Output Error Approach Research Articles

Closed-Loop Output Error Approaches for Drone's Physics Informed Trajectory Inference

The design of adequate countermeasures against drone's threats needs accurate trajectory estimation to avoid economic damage to the aerospace industry and national infrastructure. As trajectory estimation algorithms need highly accurate physics informed models or off-line learning algorithms, radical innovation in on-line trajectory inference is required. In this paper, a novel drone's physics informed trajectory inference algorithm is proposed. The algorithm constructs a physic informed model and infers the drone's trajectories simultaneously using a closed-loop output error architecture. Two different approaches are proposed based on a physics structure and an admittance filtering model which considers: i) full states measurements and ii) partial states measurements. Stability and convergence of the proposed schemes are assessed using Lyapunov stability theory. Simulations studies are carried out to demonstrate the scope and high inference capabilities of the proposed approach.

Unstable Aircraft Parameter Estimation Using Neural Partial Differentiation

An approach based on neural partial differentiation is suggested, to overcome the numerical problems faced by classical methods, for the parameter estimation of an aerodynamically unstable aircraft. Theoretical analysis of the neural modeling, the parameter estimation process, and the nature of the estimates pertaining to unstable aircraft dynamics using the neural partial differential method, are discussed. Equation for the relative standard deviation, which is equivalent to the Cramer-Rao bound in the method like output error approach, is derived using the neural partial differential method and verified through numerical simulation. The aerodynamic derivatives are derived for the simulated and real longitudinal flight data of an unstable aircraft, and the estimates obtained using the neural partial differentiation are compared with the classical methods such as the equation error and the output error methods. The parameter estimates from the simulated noisy data are also presented to assess and support the theoretical developments presented in this paper. The theoretical analysis and the results presented in this paper make the neural partial differential approach more reliable and widely applicable.

A Closed-Loop Output Error Approach for Physics-Informed Trajectory Inference Using Online Data.

While autonomous systems can be used for a variety of beneficial applications, they can also be used for malicious intentions and it is mandatory to disrupt them before they act. So, an accurate trajectory inference algorithm is required for monitoring purposes that allows to take appropriate countermeasures. This article presents a closed-loop output error approach for trajectory inference of a class of linear systems. The approach combines the main advantages of state estimation and parameter identification algorithms in a complementary fashion using online data and an estimated model, which is constructed by the state and parameter estimates, that inform about the physics of the system to infer the followed noise-free trajectory. Exact model matching and estimation error cases are analyzed. A composite update rule based on a least-squares rule is also proposed to improve robustness and parameter and state convergence. The stability and convergence of the proposed approaches are assessed via the Lyapunov stability theory under the fulfilment of a persistent excitation condition. Simulation studies are carried out to validate the proposed approaches.

Output Error Methods for Robot Identification

Abstract Industrial robot identification is usually based on the inverse dynamic identification model (IDIM) that comes from Newton's laws and has the advantage of being linear with respect to the parameters. Building the IDIM from the measurement signals allows the use of linear regression techniques like the least-squares (LS) or the instrumental variable (IV) for instance. Nonetheless, this involves a careful preprocessing to deal with sensor noise. An alternative in system identification is to consider an output error approach where the model's parameters are iteratively tuned in order to match the simulated model's output and the measured system's output. This paper proposes an extensive comparison of three different output error approaches in the context of robot identification. One of the main outcomes of this work is to show that choosing the input torque as target identification signal instead of the output position may lead to a gain in robustness versus modeling errors and noise and in computational time. Theoretical developments are illustrated on a six degrees-of-freedom rigid robot.

Nonlinear system identification using fractional Hammerstein–Wiener models

The paper deals with identification of fractional order nonlinear systems based on Hammerstein–Wiener models. An output error approach is developed using the robust Levenberg–Marquardt algorithm. It presents the difficulty of the parametric sensitivity functions calculation which requires a heavy computational load at each iteration. To overcome this drawback, the fractional nonlinear system is reformulated under a regression form, and the gradient and the Hessian can be obtained in a closed form without using the parametric sensitivity functions. The method’s efficiency is confirmed on numerical simulations, and its feasibility is illustrated with its application to the modeling of an experimental arm robot.

Identification of Aeroelastic Models for the X-56A Longitudinal Dynamics Using Multisine Inputs and Output Error in the Frequency Domain

System identification from measured flight test data was conducted using the X-56A aeroelastic demonstrator to identify a longitudinal flight dynamics model that included the short period, first symmetric wing bending, and first symmetric wing torsion modes. Orthogonal phase-optimized multisines were used to simultaneously excite multiple control effectors while a flight control system was active. Non-dimensional stability and control derivatives parameterizing an aeroelastic model were estimated using the output-error approach to match Fourier transforms of measured output response data. The predictive capability of the identified model was demonstrated using other flight test data with different inputs and at a different flight conditions. Modal characteristics of the identified model were explored and compared with other predictions. Practical aspects of the experiment design and system identification analysis, specific to flexible aircraft, are also discussed. Overall, the approach used was successful for identifying aeroelastic flight dynamics models from flight test data.

Nonlinear and Linear Unstable Aircraft Parameter Estimations Using Neural Partial Differentiation

To overcome the numerical problems faced by conventional methods for the parameter estimation of linear and nonlinear unstable aircraft dynamics, an approach based on neural partial differentiation is proposed. An equation for the relative standard deviation, which is equivalent to the Cramer–Rao bound in methods such as output error approach, is derived for the statistical analysis of the estimates obtained using the neural partial differentiation approach and verified through numerical simulation. The neural architecture to be used for the parameter estimation is also discussed. It is shown that the neural partial differentiation approach is better than the least-squares approach for noisy data. The longitudinal axis stability and control derivatives are obtained for simulated data, with and without noise for an unstable aircraft, using the neural partial differentiation approach and compared with the least-squares and stabilized output error methods. Moreover, the longitudinal axis stability and control derivatives estimated from actual flight data of the unstable X-31A aircraft are compared with the least-squares and stabilized output error approaches, proving the efficacy and superiority of the proposed neural approach.

Black box model identification of nonlinear input–output models: A Wiener–Hammerstein benchmark

This work analyzes the performance of several black box nonlinear model identification techniques for input–output models with polynomial nonlinearities on a benchmark identification problem. The case study, proposed in Schoukens, Suykens, and Ljung (2008), concerns a nonlinear SISO electronic system with a Wiener–Hammerstein structure, originally documented in Vandersteen (1997). The objective being the obtainment of an accurate simulation model, capable of replicating the dynamic behavior of the system without using past measured output data, various output-error approaches have been tested and compared with more standard equation-error techniques. The provided analysis shows that excellent modeling performance can be obtained with these methods even without explicitly taking into account the block structure of the nonlinear system.

Results of Short-Period Helicopter System Identification Using Output-Error and Hybrid Search-Gradient Optimization Algorithm

This article focuses on the problem of parameter estimation of the uncoupled, linear, short-period aerodynamic derivatives of a “Twin Squirrel” helicopter in level flight and constant speed. A flight test campaign is described with respect to maneuver specification, flight test instrumentation, and experimental data collection used to estimate the aerodynamic derivatives. The identification problem is solved in the time domain using the output-error approach, with a combination of Genetic Algorithm (GA) and Levenberg-Marquardt optimization algorithms. The advantages of this hybrid GA and gradient-search methodology in helicopter system identification are discussed.

Frequency Band Averaging of Spectral Densities for Updating Finite Element Models

The successful operation of proposed precision spacecraft will require finite element models that are accurate to much higher frequencies than the standard application. The hallmark of this mid-frequency range, between low-frequency modal analysis and high-frequency statistical energy analysis, is high modal density. The modal density is so high, and the sensitivity of the modes with respect to modeling errors and uncertainty is so great that test/analysis correlation and model updating based on traditional modal techniques no longer work. This paper presents an output error approach for finite element model updating that uses a new test/analysis correlation metric that maintains a direct connection to physical response. The optimization is gradient based. The metric is based on frequency band averaging of the output power spectral densities with the central frequency of the band running over the complete frequency range of interest. The results of this computation can be interpreted in several different ways, but the immediate physical connection is that it produces the mean-square response, or energy, of the system to random input limited to the averaging frequency band. The use of spectral densities has several advantages over using frequency response directly, such as the ability to easily include data from all inputs at once, and the fact that the metric is real. It is shown that the averaging process reduces the sensitivity of the optimization due to resonances that plague many output error model updating approaches.

NONLINEAR MULTIVARIABLE CONTROL OF AN OMNIDIRECTIONAL VEHICLE

This paper describes the multi-level control of a three-wheel omnidirectional vehicle. The vehicle was developed to be an autonomous robotic soccer player with respect to the Robocup F180 small-size league rules. The two inner control levels are model nonlinear reference controllers (MNRC) while the last level of control relies on a modified Smith Predictor. The paper covers the modeling of the vehicle, the parameter identification using an output-error approach, and the design and implementation of the controllers. Some results illustrate the good performances.

Retrospective and Recent Examples of Aircraft Parameter Identification at NASA Dryden Flight Research Center

A brief retrospective is presented on the development of aircraft aerodynamic parameter identification at NASA Dryden Flight Research Center, tracing its origins from the mid-1960s through recent flight examples. The maximum-likelihood output-error approach is summarized, leaving details to ample references. A partial listing is provided of flight programs at Dryden over the last 40 years that have used parameter identification to support flight testing. In particular, highlights and lessons learned within the last 12 years are described from the X-29A, F-18, SR-71, and space shuttle programs

A cumulant based algorithm for the identification of input–output quadratic systems

The identification of a special class of polynomial models is pursued in this paper. In particular a parameter estimation algorithm is developed for the identification of an input–output quadratic model excited by a zero mean white Gaussian input and with the output corrupted by additive measurement noise. Input–output crosscumulants up to the fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of successive triangular linear systems of equations that are solved at each step of the algorithm. Simulation studies are carried out and the proposed methodology is compared with two least squares type identification algorithms, the output error method and a combination of the instrumental variables and the output error approach. The proposed cumulant based algorithm and the output error method are tested with real data produced by a robotic manipulator.

An adaptive IIR filter algorithm based on observers

The output error approach to adaptive IIR filtering is considered from a state observation perspective, and a new algorithm, termed the observer-based regressor filtering (OBRF) algorithm, is developed. The convergence requirements of the OBRF are established as a persistent excitation condition on the regressor and a strict positive reality (SPR) condition on an operator arising in the algorithm. Speed of convergence experiments show that the OBRF algorithm converges more quickly than the related output error algorithm for the hyperstable adaptive recursive filter (HARF), although the OBRF algorithm converges as quickly as typical equation error schemes. The OBRF is shown to compare favorably with equation error with respect to parameter bias in the presence of output measurement noise. Thus, OBRF is a compromise between the equation error and output error approaches. In addition, algorithm parameter selection to satisfy the SPR condition for OBRF is explored and compared with the related conditions for HARF.

Learning neural networks with noisy inputs using the errors-in-variables approach

Currently, most learning algorithms for neural-network modeling are based on the output error approach, using a least squares cost function. This method provides good results when the network is trained with noisy output data and known inputs. Special care must be taken, however, when training the network with noisy input data, or when both inputs and outputs contain noise. This paper proposes a novel cost function for learning NN with noisy inputs, based on the errors-in-variables stochastic framework. A learning scheme is presented and examples are given demonstrating the improved performance in neural-network curve fitting, at the cost of increased computation time.

Identification of Helicopter Rigid Body Dynamics from Flight Data.

This paper discusses helicopter modelling and identification related aspects. By applying thesystem identification methodology, longitudinal and lateral-directional rigid body helicopter dynamics are identified from flight data. Aerodynamic parameters from single input excitation as wellas multimanoeuver evaluation are estimated utilising output-error approach. The formulatedmathematical models yield adequate fit to measured time histories. Results obtained from the proof-of-match for model validation indicate that the identified derivatives can satisfactorily predictlongitudinal dynamics to a given arbitrary input. It is further demonstrated for the present study thatlateral body dynamics can be adequately predicted by including cross-coupling terms in the estimation model.

Damage Detection in Composite Materials Using Identification Techniques

The present paper describes an approach for damage detection in composite structures that has its basis in methods of system identification. Response of a damaged structure differs from predictions obtained from a mathematical model of the original structure, where such a model is typically a finite-element representation of the structure. In the present work dealing with composite materials, two distinct analytical models, one using two-dimensional (2D) elements in conjunction with the classical lamination theory and another using three-dimensional (3D) elements were considered. The output error approach of system identification was employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response. The proposed method is an extension of the stiffness-reduction approach for damage detection to realistic structures. Numerical simulation of measurements of static deflections, strains, and vibration modes were used in the identification procedure. The methodology was implemented for representative composite structures. Principal shortcomings in the proposed approach and possible methods to circumvent these problems are discussed in the paper.

Parameter bounds for ARMAX models from records with bounded errors in variables

The errors in variables problem is that of parameter estimation where all observed variables are corrupted by noise. So far, the computation of parameter bounds for dynamical models has been performed using equation-error and output-error approaches. In this paper, parameter bounds for autoregres-sive-moving-average-exogenous (ARMAX) models are derived on the assumption that both input and output are affected by bounded noise. Parameter bounding by both the ‘bounded equation error’ and the ‘bounded errors-in-variables’ approach is outlined, together with the approximation of the feasible parameter region by an orthotope outer-bounding set, and is tested on simulated data.

Identification of time-varying structural dynamic systems - An artificial intelligence approach

An application of the artificial intelligence-derived methodologies of heuristic search and object-oriented programming to the problem of identifying the form of the model and the associated parameters of a time-varying structural dynamic system is presented in this paper. Possible model variations due to changes in boundary conditions or configurations of a structure are organized into a taxonomy of models, and a variant of best-first search is used to identify the model whose simulated response best matches that of the current physical structure. Simulated model responses are verified experimentally. An output-error approach is used in a discontinuous model space, and an equation-error approach is used in the parameter space. The advantages of the AI methods used, compared with conventional programming techniques for implementing knowledge structuring and inheritance, are discussed. Convergence conditions and example problems have been discussed. In the example problem, both the time-varying model and its new parameters have been identified when changes occur.

Process control by on-line trained neural controllers

The question of how to perform online training of multilayer neural controllers in order to reduce the training time is addressed. First, based on multilayer neural networks, structures for a plant emulator and a controller are described. Basic control configurations are briefly presented, and new online training methods, based on performing multiple updating operations during each sampling period, are proposed and described in algorithmic form. One method, the direct inverse control error approach, is effective for small adjustments of the neural controller when it is already reasonably trained; another, the predicted output error approach, directly minimizes the control error and greatly improves convergence of the controller. Simulation and experimental results using a simple plant show the effectiveness of the proposed control structures and training methods. >