Direct Inverse Model Research Articles

用于异形孔精密加工的超磁致伸缩构件的线性化迟滞建模

According to the tool path characters of non-cylindrical hole precision machining by giant magnetostrictive components,a dynamic hysteresis model of giant magnetostrictive components was established by a pure delay transfer function and the linearity model between high-frequency driving currents and micro-displacement responses.The pure delay compensation parameters of the system were obtained by the relevant identification of driven currents and output displacements with a certain frequency.Then,a mapping model of the driven currents and output displacements without delay was established.The output displacement met the ideal tool paths of non-cylindrical hole boring by direct inverse model and delay compensation in real-time control.The results in verification experiments indicate that the maximum control error is 2.7 μm,and the maximum relative error is about 10%.By integration of micro-displacement feedback control,the accuracy of the component is improved further,the maximum control error is 1.2 μm,and the maximum relative error is about 7%.

Four models of the functional contribution of mirror systems

Four distinct models of the functional contribution of mirror neurons to social cognition can be distinguished: direct matching, inverse modeling, response modeling, and predictive coding. Each entails a different way in which an agent's own capacities for action and affective experience contribute to understanding and/or predicting others' actions and affective experience. In this paper, the four models and their theoretical frameworks are elucidated, empirical data and theoretical arguments bearing upon each are reviewed, and falsifiable predictions that could help to distinguish empirically among the models are proposed.

Control of a hydrolyzer in an oleochemical plant using neural network based controllers

Hydrolyzer is a commonly found unit operation in the splitting of crude palm oil into fatty acids and glycerol in the oleochemical industry of Malaysia. The control of this hydrolyzer has to be done carefully since efficiency in the control of this unit will affect the further yield of the process. At present conventional controllers such as the PID controller have been used to control the unit especially during startup and shutdown of the plant and under presence of disturbances. However experience shows that these PID controllers cannot efficiently handle random disturbance entering the plant. In this study, neural network have been applied as an alternative to cope with the nonlinear dynamics of the hydrolyzer. A mathematical model had been developed and used to simulate the dynamic responses of the temperatures when the controllers were applied into the system. Two types of control strategies namely, direct inverse controller (DIC) and internal model controller (IMC) were implemented, in simulation with actual industrial data, within the control system. The controllers were evaluated on the ability to track set-point and the ability to control the temperature when disturbances and noise appeared in the system. Based on the results, IMC was found to perform very well in the temperature control of the hydrolyzer during set-point tracking and disturbance tests. The responses generated by the IMC was much more stable as compared to the conventional controllers and when noise disturbance was taken into consideration, the IMC also performs better than the DIC controller.

Stable modeling based control methods using a new RBF network

This paper presents a novel model with radial basis functions (RBFs), which is applied successively for online stable identification and control of nonlinear discrete-time systems. First, the proposed model is utilized for direct inverse modeling of the plant to generate the control input where it is assumed that inverse plant dynamics exist. Second, it is employed for system identification to generate a sliding-mode control input. Finally, the network is employed to tune PID (proportional + integrative + derivative) controller parameters automatically. The adaptive learning rate (ALR), which is employed in the gradient descent (GD) method, provides the global convergence of the modeling errors. Using the Lyapunov stability approach, the boundedness of the tracking errors and the system parameters are shown both theoretically and in real time. To show the superiority of the new model with RBFs, its tracking results are compared with the results of a conventional sigmoidal multi-layer perceptron (MLP) neural network and the new model with sigmoid activation functions. To see the real-time capability of the new model, the proposed network is employed for online identification and control of a cascaded parallel two-tank liquid-level system. Even though there exist large disturbances, the proposed model with RBFs generates a suitable control input to track the reference signal better than other methods in both simulations and real time.

Comparison of Two Mathematical Models for 3D Groundwater Flow: Block-Centered Heads and Edge-Based Stream Functions

Traditionally, groundwater flow models, as well as oil reservoir models, are based on the block-centered finite difference method. Well-known models based on this approach are MODFLOW (groundwater) and ECLIPSE (oil and gas). Such models are well proven and robust; their underlying principles are well understood by hydrologists and petroleum reservoir engineers. Nevertheless, the desire to improve the block-centered finite difference paradigm has always been alive, for instance, to be able to apply deformed grid blocks, or to model anisotropy that is not aligned along the coordinate axes. This article introduces the edge-based stream function as a potential alternative to the paradigmatic model, not only to mitigate the above mentioned limitations, but especially for its promise to inverse modeling. Computer programs have been developed for the discrete analog equations of the stream function method and the conventional method. The two methods are tested by using synthetic forward modeling problems of uniform and radial flow. The theoretical formulation and the numerical results show that the two methods are algebraically equivalent and yield the same flux output. However, for rectangular grid blocks and anisotropy aligned along the coordinate axes, the block-centered method is shown to be computationally more efficient than the edge-based stream function method. The major advantage of the stream function method is that it is linear in the resistivities, proving it an ideal candidate for direct inverse modeling. Moreover, any arbitrary specification of stream functions yields a solution that satisfies the mass balance.

A Direct Inverse Model to Determine Permeability Fields from Pressure and Flow Rate Measurements

The determination of the permeability field from pressure and flow rate measurements in wells is a key problem in reservoir engineering. This paper presents a Double Constraint method for inverse modeling that is an example of direct inverse modeling. The method is used with a standard block-centered finite difference method. With an a priori grid block permeability field as input, two forward runs are made: the first is constrained with the measured pressures; the second is constrained with the measured flow rates. We calculate the pressures in the grid block centers from the first run, while from the second run we calculate the fluxes through the faces between the grid blocks. Substitution of these pressures and fluxes into Darcy's law then yields the transmissibilities at the faces and hence the permeabilities in the grid blocks. In this way the "hard" data (measured pressures and flow rates) are always honored while the "soft", geological data can be incorporated at the discretion of the geologist. Using a synthetic example, we demonstrate the method and compare the results with another method: Ensemble Kalman Filtering. The two methods agree within the scope of their applicability. The Double Constraint method focuses initially on determining spatial distributions of the permeability field for single-phase, steady state flow. For history matching an extension is required to non-steady state, two-phase flow conditions, which is already possible with EnKF. We are currently investigating the possibility of combining the two methods, whereby the strengths of the two methods could be fully exploited. © International Association for Mathematical Geology 2008.

Neural Network Inverse Modeling and Applications to Microwave Filter Design

In this paper, systematic neural network modeling techniques are presented for microwave modeling and design using the concept of inverse modeling where the inputs to the inverse model are electrical parameters and outputs are geometrical parameters. Training the neural network inverse model directly may become difficult due to the nonuniqueness of the input-output relationship in the inverse model. We propose a new method to solve such a problem by detecting multivalued solutions in training data. The data containing multivalued solutions are divided into groups according to derivative information using a neural network forward model such that individual groups do not have the problem of multivalued solutions. Multiple inverse models are built based on divided data groups, and are then combined to form a complete model. A comprehensive modeling methodology is proposed, which includes direct inverse modeling, segmentation, derivative division, and model combining techniques. The methodology is applied to waveguide filter modeling and more accurate results are achieved compared to the direct neural network inverse modeling method. Full electromagnetic simulation and measurement results of Ku-band circular waveguide dual-mode pseudoelliptic bandpass filters are presented to demonstrate the efficiency of the proposed neural network inverse modeling methodology.

Difference inversion model of wave equation

A numerical iterative model was derived from the difference method and a perturbation assumption to calculate the coefficient function of a wave equation. The method was used to solve the disaccord problem of numerical precision between the direct problem model and inverse problem model, and its serial problems using the old method. Numerical simulation calculation shows that the method is feasible and effective.

Learning to Control in Operational Space

One of the most general frameworks for phrasing control problems for complex, redundant robots is operational-space control. However, while this framework is of essential importance for robotics and well understood from an analytical point of view, it can be prohibitively hard to achieve accurate control in the face of modeling errors, which are inevitable in complex robots (e.g. humanoid robots). In this paper, we suggest a learning approach for operational-space control as a direct inverse model learning problem. A first important insight for this paper is that a physically correct solution to the inverse problem with redundant degrees of freedom does exist when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component of our work is based on the insight that many operational-space controllers can be understood in terms of a constrained optimal control problem. The cost function associated with this optimal control problem allows us to formulate a learning algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational-space controller. From the machine learning point of view, this learning problem corresponds to a reinforcement learning problem that maximizes an immediate reward. We employ an expectation-maximization policy search algorithm in order to solve this problem. Evaluations on a three degrees-of-freedom robot arm are used to illustrate the suggested approach. The application to a physically realistic simulator of the anthropomorphic SARCOS Master arm demonstrates feasibility for complex high degree-of-freedom robots. We also show that the proposed method works in the setting of learning resolved motion rate control on a real, physical Mitsubishi PA-10 medical robotics arm.

Control of a Batch Polymerization System Using Hybrid Neural Network ‐ First Principle Model

AbstractIn this work, the utilization of neural network in hybrid with first principle models for modelling and control of a batch polymerization process was investigated. Following the steps of the methodology, hybrid neural network (HNN) forward models and HNN inverse model of the process were first developed and then the performance of the model in direct inverse control strategy and internal model control (IMC) strategy was investigated. For comparison purposes, the performance of conventional neural network and PID controller in control was compared with the proposed HNN. The results show that HNN is able to control perfectly for both set points tracking and disturbance rejection studies.

Neural Network Based Modelling and Control in Batch Reactor

The use of neural networks (NNs) in all aspects of process engineering activities, such as modelling, design, optimization and control has considerably increased in recent years (Mujtaba and Hussain, 2001). In this work, three different types of nonlinear control strategies are developed and implemented in batch reactors using NN techniques. These are generic model control (GMC), direct inverse model control (DIC) and internal model control (IMC) strategies. Within the control strategies, NNs have been used as dynamic estimator, dynamic model (forward model) and control (inverse model). An exothermic complex reaction scheme in a batch reactor is considered to explain all these control strategies and their robustness. A dynamic optimization problem with a simple model is solved a priori to obtain optimal operation policy in terms of the reactor temperature with an objective to maximize the desired product in a given batch time. The resulting optimal temperature policy is used as set-point in the control study. All types of controllers performed well in tracking the optimal temperature profile and achieving target conversion to the desired product. However, the NNs used in DIC and IMC controllers need training beyond the nominal operating condition to cope with uncertainties better.

A simulational comparison of intelligent control algorithms on a direct drive manipulator

This paper investigates the control of nonlinear systems by neural networks and fuzzy logic. As the control methods, Gaussian neuro-fuzzy variable structure (GNFVS), feedback error learning architecture (FELA) and direct inverse modeling architecture (DIMA) are studied, and their performances are comparatively evaluated on a two degrees of freedom direct drive robotic manipulator with respect to trajectory tracking performance, computational complexity, design complexity, RMS errors, necessary training time in learning phase and payload variations.

Bayesian Analysis of the Scatterometer Wind Retrieval Inverse Problem: Some New Approaches

SummaryThe retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.

Data assimilation and horizontal structure of the barotropic diurnal tides on the Newfoundland and southern Labrador shelves

A large set of in situ currents and elevation data, and a direct inverse data assimilation model are used in conjunction ‐with global inverse tidal solutions to obtain high‐resolution regional assimilative model solutions for the barotropic K1 and 01 tides on the southern Labrador and Newfoundland Shelves. The regional model assimilates the in situ data and a first estimate of the boundary conditions provided by the global model, so that the regional solutions draw on both regional and larger‐scale observations and dynamics. The regional assimilative solutions have r.m.s. observational misfit values of the order of 2 cm for elevation and 2 cm s−1 for currents, which are reduced (compared with non‐assimilative regional solutions) by 21% and 61% for K1 and O1 elevations respectively, and by 61% and 54% for K1 and O1 currents. A striking feature of the regional model solutions is a series of small‐scale (radius of approximately 100 km) eddy‐like features along the shelf edge. Singular value decomposition (SVD) of the assimilative elevation fields reveals the existence of topographically‐trapped waves at the shelf edge. There are amplified diurnal currents over the outer shelf and slope associated with the topographic waves, pointing to the potential for topographic amplification of other subinertial currents in the region.

A human system learning model for solving the inverse kinematics problem by direct inverse modeling

AbstractThe problem of computing a human arm posture that will take the hand to a desired hand position given by vision is called an inverse kinematics problem. To solve this problem, the human nervous system has a system for solving the inverse kinematics problem computing the proper joint angles from the desired hand position.Although the direct inverse modeling method is popular for the acquisition of an inverse kinematics model, a sufficient inverse model cannot be obtained for such systems with many‐to‐one input‐output correspondence as a human arm system.This paper, proposes a new model of a human inverse kinematics solver which uses the learned inverse model of the linearized model of the human arm. This inverse model transforms the hand position error to the update vector of the joint angles. The solver inverse kinematics problems by using the hand position error feedback. The performance of the solver is shown using numerical simulations.

Discrete time neural network synthesis using input and output activation functions

A new very fast algorithm for synthesis of a new structure of discrete-time neural networks (NN) is proposed. For this purpose the following concepts are employed: (i) combination of input and output activation functions, (ii) input time-varying signal distribution, (iii) time-discrete domain synthesis and (iv) one-step learning iteration approach. The problem of input-output mappings of time-varying vectors is solved. Simulation results based on the synthesis of a new structure of feedforward NN of an universal logical unit are presented. The proposed NN synthesis procedure is useful for applications to identification and control of nonlinear, very fast, dynamical systems. In this sense a feedforward NN for an adaptive nonlinear robot control is designed. Finally, a new algorithm for the direct inverse modeling of input/output nonquadratic systems is discussed.

Understanding Musical Sound with Forward Models and Physical Models

Abstract This research report describes an approach to parameter estimation for physical models of sound-generating systems using distal teachers and forward models (Jordan & Rumelhart, 1992; Jordan, 1990). The general problem is to find an inverse model of a sound-generating system that transforms sounds to action parameters; these parameters constitute a model-based description of the sound. We first show that a two-layer feedforward model is capable of performing inverse mappings for a simple physical model of a violin string. We refer to this learning strategy as direct inverse modeling; it requires an explicit teacher and it is only suitable for convex regions of the parameter space. A model of two strings was implemented that had non-convex regions in its parameter space. We show how the direct modeling strategy failed at the task of learning the inverse model in this case and that forward models can be used, in conjunction with distal teachers, to bias the learning of an inverse model so that non-convex regions are mapped to single-point solutions in the parameter space. Our results show that forward models are appropriate for learning to map sounds to parametric representations.

Manipulator Trajectory Control by Momentum Change Inverse Models Using Multilayer Neural Networks

This paper proposes a learning method of inverse manipulator dynamics model using only position and velocity. The direct inverse modeling method that was proposed as a learning method using neural network requires sensing manipulator position, velocity, and acceleration, because this method is formularized on the basis of manipulator. motion equation. However, since it is difficult at present to sense accurately manipulator acceleration, we could hardly implement this method by original formula. In the momentum change inverse modeling; the learning method that we proposed in this paper, manipulator motion causality is modeled not on the basis of manipulator motion equation but on the manipulator momentum change equation. With this formulation, sensing acceleration becomes unnecessary, inverse manipulator dynamics model can be learned using sensible position and velocity.

A neural network model rapidly learning gains and gating of reflexes necessary to adapt to an arm's dynamics.

Effects of dynamic coupling, gravity, inertia and the mechanical impedances of the segments of a multi-jointed arm are shown to be neutralizable through a reflex-like operating three layer static feedforward network. The network requires the proprioceptively mediated actual state variables (here angular velocity and position) of each arm segment. Added neural integrators (and/or differentiators) can make the network exhibit dynamic properties. Then, actual feedback is not necessary and the network can operate in a pure feedforward fashion. Feedforward of an additional load can easily be implemented into the network using "descendent gating", and a negative feedback control loop added to the feedforward control reduces errors due to external noise. A training, which combines a least squared error based simultaneous learning rule (LSQ-rule) with a "self-imitation algorithm" based on direct inverse modeling, enables the network to acquire the whole inverse dynamics, limb parameters included, during one short training movement. The considerations presented also hold for multi-jointed manipulators.