Pair Of Sensors Research Articles

Active Vibration Control of Timoshenko Sigmoid Functionally Graded Porous Composite Beam with Distributed Piezoelectric Sensor/Actuator in a Thermal Environment

This work presents the study of the dynamics and active control of a cantilever sigmoid FGM beam with porosities in a thermal environment. During this study, we considered the Timoshenko beam’s theory combined with the finite element method (FEM). This work also presents a comparative study with an experimental study for the vibration of a functionally graded piezoelectric beam (FGPM) to validate the numerical model. Linear quadratic Gaussian (LQG) optimal control with a Kalman filter was used for the vibration control using piezoelectric sensors and actuators as symmetrical layers to eliminate membrane effects. The controlled and uncontrolled responses are presented, considering the influence of thermal effect, the porosity of the FGM material, and the location of the sensor pair on the smart structure. The results indicate that the porosity effect of the FGM material, as well as the application of the thermal effect, involves an increase in vibration frequencies, in contrast to the increase in the power law index. The study also shows that the thermal and porosity effects result in an increase in vibration amplitudes.

Correction and Accuracy of PurpleAir PM2.5 Measurements for Extreme Wildfire Smoke.

PurpleAir particulate matter (PM) sensors are increasingly used in the United States and other countries for real-time air quality information, particularly during wildfire smoke episodes. Uncorrected PurpleAir data can be biased and may exhibit a nonlinear response at extreme smoke concentrations (>300 µg/m3). This bias and nonlinearity result in a disagreement with the traditional ambient monitoring network, leading to the public’s confusion during smoke episodes. These sensors must be evaluated during smoke-impacted times and then corrected for bias, to ensure that accurate data are reported. The nearby public PurpleAir sensor and monitor pairs were identified during the summer of 2020 and were used to supplement the data from collocated pairs to develop an extended U.S.-wide correction for high concentrations. We evaluated several correction schemes to identify an optimal correction, using the previously developed U.S.-wide correction, up to 300 µg/m3, transitioning to a quadradic fit above 400 µg/m3. The correction reduces the bias at each air quality index (AQI) breakpoint; most ambient collocations that were studied met the Environmental Protection Agency’s (EPA) performance targets (twelve of the thirteen ambient sensors met the EPA’s targets) and some smoke-impacted sites (5 out of 15 met the EPA’s performance targets in terms of the 1-h averages). This correction can also be used to improve the comparability of PurpleAir sensor data with regulatory-grade monitors when they are collectively analyzed or shown together on public information websites; the methods developed in this paper can also be used to correct future air-sensor types. The PurpleAir network is already filling in spatial and temporal gaps in the regulatory monitoring network and providing valuable air-quality information during smoke episodes.

A rapid technique for detecting and localizing damage in composite laminates

Composite materials are prone to impact damage, which affects structural stability and causes safety concerns. Due to the complexity and diversity of them, the damage localization in composite materials is very challenging and is getting more attention in the research community. This paper presents a rapid technique for composite damage localization without any prior knowledge of direction-dependent velocity profile. The proposed solution technique uses the time difference of arrival (TDOA) of Lamb waves. The TDOA is obtained by the cross-correlation technique applied to the received signals at different sensor pairs in two “L” shaped sensor clusters (LSSCs). With the help of the LSSC, only seven sensors are required to quickly predict the delamination damage location for quasi-isotropic and anisotropic composite materials (QACM). A simulation model was established to study the influence of damage location and different layup directions on the localization results. The experimental verification was carried out on a T300 carbon fiber board. The localization results of simulation and experiment showed good matching, which proves that the technique is suitable for QACM.

Validation of Expanded Trend-to-Trend Cross-Calibration Technique and Its Application to Global Scale

The expanded Trend-to-Trend (T2T) cross-calibration technique has the potential to calibrate two sensors in much less time and provides trends on a daily assessment basis. The trend obtained from the expanded technique aids in evaluating the differences between satellite sensors. Therefore, this technique was validated with several trusted cross-calibration techniques to evaluate its accuracy. Initially, the expanded T2T technique was validated with three independent RadCaTS RRV, DIMITRI-PICS, and APICS models, and results show a 1% average difference with other models over all bands. Further, this technique was validated with other SDSU techniques to calibrate the newly launched satellite Landsat 9 with 8, demonstrating good agreement in all bands within 0.5%. This technique was also validated for Terra MODIS and ETM+, showing consistency within 1% for all bands compared to four PICS sites. Additionally, the T2T technique was applied to a global scale using EPICS Global sites. The expanded T2T cross-calibration gain result obtained for Landsat 8 versus Landsat 7/8, Sentinel 2A/2B, and Terra/Aqua MODIS presented that the difference between these pairs was within 0.5–1% for most of the spectral bands. Total uncertainty obtained for these pairs of sensors using Monte Carlo Simulation varies from 2.5–4% for all bands except for SWIR2 bands, which vary up to 5%. The difference between EPICS Global and EPICS North Africa was calculated using the ratio of trend gain; the difference among them was within 0.5–1% difference on average for all the sensors and bands within a 0.5% uncertainty level difference.

Geometrically engineered two-color time orderings in a laser-dressed atomic antenna: Shaping space-time photon correlations

The space-time connection between the Mollow cascaded transitions with time orderings and the spatially directional correlated emissions of Mollow photons is analyzed theoretically in a strong laser-dressed subwavelength two-atom antenna, which supports only two-level electric dipole transitions. It can be regarded as the most prototypical collective quantum radiator to exploit the space-time quantum characteristics of the Mollow physics of resonance fluorescence. By constructing the photon filtering dynamics from the dressed two-atom antenna to a pair of quantum sensors, the frequency-resolved spatial two-point two-time correlations of different Mollow spectral lines are examined analytically in terms of the quantum sensor modes. It is shown that a rich significance of spatial directionality lies in the time orderings of cascaded emissions between different Mollow spectral lines. This feature enables the time orderings of different Mollow spectral lines to be tailored geometrically and thus prepared deterministically to produce highly directional temporal bunching effects of the Mollow photons with giant nonclassicality only for a specific two-photon detection order. The dressed two-atom system is therefore able to operate as a highly directional atomic antenna that may provide versatile applications in the fields of atom-photon-based quantum precise measurement physics and Mollow spectroscopy.

Investigation on the pattern for train-induced strains of the long-span steel truss railway bridge

Detecting abnormal changes in bridge behavior is essential for bridge management. Influence lines are a generally accepted method to describe the quasi-static bridge behavior. Researchers have proposed that the ratio between the influence lines associated structural strains for a pair of sensors can be used as an indicator of abnormal structural condition. However, these methods have been developed for highway bridges; direct application to railway bridges is challenging, because (i)measured responses corresponding to each axle load are coupled, and (ii)train-induced longitudinal forces and bearing restraint produce additional strains in structural members. This research seeks to resolve these challenges to enable application to long-span railway bridges with spherical bearings. First, the concept of influence lines is illustrated using the elastic beam theory, providing an understanding of the underlying mechanisms of the train-induced responses. Accordingly, two condition indicators base on the axial strain in a pair of structural members are given (i.e., the ratio between integral areas of pseudo-static strains and the ratio between average pseudo-static strain amplitude). In addition, the statistical patterns of the indicators are studied using numerical simulation. Subsequently, the strain patterns are illustrated for field monitoring data from a long-span steel truss railway bridge. Herein, the calculations for the condition indicators from strain measurements are presented, and the pre-processing of the indicators is conducted to consider bridge bearing properties. Results show that the condition indicators are naturally clustered according to tracks and the directions of two consecutive trains; each cluster can be represented using a normal distribution. Note that these distributions do not change with the variation of train loads (i.e., train weight and train speed). The recognized pattern provides a potential approach for the identification of abnormal behavior of railway bridges.

Analysis of the Threshold for Energy Consumption in Displacement of Random Sensors.

The fundamental problem of energy-efficient reallocation of mobile random sensors to provide full coverage without interference is addressed in this paper. We consider n mobile sensors with the identical sensing range placed randomly on the unit interval and on the unit square. The sensors move from their initial random positions to the final locations so that: (a) every point on the unit interval or on the unit square is within the range of a sensor; (b) each pair of sensors is at a Euclidean distance greater than or equal to s; (c) the energy consumption for the movement of the sensors to the final positions is minimized. As a cost measure for the energy in the movement of sensors, we consider a-total movement defined as the sum ∑i=1ndia, for some constant a>0, provided that the i-th sensor is displaced the distance di. The main contribution is summarized as follows: (1) if the sensors are placed on the unit interval, we explain the sharp increase around the sensing radius equal to 12n and the interference distance equal to 1n for the expected minimal a-total displacement; (2) if the sensors are placed on the unit square, we explain the sharp increase around the square sensing radius equal to 12n and the interference distance equal to 1n for the expected minimal a-total displacement. We designed and analysed three algorithms. The probabilistic analysis of our protocols is based on a novel mathematical theory of the Beta distribution.

Stabilization by switching of parabolic PDEs with spatially scheduled actuators and sensors

This paper addresses a switched sampled-data control design for stabilization of Kuramoto-Sivashinsky equation under the Dirichlet/periodic boundary conditions with spatially scheduled actuators. It is supposed that discrete-time point-like or averaged measurements are available. The system is known to be stabilizable by static output-feedback employing several distributed in space actuators and sensors, but is not stabilizable by only one of the actuator–sensor pairs. Does there exist a switching stabilizing static output-feedback such that at all times, only one actuator–sensor pair is active? We give a positive answer and find the appropriate switching sampled-data control law. The proposed switching controller can be implemented either by N actuators and sensors placed in each subdomain (here switching control may reduce the energy that the system spends) or by using one actuator–sensor pair that can move to the active subdomain. For implementation of the control law by moving actuators and sensors, we take into account a moving time by treating it as an additional switching between the open-loop system and the closed-loop switched system. The guidance of active (or mobile) actuators and sensors is provided by using output-dependent switching. Constructive conditions are derived to ensure that the resulting closed-loop system is regionally stable by means of the Lyapunov approach. Numerical example illustrates the efficiency of the method.

A Simple Configuration of an Actively Synthesized Gyroscopic-Nonreciprocal Acoustic Metamaterial

Abstract A simple configuration of an active nonreciprocal gyroscopic metamaterial (NGMM) is presented. In the proposed NGMM system, a one-dimensional acoustic cavity is provided with piezoelectric boundaries acting as a collocated pair of sensors and actuators. The active piezo-boundaries are controlled by a simple control algorithm that synthesizes a virtual gyroscopic control action to impart desirable nonreciprocal characteristics which are tunable both in magnitude and phase. The dynamic model of a prototype of the NGMM cell is experimentally identified in an attempt to provide means for predicting the characteristics of the virtual gyroscopic controller for various control gains during forward and backward propagations. The theoretical predictions are validated experimentally without the need for any physical dynamic controller which was provided, in earlier studies, by using a dummy NGMM cell. Such a simplified arrangement enables the fast execution of the controller with enhanced frequency bandwidth capabilities. The experimental and theoretical characteristics of the NGMM cell are monitored and predicted for different control gains in order to evaluate its behavior for both forward and backward propagations. The obtained experimental results are compared with the theoretical predictions and found to be in close agreement. The presented concepts provide the foundation necessary for the implementation of NGMM that can be employed in more complex 2D and 3D critical structures in order to achieve nonreciprocal behavior in a simple and programmable manner.

Development of a device that generates a temperature gradient in a microtiter plate for microbial culture.

Although temperature is a fundamental parameter in biology, testing various temperature conditions simultaneously is often difficult. In the present study, we developed a device for generating a temperature gradient in arrays of wells on a microtiter plate. This device consists of a pair of Peltier elements and temperature sensors placed on both ends of a flat aluminum bar to generate a linear temperature gradient. The device loads a microtiter plate at the center of the aluminum bar and transfers the temperature gradient to the bottom of the wells in the plate. This device successfully maintained a temperature gradient of 38.2 to 43.1°C on the horizontal axis of a 96-well microtiter plate in an incubator at 31°C. Furthermore, using this device, we demonstrated a laboratory evolution experiment of Escherichia coli, which was selected on the basis of its ability to grow at high temperatures. The developed device also facilitates a two-dimensional assay to determine the effects of temperature and drug concentrations on cellular growth.

Automatic Extrinsic Calibration Method for LiDAR and Camera Sensor Setups

Most sensor setups for onboard autonomous perception are composed of LiDARs and vision systems, as they provide complementary information that improves the reliability of the different algorithms necessary to obtain a robust scene understanding. However, the effective use of information from different sources requires an accurate calibration between the sensors involved, which usually implies a tedious and burdensome process. We present a method to calibrate the extrinsic parameters of any pair of sensors involving LiDARs, monocular or stereo cameras, of the same or different modalities. The procedure is composed of two stages: first, reference points belonging to a custom calibration target are extracted from the data provided by the sensors to be calibrated, and second, the optimal rigid transformation is found through the registration of both point sets. The proposed approach can handle devices with very different resolutions and poses, as usually found in vehicle setups. In order to assess the performance of the proposed method, a novel evaluation suite built on top of a popular simulation framework is introduced. Experiments on the synthetic environment show that our calibration algorithm significantly outperforms existing methods, whereas real data tests corroborate the results obtained in the evaluation suite. Open-source code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/beltransen/velo2cam_calibration</uri> .

Using a source of opportunity for self-localization of mobile underwater vector sensor platforms

Transforming a network of few compact mobile underwater platforms, each equipped with a single acoustic sensor, into a distributed sensing array requires precise positioning of each mobile sensor. But conventional accurate underwater positioning tools rely on active acoustic sources (e.g., acoustic pingers), which imposes additional hardware and operational complexity. Hence self-localization (i.e., totally passive) methods using only acoustic sources of opportunity (such as surface vessels) for locating the mobile sensors of a distributed array appear as an attractive alternative. Existing underwater self-localization methods have mainly been developed for mobile platform equipped with time-synchronized hydrophones and rely only on the time-difference of arrivals between multiple pairwise combinations of the mobile hydrophones as inputs for a complex non-linear inversion procedure. Instead, we introduce a self-localization method, which uses a linear least square formulation, for two mobile time-synchronized vector sensor platforms based on their acoustic recordings of a distant surface vessel and their inertial navigation systems (INS) measurements. This method can be generalized to multiple vector sensor pairs to provide additional robustness towards input parameter errors (e.g., due to a faulty INS) as demonstrated experimentally using drifting buoys with inertial vector sensors deployed ∼100 m apart in shallow water.

Armband Sensors Location Assessment for Left Arm-ECG Bipolar Leads Waveform Components Discovery Tendencies around the MUAC Line.

Sudden cardiac death (SCD) risk can be reduced by early detection of short-lived and transient cardiac arrhythmias using long-term electrocardiographic (ECG) monitoring. Early detection of ventricular arrhythmias can reduce the risk of SCD by allowing appropriate interventions. Long-term continuous ECG monitoring, using a non-invasive armband-based wearable device is an appealing solution for detecting early heart rhythm abnormalities. However, there is a paucity of understanding on the number and best bipolar ECG electrode pairs axial orientation around the left mid-upper arm circumference (MUAC) for such devices. This study addresses the question on the best axial orientation of ECG bipolar electrode pairs around the left MUAC in non-invasive armband-based wearable devices, for the early detection of heart rhythm abnormalities. A total of 18 subjects with almost same BMI values in the WASTCArD arm-ECG database were selected to assess arm-ECG bipolar leads quality using proposed metrics of relative (normalized) signal strength measurement, arm-ECG detection performance of the main ECG waveform event component (QRS) and heart-rate variability (HRV) in six derived bipolar arm ECG-lead sensor pairs around the armband circumference, having regularly spaced axis angles (at 30° steps) orientation. The analysis revealed that the angular range from −30° to +30°of arm-lead sensors pair axis orientation around the arm, including the 0° axis (which is co-planar to chest plane), provided the best orientation on the arm for reasonably good QRS detection; presenting the highest sensitivity (Se) median value of 93.3%, precision PPV median value at 99.6%; HRV RMS correlation (p) of 0.97 and coefficient of determination (R2) of 0.95 with HRV gold standard values measured in the standard Lead-I ECG.

Correlation and agreement of regional cerebral oxygen saturation measured from sensor sites at frontal and temporal areas in adult patients undergoing cardiovascular anesthesia.

BackgroundThe function and viability of the brain depend on adequate oxygen supply. A decrease in cerebral blood supply causing cerebral desaturation may lead to many neurological complications. Direct measurement of regional cerebral oxygen saturation (rScO2) assists in early detection and management. Near-infrared spectroscopy (NIRS) has been introduced for measuring rScO2. A pair of sensors are attached to the right and left forehead. However, there are some situations where the forehead of the patient is not accessible for sensor attachment (e.g., neurosurgery involving the frontal area; a bispectral index (BIS) sensor already attached, or a wound to the forehead); therefore, alternate sites for sensor attachment are required. The temporal area was proposed as an alternate site. The objective of this study was to assess the correlation and agreement of rScO2 measured at the forehead vs. the temporal area.MethodsAdult patients undergoing cardiothoracic or vascular surgery were monitored for rScO2 using two pairs of ForeSight sensors. The first pair (A1 and A2) were attached to the right and left forehead, while the second pair (B1 and B2) were attached to the right and left temporal area. The rScO2 values measured from A1 vs. B1 and A2 vs. B2 were assessed for correlation and agreement using the Bland-Altman analysis.ResultsData from 19 patients with 14,364 sets of data were analyzed. The data from A1 vs. B1 and A2 vs. B2 showed moderate positive correlation (r = 0.627; P < 0.0001 and r = 0.548; P < 0.0001). The biases of A1 vs. B1 and A2 vs. B2 were −2.3% (95% CI [−2.5 to −2.2]; P < 0.0001) and 0.7% (95% CI [0.6–0.8]; P < 0.0001). The lower and upper limits of agreement of A1 vs. B1 were −17.5% (95% CI [−17.7 to −17.3]) and 12.8% (95% CI [12.6–13.0]). The lower and upper limits of agreement of A2 vs. B2 were −14.6% (95% CI [−14.8 to −14.4]) and 16.0% (95% [CI 15.8–16.3]).ConclusionsThe rScO2 values measured from sensors at the frontal and temporal areas show a moderate correlation with sufficiently good agreement. The temporal area may be an alternative to the frontal area for cerebral oximetry monitoring.

A novel methodology for quantitative identification of pipeline leakage and negative pressure wave velocity

The detection of negative pressure waves (NPWs) is commonly used to localize leakage in pipeline integrity monitoring. However, the velocity of NPWs cannot always be accurately determined under complicated environmental and operational conditions, resulting in localization errors inevitably. Based on a fluid dynamics model of the pipeline, a relationship between the leakage properties and the NPW transient dynamics was established, and then a novel method was proposed to quantitatively identify the leakage location as well as the NPW velocity in the pipeline. The proposed method requires only one pair of dynamic pressure sensors to monitor the leakage between the proper distance in the pipeline. A series of experiments were conducted on a scaled model pipeline to verify the feasibility of the method. The experimental results demonstrate that the presented method can accurately identify the location and severity of the leakage without the NPW velocity in advance, which overcomes the limitations of the traditional approach. The novel method provides a promising technique of leakage detection for pipeline integrity management.

Programmable bulk modulus in acoustic metamaterials composed of strongly interacting active cells

Active acoustic metamaterials are one path to acoustic properties difficult to realize with passive structures, especially for broadband applications. Here, we experimentally demonstrate a 2D metamaterial composed of coupled sensor-driver unit cells with effective bulk modulus (κeff) precisely tunable through adjustments of the amplitude and phase of the transfer function between pairs of sensors and drivers present in each cell. This work adopts the concepts of our previous theoretical study on polarized sources to realize acoustic metamaterials in which the active unit cells are strongly interacting with each other. To demonstrate the capability of our active metamaterial to produce on-demand negative, fractional, and large κeff, we matched the scattered field from an incident pulse measured in a 2D waveguide with the sound scattered by equivalent continuous materials obtained in numerical simulations. Our approach benefits from being highly scalable, as the unit cells are independently controlled and any number of them can be arranged to form arbitrary geometries without added computational complexity.

Comparing Loose Clothing-Mounted Sensors with Body-Mounted Sensors in the Analysis of Walking.

A person’s walking pattern can reveal important information about their health. Mounting multiple sensors onto loose clothing potentially offers a comfortable way of collecting data about walking and other human movement. This research investigates how well the data from three sensors mounted on the lateral side of clothing (on a pair of trousers near the waist, upper thigh and lower shank) correlate with the data from sensors mounted on the frontal side of the body. Data collected from three participants (two male, one female) for two days were analysed. Gait cycles were extracted based on features in the lower-shank accelerometry and analysed in terms of sensor-to-vertical angles (SVA). The correlations in SVA between the clothing- and body-mounted sensor pairs were analysed. Correlation coefficients above 0.76 were found for the waist sensor pairs, while the thigh and lower-shank sensor pairs had correlations above 0.90. The cyclical nature of gait cycles was evident in the clothing data, and it was possible to distinguish the stance and swing phases of walking based on features in the clothing data. Furthermore, simultaneously recording data from the waist, thigh, and shank was helpful in capturing the movement of the whole leg.

Ultrasonic evaluation of a steel-concrete structure using embedded Fiber Bragg Gratings (FBG) and piezoelectric sensors

Concrete is one of the most widely used materials for civil engineering structures. The casting process is particularly well suited to the deployment of buried sensors able to sample a ultrasonic wave field in three dimensions, a valuable piece of information to evaluate the internal properties of a structure, its health state and its evolution over time. Fiber Bragg Gratings (FBGs) sensors can be used as embedded acoustic receivers to acquire such point-wise ultrasonic data. The technical advantages of this sensing technology are numerous: the reduced size of the optical fiber offers a very small footprint on the studied structure, it can be used over a very broad frequency range with very small phase or amplitude distortions, FBGs are highly resistant to harsh environments such as high temperatures, salinity or radioactive environments, thus increasing the longevity of the embedded sensors. The interrogation of FBG requires dedicated state-of-the-art opto-electronics that must be adapted to the imaging problem (bandwidth, size of the heterogeneities/aggregates, nature of the source). In this study, we present a Steel-Concrete wall model equipped with several embedded optical fibers as well as several embedded and surface piezoelectric (PZT) sensors. We compare the performances of the different embedded sensors for several sources of ultrasonic waves applied on the surface of the wall for frequencies ranging from a few tens to a few hundreds of kHz. The analysis of the signals reveal that a significant part of the energy is transmitted to the concrete through the surface liner. Using a collection of random hammer impacts applied on the surface, we evaluate our ability to reconstruct empirical Green’s functions between pairs of sensors buried into the structure using passive imaging methods. These measurements will provide useful information on the internal structure of a steel-concrete model and its temporal evolution.

Graph Construction for Traffic Prediction: A Data-Driven Approach

Graph learning-based algorithms are becoming the prevalent traffic prediction solutions due to their capability of exploiting non-Euclidean spatial-temporal traffic data correlation. However, current predictors primarily employ heuristically constructed static traffic graphs in forecasting, which may not describe the latent traffic dynamics well. Existing attempts on dynamically generated traffic graphs also face challenges like prolonged model training time and undermined model expressibility. In this paper, a novel data-driven graph construction scheme based on graph adjacency learning is proposed for graph learning-based traffic predictors. The proposed scheme explores inter-time-series dependency with the graph attention mechanism to embed the sensor correlation in a latent attention space, which determines the correlation of any possible sensor pairs for traffic graph construction. Comprehensive case studies on three real-world traffic datasets reveal that the proposed scheme outperforms state-of-the-art static and dynamic graph construction baselines. Additionally, time-varying and sparse graph construction schemes are devised and assessed to boost the efficacy, and a hyper-parameter test develops guidelines for parameter and model architecture selection.

Wrist Movement Variability Assessment in Individuals with Parkinson's Disease.

(1) Background: Parkinson’s disease (PD) is a neurodegenerative disorder represented by the progressive loss of dopamine-producing neurons, it decreases the individual’s motor functions and affects the execution of movements. There is a real need to include quantitative techniques and reliable methods to assess the evolution of PD. (2) Methods: This cross-sectional study assessed the variability of wrist RUD (radial and ulnar deviation) and FE (flexion and extension) movements measured by two pairs of capacitive sensors (PS25454 EPIC). The hypothesis was that PD patients have less variability in wrist movement execution than healthy individuals. The data was collected from 29 participants (age: 62.13 ± 9.7) with PD and 29 healthy individuals (60.70 ± 8). Subjects performed the experimental tasks at normal and fast speeds. Six features that captured the amplitude of the hand movements around two axes were estimated from the collected signals. (3) Results: The movement variability was greater for healthy individuals than for PD patients (p < 0.05). (4) Conclusion: The low variability seen in the PD group may indicate they execute wrist RUD and FE in a more restricted way. The variability analysis proposed here could be used as an indicator of patient progress in therapeutic programs and required changes in medication dosage.