Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform

This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression. This approach has the additional practical advantage of requiring no a priori knowledge of the source of the excitation (or, alternatively, the initial conditions). By using training data, we devise a coarse regression procedure to recover different PDE parameters from the PDE solution measured at a single location. Numerical experiments show that the proposed regression procedure is capable of detecting and estimating PDE parameters with superior accuracy compared to a number of recently developed machine learning methods. Furthermore, a damage identification experiment conducted on a publicly available dataset provides strong evidence of the proposed method's effectiveness in structural health monitoring (SHM) applications. The Python implementation of the proposed system identification technique is integrated as a part of the software package PyTransKit [1].

Augmented Reality-Based Real-Time Visualization for Structural Modal Identification

In the era of aging civil infrastructure and growing concerns about rapid structural deterioration due to climate change, the demand for real-time structural health monitoring (SHM) techniques has been predominant worldwide. Traditional SHM methods face challenges, including delays in processing acquired data from large structures, time-intensive dense instrumentation, and visualization of real-time structural information. To address these issues, this paper develops a novel real-time visualization method using Augmented Reality (AR) to enhance vibration-based onsite structural inspections. The proposed approach presents a visualization system designed for real-time fieldwork, enabling detailed multi-sensor analyses within the immersive environment of AR. Leveraging the remote connectivity of the AR device, real-time communication is established with an external database and Python library through a web server, expanding the analytical capabilities of data acquisition, and data processing, such as modal identification, and the resulting visualization of SHM information. The proposed system allows live visualization of time-domain, frequency-domain, and system identification information through AR. This paper provides an overview of the proposed technology and presents the results of a lab-scale experimental model. It is concluded that the proposed approach yields accurate processing of real-time data and visualization of system identification information by highlighting its potential to enhance efficiency and safety in SHM by integrating AR technology with real-world fieldwork.

Design and verification of a parallel elastic robotic leg

This paper presents the design and experimental verification of a parallel elastic robotic leg mechanism that aims to capture the dynamics of the linear mass-spring-damper model. The mechanism utilizes a wrapping cam mechanism to linearize the non-linear force resulting from the elongation of the parallel elastic element. Firstly, we explain the desired dynamics of the mass-spring-damper model, including the impact transitions, and the design of the wrapping cam mechanism. We then introduce a system identification procedure to estimate the parameters of the leg mechanism corresponding to the dynamic model. The estimated parameters are tested with a cross-validation approach to evaluate the mechanism's performance in tracking the desired model. The experimental results show that the passive dynamics of the mechanism resemble the linear model as intended. Thus, the robot provides a basis for using parallel elastic actuation while using model-based controllers that benefit the analytic solutions of the linear model.

Manufacture and Deformation Angle Control of a Two-Direction Soft Actuator Integrated with SMAs

In this contribution, the development of a 3D-printed soft actuator integrated with shape memory alloys (SMA) wires capable of bending in two directions is presented. This work discusses the design, manufacturing, modeling, simulation, and feedback control of the actuator. The SMA wires are encased in Polytetrafluoroethylene (PTFE) tubes and then integrated into the 3D-printed matrix made of thermoplastic polyurethane (TPU). To measure and control the deformation angle of the soft actuator, a computer vision system was implemented. Based on the experimental results, a mathematical model was developed using the system identification method and simulated to describe the dynamics of the actuator, contributing to the design of a controller. However, achieving precise control of the deformation angle in systems actuated by SMA wires is challenging due to their inherent nonlinearities and hysteretic behavior. A proportional-integral (PI) controller was designed to address this challenge, and its effectiveness was validated through real experiments.

Esophageal balloon catheter system identification to improve respiratory effort time features and amplitude determination

Objective. Understanding a patient's respiratory effort and mechanics is essential for the provision of individualized care during mechanical ventilation. However, measurement of transpulmonary pressure (the difference between airway and pleural pressures) is not easily performed in practice. While airway pressures are available on most mechanical ventilators, pleural pressures are measured indirectly by an esophageal balloon catheter. In many cases, esophageal pressure readings take other phenomena into account and are not a reliable measure of pleural pressure.Approach.A system identification approach was applied to provide accurate pleural measures from esophageal pressure readings. First, we used a closed pressurized chamber to stimulate an esophageal balloon and model its dynamics. Second, we created a simplified version of an artificial lung and tried the model with different ventilation configurations. For validation, data from 11 patients (five male and six female) were used to estimate respiratory effort profile and patient mechanics.Main results.After correcting the dynamic response of the balloon catheter, the estimates of resistance and compliance and the corresponding respiratory effort waveform were improved when compared with the adjusted quantities in the test bench. The performance of the estimated model was evaluated using the respiratory pause/occlusion maneuver, demonstrating improved agreement between the airway and esophageal pressure waveforms when using the normalized mean squared error metric. Using the corrected muscle pressure waveform, we detected start and peak times 130 ± 50 ms earlier and a peak amplitude 2.04 ± 1.46 cmH2O higher than the corresponding estimates from esophageal catheter readings.Significance.Compensating the acquired measurements with system identification techniques makes the readings more accurate, possibly better portraying the patient's situation for individualization of ventilation therapy.

Identifying the Sweet Spot of Padel Rackets with a Robot

Although the vibration of rackets and the location of the sweet spot for players when hitting the ball is crucial, manufacturers do not specify this behavior precisely. This article analyses padel rackets, provides a solution to determine the sweet spot position (SSP), quantifies its behavior, and determines the level of vibration transmitted along the racket handle. The proposed methods serve to locate the SSP without quantifying it. This article demonstrates the development of equipment capable of analyzing the vibration behavior of padel rackets. To do so, it employs a robot that moves along the surface of the padel racket, striking it along its central line. Accelerometers are placed on a movable cradle where rackets are positioned and adjusted. A method for analyzing accelerometer signals to quantify vibration severity is proposed. The SSP and vibration behavior along the central line are determined and quantified. As a result of the study, 225 padel rackets are analyzed and compared. SSP is independent of the padel racket shape, balance, weight, moment of inertia, and padel racket shape (tear, diamond, or round) and is not located at the same position as the center of percussion.

Viability Under Degraded Control Authority

In this letter, we solve the problem of quantifying and mitigating control authority degradation in real time. Here, our target systems are controlled nonlinear affine-in-control evolution equations with finite control input and finite- or infinite-dimensional state. We consider two cases of control input degradation: finitely many affine maps acting on unknown disjoint subsets of the inputs and general Lipschitz continuous maps. These degradation modes are encountered in practice due to actuator wear and tear, hard locks on actuator ranges due to over-excitation, as well as more general changes in the control allocation dynamics. We derive sufficient conditions for identifiability of control authority degradation, and propose a novel real-time algorithm for identifying or approximating control degradation modes. We demonstrate our method on a nonlinear distributed parameter system, namely a one-dimensional heat equation with a velocity-controlled moveable heat source, motivated by autonomous energy-based surgery.

Curriculum-based humanoid robot identification using large-scale human motion database

Identifying an accurate dynamics model remains challenging for humanoid robots. The difficulty is mainly due to the following two points. First, a good initial model is required to evaluate the feasibility of motions for data acquisition. Second, a highly nonlinear optimization problem needs to be solved to design movements to acquire the identification data. To cope with the first point, in this paper, we propose a curriculum of identification to gradually learn an accurate dynamics model from an unreliable initial model. For the second point, we propose using a large-scale human motion database to efficiently design the humanoid movements for the parameter identification. The contribution of our study is developing a humanoid identification method that does not require the good initial model and does not need to solve the highly nonlinear optimization problem. We showed that our curriculum-based approach was able to more efficiently identify humanoid model parameters than a method that just randomly picked reference motions for identification. We evaluated our proposed method in a simulation experiment and demonstrated that our curriculum was led to obtain a wide variety of motion data for efficient parameter estimation. Consequently, our approach successfully identified an accurate model of an 18-DoF, simulated upper-body humanoid robot.

Learning-based sliding mode synchronization for fractional-order Hindmarsh-Rose neuronal models with deterministic learning

Introduction

In recent years, extensive research has been conducted on the synchronous behavior of neural networks. It is found that the synchronization ability of neurons is related to the performance of signal reception and transmission between neurons, which in turn affects the function of the organism. However, most of the existing synchronization methods are faced with two difficulties, one is the structural parameter dependency, which limits the promotion and application of synchronous methods in practical problems. The other is the limited adaptability, that is, even when faced with the same control tasks, for most of the existing control methods, the control parameters still need to be retrained. To this end, the present study investigates the synchronization problem of the fractional-order HindmarshRose (FOHR) neuronal models in unknown dynamic environment.

Methods

Inspired by the human experience of knowledge acquiring, memorizing, and application, a learning-based sliding mode control algorithm is proposed by using the deterministic learning (DL) mechanism. Firstly, the unknown dynamics of the FOHR system under unknown dynamic environment is locally accurately identified and stored in the form of constant weight neural networks through deterministic learning without dependency of the system parameters. Then, based on the identified and stored system dynamics, the model-based and relearning-based sliding mode controller are designed for similar as well as new synchronization tasks, respectively.

Results

The synchronization process can be started quickly by recalling the empirical dynamics of neurons. Therefore, fast synchronization effect is achieved by reducing the online computing time. In addition, because of the convergence of the identification and synchronization process, the control experience can be constantly replenished and stored for reutilization, so as to improve the synchronization speed and accuracy continuously.

Discussion

The thought of this article will also bring inspiration to the related research in other fields.

A NARX Model-Based Condition Monitoring Method for Rotor Systems

In this study, we developed a data-driven frequency domain analysis method for rotor systems using the NARX (Nonlinear Auto-Regressive with eXternal input) model established by system vibration signals. We propose a model-based index of fault features calculated in a multi-frequency range to facilitate condition monitoring of rotor systems. Four steps are included in the proposed method. Firstly, displacement vibration signals are collected at multiple monitored rotating speeds. Secondly, the collected signals are processed as output data and the corresponding input data is generated. Then, NARX models are developed with input and output data to characterize the rotor system. Finally, the NRSF (Nonlinear Response Spectrum Function)-based nonlinear fault index is calculated and compared to the healthy condition. An experimental application to the misaligned rotor system is also demonstrated to verify its effectiveness. Our results indicate that the value of the index directly reflects the severity of the misaligned fault.

Detection of Sensor Faults with or without Disturbance Using Analytical Redundancy Methods: An Application to Orifice Flowmeter

Sensors and transducers play a vital role in the productivity of any industry. A sensor that is frequently used in industries to monitor flow is an orifice flowmeter. In certain instances, faults can occur in the flowmeter, hindering the operation of other dependent systems. Hence, the present study determines the occurrence of faults in the flowmeter with a model-based approach. To do this, the model of the system is developed from the transient data obtained from computational fluid dynamics. This second-order transfer function is further used for the development of linear-parameter-varying observers, which generates the residue for fault detection. With or without disturbance, the suggested method is capable of effectively isolating drift, open-circuit, and short-circuit defects in the orifice flowmeter. The outcomes of the LPV observer are compared with those of a neural network. The open- and short-circuit faults are traced within 1 s, whereas the minimum time duration for the detection of a drift fault is 5.2 s and the maximum time is 20 s for different combinations of threshold and slope.

The Dynamic Sensorium competition for predicting large-scale mouse visual cortex activity from videos

Understanding how biological visual systems process information is challenging due to the complex nonlinear relationship between neuronal responses and high-dimensional visual input. Artificial neural networks have already improved our understanding of this system by allowing computational neuroscientists to create predictive models and bridge biological and machine vision. During the Sensorium 2022 competition, we introduced benchmarks for vision models with static input (i.e. images). However, animals operate and excel in dynamic environments, making it crucial to study and understand how the brain functions under these conditions. Moreover, many biological theories, such as predictive coding, suggest that previous input is crucial for current input processing. Currently, there is no standardized benchmark to identify state-of-the-art dynamic models of the mouse visual system. To address this gap, we propose the Sensorium 2023 Benchmark Competition with dynamic input (https://www.sensorium-competition.net/). This competition includes the collection of a new large-scale dataset from the primary visual cortex of five mice, containing responses from over 38,000 neurons to over 2 hours of dynamic stimuli per neuron. Participants in the main benchmark track will compete to identify the best predictive models of neuronal responses for dynamic input (i.e. video). We will also host a bonus track in which submission performance will be evaluated on out-of-domain input, using withheld neuronal responses to dynamic input stimuli whose statistics differ from the training set. Both tracks will offer behavioral data along with video stimuli. As before, we will provide code, tutorials, and strong pre-trained baseline models to encourage participation. We hope this competition will continue to strengthen the accompanying Sensorium benchmarks collection as a standard tool to measure progress in large-scale neural system identification models of the entire mouse visual hierarchy and beyond.

Full Bayesian identification of linear dynamic systems using stable kernels

System identification learns mathematical models of dynamic systems starting from input-output data. Despite its long history, such research area is still extremely active. New challenges are posed by identification of complex physical processes given by the interconnection of dynamic systems. Examples arise in biology and industry, e.g., in the study of brain dynamics or sensor networks. In the last years, regularized kernel-based identification, with inspiration from machine learning, has emerged as an interesting alternative to the classical approach commonly adopted in the literature. In the linear setting, it uses the class of stable kernels to include fundamental features of physical dynamical systems, e.g., smooth exponential decay of impulse responses. Such class includes also unknown continuous parameters, called hyperparameters, which play a similar role as the model discrete order in controlling complexity. In this paper, we develop a linear system identification procedure by casting stable kernels in a full Bayesian framework. Our models incorporate hyperparameters uncertainty and consist of a mixture of dynamic systems over a continuum spectrum of dimensions. They are obtained by overcoming drawbacks related to classical Markov chain Monte Carlo schemes that, when applied to stable kernels, are proved to become nearly reducible (i.e., unable to reconstruct posteriors of interest in reasonable time). Numerical experiments show that full Bayes frequently outperforms the state-of-the-art results on typical benchmark problems. Two real applications related to brain dynamics (neural activity) and sensor networks are also included.

In Search of a Feedback Signal for Closed-Loop Deep Brain Stimulation: Stimulation of the Subthalamic Nucleus Reveals Altered Glutamate Dynamics in the Globus Pallidus in Anesthetized, 6-Hydroxydopamine-Treated Rats

Deep Brain Stimulation (DBS) of the subthalamic nucleus (STN) is a surgical procedure for alleviating motor symptoms of Parkinson's Disease (PD). The pattern of DBS (e.g., the electrode pairs used and the intensity of stimulation) is usually optimized by trial and error based on a subjective evaluation of motor function. We tested the hypotheses that DBS releases glutamate in selected basal ganglia nuclei and that the creation of 6-hydroxydopamine (6-OHDA)-induced nigrostriatal lesions alters glutamate release during DBS in those basal ganglia nuclei. We studied the relationship between a pseudo-random binary sequence of DBS and glutamate levels in the STN itself or in the globus pallidus (GP) in anesthetized, control, and 6-OHDA-treated rats. We characterized the stimulus-response relationships between DBS and glutamate levels using a transfer function estimated using System Identification. Stimulation of the STN elevated glutamate levels in the GP and in the STN. Although the 6-OHDA treatment did not affect glutamate dynamics in the STN during DBS in the STN, the transfer function between DBS in the STN and glutamate levels in the GP was significantly altered by the presence or absence of 6-OHDA-induced lesions. Thus, glutamate responses in the GP in the 6-OHDA-treated animals (but not in the STN) depended on dopaminergic inputs. For this reason, measuring glutamate levels in the GP may provide a useful feedback target in a closed-loop DBS device in patients with PD since the dynamics of glutamate release in the GP during DBS seem to reflect the loss of dopaminergic neurons in the SNc.

Reliability Assessment of a Vision-Based Dynamic Displacement Measurement System Using an Unmanned Aerial Vehicle

In recent years, many studies have been conducted on the vision-based displacement measurement system using an unmanned aerial vehicle, which has been used in actual structure measurements. In this study, the dynamic measurement reliability of a vision-based displacement measurement system using an unmanned aerial vehicle was examined by measuring various vibrations with a frequency of 0 to 3 Hz and a displacement of 0 to 100 mm. Furthermore, free vibration was applied to model structures with one and two stories, and the response was measured to examine the accuracy of identifying structural dynamic characteristics. The vibration measurement results demonstrated that the vision-based displacement measurement system using an unmanned aerial vehicle has an average root mean square percentage error of 0.662% compared with the laser distance sensor in all experiments. However, the errors were relatively large in the displacement measurement of 10 mm or less regardless of the frequency. In the structure measurements, all sensors demonstrated the same mode frequency based on the accelerometer, and the damping ratios were extremely similar, except for the laser distance sensor measurement value of the two-story structure. Mode shape estimation was obtained and compared using the modal assurance criterion value compared with the accelerometer, and the values for the vision-based displacement measurement system using an unmanned aerial vehicle were close to 1. According to these results, the vision-based displacement measurement system using an unmanned aerial vehicle demonstrated results similar to those of conventional displacement sensors and can thus replace conventional displacement sensors.

Model-Based Approach Shows ON Pathway Afferents Elicit a Transient Decrease of V1 Responses

Neurons in the primary visual cortex (V1) receive excitation and inhibition from distinct parallel pathways processing lightness (ON) and darkness (OFF). V1 neurons overall respond more strongly to dark than light stimuli, consistent with a preponderance of darker regions in natural images, as well as human psychophysics. However, it has been unclear whether this "dark-dominance" is because of more excitation from the OFF pathway or more inhibition from the ON pathway. To understand the mechanisms behind dark-dominance, we record electrophysiological responses of individual simple-type V1 neurons to natural image stimuli and then train biologically inspired convolutional neural networks to predict the neurons' responses. Analyzing a sample of 71 neurons (in anesthetized, paralyzed cats of either sex) has revealed their responses to be more driven by dark than light stimuli, consistent with previous investigations. We show that this asymmetry is predominantly because of slower inhibition to dark stimuli rather than to stronger excitation from the thalamocortical OFF pathway. Consistent with dark-dominant neurons having faster responses than light-dominant neurons, we find dark-dominance to solely occur in the early latencies of neurons' responses. Neurons that are strongly dark-dominated also tend to be less orientation-selective. This novel approach gives us new insight into the dark-dominance phenomenon and provides an avenue to address new questions about excitatory and inhibitory integration in cortical neurons.SIGNIFICANCE STATEMENT Neurons in the early visual cortex respond on average more strongly to dark than to light stimuli, but the mechanisms behind this bias have been unclear. Here we address this issue by combining single-unit electrophysiology with a novel machine learning model to analyze neurons' responses to natural image stimuli in primary visual cortex. Using these techniques, we find slower inhibition to light than to dark stimuli to be the leading mechanism behind stronger dark responses. This slower inhibition to light might help explain other empirical findings, such as why orientation selectivity is weaker at earlier response latencies. These results demonstrate how imbalances in excitation versus inhibition can give rise to response asymmetries in cortical neuron responses.

Practical Application of Drive-By Monitoring Technology to Road Roughness Estimation Using Buses in Service

The efficiency of vehicles and travel comfort are maintained by the effective management of road pavement conditions. Pavement conditions can be inspected at a low cost by drive-by monitoring technology. Drive-by monitoring technology is a method of collecting data from sensors installed on a running vehicle. This technique enables quick and low-cost inspections. However, most existing technologies assume that the vehicle runs at a constant speed. Therefore, this study devises a theoretical framework that estimates road unevenness without prior information about the vehicle's mechanical parameters even when the running speed changes. This paper also shows the required function of sensors for this scheme. The required ability is to collect the three-axis acceleration vibration and position data simultaneously. A field experiment was performed to examine the applicability of sensors with both functions to the proposed methods. Each sensor was installed on a bus in service in this field experiment. The vehicle's natural frequency estimated from the measured data ranges from 1 to 2 Hz, but the natural frequency estimated by the proposed method is 0.71 Hz. However, the estimated road unevenness does not change significantly with changes in the vehicle's estimated parameters. The results found that the accuracy of road unevenness estimation seems to be acceptable with the conventional method and the new method. Future work will include improving the algorithm and accuracy verification of the schemes.

Discussion on a Vehicle-Bridge Interaction System Identification in a Field Test

For infrastructures to be sustainable, it is essential to improve maintenance and management efficiency. Vibration-based monitoring methods are being investigated to improve the efficiency of infrastructure maintenance and management. In this paper, signals from acceleration sensors attached to vehicles traveling on bridges are processed. Methods have been proposed to individually estimate the modal parameters of bridges and road unevenness from vehicle vibrations. This study proposes a method to simultaneously estimate the mechanical parameters of the vehicle, bridge, and road unevenness with only a few constraints. Numerical validation examined the effect of introducing the Kalman filter on the accuracy of estimating the mechanical parameters of vehicles and bridges. In field tests, vehicle vibration, bridge vibration, and road unevenness were measured and verified, respectively. The road surface irregularities estimated by the proposed method were compared with the measured values, which were somewhat smaller than the measured values. Future studies are needed to improve the efficiency of vehicle vibration preprocessing and optimization methods and to establish a methodology for evaluating accuracy.

Mixed-integer quadratic programming approach for noninvasive estimation of respiratory effort profile during pressure support ventilation

Information about respiratory mechanics such as resistance, elastance, and muscular pressure is important to mitigate ventilator-induced lung injury. Particularly during pressure support ventilation, the available options to quantify breathing effort and calculate respiratory system mechanics are often invasive or complex. We herein propose a robust and flexible estimation of respiratory effort better than current methods. We developed a method for non-invasively estimating breathing effort using only flow and pressure signals. Mixed-integer quadratic programming (MIQP) was employed, and the binary variables were the switching moments of the respiratory effort waveform. Mathematical constraints, based on ventilation physiology, were set for some variables to restrict feasible solutions. Simulated and patient data were used to verify our method, and the results were compared to an established estimation methodology. Our algorithm successfully estimated the respiratory effort, resistance, and elastance of the respiratory system, resulting in more robust performance and faster solver times than a previously proposed algorithm that used quadratic programming (QP) techniques. In a numerical simulation benchmark, the worst-case errors for resistance and elastance were 25% and 23% for QP versus <0.1% and <0.1% for MIQP, whose solver times were 4.7 s and 0.5 s, respectively. This approach can estimate several breathing effort profiles and identify the respiratory system's mechanical properties in invasively ventilated critically ill patients.

Predictive neuromodulation of cingulo-frontal neural dynamics in major depressive disorder using a brain-computer interface system: A simulation study

Introduction

Deep brain stimulation (DBS) is a promising therapy for treatment-resistant major depressive disorder (MDD). MDD involves the dysfunction of a brain network that can exhibit complex nonlinear neural dynamics in multiple frequency bands. However, current open-loop and responsive DBS methods cannot track the complex multiband neural dynamics in MDD, leading to imprecise regulation of symptoms, variable treatment effects among patients, and high battery power consumption.

Methods

Here, we develop a closed-loop brain-computer interface (BCI) system of predictive neuromodulation for treating MDD. We first use a biophysically plausible ventral anterior cingulate cortex (vACC)-dorsolateral prefrontal cortex (dlPFC) neural mass model of MDD to simulate nonlinear and multiband neural dynamics in response to DBS. We then use offline system identification to build a dynamic model that predicts the DBS effect on neural activity. We next use the offline identified model to design an online BCI system of predictive neuromodulation. The online BCI system consists of a dynamic brain state estimator and a model predictive controller. The brain state estimator estimates the MDD brain state from the history of neural activity and previously delivered DBS patterns. The predictive controller takes the estimated MDD brain state as the feedback signal and optimally adjusts DBS to regulate the MDD neural dynamics to therapeutic targets. We use the vACC-dlPFC neural mass model as a simulation testbed to test the BCI system and compare it with state-of-the-art open-loop and responsive DBS treatments of MDD.

Results

We demonstrate that our dynamic model accurately predicts nonlinear and multiband neural activity. Consequently, the predictive neuromodulation system accurately regulates the neural dynamics in MDD, resulting in significantly smaller control errors and lower DBS battery power consumption than open-loop and responsive DBS.

Discussion

Our results have implications for developing future precisely-tailored clinical closed-loop DBS treatments for MDD.

System Identification and Mathematical Modeling of A Piezoelectric Actuator through A Practical Three-Stage Mechanism

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper, we developed a full analytical model and a simple system identification (SI) method of a piezoelectric actuator, which includes piezostack elements and a three-stage amplification mechanism. The model was derived separately for each unit of the system. Next, the units were combined, while taking into account their coupling. The hysteresis phenomenon, which is significant in piezoelectric materials, is described extensively. The theoretical model was verified in a laboratory setup. This setup includes a piezoelectric actuator, measuring devices and an acquisition system. The measured results were compared to the theoretical results. Some of the most well-known forms of system identification are shown briefly, while a new and simple algorithm is described systematically and verified by the model. The main advantage of this work is to provide a solid background and domain knowledge of modelling and system identification methods for further investigations in the field of piezoelectric actuators. Due to their simplicity, both the model and the system identification method can be easily modified in order to be applied to other PEMs or other amplification mechanism methods. The main novelty of this work lies in applying a simple system identification algorithm while using the system-level approach for piezoelectric actuators. Lastly, this review work is concluded and some recommendations for researchers working in this area are presented.

Influence of Noise in Computer-Vision-Based Measurements on Parameter Identification in Structural Dynamics

Nowadays, consumer electronics offer computer-vision-based (CV) measurements of dynamic displacements with some trade-offs between sampling frequency, resolution and low cost of the device. This study considers a consumer-grade smartphone camera based on complementary metal-oxide semiconductor (CMOS) technology and investigates the influence of its hardware limitations on the estimation of dynamic displacements, modal parameters and stiffness parameters of bolted connections in a laboratory structure. An algorithm that maximizes the zero-normalized cross-correlation function is employed to extract the dynamic displacements. The modal parameters are identified with the stochastic subspace identification method. The stiffness parameters are identified using a model-updating technique based on modal sensitivities. The results are compared with the corresponding data obtained with accelerometers and a laser distance sensor. The CV measurement allows lower-order vibration modes to be identified with a systematic (bias) error that is nearly proportional to the vibration frequency: from 2% for the first mode (9.4 Hz) to 10% for the third mode (71.4 Hz). However, the measurement errors introduced by the smartphone camera have a significantly lower influence on the values of the identified stiffness parameters than the numbers of modes and parameters taken into account. This is due to the bias-variance trade-off. The results show that consumer-grade electronics can be used as a low-cost and easy-to-use measurement tool if lower-order modes are required.

High-Precision Semiconductor Laser Current Drive and Temperature Control System Design

To solve the problem in which the output power and wavelength of semiconductor lasers in fiber optic sensing systems are easily affected by the drive current and temperature, a high-precision current drive and temperature control system was developed in this study. The embedded system was used to provide a stable drive current for the semiconductor laser through closed-loop negative feedback control; moreover, some measures, such as linear slow-start, current-limiting protection, and electrostatic protection, were adopted to ensure the stability and safety of the laser's operation. A mathematical model of the temperature control system was constructed using mechanism analysis, and model identification was completed using the M sequence and differential evolution (DE) algorithms. Finally, the control rules of the fuzzy proportional integral differentiation (PID) algorithm were optimized through system simulation to make it more suitable for the temperature control system designed in this research, and the accurate control of the working temperature of the semiconductor laser was realized. Experimental results showed that the system could achieve a linearly adjustable drive current in the range of 0-100 mA, with an output current accuracy of 0.01 mA and a temperature control accuracy of up to 0.005 °C.

Automatic Speaker Recognition System Based on Gaussian Mixture Models, Cepstral Analysis, and Genetic Selection of Distinctive Features

This article presents the Automatic Speaker Recognition System (ASR System), which successfully resolves problems such as identification within an open set of speakers and the verification of speakers in difficult recording conditions similar to telephone transmission conditions. The article provides complete information on the architecture of the various internal processing modules of the ASR System. The speaker recognition system proposed in the article, has been compared very closely to other competing systems, achieving improved speaker identification and verification results, on known certified voice dataset. The ASR System owes this to the dual use of genetic algorithms both in the feature selection process and in the optimization of the system's internal parameters. This was also influenced by the proprietary feature generation and corresponding classification process using Gaussian mixture models. This allowed the development of a system that makes an important contribution to the current state of the art in speaker recognition systems for telephone transmission applications with known speech coding standards.

Simultaneous Quantification of Ankle, Muscle, and Tendon Impedance in Humans

OBJECTIVE

Regulating the impedance of our joints is essential for the effective control of posture and movement. The impedance of a joint is governed mainly by the mechanical properties of the muscle-tendon units spanning it. Many studies have quantified the net impedance of joints but not the specific contributions from the muscles and tendons. The inability to quantify both muscle and tendon impedance limits the ability to determine the causes underlying altered movement control associated with aging, neuromuscular injury, and other conditions that have different effects on muscle and tendon properties. Therefore, we developed a technique to quantify joint, muscle, and tendon impedance simultaneously and evaluated this technique at the human ankle.

METHODS

We used a single degree of freedom actuator to deliver pseudorandom rotations to the ankle while measuring the corresponding torques. We simultaneously measured the displacement of the medial gastrocnemius muscle-tendon junction with B-mode ultrasound. From these experimental measurements, we were able to estimate ankle, muscle, and tendon impedance using non-parametric system identification.

RESULTS

We validated our estimates by comparing them to previously reported measurements of muscle and tendon stiffness, the position-dependent component of impedance, to demonstrate that our technique generates reliable estimates of these properties.

CONCLUSION

Our approach can be used to clarify the respective contributions from the muscle and tendon to the net mechanics of a joint.

SIGNIFICANCE

This is a critical step forward in the ultimate goal of understanding how muscles and tendons govern ankle impedance during posture and movement.

Identifying the Inertial Properties of a Padel Racket: An Experimental Maneuverability Proposal

Although the moment of inertia of padel rackets is one of their fundamental properties and of particular interest to the players, hardly any manufacturer specifies the parameter for its rackets. The present paper offers a solution to determine the moment of inertia around different axes of padel rackets and makes a standardized comparison possible. After a short overview of the physical background of the problem and the existing solutions for inertia testing, the developed concept for a test stand is described in detail. The approach uses the fact that a pendulum swings with its natural frequency, which depends directly on its moment of inertia. The inertia can be calculated by measuring the cycle time of the swing. Two different test stands, a trifilar and a swing pendulum, are designed to enable an oscillation of the rackets with different rotation axes, and an acceleration sensor is used to measure its natural frequency. A user-friendly interface acquires and processes accelerometer data providing inertial moments. A calibration model defines sensor accuracy. Precision is estimated by calculating the influence of the measurement errors and by testing the repeatability. The maneuverability parameter is created, and in the last step, various rackets are evaluated to create a database with the main properties. As a result of the study of the racket population, a maneuverability parameter is proposed to classify the rackets in a comprehensible way for users. The classification method is tested with users to explore the matching between the scientific classification and the player's feelings. The results are shown and explained.

Robust Synchronization of Ambient Vibration Time Histories Based on Phase Angle Compensations and Kernel Density Function

The output-only modal analysis is ubiquitously used for structural health monitoring of civil engineering systems. The measurements for such applications require the use of multiple data acquisition systems (DAS) to avoid complicated meshes of cables in high-rise buildings, avoid traffic constriction on a bridge during measurements, or to avoid having limited channels in a single DAS. Nevertheless, such requirements introduce time synchronization problems which potentially lead to erroneous structural dynamic characterization and hence misleading or inconclusive structural health monitoring results. This research aims at proposing a system-identification-based time synchronization algorithm for output-only modal analysis using multiple DAS. A new procedure based on the compensation of the phase angle shifts is proposed to identify and address the time synchronization issue in ambient vibration data measured through multiple DAS. To increase the robustness of the proposed algorithm to the inherent inconsistencies in these datasets, the kernel density function is applied to rank multiple time-shift estimates that are sometimes detected by the algorithm when inaccuracies exist in the data arising from low signal-to-noise ratio and/or presence of colored noise in the ambient excitations. First, the synchronized ambient vibration dataset of a full-scale bridge is artificially de-synchronized and used to present a proof of concept for the proposed algorithm. Next, the algorithm is applied to ambient vibration data of a 30-story, reinforced concrete building, where the synchronization of the data could not be achieved using two DAS despite best efforts. The application of the proposed time synchronization algorithm is shown to both detect and correct the time synchronization discrepancies in the output-only modal analysis.

Identification and Compensation for D-Dot Measurement System in Transient Electromagnetic Pulse Measurement

The measurement of the transient pulsed electromagnetic (EM) field is essential for analyzing electromagnetic compatibility. Due to their good performance, D-dot sensors, combined with numerical integration computation for signal recovery, are commonly used to measure electromagnetic pulses (EMPs). However, the integration approach is occasionally flawed due to a non-ideal frequency response or noise, causing distortions in the reconstructed signal. In order to better understand the dynamic performance of the sensor, a nonlinear Hammerstein model is employed in the system identification for the sensor with the calibration data collected in the laboratory environment. When identifying the linear component based on the ultra-wideband characteristics of the measured transient pulse, a two-step identification approach with two different pulse excitation modes, low frequency and high frequency, is utilized to conduct the modeling across the entire frequency range. Based on the reliable identification and modeling of the D-dot sensor, a compensation system that corresponds to the nonlinear Hammerstein model has been developed for the practical signal recovery of the incident E-field. After compensation, the dynamic characteristics of the sensor are significantly improved, and the system compensation approach outperforms the integration method in signal recovery for the incident E-field.

Research on the Physics-Intelligence Hybrid Theory Based Dynamic Scenario Library Generation for Automated Vehicles

The testing and evaluation system has been the key technology and security with its necessity in the development and deployment of maturing automated vehicles. In this research, the physics-intelligence hybrid theory-based dynamic scenario library generation method is proposed to improve system performance, in particular, the testing efficiency and accuracy for automated vehicles. A general framework of the dynamic scenario library generation is established. Then, the parameterized scenario based on the dimension optimization method is specified to obtain the effective scenario element set. Long-tail functions for performance testing of specific ODD are constructed as optimization boundaries and critical scenario searching methods are proposed based on the node optimization and sample expansion methods for the low-dimensional scenario library generation and the reinforcement learning for the high-dimensional one, respectively. The scenario library generation method is evaluated with the naturalistic driving data (NDD) of the intelligent electric vehicle in the field test. Results show better efficient and accuracy performances compared with the ideal testing library and the NDD, respectively, in both low- and high-dimensional scenarios.

Effective Stiffness of Hydrated Atomic Force Microscopy Tips

When generating force curves with atomic force microscopy (AFM), the conventional assumption is that the silicon tip's apex is infinitely stiffer than the force gradient acting between the apex and test object. Although true for measurements in vacuum or at long distances, we show this assumption fails badly at short distances in aqueous environments. In this case, the effective apex is an adsorbed water molecule, bound by a weak O-H···O-H H-bond. At short distances, the magnitude of the force gradient exceeds the stiffness of this bond. This causes conventional AFM measurements to be dominated by the mechanical H-bond stiffness, instead of the force gradient. Here, we introduce a new multifrequency technique that is able to measure the surface force gradient independently from the H-bond. We compare our results to conventional FM-AFM and show that due to the H-bond, FM-AFM can give extremely erroneous measurements and even the wrong force polarity.

Online Weak-form Sparse Identification of Partial Differential Equations

This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in the sense that if performs the identification task by processing solution snapshots that arrive sequentially. The core of the method combines a weak-form discretization of candidate PDEs with an online proximal gradient descent approach to the sparse regression problem. In particular, we do not regularize the ℓ 0 -pseudo-norm, instead finding that directly applying its proximal operator (which corresponds to a hard thresholding) leads to efficient online system identification from noisy data. We demonstrate the success of the method on the Kuramoto-Sivashinsky equation, the nonlinear wave equation with time-varying wavespeed, and the linear wave equation, in one, two, and three spatial dimensions, respectively. In particular, our examples show that the method is capable of identifying and tracking systems with coefficients that vary abruptly in time, and offers a streaming alternative to problems in higher dimensions.

System identification and mathematical modeling of the pandemic spread COVID-19 in Serbia

This paper presents applications of control system theory in biomedical engineering. These methodologies are used in engineering sciences to obtain a mathematical model of systems, but system identification as scientific methodology is rarely used in biomedical engineering. The paper presents exemplarily control theory and system identification as methods for obtaining a mathematical model of the spread SARS-CoV-2 virus. The models obtained in the course of this are data-driven and strongly data-dependent. The available dataset allowed us to consider a model of a pandemic spread in the context of both the number of tested individuals and the number of infected individuals and with a resultant model that is nonlinear. We also considered a mathematical model for the dependence between the number of confirmed infected individuals and the number of deaths caused by the disease. The resulting model is linear given with the transfer function corresponding to the second-order differential equation. The mathematical models developed were additionally analyzed in accordance with controllability and observability.

[A decision framework for an adaptive behavioral intervention for physical activity using hybrid model predictive control: illustration with Just Walk]

Physical inactivity is a major contributor to morbidity and mortality worldwide. Many current physical activity behavioral interventions have shown limited success addressing the problem from a long-term perspective that includes maintenance. This paper proposes the design of a decision algorithm for a mobile and wireless health (mHealth) adaptive intervention that is based on control engineering concepts. The design process relies on a behavioral dynamical model based on Social Cognitive Theory (SCT), with a controller formulation based on hybrid model predictive control (HMPC) being used to implement the decision scheme. The discrete and logical features of HMPC coincide naturally with the categorical nature of the intervention components and the logical decisions that are particular to an intervention for physical activity. The intervention incorporates an online controller reconfiguration mode that applies changes in the penalty weights to accomplish the transition between the behavioral initiation and maintenance training stages. Controller performance is illustrated using an ARX model estimated from system identification data of a representative participant for Just Walk, a physical activity intervention designed on the basis of control systems principles.

Discovery of nonlinear dynamical systems using a Runge-Kutta inspired dictionary-based sparse regression approach

In this work, we blend machine learning and dictionary-based learning with numerical analysis tools to discover differential equations from noisy and sparsely sampled measurement data of time-dependent processes. We use the fact that given a dictionary containing large candidate nonlinear functions, dynamical models can often be described by a few appropriately chosen basis functions. As a result, we obtain parsimonious models that can be better interpreted by practitioners, and potentially generalize better beyond the sampling regime than black-box modelling. In this work, we integrate a numerical integration framework with dictionary learning that yields differential equations without requiring or approximating derivative information at any stage. Hence, it is utterly effective for corrupted and sparsely sampled data. We discuss its extension to governing equations, containing rational nonlinearities that typically appear in biological networks. Moreover, we generalized the method to governing equations subject to parameter variations and externally controlled inputs. We demonstrate the efficiency of the method to discover a number of diverse differential equations using noisy measurements, including a model describing neural dynamics, chaotic Lorenz model, Michaelis-Menten kinetics and a parameterized Hopf normal form.

Wavelet-Based Identification for Spinning Projectile with Gasodynamic Control Aerodynamic Coefficients Determination

Identification of a spinning projectile controlled with gasodynamic engines is shown in this paper. A missile model with a measurement inertial unit was developed from Newton’s law of motion and its aerodynamic coefficients were identified. This was achieved by applying the maximum likelihood principle in the wavelet domain. To assess the results, this was also performed in the time domain. The outcomes were obtained for two cases: when noise was not present and when it was included in the data. In all cases, the identification was performed in the passive mode, i.e., no special system identification experiments were designed. In the noise-free case, aerodynamic coefficients were estimated with high accuracy. When noise was included in the data, the wavelet-based estimates had a drop in their accuracy, but were still very accurate, whereas for the time domain approach the estimates were considered inaccurate.

Impulse Response Functions for Nonlinear, Nonstationary, and Heterogeneous Systems, Estimated by Deconvolution and Demixing of Noisy Time Series

Impulse response functions (IRFs) are useful for characterizing systems’ dynamic behavior and gaining insight into their underlying processes, based on sensor data streams of their inputs and outputs. However, current IRF estimation methods typically require restrictive assumptions that are rarely met in practice, including that the underlying system is homogeneous, linear, and stationary, and that any noise is well behaved. Here, I present data-driven, model-independent, nonparametric IRF estimation methods that relax these assumptions, and thus expand the applicability of IRFs in real-world systems. These methods can accurately and efficiently deconvolve IRFs from signals that are substantially contaminated by autoregressive moving average (ARMA) noise or nonstationary ARIMA noise. They can also simultaneously deconvolve and demix the impulse responses of individual components of heterogeneous systems, based on their combined output (without needing to know the outputs of the individual components). This deconvolution–demixing approach can be extended to characterize nonstationary coupling between inputs and outputs, even if the system’s impulse response changes so rapidly that different impulse responses overlap one another. These techniques can also be extended to estimate IRFs for nonlinear systems in which different input intensities yield impulse responses with different shapes and amplitudes, which are then overprinted on one another in the output. I further show how one can efficiently quantify multiscale impulse responses using piecewise linear IRFs defined at unevenly spaced lags. All of these methods are implemented in an R script that can efficiently estimate IRFs over hundreds of lags, from noisy time series of thousands or even millions of time steps.

Identification of tissue optical properties during thermal laser-tissue interactions: An ensemble Kalman filter-based approach

In this article, we propose a computational framework to estimate the physical properties that govern the thermal response of laser-irradiated tissue. We focus in particular on two quantities, the absorption and scattering coefficients, which describe the optical absorption of light in the tissue and whose knowledge is vital to correctly plan medical laser treatments. To perform the estimation, we utilize an implementation of the ensemble Kalman filter (EnKF), a type of Bayesian filtering algorithm for data assimilation. Unlike prior approaches, in this work, we estimate the tissue optical properties based on observations of the tissue thermal response to laser irradiation. This method has the potential for straightforward implementation in a clinical setup, as it would only require a simple thermal sensor, for example, a miniaturized infrared camera. Because the optical properties of tissue can undergo shifts during laser exposure, we employ a variant of EnKF capable of tracking time-varying parameters. Through simulated experimental studies, we demonstrate the ability of the proposed technique to identify the tissue optical properties and track their dynamic changes during laser exposure, while simultaneously tracking changes in the tissue temperature at locations beneath the surface. We further demonstrate the framework's capability in estimating additional unknown tissue properties (i.e., the volumetric heat capacity and thermal conductivity) along with the optical properties of interest.

Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modelling high-dimensional systems from data. However, the quality of the linear DMD model is known to be fragile with respect to strong nonlinearity, which contaminates the model estimate. By contrast, sparse identification of nonlinear dynamics learns fully nonlinear models, disambiguating the linear and nonlinear effects, but is restricted to low-dimensional systems. In this work, we present a kernel method that learns interpretable data-driven models for high-dimensional, nonlinear systems. Our method performs kernel regression on a sparse dictionary of samples that appreciably contribute to the dynamics. We show that this kernel method efficiently handles high-dimensional data and is flexible enough to incorporate partial knowledge of system physics. It is possible to recover the linear model contribution with this approach, thus separating the effects of the implicitly defined nonlinear terms. We demonstrate our approach on data from a range of nonlinear ordinary and partial differential equations. This framework can be used for many practical engineering tasks such as model order reduction, diagnostics, prediction, control and discovery of governing laws.

Data-driven geometric system identification for shape-underactuated dissipative systems

Modeling system dynamics becomes challenging when the properties of individual system components cannot be directly measured, and often requires identification of properties from observed motion. In this paper, we show that systems whose movement is highly dissipative have features which provide an opportunity to more easily identify models and more quickly optimize motions than would be possible with general techniques. Geometric mechanics provides means for reduction of the dynamics by environmental homogeneity, while the dissipative nature minimizes the role of second order (inertial) features in the dynamics. Here we extend the tools of geometric system identification to 'shape-underactuated dissipative systems (SUDS)'-systems whose motions are more dissipative than inertial, but whose actuation is restricted to a subset of the body shape coordinates. Many animal motions are SUDS, including micro-swimmers such as nematodes and flagellated bacteria, and granular locomotors such as snakes and lizards. Many soft robots are also SUDS, particularly robots that incorporate highly damped series elastic actuators to reduce the rigidity of their interactions with their environments during locomotion and manipulation. We motivate the use of SUDS models, and validate their ability to predict motion of a variety of simulated viscous swimming platforms. For a large class of SUDS, we show how the shape velocity actuation inputs can be directly converted into torque inputs, suggesting that systems with soft pneumatic or dielectric elastomer actuators can be modeled with the tools presented. Based on fundamental assumptions in the physics, we show how our model complexity scales linearly with the number of passive shape coordinates. This scaling offers a large reduction on the number of trials needed to identify the system model from experimental data, and may reduce overfitting. The sample efficiency of our method suggests its use in modeling, control, and optimization in robotics, and as a tool for the study of organismal motion in friction dominated regimes.

Comparing system identification techniques for identifying human-like walking controllers

While human walking has been well studied, the exact controller is unknown. This paper used human experimental walking data and system identification techniques to infer a human-like controller for a spring-loaded inverted pendulum (SLIP) model. Because the best system identification technique is unknown, three methods were used and compared. First, a linear system was found using ordinary least squares. A second linear system was found that both encoded the linearized SLIP model and matched the first linear system as closely as possible. A third nonlinear system used sparse identification of nonlinear dynamics (SINDY). When directly mapping states from the start to the end of a step, all three methods were accurate, with errors below 10% of the mean experimental values in most cases. When using the controllers in simulation, the errors were significantly higher but remained below 10% for all but one state. Thus, all three system identification methods generated accurate system models. Somewhat surprisingly, the linearized system was the most accurate, followed closely by SINDY. This suggests that nonlinear system identification techniques are not needed when finding a discrete human gait controller, at least for unperturbed walking. It may also suggest that human control of normal, unperturbed walking is approximately linear.

System Identification of Conveyor Belt Microwave Drying Process of Polymer Foams Using Electrical Capacitance Tomography

The microwave drying process has a wide application in industry, including drying polymer foams after the impregnation process for sealings in the construction industry. The objective of the drying process is to reach a certain moisture in the foam by adjusting the power levels of the microwave sources. A moisture controller can be designed to achieve this goal; however, a process model is required to design model-based controllers. Since complex physics governs the microwave drying process, system identification tools are employed in this paper to exploit the process input and output information and find a simplified yet accurate model of the process. The moisture content of the foam that is the process output is measured using a designed electrical capacitance tomography (ECT) sensor. The ECT sensor estimates the 2D permittivity distribution of moving foams, which correlates with the foam moisture. Experiments are conducted to collect the ECT measurements while giving different inputs to the microwave sources. A state-space model is estimated using one of the collected datasets and is validated using the other datasets. The comparison between the model response and the actual measurements shows that the model is accurate enough to design a controller for the microwave drying process.

Dynamic Expectation Maximization Algorithm for Estimation of Linear Systems with Colored Noise

The free energy principle from neuroscience has recently gained traction as one of the most prominent brain theories that can emulate the brain's perception and action in a bio-inspired manner. This renders the theory with the potential to hold the key for general artificial intelligence. Leveraging this potential, this paper aims to bridge the gap between neuroscience and robotics by reformulating an FEP-based inference scheme-Dynamic Expectation Maximization-into an algorithm that can perform simultaneous state, input, parameter, and noise hyperparameter estimation of any stable linear state space system subjected to colored noises. The resulting estimator was proved to be of the form of an augmented coupled linear estimator. Using this mathematical formulation, we proved that the estimation steps have theoretical guarantees of convergence. The algorithm was rigorously tested in simulation on a wide variety of linear systems with colored noises. The paper concludes by demonstrating the superior performance of DEM for parameter estimation under colored noise in simulation, when compared to the state-of-the-art estimators like Sub Space method, Prediction Error Minimization (PEM), and Expectation Maximization (EM) algorithm. These results contribute to the applicability of DEM as a robust learning algorithm for safe robotic applications.

Neural-Network Based Modeling of I/O Buffer Predriver under Power/Ground Supply Voltage Variations

This paper presents a neural-network based nonlinear behavioral modelling of I/O buffer that accounts for timing distortion introduced by nonlinear switching behavior of the predriver electrical circuit under power and ground supply voltage (PGSV) variations. Model structure and I/O device characterization along with extraction procedure were described. The last stage of the I/O buffer is modelled as nonlinear current-voltage (I-V) and capacitance voltage (C-V) functions capturing the nonlinear dynamic impedances of the pull-up and pull-down transistors. The mathematical model structure of the predriver was derived from the analysis of the large-signal electrical circuit switching behavior. Accordingly, a generic and surrogate multilayer neural network (NN) structure was considered in this work. Timing series data which reflects the nonlinear switching behavior of the multistage predriver's circuit PGSV variations, were used to train the NN model. The proposed model was implemented in the time-domain solver and validated against the reference transistor level (TL) model and the state-of-the-art input-output buffer information specification (IBIS) behavioral model under different scenarios. The analysis of jitter was performed using the eye diagrams plotted at different metrics values.

Characterization of the Force Production Capabilities of Paralyzed Trunk Muscles Activated With Functional Neuromuscular Stimulation in Individuals With Spinal Cord Injury

Paralysis of the trunk results in seated instability leading to difficulties performing activities of daily living. Functional neuromuscular stimulation (FNS) combined with control systems have the potential to restore some dynamic functions of the trunk. However, design of multi-joint, multi-muscle control systems requires characterization of the stimulation-driven muscles responsible for movement.

OBJECTIVE

This study characterizes the input-output properties of paralyzed trunk muscles activated by FNS, and explores co-activation of muscles.

METHODS

Four participants with various spinal cord injuries (C7 AIS-B, T4 AIS-B, T5 AIS-A, C5 AIS-C) were constrained so lumbar forces were transmitted to a load cell while an implanted neuroprosthesis activated otherwise paralyzed hip and paraspinal muscles. Isometric force recruitment curves in the nominal seated position were generated by inputting the level of stimulation (pulse width modulation) while measuring the resulting muscle force. Two participants returned for a second experiment where muscles were co-activated to determine if their actions combined linearly.

RESULTS

Recruitment curves of most trunk and hip muscles fit sigmoid shaped curves with a regression coefficient above 0.75, and co-activation of the muscles combined linearly across the hip and lumbar joint. Subject specific perturbation plots showed one subject is capable of resisting up to a 300N perturbation anteriorly and 125N laterally; with some subjects falling considerably below these values.

CONCLUSION

Development of a trunk stability control system can use sigmoid recruitment dynamics and assume muscle forces combine linearly.

SIGNIFICANCE

This study informs future designs of multi-muscle, and multi-dimensional FNS systems to maintain seated posture and stability.

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after excitations taking the system out of its equilibrium (e.g., physical effort during cardiac stress testing). Such approach can be applied to a broad range of outcomes such as physiological processes in medicine and psychosocial processes in social sciences, and it allows to extract simple characteristics of the signal studied. The model is based on a first order linear differential equation with constant coefficients defined by three main parameters corresponding to the initial equilibrium value, the dynamic characteristic time, and the reaction to the excitation. Assuming the presence of interindividual variability (random effects) on these three parameters, we propose a two-step procedure to estimate them. We then compare the results of this analysis to several other estimation procedures in a simulation study that clarifies under which conditions parameters are accurately estimated. Finally, applications of this model are illustrated using cardiology data recorded during effort tests.

Using System Identification to Construct an Inherent Model of Pupillary Light Reflex to Explore Diabetic Neuropathy

This study proposed a pupillary light reflex (PLR) inherent model based on the system identification method to demonstrate the dynamic physiological mechanism of the PLR, in which pupillary constriction and dilation are controlled by the sympathetic and parasympathetic nervous system. This model was constructed and verified by comparing the simulated and predicted PLR response with that of healthy participants. The least root-mean-square error (RMSE) of simulated PLR response was less than 0.7% when stimulus duration was under 3 ms. The RMSE of predicted PLR response increased by approximately 6.76%/s from the stimulus duration of 1 ms to 3 s, when the model directly used the parameters extracted from the PLR at the stimulus duration of 10 ms. When model parameters were derived from the regression by the measured PLR response, the RMSE kept under 8.5%. The model was applied to explore the PLR abnormalities of the people with Diabetic Mellitus (DM) by extracting the model parameters from 42 people with DM and comparing these parameters with those of 42 healthy participants. The parameter in the first-order term of the elastic force of the participants with DM was significantly lower than that of the healthy participants (p < 0.05). The sympathetic force and sympathetic action delay of the participants with DM were significantly larger (p < 0.05) and longer (p < 0.0001) than that of the healthy ones, respectively. The reason might be that the sympathetic nervous system, which controls the dilator muscle, degenerated in diabetic patients.

Dynamic Systems Approach in Sensorimotor Synchronization: Adaptation to Tempo Step-Change

This paper presents a dynamic systems model of a sensorimotor synchronization (SMS) task. An SMS task typically gives temporally discrete human responses to some temporally discrete stimuli. Here, a dynamic systems modeling approach is applied after converting the discrete events to regularly sampled time signals. To collect data for model parameter fitting, a previously published pilot study was expanded. Three human participants took part in an experiment: to tap a finger on a keyboard, following a metronome which changed tempo in steps. System identification was used to estimate the transfer function that represented the relationship between the stimulus and the step response signals, assuming a separate linear, time-invariant system for each tempo step. Different versions of model complexity were investigated. As a minimum, a second-order linear system with delay, two poles, and one zero was needed to model the most important features of the tempo step response by humans, while an additional third pole could give a somewhat better fit to the response data. The modeling results revealed the behavior of the system in two distinct regimes: tempo steps below and above the conscious awareness of tempo change, i.e., around 12% of the base tempo. For the tempo steps above this value, model parameters were derived as linear functions of step size for the group of three participants. The results were interpreted in the light of known facts from other fields like SMS, psychoacoustics and behavioral neuroscience.

Experimental Investigation on a Bladed Disk with Traveling Wave Excitation

Bladed disks are key components of turbomachines and their dynamic behavior is strongly conditioned by their small accidental lack of symmetry referred to as blade mistuning. The experimental identification of mistuned disks is complicated due to several reasons related both to measurement and data processing issues. This paper describes the realization of a test rig designed to investigate the behavior of mistuned disks and develop or validate data processing techniques for system identification. To simplify experiments, using the opposite than in the real situation, the disk is fixed, while the excitation is rotating. The response measured during an experiment carried out in the resonance-crossing condition is used to compare three alternative techniques to estimate the frequency-response function of the disk.

Vibration-based monitoring of a small-scale wind turbine blade under varying climate conditions. Part I: An experimental benchmark

Structural health monitoring (SHM) has been increasingly exploited in recent years as a valuable tool for assessing performance throughout the life cycle of structural systems, as well as for supporting decision-making and maintenance planning. Although a great assortment of SHM methods has been developed, only a limited number of studies exist serving as reference basis for the comparison of different techniques. In this paper, the vibration-based assessment of a small-scale wind turbine (WT) blade is experimentally investigated, with the aim of establishing a benchmark case study for the SHM community. The structure under consideration, provided by Sonkyo Energy as part of the Windspot 3.5 kW WT model, is tested in both healthy and damaged states under varying environmental, that is, temperature, conditions as imposed by means of a climatic chamber. This study offers a thorough documentation of the configuration of this experimental benchmark, including the types of deployed sensors, the nature of excitation and available measurements, and the investigated damage scenarios and environmental variations enforced. Lastly, an overview of the raw and processed measurement data, made available to researchers via an open access Zenodo repository, is herein provided.

Nonlinear stochastic modelling with Langevin regression

Many physical systems characterized by nonlinear multiscale interactions can be modelled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behaviour are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence where the perturbations do not behave like Gaussian white noise, introducing non-Markovian behaviour to the dynamics. We address these challenges with a framework for identifying interpretable stochastic nonlinear dynamics from experimental data, using forward and adjoint Fokker-Planck equations to enforce statistical consistency. If the form of the Langevin equation is unknown, a simple sparsifying procedure can provide an appropriate functional form. We demonstrate that this method can learn stochastic models in two artificial examples: recovering a nonlinear Langevin equation forced by coloured noise and approximating the second-order dynamics of a particle in a double-well potential with the corresponding first-order bifurcation normal form. Finally, we apply Langevin regression to experimental measurements of a turbulent bluff body wake and show that the statistical behaviour of the centre of pressure can be described by the dynamics of the corresponding laminar flow driven by nonlinear state-dependent noise.