Optimal Input Design Research Articles

Multi-objective optimal input design for grey-box identification modelling of ship manoeuvring motion

ABSTRACT Grey-box modelling has been widely used to predict the ship manoeuvring motion. In order to design input signals for the grey-box model of ship manoeuvring motion, a multi-objective optimal input design (MOID) method is proposed in this paper. In the proposed method, the MOID is regarded as a multi-objective optimization problem (MOP), where both of D-optimality criterion and condition number are taken as two-objective functions to improve the accuracy and robustness of identifying the grey-box model. The correlation factor is also presented as a constraint for reducing the parameter drift. The MOP is solved by the non-dominated sorting genetic algorithm-II (NSGA-II) with a constraint handling technique. The technique for order preference by similarity to an ideal solution (TOPSIS) is also adopted to screen out an optimal solution from the Pareto solutions. The effectiveness of MOID signals is validated by Monte Carlo analysis and grey-box identification of the MMG model.

Optimal Period Input Design in FIR System Identification With Binary-Valued Observations and Event-Triggered Communication

In the identification of networked systems, the sender uses the event-triggered mechanism to reduce the times of sending data to save communication resources, but the receiver needs as much data as possible to improve the estimation accuracy. This paper tries to mediate the contradiction between the two by means of input design. First, based on the communication rate and the convergence rate of the identification algorithm, the problem of optimal input design is became an optimization problem with constraints. Then, the algorithm for solving this optimization problem is given. Next, the two-time-scale implementation method of optimal input is proposed, where the updated time of the parameter estimation constitutes the identified time scale, and the input is updated based on the estimated value of the system parameter and lasts for a period of time that constitutes the duration time scale of the input. Finally, the validity of the algorithm is verified by numerical simulation.

Optimal experiment design for multivariable system identification using simultaneous excitation

Having an accurate model of a system is essential for many applications today, especially those related to advanced process control (APC). When executing an industrial delivery project of APC, often significant time is spent performing experiments on the real process to identify a model. By designing higher quality experiments the time needed on site carrying out experiments can be reduced, saving both resources and engineering efforts. This paper investigates optimal input design to minimize the time needed to identify a linear time-invariant multi-variable system fulfilling certain requirements on the model accuracy. This is an extension of previous work which focused on sequential excitation on one input signal at the time. Here, however, the effects of using combined simultaneous and sequential excitation is investigated. The resulting non-convex optimization problem is relaxed using binary decision variables. An important feature of the approach is that the experiment is carried out in closed-loop using a model predictive controller with zone constraints to further guarantee that the output constraints are not violated. Simulation results indicate that there are many cases where using combined simultaneous and sequential excitation outperforms the previous sequential approach.

Advancements in the Theory and Practice of Flight Vehicle System Identification

System identification methods have played an essential role in the research and industry projects at the Institute of Flight System Dynamics of the Technical University of Munich. Besides the application of the established system identification approaches to multiple aircraft, novel methods have been developed at the institute to deal with the challenges associated with fixed- and rotary-wing aircraft system identification in the time and frequency domains. This paper provides an overview of these new developments, as well as practical application examples from the past and ongoing projects at the institute. After a brief introduction to the work at the institute, the paper describes the new advancements in the fields of time domain system identification and optimal input design by introducing optimal control methods. It continues with an alternative problem formulation for applying frequency domain system identification and parameter estimation methods to a novel flight control design and tuning approach. Additional topics from the past and ongoing research at the institute such as novel methods and practical findings in rotorcraft system identification and flight path reconstruction for different applications will be discussed and referenced.

Adaptive actor‐critic neural optimal control for constrained nonstrict feedback nonlinear systems via command filter

AbstractThe actor‐critic neural optimal control is investigated for the state‐constrained nonlinear systems in the nonstrict feedback form with unmodeled dynamics in this paper. The filtering errors in the traditional dynamic surface control (DSC) are countervailed by the introduced compensation signals. Two design phases together determine the input: the feedforward input design and the near optimal input design. In the feedforward input design, a mapping rule is established to keep all the states in the finite range, and a first‐order adjunctive signal is designed to treat the unmodeled dynamics. In the near optimal input design, the cost function relying on the reconstructed error system is minimized by the near optimal input via adaptive dynamic programming (ADP). In the whole design processing, the unknown nonlinear uncertain parts are fitted by the radial basis function neural networks (RBFNNs). The stability analysis illustrates all the signals are bounded in the controlled system. Two simulation examples are employed to verify the theoretical findings.

An Energy-Efficient Optimal Operation Control Strategy for High-Speed Trains via a Symmetric Alternating Direction Method of Multipliers

Train operation control is of great importance in reducing train operation energy consumption and improving railway operation efficiency. This paper investigates the design of optimal control inputs for multiple trains on a single railway line with several stations. Firstly, a distributed optimal control problem for multiple train operation is formulated to reduce the energy consumption and improve the punctuality of trains. Then, we propose an efficient algorithm based on the framework of the symmetric alternating direction method of multipliers to solve this optimization problem. Finally, numerical simulations show that the method can obtain the optimal train control sequence in fewer iterative steps compared to the alternating direction multiplier method, thus illustrating the effectiveness of the algorithm.

A novel geometry optimization strategy to online active fault diagnosis of LPV systems

This paper proposes a novel geometry optimization strategy for the online robust active fault diagnosis (AFD) of discrete-time linear parameter varying (LPV) systems under set-theoretic framework. By establishing a bank of zonotopic set-value observers to match healthy/faulty system modes, the key of the optimization strategy comes down to the design of the optimal system inputs and gain matrices simultaneously. The criterion on the design of optimal inputs is characterized by fully utilizing the geometry property of zonotopes, which formulates a non-convex fractional programming problem able to be solved under 0–1 mixed integer quadratic programming framework based on a series of transformations. While the optimal gain matrices can be obtained analytically based on a so-called zonotopic kalman filtering process. The proposed method can improve the sensitivity of AFD as much as possible while ensuring the stability of the designed observer. At the end, two physical models are used to verify the effectiveness of our proposed method.

Application-Oriented Input Design With Low Coherence Constraint

In optimal input design input sequences are typically generated without paying attention to the correlations between the regressors of the model to be estimated. In fact, in many cases high correlations are beneficial. This is in contrast to the requirements in sparse estimation. Mutual coherence is the maximum of these correlations, and in case the parameter vector is known to be sparse, we need a low mutual coherence in order to estimate it accurately. This contribution proposes adding a constraint on the mutual coherence to the optimal input design problem to improve the accuracy of estimated sparse models. The proposed method can be combined with any sparse estimation algorithm to estimate the parameters of a model. However, we focus in particular on the bound on the mutual coherence required for Orthogonal Matching Pursuit (OMP), a well-known algorithm in sparse estimation. Furthermore, we analyze the effect of the proposed method on the required input power. Finally, we evaluate, in a numerical study, the performance of the proposed method compared to state-of-the-art algorithms for input design.

Tractable model discrimination for safety–critical systems with disjunctive and coupled constraints

This paper considers the model discrimination problem among a finite number of models in safety–critical systems that are subjected to constraints that can be disjunctive and where state and input constraints can be coupled with each other. In particular, we consider both the optimal input design problem for active model discrimination that is solved offline as well as the online passive model discrimination problem via a model invalidation framework. To overcome the issues associated with non-convex and generalized semi-infinite constraints due to the disjunctive and coupled constraints, we propose some techniques for reformulating these constraints in a computationally tractable manner by leveraging the Karush–Kuhn–Tucker (KKT) conditions and introducing binary variables, thus recasting the active and passive model discrimination problems into tractable mixed-integer linear/quadratic programming (MILP/MIQP) problems. When compared with existing approaches, our method is able to obtain the optimal solution and is observed in simulations to also result in less computation time. Finally, we demonstrate the effectiveness of the proposed active model discrimination approach for estimating driver intention with disjunctive safety constraints and state–input coupled curvature constraints, as well as for fault identification.

Trust-Region RB Methods for PDE-Constrained Optimization and Optimal Input Design

In this paper we propose an algorithm for the bi-level optimal input design involving a parameter-dependent evolution problem. In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trust-region reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.

Data Driven Strategy for Linear Parameter Varying Control Design

In this paper, we propose a novel data driven strategy framework for linear parameter varying closed loop system which consists of linear parameter varying system and linear parameter varying controller simultaneously. Firstly, we consider the model based control framework whose controller design is dependent of the considered system. In particular, due to the unknown system and unknown controller, data driven strategy is applied to obtain the system and controller respectively in their nonparametric and parametric forms. Such two different forms are related with system identification, power spectral and numerical optimization ,etc. with a choice of the optimal input signal design. Secondly, to avoid the identification process of that system, data driven strategy is modified to design the controller directly from the observed input-output data sequence without providing any priori information on the considered system. We show that various techniques for data driven strategy to identify system or design controller, such as system identification, numerical optimization, power spectral and optimal input design etc within the proposed general framework.

Dynamic Optimization Approach to Estimate Kinetic Parameters of Monod-Based Microalgae Growth Models.

The biomass concentration of microalgae growth in photobioreactor was predicted using the Monod-based growth models. Kinetic parameters such as maximum specific growth rate and saturation constant of light intensity were evaluated by nonlinear least squares methods that focused on minimizing the sum of squares error (SSE). The importance of good initial guess for the nonlinear least squares method was also discussed. The optimal control problem of the microalgae growth model was determined based on parameter sensitivity. Therefore, a dynamic optimization approach was used where an optimal input design method was formulated to obtain a control function of a problem. The dynamic state equations, additional state equations, cost function, and Hamiltonian function were used to establish a control function of microalgae growth in a photobioreactor. Hence, the biomass production of microalgae can be predicted using numerical methods such as the Taylor series method.

Optimal Input Design for Aircraft Stability and Control Flight Testing

Optimal Input Design for Aircraft Stability and Control Flight Testing

Estimation of the microalgae growth using the optimization approach

This study estimates the parameters value of the microalgae growth kinetic model which are Monod, Tessier and modified Moser model using the Levenberg-Marquardt method, by minimizing the sum of squares error. The optimal control problem for microalgae growth in photobioreactor is formulated and solved by the optimal input design method and taking into account the parametric sensitivities in order to obtain the control function. Hence, the fourth-order Runge-Kutta method is implemented to predict the microalgae biomass concentration by solving the state equations of the optimal control problem. The result shows the Tessier model best describes the growth of microalgae with the produced biomass concentration of weight 1.813 × 1010 g.

A Study of Convolutional Neural Networks Learning Mechanisms for Machine Health Monitoring Applications

In recent years, Deep Learning (DL) and Internet of Things (IoT) technologies have been used and deployed jointly to solve a wide range of modern technical challenges in different areas. With the continuous advancement of IoT connectivity solutions, the range of applications that can benefit from such an increase is limitless. One area that can benefit significantly from the combined strength of DL and IoT technologies is Machine Health Monitoring (MHM) Systems. MHM utilizes different analytical approaches and tools to determine the state and health of different components in running machinery. The traditional MHM system uses control limits from predetermining values that determine if a component has failed depending on the preset limits of the machinery. The main disadvantage of using such technique us the unpredictable nature of the timing and component failure. This type of failure causes unplanned production time loss and increases the cost of maintenance due to the unpredictability of the failure events. With DL and low-cost sensors that use different IoT connectivity solutions, MHM systems can utilize the learning capabilities of the DL network to perform end-to-end prognosis. One crucial fact is that features learned by Deep Neural Networks (DNN) are part of a large black box, and there are valuable underlying physical meanings embedded within the features. Hence, there is an exciting research area to explore underlying mechanisms and interpret physical meanings within DNN. In this paper, DNN learning mechanisms are evaluated using three different models: stacked autoencoders (SAE), denoising autoencoders (DAE), and convolutional neural networks (CNN). Initial results indicate that the input layer behaves similarly to a band-pass filter. However, deep layers require optimal input design to maximize neuron activation, which leads to an extensive understanding of deep layer learning consequently (In progress).

Data-driven modeling of product crystal size distribution and optimal input design for batch cooling crystallization processes

In this paper, a novel data-driven model building method is proposed for predicting one-dimensional product crystal size distribution (CSD) or chord length distribution (CLD) of batch cooling crystallization processes, based on only batch run data. The proposed model relating the manipulated variable of cooling rate to the product CSD are constructed by two classes of basis functions, one is the wavelet basis function for reshaping the CSD and the other is the polynomial basis function for weighting the chosen wavelet basis functions to reflect the nonlinear relationship between the input and the density of individual crystal size among the product crystals. Correspondingly, a double-layer least-squares algorithm is established to estimate the model parameters, along with an adaptive strategy to determine the location and number of wavelet basis functions. By introducing an objective function that combines the information entropy of product CSD and the sample deviation of product crystals in each batch with respect to the target crystal size, the optimal input design of cooling rate for the desired product CSD is carried out by using a particle swarm optimization (PSO) algorithm to solve the non-convex optimization problem with the established CSD model. Simulation tests on the hen-egg-white lysozyme crystallization process along with experiments on the L-glutamic acid cooling crystallization process are performed to demonstrate the effectiveness and advantage of the proposed method.

Innovative Analysis for Parameter Estimation Quality

This paper performs an analysis of the solution space influence of a nonlinear dynamic system on the parameter estimation quality. For parameters estimation, the proposed approach uses an Optimal Input Design (OID) as the Suboptimal Excitation Signal Generation and Optimal Parameter Estimation (SOESGOPE). Based on the studies of a small mobile robot that is represented by a parametric mathematical model indicate that the model reliability level maximizes using the shortest set of parameters. Applications, qualities, and limitations of the method are analyzed considering the solution space. Through an in-depth analysis of the identification process of a differential mobile robot, the paper becomes a reference for a review of a nonlinear dynamic system, aiming to select the most suitable model for the identification process.

Experimental Verification of Fault Identification for Overactuated System With a Scaled-Down Electric Vehicle

The experimental verification of the optimal input design method for fault identification is performed using a scaled-down overactuated electric vehicle. In the previous study, online fault identification was achieved by utilizing all the characteristics of an overactuated system (Park and Park, 2016). The perturbation input signal for the actuator fault identification can be applied to the faulty actuators to suppress most of the control performance loss. The scaled-down vehicle contains four independent driving motors and four independent wheel steering motors to model an extremely overactuated system. The lateral velocity and yaw rate are estimated using the state observer to realize feedback control, and the cornering stiffness is determined based on the estimated values. Experimental verification is performed using steady state cornering maneuvers with sudden actuator faults. The experiments with the scaled-down vehicle support the performance of the optimal input design method. When sensor noise and modeling uncertainties exist, the results from our method were much more precise than the results obtained using the conventional white noise perturbation input signal.

Recursive Approach of Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation

Optimal Input Design (OID) methodologies are developed to find a signal that could best estimate a set of parameters of a given model. Their application in constrained nonlinear systems, especially when the search space limits or the initial conditions are unknown, may present several difficulties due to the numerical instability related to the optimization processes. A good choice over the parameters possible ranges is a trade-off among numerical stability, search space size, and effectiveness, and it is hardly found. To deal with this problem, this paper proposes a series of changes in the Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation (SOESGOPE) methodology. First, the limits over the parameters are tightly adjusted according to their confidence. A recursive approach runs the optimization methodology, analyzes the solution’s feasibility and marginal costs given by the Lagrange Multipliers, and selects a direction that could improve the system’s response. This approach improves the convergence and the assertiveness of the estimation process. To validate this approach, some cases, including a parameters estimation of a mobile robot nonlinear system, are tested.

Statistical accuracy analysis for virtual reference feedback tuning with two degrees of freedom controllers*

Virtual reference feedback tuning is one of data-driven control method, as only input–output data are used to design two degrees of freedom controller directly, i.e. feed-forward and feedback controller. Given two desired closed-loop transfer functions, virtual input and virtual disturbance are constructed, respectively to obtain one cost function, whose decision variables correspond to the two unknown controller parameters. Then after formulating the cost function as a linear regression form, the classical least squares algorithm is applied to identify the unknown parameter estimators. To quantify the quality or approximation error of the parameter estimators, statistical accuracy analysis is studied for virtual reference feedback tuning control. The detailed computational process about the asymptotic variance matrix is given by using some knowledge from probability theory and matrix theory. Based on our obtained asymptotic variance matrix, two applications of optimal input design and model structure validation are used to illustrate how to use the obtained asymptotic variance matrix. Finally, one simulation example has been performed to demonstrate the effectiveness of the theories proposed in this paper.