Nonlinear Identification Research Articles

Change surface regression for nonlinear subgroup identification with application to warfarin pharmacogenomics data.

Pharmacogenomics stands as a pivotal driver toward personalized medicine, aiming to optimize drug efficacy while minimizing adverse effects by uncovering the impact of genetic variations on inter-individual outcome variability. Despite its promise, the intricate landscape of drug metabolism introduces complexity, where the correlation between drug response and genes can be shaped by numerous nongenetic factors, often exhibiting heterogeneity across diverse subpopulations. This challenge is particularly pronounced in datasets such as the International Warfarin Pharmacogenetic Consortium (IWPC), which encompasses diverse patient information from multiple nations. To capture the between-patient heterogeneity in dosing requirement, we formulate a novel change surface model as a model-based approach for multiple subgroup identification in complex datasets. A key feature of our approach is its ability to accommodate nonlinear subgroup divisions, providing a clearer understanding of dynamic drug-gene associations. Furthermore, our model effectively handles high-dimensional data through a doubly penalized approach, ensuring both interpretability and adaptability. We propose an iterative 2-stage method that combines a change point detection technique in the first stage with a smoothed local adaptive majorize-minimization algorithm for surface regression in the second stage. Performance of the proposed methods is evaluated through extensive numerical studies. Application of our method to the IWPC dataset leads to significant new findings, where 3 subgroups subject to different pharmacogenomic relationships are identified, contributing valuable insights into the complex dynamics of drug-gene associations in patients.

Multi-DoFs nonlinear joint identification through substructure decoupling

Multi-DoFs nonlinear joint identification through substructure decoupling

Neuro-Fuzzy: Multivariable Identification of a Pumping System with Variable Demand

Water supply systems (WSS) comprise a set of equipment, works and services aimed at supplying water, covering domestic, industrial and public consumption. WSS face challenges arising from hourly variation in demand, influenced by society's consumption patterns. These variations cause fluctuations in system pressures and energy inefficiencies. As a way of analyzing this aspect, intelligent techniques were used to identify an automated WSS with variable demand for the development of computational models. Two multivariable and non-linear models were developed based on Artificial Neural Networks (ANN) and Neuro-Fuzzy system (NF). The objective is to enable simulations of operation scenarios, analysis, design and implementation of new intelligent control algorithms. To collect the data used in training and validation, experiments were carried out throughout the system's operating region. For cross validation, tests were carried out in operating regions different from those used for training. The models were evaluated using performance criteria, such as: Root Mean Square Error (RMSE), Normalized Root Mean Square Error (NRMSE), Final Prediction Error (FPE) and Adjustment percentage. The results were obtained using an experimental bench and showed adjustments greater than 99%. The cross-validation results evaluated with performance indicators show the superiority of intelligent models in comparison to parametric and mathematical models in the multivariable and non-linear identification of water pumping systems for simulation and dynamics prediction purposes.

Nonlinear Parameter Identification of the Franka Emika PANDA Robot

This research addresses the problem of dynamic parameter identification for robot manipulators. As the complex manipulation of tasks increases, traditional control methods become insufficient, necessitating accurate model-based control. Previous studies have explored various parameter identification methods for robot manipulators. Still, the impact of different friction models on dynamic parameter identification, particularly for the Franka Emika PANDA robot, is yet to be comprehensively investigated. The linear and nonlinear parameter identification methods and nonlinear friction models (Lugre, Stribeck, and Sigmoidal) were studied on the PANDA robot. A linear inverse dynamic model was developed using the Newton-Euler method. Identification and validation trajectories were designed. Nonlinear constraints and bounds were applied for easier convergence, ensuring a positive definite inertia tensor in the center of mass (COM) frame. Using constrained least squares with Lasso regularisation, model-estimated torques comparison to measurements was done to estimate the physical parameters, considering the PANDA robot’s hand as a payload. We obtained the PANDA robot’s physical parameters, including the hand’s mass, without a friction model where discrepancies in joint torques were observed. Incorporating friction models reduced these discrepancies, validated by another trajectory comparison between the measured and the model’s predicted joint torques. Stribeck friction model exhibited the best performance in estimating parameters from its Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), indicating its effectiveness in capturing nonlinearities in the PANDA robot.

An analytical model for nonlinear bending mode identification of the circumferential joints of assembled underground structures

The circumferential joints of assembled underground structures are generally subjected to loads from construction and the environment, resulting in significant nonlinear characteristics. To elucidate the nonlinear characteristics of the bending deformation law of circumferential joints, a comprehensive mechanical model containing five bending modes is proposed. The model determines the variation in bending stiffness by solving expressions for the bending moment, axial force, and rotation angle. To directly apply monitored strain data in practical engineering without conversion, strain regional distribution diagrams are presented to rapidly and accurately identify the joint bending modes. Finally, the above model is applied to two case studies: the Zhanjiang Bay undersea shield tunnel and the Shenzhen assembled metro station in China. Through inverse calculations of internal forces at the joint sections, the underlying causes of the bending deformation development are revealed, and the differences in the joint mechanical characteristics between the two projects are studied. The results indicate that the strain regional distribution diagrams can quickly and effectively identify the bending patterns of circumferential joints in assembled underground structures. While the axial forces in the joint section of both projects are comparable, the bending moments in the assembled metro station are approximately ten times greater than those in the undersea shield tunnel due to distinct joint structures, assembly processes, and surrounding loads. In these case studies, most joints of both structures are in Mode I under axial compression and low bending moment. However, a small portion of joints develop into Mode III in the case of tension/low compression and high bending moment, which exhibits nonlinear mechanical characteristics.

Identification of Nonlinearity in Bolted Beam using ResponseControlled Testing and ForceControlled Testing

Nonlinear phenomena such as super-and sub-harmonics and unstable branches in frequency response functions (FRFs) often occur in slender structures, which are common in the aerospace, civil and wind power domains. The widely used methods of linear modal analysis are invalid for the identification of these phenomena, which play an important role in nonlinear structural analysis as they can significantly affect the behaviour and stability of structures under various excitations. This paper proposes the methodology of Response-Controlled Stepped Sine Testing (RCT) and Force-Controlled Stepped Sine Testing (FCT) to identify nonlinear phenomena in a bolted beam. The bolted beam was excited with two different sets of predefined displacement and force amplitudesto measure the Nonlinear Frequency Response Functions (NLFRFs) of the bolted beam. The measurements were performed with RCT and FCT, using Stepped Sine signals to control the displacement and force amplitudes. The Harmonic Force Surface (HFS) technique was used as means of obtaining the NFRFs. It was found that RCT with HFS successfully identifiedthe nonlinearity that is very similar to the identification results obtained with FCT. In addition, RCT was computationally faster than FCT in identifying nonlinear bolted beams and avoided dealing with jump phenomena. These advantages of RCT and HFS can provide engineers and researchers with a great technique to accurately and efficiently identify nonlinearities in structures.

An efficient Volterra series approach for identifying nonlinear system vibration responses to an excitation

This paper focuses on the issue of nonlinear vibration responses identification of nonlinear systems. An efficient algorithm is presented, in which the nonlinear vibration system under studied is decomposed into a multiple-input/single-output (MISO) linear system with a series of power characterized inputs based on Volterra series, and the nonlinear output responses of different orders are identified by taking power spectra operation to the input and output data, revealing the contributions of each order nonlinearity to the output of the system. Compared to the existing method, the input signal of the system required in the presented approach need not remain unchanged in waveform and adjustable in magnitude. To verify the approach, a classic Duffing–Van der Pol oscillator was simulated, obtaining results very close to the fourth order Runge–Kutta method. Finally, an experiment analysis was carried out, in which the vibration transmission properties of a bolt connection were tested when the bolt was tight and loose, respectively. The results proved that the approach is effective in identifying nonlinear vibration frequency responses.

Nonlinear second order plus time delay model identification and nonlinear PID controller tuning based on extended linearization method

PID control systems based on the first order plus time delay model (FOPTD), which approximate the full system dynamics, are well-accepted for a wide range of linear processes. While such controllers can be applied to overdamped nonlinear processes, they often experience excessive overshoots and oscillations for general nonlinear processes. To overcome this limitation, we propose a novel method to design a nonlinear PID controller based on the second order plus time delay (SOPTD) model. The system nonlinearity requires parameter adjustments of the linearized model across operational ranges. Hence, in this work, it is handled by the extended linearization method (ELM), ensuring local stability under the assumptions of slow and small changes in operating points. Importantly, the model achieves global input-to-output stability even without the above constraints, provided there are no structural and parametric errors. The resulting nonlinear SOPTD model can describe changes in process gain and two time constants as the operation point varies. We demonstrate the applicability of our approach with a polymerization reactor simulation and liquid-level control experiments.

Auxiliary model nonlinear innovation least squares algorithm for identification ship 4-DOF via full-scale test data

For the ship motion with large inertia coupled system identification modeling inaccuracy, the ship scale effect and the existence of partial unmeasured ship data problems. In this paper, an auxiliary model nonlinear innovation least squares identification algorithm is proposed. The new algorithm uses the output of the auxiliary model instead of the unmeasurable variables in the full-scale test data of the ship, and optimizes the error using the tangent function. Compared with the existing algorithm, the error of the improved algorithm decreases with the increase of time and continuously approaches to zero, which greatly improves the identification accuracy and convergence efficiency. The results show that the improved algorithm has significant identification accuracy and reliability. The identification method designed in this paper can be applied to the field of ship intelligent navigation engineering.

A Self-Calibration Method for Robot End-Effector Using Spherical Constraints

A self-calibration method utilizing spherical constraints is proposed for calibration of robot end-effectors. The method establishes a mathematical model to account for both the geometric errors of the robot and the deformation errors of the end-effector. A nonlinear least-squares parameter identification technique based on spherical constraints is employed to achieve autonomous calibration of the end-effector. Contrasted with methodologies relying on point plane or distance constraints, this novel technique delivers superior positioning accuracy, streamlined operational procedures and enhanced efficiency. Both simulation and experimental validation confirm that the self-calibration method using spherical constraints improves the positioning accuracy of the robot end-effector from 3 mm to 0.3 mm, showing the effectiveness of the method.

Web-платформа для організації хмарних обчислень у нейрофізіологічних дослідженнях на основі даних айтрекінгу

The purpose of the work is to develop the architecture and web version of the software complex based on the proposed new concept of cloud computing organization, which allows to expand the diagnostic capabilities of the tools of model-oriented information technology for assessing the neurophysiological state of a person using methods of nonlinear dynamic identification of the oculomotor system based on eye tracking data. The concept of cloud computing is proposed, which is based on the combination of PaaS and SaaS services as part of the developed software complex, due to which the cross-platform nature of cloud computing is ensured, the productivity and efficiency of scientific research increases. The developed architecture allows you to easily expand the functionality of the software complex and adapt it to different application conditions. The key feature of the complex is its undemanding hardware on the client side thanks to the use of cloud computing and its modular structure, which allows for easy scaling of the complex, as well as the isolation of the script code execution process in the cloud computing environment to increase the level of security when interpreting the script code on the server . Compared to other similar services, the complex has several advantages: it provides effective work in research and educational applications, supports Python and JavaScript programming languages, and also allows the use of software-implemented identification methods through specially developed GUI interfaces. In addition, the complex offers social opportunities and a high level of abstraction, which allows to optimize the research process.

Method of reference models for synthesis of intellectual systems of nonlinear dynamic objects identification

The paper is devoted to resolving the contradiction between the accuracy of modeling nonlinear dynamic objects and the speed of models building under conditions of limited computing resources. The purpose of the work is to reduce the time for building models of nonlinear dynamic objects with continuous characteristics while ensuring a given modeling accuracy. This goal is achieved by further developing the method of synthesing intelligent systems based on the superposition of pre-trained reference models in the form of neural networks reflecting the basic properties of the object. The scientific novelty of the work novelty consists in the development of a method for identifying nonlinear dynamic objects in the form of neural networks with time delays based on a set of pre-trained neural network models that reflect the basic properties of the subject area. In contrast to the traditional approach based on pre-trained neural networks the developed method allows building models of lower complexity and with shorter training time while ensuring the required accuracy. To determine the initial parameters of the model, expressions based on the superposition of reference models in the form of neural networks are proposed. The practical usefullness of the work consists in the development of an algorithm for the method of reference models for training neural networks with time delays in the tasks of identifying nonlinear dynamic objects with continuous characteristics, which can significantly reduce the training time of neural networks without losing the accuracy of the model. The value of the study lies in determining the area of effective use of the proposed method, namely, in the availability of a sufficient amount of qualitative data for the building of reference models. Insufficient data or poor data quality can significantly reduce the accuracy of reference models and, as a result, significantly reduce the training time of the target model.

Nonparametric identification of multi-degree-of-freedom nonlinear systems from partially measured responses under uncertain dynamic excitations

With the rapid advent of new materials and novel structures, it becomes difficult, if not impossible, to accurately model and simulate the nonlinear response of complex systems under uncertain dynamic excitations based on close-formed nonlinear functions and parametric identification. In this study, a two-step structural nonlinearity localization and identification approach for multi-degree-of-freedom (MDOF) nonlinear systems under uncertain dynamic excitations is developed by integrating an extended Kalman filter with unknown inputs into the equivalent linearized systems. In the first step, unmeasured responses and excitations are estimated as well as unknown structural parameters and nonlinearity locations are identified by fusing acceleration with displacement time histories at the observed degrees of freedom (DOFs). In the second step, the nonlinear restoring force of the detected nonlinear structural members is identified nonparametrically using three polynomial models, including a power series polynomial model (PSPM), a double Chebyshev polynomial model (DCPM), and a Legendre polynomial model (LPM). Linear multi-story shear frames controlled by nonlinear magnetorheological (MR) dampers are modelled computationally to demonstrate the generality of the proposed methodology. The multi-source uncertainties considered in these representative examples include the location and the type of nonlinearities represented by a Bingham model and a modified Dahl model of the dampers, the location of response measurements, the location and intensity of dynamic excitations, the level of measurement noise, and the initial assignment of structural parameters. The acceleration, velocity, and displacement time histories of structures can be evaluated accurately with a maximum error of 2.62% even with the presence of 8% measurement noise, while the external excitations can be estimated within an error of 1.77%. The location of nonlinear elements can be detected correctly. The structural parameters, the NRFs provided by MR dampers and the corresponding energy dissipation can be identified with a maximum error of 2.08%, 1.19% and 0.39%, respectively, even 8% measurement noise and very rough initial assignment of structure parameters (−70%) are considered. Moreover, the numerical results change little (<0.20%) even the initial assignment of structural parameters varies from 50% to 30% of their original values, no matter which nonparametric model is employed. Results indicate that the presented algorithm can effectively identify unmeasured dynamic responses, structural parameters, unknown excitations, nonlinear locations, and NRF of nonlinear elements in a nonparametric way.

Optimal operational planning of a bio-fuelled cogeneration plant: Integration of sparse nonlinear dynamics identification and deep reinforcement learning

This paper presents a novel data-driven approach for short-term operational planning of a cogeneration plant. The proposed methodology utilizes sparse identification of nonlinear dynamics (SINDy) to extract a dynamic model of heat generation from operational data. This model is then employed to simulate the plant dynamics during the training of a reinforcement learning (RL) agent, enabling online stochastic optimization of the production plan in real-time. The incorporation of SINDy enhances the accuracy of capturing the plant's nonlinear dynamics and significantly improves the computational speed of plant simulations, enabling efficient RL agent training within a reasonable timeframe. The performance of operational planning with the RL agent is compared to that of dynamic programming, a widely used method in the literature. The evaluation metric encompasses energy efficiency, unmet demands, and wasted heat. The comparison investigates the effectiveness of RL and dynamic programming under various scenarios with different qualities of energy demand forecasts. The RL agent exhibits robustness and notably improves the operational planning performance, particularly when faced with uncertain energy demands in the environment. Furthermore, the findings show that the RL agent, trained on a school building data, could successfully perform planning tasks for a hotel building, indicating the transferability of learned planning knowledge across different cogeneration use cases.

Predicting the Maximum Displacements of Structures during an Earthquake based on Chaos Theory

The maximum displacements are an important index for the structural health monitoring (SHM) after an earthquake. However, the measurement of displacements is not easy compared to that of accelerations, and nonlinear structural identification is problematic. This study estimates displacements using input and output accelerations with a small database without assuming any physical models. A nonlinear-dynamics prediction algorithm based on chaos theory is proposed combining Takens’s embedding theorem and nearest-neighbor method. Using 12 ground motions in simulation and three motions in experimental cases, the maximum displacements are predicted with 8 % to 25 % mean absolute errors (MAEs). A practical method is developed for robustly and accurately evaluating displacements.

Investigation of the accuracy of integral models of the oculo-motor system

For mathematical modeling of the human oculomotor system (OMS), integral nonlinear models are used, which simultaneously take into account the nonlinear and inertial properties of the research object. Based on the data of experimental studies of the OMS "input-output", transient and diagonal intersections of transient functions of the second and third orders are determined. To obtain experimental data, an innovative eye tracking technology is used, which allows recording eye responses to test visual stimuli. Thus test signals are displayed on the computer monitor at different distances from the starting position in the horizontal direction. The aim of the research is to study the accuracy of OMS identification using eye-tracking data by evaluating the calculation errors of multidimensional transient functions when using methods of nonlinear dynamic identification based on models in the form of Volterra series and polynomials. The object of the study is the process of nonparametric identification of the OMS based on Volterra models in the time domain. The subject of the research is algorithmic and software tools for calculating the dynamic characteristics of OMS based on eye-tracking data, analyzing the accuracy of the obtained models using two identification methods: the approximation method and the least squares method (LSM). The means of nonlinear dynamic identification of the human OMS based on Volterra series and polynomials were developed in the Python programming environment. The accuracy estimates of various OMS (linear, quadratic, and cubic) models were obtained based on data from three responses to test signals of different amplitudes. For the same test signals, the same models in the form of the Volterra series and polynomials were obtained, as these models coincide in the region of convergence of the Volterra series. The analysis of errors in the assessment of the dynamic characteristics of the OMS demonstrated that the model in the form of an integral polynomial of the second degree, which was built using the LSM based on three responses, has an accuracy twice as high as the accuracy of similar models built using the data of two responses. Thus, in further studies of the psychophysiological state of a person based on nonlinear dynamic models of the OMS according to the data of three responses, it is advisable to use a model in the form of a quadratic Volterra polynomial. Figs.: 17. Tabl. 3. Refs.: 10 titles.

Nonlinear dynamic model identification of robots: application to collision detection using a finite-time nonlinear momentum observer

Nonlinear dynamic model identification of robots: application to collision detection using a finite-time nonlinear momentum observer

Flight Test Design and Nonlinear Model Identification for Landing Gear Aerodynamics

Flight Test Design and Nonlinear Model Identification for Landing Gear Aerodynamics

Nonlinear Identification for Control by Using NARMAX Models

The identification (and control) of nonlinear systems is one of the most important and actual research directions. Moreover, many systems are multivariable. Different from linear system identification (where only a few classes of models are available), in the case of nonlinear systems, the class set of models is quite diverse. One of the most appealing nonlinear models belongs to the nonlinear ARMAX (NARMAX) class. This article focusses on the identification of such a model, which can be compared with other models (such as nonlinear ARX (NARX) and linear ARMAX) in an application based on the didactical installation ASTANK2. The mathematical foundation of NARMAX models and their identification method are described at length within this article. One of the most interesting parts is concerned with the identification of optimal models not only in terms of numerical parameters but also as structure. A metaheuristic (namely, the Cuckoo Search Algorithm) is employed with the aim of finding the optimal structural indices based on a special cost function, referred to as fitness. In the end, the performances of all three models (NARMAX, NARX, and ARMAX) are compared after the identification of the ASTANK2 installation.

AN ADAPTIVE DIFFERENTIAL EVOLUTION ALGORITHM WITH A BOUND ADJUSTMENT STRATEGY FOR SOLVING NONLINEAR PARAMETER IDENTIFICATION PROBLEMS

Real-world parameter identification problems require determining the bounds that cover the unknown solutions. This paper presents an adaptive differential evolution algorithm with a bound adjustment strategy (ADEBAS) for solving nonlinear parameter identification problems. The adjustment strategy detects the parameter-bound violations of mutant vectors during the evolution process and gradually extends the bounds. The algorithm adaptively uses two mutation strategies and two ranges of crossover rate to balance the population diversity and convergence speed. Experimental results show that ADEBAS can solve 24 nonlinear regression tasks from the National Institute of Standards and Technology benchmark with accurate estimation and reliability. It also outperforms the compared methods on real-world parameter identification problems.