A Mobile Sensing Framework for Bridge Modal Identification through an Inverse Problem Solution Procedure and Moving-Window Time Series Models.

With the rise and development of smart infrastructures, there has been a great demand for installing automatic monitoring systems on bridges, which are key members of transportation networks. In this regard, utilizing the data collected by the sensors mounted on the vehicles passing over the bridge can reduce the costs of the monitoring systems, compared with the traditional systems where fixed sensors are mounted on the bridge. This paper presents an innovative framework for determining the response and for identifying modal characteristics of the bridge, utilizing only the accelerometer sensors on the moving vehicle passing over it. In the proposed approach, the acceleration and displacement response of some virtual fixed nodes on the bridge is first determined using the acceleration response of the vehicle axles as the input. An inverse problem solution approach based on a linear and a novel cubic spline shape function provides the preliminary estimations of the bridge's displacement and acceleration responses, respectively. Since the inverse solution approach is only capable of determining the response signal of the nodes with high accuracy in the vicinity of the vehicle axles, a new moving-window signal prediction method based on auto-regressive with exogenous time series models (ARX) is proposed to complete the responses in the regions with large errors (invalid regions). The mode shapes and natural frequencies of the bridge are identified using a novel approach that integrates the results of singular value decomposition (SVD) on the predicted displacement responses and frequency domain decomposition (FDD) on the predicted acceleration responses. To evaluate the proposed framework, various numerical but realistic models for a single-span bridge under the effect of a moving mass are considered; the effects of different levels of ambient noise, the number of axles of the passing vehicle, and the effect of its speed on the accuracy of the method are investigated. The results show that the proposed method can identify the characteristics of the three main modes of the bridge with high accuracy.

Testing for Serial Correlation in Autoregressive Exogenous Models with Possible GARCH Errors.

Autoregressive exogenous, hereafter ARX, models are widely adopted in time series-related domains as they can be regarded as the combination of an autoregressive process and a predictive regression. Within a more complex structure, extant diagnostic checking methods face difficulties in remaining validity in many conditions existing in real applications, such as heteroscedasticity and error correlations exhibited between the ARX model itself and its exogenous processes. For these reasons, we propose a new serial correlation test method based on the profile empirical likelihood. Simulation results, as well as two real data examples, show that our method has a good performance in all mentioned conditions.

A General Use QSAR-ARX Model to Predict the Corrosion Inhibition Efficiency of Drugs in Terms of Quantum Mechanical Descriptors and Experimental Comparison for Lidocaine.

A study of 250 commercial drugs to act as corrosion inhibitors on steel has been developed by applying the quantitative structure-activity relationship (QSAR) paradigm. Hard-soft acid-base (HSAB) descriptors were used to establish a mathematical model to predict the corrosion inhibition efficiency (IE%) of several commercial drugs on steel surfaces. These descriptors were calculated through third-order density-functional tight binding (DFTB) methods. The mathematical modeling was carried out through autoregressive with exogenous inputs (ARX) framework and tested by fivefold cross-validation. Another set of drugs was used as an external validation, obtaining SD, RMSE, and MSE, obtaining 6.76%, 3.89%, 7.03%, and 49.47%, respectively. With a predicted value of IE% = 87.51%, lidocaine was selected to perform a final comparison with experimental results. By the first time, this drug obtained a maximum IE%, determined experimentally by electrochemical impedance spectroscopy measurements at 100 ppm concentration, of about 92.5%, which stands within limits of 1 SD from the predicted ARX model value. From the qualitative perspective, several potential trends have emerged from the estimated values. Among them, macrolides, alkaloids from Rauwolfia species, cephalosporin, and rifamycin antibiotics are expected to exhibit high IE% on steel surfaces. Additionally, IE% increases as the energy of HOMO decreases. The highest efficiency is obtained in case of the molecules with the highest ω and ΔN values. The most efficient drugs are found with pKa ranging from 1.70 to 9.46. The drugs recurrently exhibit aromatic rings, carbonyl, and hydroxyl groups with the highest IE% values.

Identification of the ARX Model with Random Impulse Noise Based on Forgetting Factor Multi-error Information Entropy.

Entropy has been widely applied in system identification in the last decade. In this paper, a novel stochastic gradient algorithm based on minimum Shannon entropy is proposed. Though needing less computation than the mean square error algorithm, the traditional stochastic gradient algorithm converges relatively slowly. To make the convergence faster, a multi-error method and a forgetting factor are integrated into the algorithm. The scalar error is replaced by a vector error with stacked errors. Further, a simple step size method is proposed and a forgetting factor is adopted to adjust the step size. The proposed algorithm is utilized to estimate the parameters of an ARX model with random impulse noise. Several numerical solutions and case study indicate that the proposed algorithm can obtain more accurate estimates than the traditional gradient algorithm and has a faster convergence speed.

Direct Versus Iterated Multi-Step Forecasting of Glycaemia in Type 1 Diabetics Using Autoregressive Models.

The paper compares two approaches to multi-step ahead glycaemia forecasting. While the direct approach uses a different model for each number of steps ahead, the iterative approach applies one one-step ahead model iteratively. Although it is well known that the iterative approach suffers from the error accumulation problem, there are no clear outcomes supporting a proper choice between those two methods. This paper provides such comparison for different ARX models and shows that the iterative approach outperformed the direct method for one-hour ahead (12-steps ahead) forecasting. Moreover, the classical linear ARX model outperformed more complex non-linear versions for training data covering one-month period.

Analysis of thermoluminescence characteristics of a lithium disilicate glass ceramic using a nonlinear autoregressive with exogenous input model.

Dental ceramics because of their translucency exemplify the most biologically realistic restorative materials for aesthetic rehabilitation and can be used to estimate dose accumulated as a result of a nuclear accident or attack. In this study, lithium disilicate ceramic obtained from Vivadent Ivoclar, Turkey was studied for its thermoluminescence (TL) properties. The lithium disilicate glass ceramic was irradiated with a 90 Sr-90 Y ß-source from 10 Gy to 6.9 kGy and the results read on a Harshaw 3500 reader. The TL peak of lithium disilicate ceramic showed sublinearity in the range 12 Gy to 6 kGy. The area under the TL glow curve increased by about 25% by the end of 10th measurement cycle. Fading values were also considered after irradiation. Lithium disilicate ceramic samples underwent 37% fading after 1 h and 59% fading after 1 week. In addition to the experimental study, a software-based simulation study was also undertaken using a MATLAB system identification tool. Experimental studies are generally time consuming and some materials used for experiments are very expensive. In this study, experimental, and simulation results were compared and produced almost the same outcome with a similarity of more than 98%.

ARX model decomposed on Meixner-Like orthonormal bases.

The present study provides a new modeling of linear slowly starting systems. More precisely, this new approach extends the technique of filtering only the input using Meixner-Like (M-L) filters to filter both the output and input of the system outlined by an ARX model. Therefore, the idea is to develop the input and output parameters of ARX modeling over 2 M-L bases. So as to ensure an optimal representation, the two M-L poles are optimized using Newton-Raphson (N-R) and Genetic Algorithms (GA) methods. A new method is proposed for Model Predictive Control (MPC) using the obtained optimal model that is called ARXMeixner-Like (ARXM-L). A numerical example of system having delay and three examples of experimental research: A supersonic jet engine inlet, a Process Trainer PT326 and a Quanser aero experiment with one degree of freedom attitude control are made.

RBF-ARX model-based fast robust MPC approach to an inverted pendulum.

In general, the online computation burden of robust model predictive control (RMPC) is very heavy, and the mechanical model of a plant, which is used in RMPC, is hard to obtain precisely in real industry. These issues may largely restrict the applicability of RMPC in real applications. This paper proposes a RBF-ARX (state-dependent Auto-Regressive model with eXogenous input and Radial Basis Function network type coefficients) model-based efficient robust predictive control (RBF-ARX-ERPC) approach to an inverted pendulum system, which is a complete and systematic method for designing robust MPC controller because it integrates the RBF-ARX modeling method and a fast RMPC approach. First, based on the offline identified RBF-ARX model without offset term, two convex polytopic sets are constructed to wrap the globally nonlinear behavior of the system. Then, the optimization problem of implementing a quasi-min-max MPC algorithm including several linear matrix inequalities (LMIs) is formulated, and it is solved offline to synthesize a sequence of explicit control laws that correspond to a sequence of asymptotically stable invariant ellipsoids, of which all the optimization results are stored in a look-up table. During the online real-time control, the controller only needs to carry out a simple state-vector computation and bisection search. The proposed approach is applied to an actual linear one-stage inverted pendulum (LOSIP), which is a fast-responding and nonlinear plant. The real-time control experiments demonstrate the effectiveness of the proposed RBF-ARX model-based efficient RMPC approach.

Diurnal Transcriptome and Gene Network Represented through Sparse Modeling in Brachypodium distachyon.

We report the comprehensive identification of periodic genes and their network inference, based on a gene co-expression analysis and an Auto-Regressive eXogenous (ARX) model with a group smoothly clipped absolute deviation (SCAD) method using a time-series transcriptome dataset in a model grass, Brachypodium distachyon. To reveal the diurnal changes in the transcriptome in B. distachyon, we performed RNA-seq analysis of its leaves sampled through a diurnal cycle of over 48 h at 4 h intervals using three biological replications, and identified 3,621 periodic genes through our wavelet analysis. The expression data are feasible to infer network sparsity based on ARX models. We found that genes involved in biological processes such as transcriptional regulation, protein degradation, and post-transcriptional modification and photosynthesis are significantly enriched in the periodic genes, suggesting that these processes might be regulated by circadian rhythm in B. distachyon. On the basis of the time-series expression patterns of the periodic genes, we constructed a chronological gene co-expression network and identified putative transcription factors encoding genes that might be involved in the time-specific regulatory transcriptional network. Moreover, we inferred a transcriptional network composed of the periodic genes in B. distachyon, aiming to identify genes associated with other genes through variable selection by grouping time points for each gene. Based on the ARX model with the group SCAD regularization using our time-series expression datasets of the periodic genes, we constructed gene networks and found that the networks represent typical scale-free structure. Our findings demonstrate that the diurnal changes in the transcriptome in B. distachyon leaves have a sparse network structure, demonstrating the spatiotemporal gene regulatory network over the cyclic phase transitions in B. distachyon diurnal growth.

NIRS-EEG joint imaging during transcranial direct current stimulation: Online parameter estimation with an autoregressive model.

BACKGROUND: Transcranial direct current stimulation (tDCS) has been shown to perturb both cortical neural activity and hemodynamics during (online) and after the stimulation, however mechanisms of these tDCS-induced online and after-effects are not known. Here, online resting-state spontaneous brain activation may be relevant to monitor tDCS neuromodulatory effects that can be measured using electroencephalography (EEG) in conjunction with near-infrared spectroscopy (NIRS). METHOD: We present a Kalman Filter based online parameter estimation of an autoregressive (ARX) model to track the transient coupling relation between the changes in EEG power spectrum and NIRS signals during anodal tDCS (2mA, 10min) using a 4×1 ring high-definition montage. RESULTS: Our online ARX parameter estimation technique using the cross-correlation between log (base-10) transformed EEG band-power (0.5-11.25Hz) and NIRS oxy-hemoglobin signal in the low frequency (≤0.1Hz) range was shown in 5 healthy subjects to be sensitive to detect transient EEG-NIRS coupling changes in resting-state spontaneous brain activation during anodal tDCS. Conventional sliding window cross-correlation calculations suffer a fundamental problem in computing the phase relationship as the signal in the window is considered time-invariant and the choice of the window length and step size are subjective. Here, Kalman Filter based method allowed online ARX parameter estimation using time-varying signals that could capture transients in the coupling relationship between EEG and NIRS signals. CONCLUSION: Our new online ARX model based tracking method allows continuous assessment of the transient coupling between the electrophysiological (EEG) and the hemodynamic (NIRS) signals representing resting-state spontaneous brain activation during anodal tDCS.

Modeling and control approach to a distinctive quadrotor helicopter.

The referenced quadrotor helicopter in this paper has a unique configuration. It is more complex than commonly used quadrotors because of its inaccurate parameters, unideal symmetrical structure and unknown nonlinear dynamics. A novel method was presented to handle its modeling and control problems in this paper, which adopts a MIMO RBF neural nets-based state-dependent ARX (RBF-ARX) model to represent its nonlinear dynamics, and then a MIMO RBF-ARX model-based global LQR controller is proposed to stabilize the quadrotor's attitude. By comparing with a physical model-based LQR controller and an ARX model-set-based gain scheduling LQR controller, superiority of the MIMO RBF-ARX model-based control approach was confirmed. This successful application verified the validity of the MIMO RBF-ARX modeling method to the quadrotor helicopter with complex nonlinearity.

An ARX model for light propagation in biological tissue.

For many applications in biomedical engineering, and especially for precise dosimetry in photodynamic therapy, it is essential to determine the absorption and scattering of light in biological tissue very precisely. At present it is not possible to measure the absorption and scattering coefficient separately by using an endoscopic sensor based upon the backscattering phenomenon. In this paper, we propose a solution to this problem. We present a new model derived from Kubelka and Munk's theory, which is known to be suitable for the description of optical phenomena in tissue. Then we apply an algorithm often used in signal processing, the Auto Regressive with eXternal input or ARX model, which allows us to determine both optical coefficients separately. A first validation is done by numerical simulation, then measurements with phantoms were done. The results of both tests prove the model to be reliable and effective.