Eulerian frame is performed. The algorithm entails the use of the Tikhonov regularization method, along with the L-curve method to select an optimal regularization parameter. Both the direct solution of moving boundary problem and the inverse design formulation are presented. The accuracy of the inverse method is examined by simulating the exact and noisy data with four different values of the surface-to-jet velocity ratio, and two different materials (PVC and Aluminum) for the measurement medium. The results show a greater sensitivity to the convective heat flux allowing a better estimation of heat flux distribution for the PVC layer. An alternative underdetermined inverse scheme is also studied. This configuration allows a different extend between the retrieval heat flux surface and the measurement temperature surface.

Assessment of the direct inversion scheme for the quasigeoid modeling based on applying the Levenberg–Marquardt algorithm

Methods for a spherical harmonic analysis and synthesis are often used in describing the global gravity field by means of spherical harmonics to a certain degree of spectral resolution. In local gravity field modeling, the radial basis functions (RBFs) can be used to parameterize the gravity field with a high spatial/spectral resolution because of their local support. Since the global integration is required in both cases, these two methods are somehow complementary. In physical geodesy, this is done practically by adopting a remove-compute-restore numerical scheme. According to this scheme, a long-wavelength part of the gravity spectrum is defined by means of the spherical harmonics while a residual (high-frequency) gravity contribution is treated based on using the RBFs. To find an optimal parameterization of the gravity field, the number of RBFs and their spatial configuration are optional. Moreover, the regularization is applied to stabilize the (ill-posed) gravity inversion. In this study, we utilize the Levenberg–Marquardt (LM) algorithm for finding the optimal number of RBFs and their 3-D spatial configuration (i.e., horizontal location and depth) simultaneously with a regularization parameter. The optimal choice of these parameters is based on minimizing the least-squares residuals between the predicted and observed values of the potential and gravity field. In numerical experiment, we apply the LM algorithm in two inverse schemes of solving the Molodensky’s problem. The results reveal that a direct inversion of the observed gravity data to the potential field (i.e., quasigeoid heights) yields a systematic bias. Moreover, this gravimetric solution has a low approximation quality in terms of the potential field. The systematic discrepancies are thus modeled and corrected for by combining the gravity and GPS-leveling data. We propose and apply the RBF-parameterization, which again utilizes the LM optimization algorithm in combining these data. We demonstrate that only a two-step approach provides a satisfactory approximation to both the gravity and potential field.

Efficient GPU parallel computing of population balance—Monte Carlo method for coagulation

The population balance-Monte Carlo (PBMC) method has become increasingly popular because the discrete and stochastic nature of the MCmethod is especially suited for particle dynamics. However, for the two-particle events (typically, particle coagulation), the double looping over all simulation particles is required in normal PBMCmethods, and simulating particle coagulation is in general a challenging computational task due to its numerical complexity and the computing cost. The compute unified device architecture (CUDA) is a programming approach for performing scientific calculations on a graphics processing unit (GPU) as a data-parallel computing device. In this article we present an implementation of accelerating PBMCmethod based on the Inverse scheme and the Acceptance-rejection (AR) scheme for simulating particle coagulation on the GPU. The main idea is to implement the highly threaded data-parallel processing tasks by using GPU and serial computing of complex logic and transaction processing by CPU. Furthermore, the computation accuracy of the PBMC on GPU was validated with a benchmark, a CPU-based discrete-sectional method. To evaluate the accelerating performance, the computing time on the GPU against its sequential counterpart on the CPU was compared. The speedups show that the GPU can accelerate the PBMC by a factor from decades to more than one hundred, depending on the number of simulation particle.

Computations with inverse Runge-Kutta schemes

A new subclass of schemes is considered formally reduced to the class of fully implicit Runge-Kutta schemes possessing outstanding accuracy and stability characteristics. The implementation details of the iterative algorithm for solving stiff systems of ODE and differential-algebraic systems of index 1 by means of the proposed schemes are given.

Experimental performance analysis of an inverse dynamics CNC compensation scheme for high-speed execution of curved toolpaths

Experimental results from the implementation of an inverse dynamics compensation scheme on a three-axis CNC mill with an open-architecture software controller are presented. The scheme amounts to imposing a continuously variable displacement on the commanded toolpath, which compensates for the physical limitations (inertia and damping) of each machine axis, producing accurate execution of the prescribed toolpath. Numerical values for the dimensionless parameters that characterize the second-order inverse dynamics model are determined by feeding input and output data from machine runs into a system identification software tool. For a basic P-type controller, exact a priori solutions for the modified path geometry are possible, allowing implementation by simple alterations to the real-time interpolator. The experimental results based on a P-type controller indicate that the inverse dynamics scheme is highly effective in suppressing both feed (lag/lead) error and contour error (deviation from the desired path), even at high feedrates along strongly curved toolpaths. The scheme thus provides a practical means of achieving smooth and accurate execution of free-form paths, without appealing to more complicated “active” control strategies.

Improving volcanic sulfur dioxide cloud dispersal forecasts by progressive assimilation of satellite observations

Forecasting the dispersal of volcanic clouds during an eruption is of primary importance, especially for ensuring aviation safety. As volcanic emissions are characterized by rapid variations of emission rate and height, the (generally) high level of uncertainty in the emission parameters represents a critical issue that limits the robustness of volcanic cloud dispersal forecasts. An inverse modeling scheme, combining satellite observations of the volcanic cloud with a regional chemistry-transport model, allows reconstructing this source term at high temporal resolution. We demonstrate here how a progressive assimilation of freshly acquired satellite observations, via such an inverse modeling procedure, allows for delivering robust sulfur dioxide (SO2) cloud dispersal forecasts during the eruption. This approach provides a computationally cheap estimate of the expected location and mass loading of volcanic clouds, including the identification of SO2-rich parts.

Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm

By using the finite element method and a "coarse to fine" two-stage genetic algorithm as the forward calculation method and the inverse search scheme, respectively, we perform both the unconstrained and constrained optimal design of the unit cell topology of the two-dimensional square-latticed solid phononic crystals (PnCs), to maximize the relative widths of the gaps between the adjacent energy bands of the PnCs. In the constrained optimizations, the maximization is subjected to the constraint of a predefined average density. In the numerical results, the variation patterns of the optimized structures with the order of the bandgap for both the out-plane shear and the in-plane mixed elastic wave modes are presented, and the effects of both the material contrast and the predefined average density on the obtained optimal structures are discussed.

Modeling and Inverse Compensation of Nonmonotonic Hysteresis in VO $_2$-Coated Microactuators

Vanadium dioxide ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm VO_2}$</tex></formula> ) undergoes a thermally induced solid-to-solid phase transition, which can be exploited for actuation purposes. <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm VO_2}$</tex></formula> -coated silicon cantilevers demonstrate abrupt curvature changes when their temperature is varied across the phase transition. Unlike the monotonic hysteresis phenomena observed in many other smart materials, the curvature–temperature hysteresis of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${\rm VO_2}$</tex></formula> actuators is nonmonotonic due to competing mechanisms associated with the material’s phase transition and the different thermal expansion coefficients of the materials that form the bilayered cantilever. Motivated by the underlying physics, a novel model for the nonmonotonic hysteresis that combines a monotonic Preisach hysteresis operator and a quadratic operator is presented. A constrained least-squares scheme is proposed for model identification, and an effective inverse control scheme is presented for hysteresis compensation. For comparison purposes, a Preisach operator with a signed density function and a single-valued polynomial model are considered. Experimental results show that, for a 300- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu \hbox{m}$</tex></formula> -long actuator, the largest modeling errors with the proposed model, the signed Preisach operator, and the polynomial approximation are 46.8, 80.3, and 483 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm m}^{-1}$</tex></formula> , respectively, over the actuated curvature range of [ <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm -}$</tex></formula> 104, 1846] <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm m}^{-1}$</tex></formula> . In addition, both the largest tracking error and root-mean-square error under the proposed inversion scheme are only around 10% of those under the polynomial-based inversion scheme.

Compensation of Hysteresis Nonlinearity in Magnetostrictive Actuators With Inverse Multiplicative Structure for Preisach Model

Compensation of hysteresis nonlinearities in smart material based actuators presents a challenging task for their applications. Many approaches have been proposed in the literature, including the inverse multiplicative scheme. The advantage for such a scheme is to avoid direct model inversions. However, the approach is mainly developed for the Bouc-Wen model. Focusing on the Preisach model which is utilized to describe magnetostrictive actuators, in this paper an inverse compensation approach for Preisach model using the inverse multiplicative structure is developed. Since the input signal is implicitly involved in the Preisach model, it imposes a great challenge to construct the inverse function of the model. To obtain an explicit expression of the input signal from its implicit form so that the inverse multiplicative technique can be applied, the Preisach model is decomposed into a non-memory part and memory part. Using this separation, it only requires to solve the inverse of the non-memory part to obtain an explicit expression of the input signal, thus avoiding constructing the inverse for entire complex dual integral formulation of the Preisach model. Experimental results for a magnetostrictive actuator demonstrate the effectiveness of the proposed approach.

Estimation of vertical diffusion coefficient based on a one-dimensional temperature diffusion equation with an inverse method

Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography. It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.

Neural Inverse Optimal Control via Passivity for Subcutaneous Blood Glucose Regulation in Type 1 Diabetes Mellitus Patients

This paper deals with subcutaneous blood glucose level control. Inverse optimal trajectory tracking for discrete time non-linear positive systems is applied. The scheme is developed for MIMO (multi-input, multi-output) affine systems. The control law calculates the subcutaneous insulin delivery rate in order to prevent hyperglycemia and hypoglycemia events. A neural model is obtained from an on-line neural identifier, which uses a recurrent neural network, trained with the extended Kalman filter (EKF); this neural model has an affine form, which permits the applicability of inverse optimal control scheme. The proposed algorithm is tuned to follow a desired trajectory; this trajectory reproduces the glucose absorption of a healthy person. Then this model is used to synthesize an inverse optimal controller in order to regulate the subcutaneous blood glucose level for a Type 1 Diabetes Mellitus patient the applicability of the proposed scheme is illustrated via simulation using a recurrent neural network in ...

User adaptive QoS aware selection method for cooperative heterogeneous wireless systems: A dynamic contextual approach

This paper proposes an adaptive realistic mechanism for joint network and user selection in cooperative wireless network environments. We present a novel optimization utility to incorporate the quality-of-service (QoS) dynamics of the available networks along with heterogeneous attributes of each user. The joint network and user selection is modelled by an evolutionary game theoretical approach and replicator dynamics is solved to seek an optimal stable solution. Combining both self-control of users’ preferences and self-adjustment of networks’ parameters, our study innovates over related efforts. The simulation results demonstrate that the proposed inverse cumulative ranking scheme significantly improves the overall QoS performance and system benefits as compared to other solutions. Our results also show that by incorporating the proposed Region of Interest (RoI) scheme, the complexity of the evolutionary game with and without network re-configuration can be reduced by 23% and 58 % respectively.

Research of Force Sensor-based Control on Flight Simulator Motion Platform

Six degrees of freedom (6-DOF) motion platform provides the sense of motion for pilot when the flight simulator is operating. This paper presents a new method of tracking acceleration instead of tracking displacement, while the latter has been widely used. Since the acceleration sensor poor low-frequency characteristics, a new motion platform control method based on force sensor is proposed. By means of the derivation of the dynamics equation, platform acceleration can be obtained indirectly from the force sensor information. Taking RTO (Rejected Takeoff) as an example, in which the washout filter algorithm is designed to access the parameters such as expected acceleration of the motion platform. In addition, a motion platform acceleration controller based on inverse dynamics feedforward control scheme is designed and compared to displacement tracking. Simulation results show that: using the force sensor can achieve the acceleration of the motion platform tracking control, and compared with the conventional displacement control, the acceleration tracking control can significantly improve the tracking accuracy.

Maximum Wind Energy Capturing of Wind Turbine Generator Based on Adaptive Inverse Controller

The variable speed wind turbine generator exhibits serious nonlinearity, uncertainty and difficulty accurate modeling, conventional PID controller can't achieve ideal control effect. In this paper, an adaptive inverse control scheme based on neural network identification technology is proposed to solve the above problem. The scheme firstly uses online identification of one DRNN to obtain the Jacobian information of plant. On this basis, another DRNN identifies the inverse plant model which constitutes adaptive inverse control system as controller. The simulation results verify that the adaptive inverse control scheme has excellent adaptability and robustness, which can make the actual rotational speed of wind turbine rapidly track the set point to maintain the best tip-speed ratio in order to get maximum wind energy capture in the random wind conditions.

Estimation of Grain Orientation in an Anisotropic Weld by Using a Model of Ultrasonic Propagation in an Inverse Scheme

The initial step towards a nondestructive technique that estimates grain orientation in an anisotropic weld is presented in this paper. The purpose is to aid future forward simulations of ultrasonic NDT of this kind of weld to achieve a better result. A forward model that consists of a weld model, a transmitter model, a receiver model, and a 2D ray tracing algorithm is introduced. An inversion based on a multiobjective genetic algorithm is also presented. Experiments are conducted for both P and SV waves in order to collect enough data used in the inversion. Calculation is conducted to fulfill the estimation with both the synthetic data and the experimental data. Concluding remarks are presented at the end of the paper.

Inverse Model Based Torque Vectoring Control For a Rear Wheel Driven Battery Electric Vehicle

This paper presents the torque vectoring control concept for a vehicle with two powerful wheel individual electric drives at the rear axle. The direct yaw moment control which is enabled by the torque difference offers the potential for shaping the vehicle's yaw dynamics in a considerable range. The control concept introduced here is primarily oriented at the practical target of demonstrating the potential of the prototype vehicle's innovative rear axle. Nevertheless, together with the tools presented here it is conveniently adaptable to any vehicle data. The focus is on yaw dynamics control. A reference yaw rate is determined by combining conveniently tunable linear dynamics with a nonlinear steady state gain, the latter in order to establish a desired self-steering behavior. In order to reshape the yaw response after steering inputs an inverse single track model is used as a significant part of the applied feedforward control. Moreover, the same inverse model is employed by the optional yaw rate feedback control which is based on the inverse disturbance observer scheme. Both the effectiveness of the control concept and the practical ease of control parameter tuning were validated in driving experiments.

Adaptive Inverse Control Using an Online Learning Algorithm for Neural Networks

We propose an adaptive inverse control scheme, which employs a neural network for the system identification phase and updates its weights in online mode. The theoretical basis of the method is given and its performance is illustrated by means of its application to different control problems showing that our proposal is able to overcome the problems generated by dynamic nature of the process or by physical changes of the system which originate important modifications in the process. A comparative experimental study is presented in order to show the more stable behavior of the proposed method in several working ranks.

Improved MIMO Throughput With Inverse Power Allocation—Study Using USRP Measurement in Reverberation Chamber

In this letter, we study the spatial multiplexing throughputs of multiple-input-multiple-output (MIMO) systems with fixed modulation and coding scheme (i.e., fixed peak rate) based on measurement of the universal software radio peripheral (USRP) in a reverberation chamber. In particular, we propose a simple inverse power allocation scheme for the singular value decomposition (SVD)-based MIMO system. Using the proposed power allocation, the power saving (for achieving the same throughput), compared to the SVD-MIMO without power allocation, is about 2.5 dB. Good agreement is observed between the USRP measurement and the simulation.

Fast Fourier transforms for the evaluation of convolution products: CPU versus GPU implementation

In a large variety of research areas, convolution products that relate a physical quantity in some observation points with their sources are encountered. When the sources and the observation points coincide, the numerical evaluation of the physical quantity typically leads to order N2 numerical problems. Here, fast Fourier transforms are widely used to reduce the computations to order Nlog N complexity. When adopting Fourier transforms FFT for finite physical problems, zero padding is required. Hence, in 2D and 3D problems, an optimization of the evaluation of the convolution product includes a non-execution of Fourier transforms on arrays containing only zeros in the forward 2D or 3D FFT scheme and their corresponding arrays in the inverse 2D or 3D FFT scheme. This paper describes the implementation of such an approach on graphical processing units GPUs and compares the time gains on GPU and on CPU. It is found that on CPU, the speedup corresponds with the theoretical limit, while in the GPU implementation, the memory bandwidth limits the speedup ratio. Copyright © 2013 John Wiley & Sons, Ltd.