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.

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.

Automated Seizure Detection Based on State-Space Model Identification.

In this study, we developed a machine learning model for automated seizure detection using system identification techniques on EEG recordings. System identification builds mathematical models from a time series signal and uses a small number of parameters to represent the entirety of time domain signal epochs. Such parameters were used as features for the classifiers in our study. We analyzed 69 seizure and 55 non-seizure recordings and an additional 10 continuous recordings from Thomas Jefferson University Hospital, alongside a larger dataset from the CHB-MIT database. By dividing EEGs into epochs (1 s, 2 s, 5 s, and 10 s) and employing fifth-order state-space dynamic systems for feature extraction, we tested various classifiers, with the decision tree and 1 s epochs achieving the highest performance: 96.0% accuracy, 92.7% sensitivity, and 97.6% specificity based on the Jefferson dataset. Moreover, as the epoch length increased, the accuracy dropped to 94.9%, with a decrease in sensitivity to 91.5% and specificity to 96.7%. Accuracy for the CHB-MIT dataset was 94.1%, with 87.6% sensitivity and 97.5% specificity. The subject-specific cases showed improved results, with an average of 98.3% accuracy, 97.4% sensitivity, and 98.4% specificity. The average false detection rate per hour was 0.5 ± 0.28 in the 10 continuous EEG recordings. This study suggests that using a system identification technique, specifically, state-space modeling, combined with machine learning classifiers, such as decision trees, is an effective and efficient approach to automated seizure detection.

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.

Evaluating inter-individual variability captured by the Eleveld pharmacokinetics model.

Inter-individual variability in Pharmacokinetic (PK) and Pharmacodynamic (PD) models significantly affects the accuracy of Target Controlled Infusion and closed-loop control of anesthesia. We hypothesize that the novel Eleveld PK model captures more inter-individual variability relevant to both open-loop and closed-loop control design, resulting in reduced variability in PD models identified using the Eleveld PK model's plasma prediction compared to the Schuttler or Schnider PK model. We used a dataset of propofol infusion rates and Depth of Hypnosis measurements across three demographic groups: elderly, obese, and adult. PD models are identified based on plasma concentration prediction using three PK models (Schuttler, Schnider, and Eleveld). Validation methods are presented to confirm acceptable predictive performance and comparable PK-PD model variability within each demographic group. To test our hypothesis, we compared coefficient variations in step responses for open-loop control and multiplicative uncertainty of PD model sets for closed-loop control. Validated PKPD models using the Schuttler and Schnider PK model showed no significant differences in predictive response and multiplicative uncertainty compared to the Eleveld PK model. The coefficient variations in step responses of PD model sets and the frequency ranges, corresponding to uncertainty below one, were comparable for all three PK models. The comparison of the accumulated coefficient of variation in the step-response and the uncertainty of the PD model sets indicated that the Eleveld PK model does not offer any advantage for the design of open-loop or closed-loop control of anesthesia.

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].

Non-linear properties of the Achilles tendon determine ankle impedance over a broad range of activations in humans.

Regulating ankle mechanics is essential for controlled interactions with the environment and rejecting unexpected disturbances. Ankle mechanics can be quantified by impedance, the dynamic relationship between an imposed displacement and the torque generated in response. Ankle impedance in the sagittal plane depends strongly on the triceps surae and Achilles tendon, but their relative contributions remain unknown. It is commonly assumed that ankle impedance is controlled by changing muscle activation and, thereby, muscle impedance, but this ignores that tendon impedance also changes with activation-induced loading. Thus, we sought to determine the relative contributions from the triceps surae and Achilles tendon during conditions relevant to postural control. We used a novel technique that combines B-mode ultrasound imaging with joint-level perturbations to quantify ankle, muscle and tendon impedance simultaneously across activation levels from 0% to 30% of maximum voluntary contraction. We found that muscle and tendon stiffness, the static component of impedance, increased with voluntary plantarflexion contractions, but that muscle stiffness exceeded tendon stiffness at very low loads (21±7 N). Above these loads, corresponding to 1.3% of maximal strength for an average participant in our study, ankle stiffness was determined predominately by Achilles tendon stiffness. At approximately 20% MVC for an average participant, ankle stiffness was 4 times more sensitive to changes in tendon stiffness than to changes in muscle stiffness. We provide the first empirical evidence demonstrating that the nervous system, through changes in muscle activations, leverages the non-linear properties of the Achilles tendon to increase ankle stiffness during postural conditions.

Examining the role of intrinsic and reflexive contributions to ankle joint hyper-resistance treated with botulinum toxin-A.

BACKGROUND: Spasticity, i.e. stretch hyperreflexia, increases joint resistance similar to symptoms like hypertonia and contractures. Botulinum neurotoxin-A (BoNT-A) injections are a widely used intervention to reduce spasticity. BoNT-A effects on spasticity are poorly understood, because clinical measures, e.g. modified Ashworth scale (MAS), cannot differentiate between the symptoms affecting joint resistance. This paper distinguishes the contributions of the reflexive and intrinsic pathways to ankle joint hyper-resistance for participants treated with BoNT-A injections. We hypothesized that the overall joint resistance and reflexive contribution decrease 6 weeks after injection, while returning close to baseline after 12 weeks. METHODS: Nine participants with spasticity after spinal cord injury or after stroke were evaluated across three sessions: 0, 6 and 12 weeks after BoNT-A injection in the calf muscles. Evaluation included clinical measures (MAS, Tardieu Scale) and motorized instrumented assessment using the instrumented spasticity test (SPAT) and parallel-cascade (PC) system identification. Assessments included measures for: (1) overall resistance from MAS and fast velocity SPAT; (2) reflexive resistance contribution from Tardieu Scale, difference between fast and slow velocity SPAT and PC reflexive gain; and (3) intrinsic resistance contribution from slow velocity SPAT and PC intrinsic stiffness/damping. RESULTS: Individually, the hypothesized BoNT-A effect, the combination of a reduced resistance (week 6) and return towards baseline (week 12), was observed in the MAS (5 participants), fast velocity SPAT (2 participants), Tardieu Scale (2 participants), SPAT (1 participant) and reflexive gain (4 participants). On group-level, the hypothesis was only confirmed for the MAS, which showed a significant resistance reduction at week 6. All instrumented measures were strongly correlated when quantifying the same resistance contribution. CONCLUSION: At group-level, the expected joint resistance reduction due to BoNT-A injections was only observed in the MAS (overall resistance). This observed reduction could not be attributed to an unambiguous group-level reduction of the reflexive resistance contribution, as no instrumented measure confirmed the hypothesis. Validity of the instrumented measures was supported through a strong association between different assessment methods. Therefore, further quantification of the individual contributions to joint resistance changes using instrumented measures across a large sample size are essential to understand the heterogeneous response to BoNT-A injections.

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.

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.

Decoding Electroencephalography Signal Response by Stacking Ensemble Learning and Adaptive Differential Evolution.

Electroencephalography (EEG) is an exam widely adopted to monitor cerebral activities regarding external stimuli, and its signals compose a nonlinear dynamical system. There are many difficulties associated with EEG analysis. For example, noise can originate from different disorders, such as muscle or physiological activity. There are also artifacts that are related to undesirable signals during EEG recordings, and finally, nonlinearities can occur due to brain activity and its relationship with different brain regions. All these characteristics make data modeling a difficult task. Therefore, using a combined approach can be the best solution to obtain an efficient model for identifying neural data and developing reliable predictions. This paper proposes a new hybrid framework combining stacked generalization (STACK) ensemble learning and a differential-evolution-based algorithm called Adaptive Differential Evolution with an Optional External Archive (JADE) to perform nonlinear system identification. In the proposed framework, five base learners, namely, eXtreme Gradient Boosting, a Gaussian Process, Least Absolute Shrinkage and Selection Operator, a Multilayer Perceptron Neural Network, and Support Vector Regression with a radial basis function kernel, are trained. The predictions from all these base learners compose STACK's layer-0 and are adopted as inputs of the Cubist model, whose hyperparameters were obtained by JADE. The model was evaluated for decoding the electroencephalography signal response to wrist joint perturbations. The variance accounted for (VAF), root-mean-squared error (RMSE), and Friedman statistical test were used to validate the performance of the proposed model and compare its results with other methods in the literature, including the base learners. The JADE-STACK model outperforms the other models in terms of accuracy, being able to explain around, as an average of all participants, 94.50% and 67.50% (standard deviations of 1.53 and 7.44, respectively) of the data variability for one step ahead and three steps ahead, which makes it a suitable approach to dealing with nonlinear system identification. Also, the improvement over state-of-the-art methods ranges from 0.6% to 161% and 43.34% for one step ahead and three steps ahead, respectively. Therefore, the developed model can be viewed as an alternative and additional approach to well-established techniques for nonlinear system identification once it can achieve satisfactory results regarding the data variability explanation.

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.

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.

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.

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.

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.

Identification of Sparse Volterra Systems: An Almost Orthogonal Matching Pursuit Approach.

This paper considers identification of sparse Volterra systems. A method based on the almost orthogonal matching pursuit (AOMP) is proposed. The AOMP algorithm allows one to estimate one non-zero coefficient at a time until all non-zero coefficients are found without losing the optimality and the sparsity, thus avoiding the curse of dimensionality often encountered in Volterra system identification.

Simulation and Experiment of Substation Grounding Resistance Measurement Based on Pseudorandom Signal.

The grounding resistance of a substation is an important parameter that should be designed within a reasonable range to prevent operational accidents from damaging electrical equipment due to overvoltage and ensure the safe operation of an electrical system. However, simply and accurately measuring the grounding resistance of a substation has been a difficult problem faced by engineers and technicians for a long time. This paper proposes a method of denoising by applying the m-sequence correlation identification technology to the measurement of substation resistance. We established a grounding resistance model of a grounding grid and used LabVIEW to simulate it. Based on system identification and correlation function theory, pseudorandom signals or sinusoidal signals were used as excitation signals. The output results of the system were compared when pseudorandom signals and sinusoidal signals were used as excitation signals. It was verified that the grounding resistance value measured by a pseudorandom signal was closer to the actual value, which met the design requirements. Laboratory test results verify that the method of calculating grounding resistance based on the correlation analysis method is feasible.

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.

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.