# MATHMET

## The European Centre for Mathematics and Statistics in Metrology

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Abbestr. Berlin

### Programme

Wednesday
Dynamic operation of sensors and sensing of dynamic processes: similarities, differences and challenges
Andreas Schütze, University of Saarland
This talk focuses on examples from dynamically excited sensors, such as magnetic field sensors with integrated calibration or gas sensors for sensing and detection in condition monitoring and surveillance. With regard to the employed signal processing and calibration, similarities, differences and challenges are demonstrated and discussed.
A Two-Stage Bayesian Approach for the Analysis of Multispectral Camera Measurements
Marcel Dierl, Physikalisch-Technische Bundesanstalt
Estimation of spectral reflectance from responses of multispectral imaging systems is important for numerous applications in imaging science and several reconstruction principles have been proposed to this end. These principles have in common that the calculation of spectral reflectance from measurement data requires the solution of an ill-posed inverse problem. In many practical situations appropriate prior knowledge is available that should be utilized in the reconstruction procedure for regularization. However, this is not straightforward for many of the data analysis methods currently applied in spectral measurement, and it is often realized by using suitable training data and special kernel functions.

Here we present a two-stage Bayesian approach that allows us to incorporate prior knowledge about spectral content. Such prior knowledge can originate from previous monochromator or spectrophotometer measurements. For the Bayesian analysis we apply truncated normal distributions that ensure the physical constraint of positivity and use special designed prior covariance matrices to provide smooth recovered spectra. In the first step, called calibration stage, spectral sensitivity curves for each camera channel of the multispectral imaging system are determined that connect camera responses with spectral reflectances. In the subsequent measurement stage these results are used for the estimation of the reflectance spectrum from the camera’s response. The approach yields analytical expressions for a fast and efficient estimation of spectral reflectance and is thus suitable for real-time applications. Besides point estimates, also probability distributions are obtained which completely characterize the uncertainty associated with the reconstructed spectrum.

We demonstrate the performance of our approach by using simulated data for the camera responses and spectral curves. It is shown that through incorporation of prior knowledge the Bayesian treatment yields improved reconstruction results for a wide range of standard deviations of the prior compared to methods that resort to training data only. Reflectance spectra which are not fully captured by training data can also be well estimated with our approach.
Data-driven weight measurements
Gustavo Quintana-Carapia, Vrije Universiteit Brussel
The succesful operation of most engineering systems depends on fast and accurate measurements, which in turn depends on the physical nature of the sensors. For instance, in temperature measurements, there is a heat exchange between the environment and the thermometer. In mass measurements, the scale exhibits oscilations. In general, the measurement is a dynamical process and introduces a delay. Using real-time digital signal processing allows to reduce the measurement time.

In our previous work, we proposed an approach to solve the metrology problem of speeding up a measurement device. We assume that the measurement device is a stable linear time-invariant dynamical system. The proposed algorithm predicts the measured value by recursive least-squares estimation. The algorithm is model-free and is called Data-Driven Fast Measurements (DDFM).

In this approach there is no need for identication of the dinamical system. The implementation can be done on digital signal processors of low computational resources. The DDFM algorithm has been tested on both temperature and mass measurements. The results observed in simulation validate the eectiveness of the algorithm. Experimentally, the temperature prediction with the DDFM has been performed with a test bed based on commercial LEGO NXT and EV3 devices. Using the DDFM algorithm, the temperature estimation, on the LEGO test bed, is achieved before the sensor signal transient reaches its steady value.

Currently, we are designing a experimental realization for testing the DDFM algorithm in weight mea- surements. The experimental set up will be a conveyor belt that weights an object while it is transported. Only a section of the conveyor belt has weighing capabilities. The objects are transported in such a way that they do not stop on the weighing conveyor to be measured. The objects gradually enter into the weighing section. If we assume constant speed, for the weighing sensor the mass increases linearly from zero to its maximum value. Therefore, the mass needs to be considered a time-varying parameter. We aim to gener- alize the DDFM algorithm to cover time-varying parameter situations. We have performed simulations to estimate the mass with a modied DDFM algorithm.
PyDynamic: A repository for software for the analysis of dynamic measurements
Ian Smith, National Physical Laboratory
Dynamic quantities arise and are of interest within many industrial sectors. For example, the measurement of in-cylinder pressure is of great importance to the automotive industry. Engine developers are typically faced with the problem of maximising engine efficiency while at the same time minimising emissions. Information on the in-cylinder pressure during the combustion cycle can be employed to optimise fuel injection and timing parameters, enabling the efficiency/emissions problem to be addressed.

The EMPIR Support for Impact Project (SIP) “Standards and software to maximise end user uptake of NMI calibrations of dynamic force, torque and pressure sensors”, running from 2015 to 2018, follows on from the EMRP Joint Research Project (JRP) “Traceable dynamic measurement of mechanical quantities” which ran from 2011 to 2014. The JRP was primarily concerned with establishing primary and secondary NMI-level traceability for the mechanical quantities of dynamic force, dynamic torque and dynamic pressure. One of the objectives of the SIP is to make publicly available software that allows industrial end-users to evaluate reliable estimates of dynamic mechanical quantities and their associated uncertainties. To this end, the software repository PyDynamic has been developed and populated with software that allows dynamic measurements to be analysed.

This paper provides a summary of the software currently available within PyDynamic, illustrates some of that software in action, and discusses further additions to the repository to be made during the SIP.
Analysis of impact hammer calibration measurements
Michael Kobusch, Physikalisch-Technische Bundesanstalt
Impact hammers represent a commonly used tool for the modal testing of mechanical components and interconnected mechanical structures. An integrated force transducer measures the shock force stimulus which excites the mechanical structure under test, in particular in order to determine its modal resonances and mode shapes by means of additional sensors which acquire the shock response at a specific surface point of interest.

The appropriate calibration of impact hammers has gained importance in order to satisfy increasing demands on measurement accuracy and to account for the needs of the employed quality management system. As known from the dynamic calibration of the related mechanical transducers for acceleration and force, these transducers exhibit a frequency- dependent response depending on their mechanical structure and coupling to their environment. In this context, the establishment of traceable dynamic calibration procedures is a topic of recent research activities.

This contribution presents primary calibration measurements of selected impact hammers conducted at different experimental set-ups which use a reference force signal determined from the measured acceleration of a known mass body at which the hammer impacts. To minimize friction and to assure a defined axial motion, the mass bodies (cylindrical shape, various mass values) were either suspended by strings or guided by an air bearing. The acceleration was measured by an accelerometer or by a laser vibrometer, respectively. Magnitude and duration of the shock pulses could be varied by applying differently strong strokes and by using impact tips of different hardness.

The measurement signals of impact hammer and reference force were analysed in the time and frequency domain, and the calibration results obtained with the different measurement set-ups will be compared and discussed. In the scope of joint research activities between PTB and the Mexican national metrology institute CENAM, the presented measurements were conducted at both institutes using the available impact hammer calibration set-ups. A comparison of these bilateral results of the primary calibration of impact hammers will be given for the first time.
A Dynamic Force Transfer Standard
Nicholas Vlajic, NIST
We present results of an investigation into the use of an impact hammer as a dynamic force transfer standard. Such a standard provides a practical link between a laboratory dynamic force standard and a force transducer in its application setting. In general, the dynamic response of a force transducer is not a property of the transducer alone but a property of the composite dynamic system of which the transducer is a part. The realized dynamic sensitivity of the transducer depends on the mechanics of this composite system, motivating the use of a transfer standard for in-situ dynamic calibration of working force transducers.

An impact hammer is a convenient transducer form factor for a transfer standard for many applications, being simple to use. In order to deploy it as such a standard, its response must be known with low uncertainty. We explore calibration of an impact hammer using a step-force input, thereby determining its dynamic sensitivity (i.e. the complex frequency response function $V_{out,imp} (\omega) / F_{cal} (\omega)$, where $V_{out,imp}$ is the impact hammer output voltage and $F$ cal is the applied force step). The uncertainty of the determined sensitivity incorporates variability in the use of the device, for example in the angle of impact.

Following this calibration, we demonstrate use of the transfer standard to calibrate working transducers in different settings, as may be encountered in applications. With the calibrated impact hammer, we generate known force pulses on the working transducer in its application setting. This provides the dynamic sensitivity of the working transducer $V_{out,wrk} (\omega) / F_{trans} (\omega)$, where $V_{out,wrk} (\omega)$ is the working transducer output voltage in response to the force pulse $F_{trans}$ applied by the impact hammer.

With the thus-calibrated working transducer, accurate measurements of input-force waveforms can be performed. This requires inversion of the output voltage waveform observed in the application, introducing additional uncertainty that depends on the particular force waveform being measured.

We consider limiting factors on the performance of the impact hammer as a transfer standard, including bandwidth, nonlinearity and repeatability of use.
Needs and contribution of an industry collaborator for a better determination of dynamic calibration measurement uncertainty
André Schäfer, HBM
This talks provides an overview of HBM in international research on dynamic metrology, both as a provider of precision instruments and collaborator in research.
Thursday
Measuring and modeling dynamical systems in the presence of nonlinear distortions
Johan Schoukens, Vrije Universiteit Brussel
Development of a dynamic standard to evaluate the metrological performance of absolute pressure measurement systems
Alberto Díaz Tey, Univ. Costa Rica)
Based on the recognition by the BIPM "... that the traceability of measurements from INM down to calibration laboratories is generally established under steady conditions...", the Engineering Research (INII) at the University of Costa Rica (UCR) registered a project entitled "Development of a dynamic standard to evaluate the metrological performance of absolute pressure measurement systems".

The project was formally launched on January 1st, 2015, to ensure the metrological quality of pressure measurements under the ocean, up to 50 m, in the Pacific and Caribbean coasts of Costa Rica. Such dynamic measurements are used by researchers of the Marine, River and Estuary Research Unit (IMARES) to calculate the height of the water column by using the equation of state of seawater. Other important calculations for the design of ports and marinas, such as wave profiles, are performed using the original data under the assumptions of the Airy wave theory.

In the newly created Dynamic Measurements Laboratory, there is currently a construction of a 2,4 m dynamic pressure generator based on the shock tube theory, but using an adjustable safety valve as a shooting device between the high and low pressure chambers.

The dynamic pressure generator counts on four ports for measurements. Two of the latter are located at the end of the low pressure chamber where the pressure reference transducers (HBM P3TCP) and the subject of calibration (usually with a silicone diaphragm sensor) are installed, another in the low pressure chamber for monitoring the shock wave associated with isoentropic expansion of the inert gas (nitrogen), and the last one "upstream" the safety valve for the control and monitoring of the shooting pressure.

The shock tube will be used initially as a means of comparison between the pressure reference transducers and the subject of calibration. However, the validation of the mathematical model associated with the isoentropic expansion of the inert gas is expected as well, using numerical simulation by adjusting the parameters from experimental results, and then evaluating its possible behavior as a standard.

The electrical outputs of the four pressure transducers are connected to a HBM Quantum MX440B universal amplifier, which is responsible for the digital conversion and synchronized registration on a spreadsheet using the HBM catmanAP software.

Considering the processing complexity of dynamic measurements and the evaluation of the associated the uncertainty in an environment of traceability to the SI, the results will be presented at the 9 International Workshop on Analysis of Dynamic Measurements, in order to adjust our calculations according to the procedures developed in the EURAMET research projects.

According to the developed schedule and available budget, the project should be completed in August 2018.
Dynamic Calibration of Torque Transducers – The Angular Acceleration Ramp Method
Renato Reis Machado, INMETRO
In the current international traceability chain of the torque quantity, torque transducers used in rotational and dynamic regimes are calibrated under static proceedings and systems, what constitutes a gap in this traceability chain. In order to fulﬁll the needs that differentiate static from dynamic measurements and processes, recent research on the dynamic traceability of torque has been done with different approaches for the principles, the systems and the methodologies to be adopted.

A dynamic calibration proposal is being developed by the National Institute of Metrology of Brazil (INMETRO) and it is based on the Newton's Second Law applied to the rotational case. The physical principle consists of generating the reference pulse torque value through an angular acceleration regime applied to a rotating measuring shaft, where a piece attached to it has a known mass moment of inertia. This physical principle, with high torque rates, must be consolidated with a well deﬁned measurement assembly and a consistent loading sequence, once the correct manipulations of the torque data measured by the transducer under calibration and of the calculated reference values are essential for reliable results.

This paper focus on the discussion around the two methods of calibration proposed: (a) the direct comparison, which evaluates the measurement error between the measured torque and the reference torque values for each point of a deﬁned load curve and (b) the indirect comparison, which presents the analysis of linearity of the relationship between the measured torque and the measured acceleration through linear ﬁtting curves.

The results to be presented sustain the discussions and confront the theories initially inputted to the proposal, which leads to practical conclusions to the analysis of the parameters to be included as calibration results that would better characterize the transducer under calibration.
Using a triaxial acceleration calibration device for seismometer calibration
Leonard Klaus, Physikalisch-Technische Bundesanstalt
Seismometers are used in great numbers for the analysis of seismic activities as earthquakes, but as well nuclear weapon tests. Up to now, they are only rarely calibrated traceable to national standards. Often, only internal calibration procedures are used.

Compared to accelerometers, seismometers are heavy and large. They are only designed to be mounted only in one orientation, requiring a multi-component excitation for a triaxial seismometer. While uniaxial exciters designed specifically for the purpose of seismometer calibrations were developed recently, for triaxial seismometers no calibration facilities exist at present.

Due to a request for a three-axial calibration of seismometers, PTB analysed how these seismometers could be calibrated. A feasible solution seemed to utilise the multi-component acceleration calibration device of PTB.

This device is designed to generate vibration in three degrees of freedom of much higher magnitudes of acceleration (up to 100 m/s2), up to 50 mm peak-to-peak displacement, and for higher frequencies (10 Hz – 1 kHz) than required for a seismometer calibration. The maximum weight of 100 kg for the specimen will overcome any issues with heavy seismometers, which often appear with conventional acceleration exciters.

The assessment showed that the excited sinusoidal vibrations even for small magnitudes (2.5 mm/s) and low frequencies (down to 0.4 Hz) gave only small disturbances.

The excitation signal was generated by a closed-loop vibration controller, which represents the lower frequency limit. The measurement of the generated acceleration for each axis was carried out by means of three laser-Doppler vibrometers. The calibrated velocity-proportional voltage outputs of the vibrometers were used for the calibration.

Recently, the data acquisition system was updated incorporating synchronised simultaneous sampling data acquisition cards in an PXI-system. For this reason, the measurement uncertainty was re-evaluated, the results will be presented in the final contribution.
Time-domain laser-based characterization of high-speed photodetectors
Paul Struszewski, Physikalisch-Technische Bundesanstalt
We present a procedure to characterize the time- and frequency-domain responses of high-speed photodetectors (PDs). For this purpose, we utilize an all-optical laser-based vector network analyser (VNA). This device features a novel measurement technique with which we are able to obtain complex scattering parameters at the measurement plane. This allows for full mismatch correction being crucial for characterization of high-frequency devices. The analysis of the time-domain measurements includes several deconvolution operations. We demonstrate that in our case the usage of a Tikhonov regularisation algorithm is essential to overcome the ill- posed problem of deconvolution. This results in a numerically demanding analysis for a dynamic system with time traces having several thousand data points. In order to quantify the uncertainty of PD responses constituting a highly multivariate problem, we apply a Monte-Carlo simulation according to the GUM. Our technique not only enables accurate calibration of PDs but will also prove to be important for general waveform metrology applications.
Uncertainty evaluation for determination of electrical grid characteristics using the Nodal Load Observer
Natallia Makarava, Physikalisch-Technische Bundesanstalt
The Nodal load observer (NLO) is a state estimation method which is based on the extended Kalman ﬁlter and aims for the online estimation of complex nodal electric power and voltage in middle and low voltage electrical grids. Due to an insucient instrumentation of such grids, so-called pseudo- measurements have to be applied at nodes with missing information in order to enable observability of the network. Pseudo-measurements are typically derived from historical data and are known be error prone. Therefore, the basic idea of the NLO is the treatment of the (unknown) error of the pseudo-measurements as system states, and their estimation by means of Kalman ﬁltering prior to the actual estimation of the grid characteristics. In this way the reliability and accuracy of the state estimation can be improved signiﬁcantly, provided an appropriate dynamic model for the pseudo-measurement errors is available.

The main sources of uncertainty in the application of the NLO are the measurements of voltage and electrical power. In addition, some not precisely known network parameters, such as line impedances of some lines, can be sources of un- certainty. Application of the NLO thus requires determining a GUM-compliant uncertainty evaluation for the extended Kalman ﬁlter in the case of an uncer- tain state-space model. It was shown that the covariance matrix produced by the extended Kalman ﬁlter corresponds to the result of GUM linearized uncertainty propagation. However, the extended Kalman ﬁlter is known to suer from linearization errors. A GUM Monte Carlo method for uncertainty propagation with the NLO can thus mitigate the eect of linearization errors only to a certain extent.
Research on Quasi-δ temperature pulse dynamic calibration technology of thermocouple sensor
Yanfeng Li, North University of China
Because of the shortage of the working frequency bandwidth of thermocouple, there is the dynamic measurement error in the field of transient temperature measurement. Therefore, the dynamic calibration of the thermocouple shuold be done, and the dynamic characteristics should be analyzed before measurement. In this paper, the Quasi-δ dynamic calibration system for the contact temperature sensors was built by Quasi-δ dynamic calibration theory.

The ideal impulse function cannot be achieved in physical; commonly we replace it with narrow pulse (Quasi-δ) signal. The frequency spectrum of Quasi-δ function is a constant from zero to certain frequency. There are four Quasi-δ pulse signals with different shapes and different pulse width and same amplitude in Fig. 1. Fig. 2 shows the normalized spectrums diagram of the four signals. The Figs. 1 and 2 show that frequency spectrum of Quasi-δ pulse signal is associated with the pulse width, and the signal waveform has little influence on frequency spectrum. The narrower the pulse width is, the longer the straight section is, the higher the calibration frequency.
Posters
Dynamic Pressure Measurement System at UME
Yasin Durgut, TUBITAK/UME
In dynamic pressure measurement phenomena, dynamic pressure calibration of the measurement chain including pressure sensor, signal conditioning amplifier and data acquisition part is required. A drop mass system which is used for the dynamic calibration in hydraulic media was designed and developed in TÜBİTAK UME, National Metrology Institute of Turkey. This study presents a research study and measurement results on the dynamic calibration of pressure transducers by using newly developed system.
Primary standard for dynamic pressures in the range 20 MPa to 500 MPa
Richard Högström, MIKES
Dynamic pressure measurements are important in many fields of industry, such as combustion engines, ballistics and turbomachinery. However, the accuracy of dynamic pressure sensors is not well known, because there doesn’t exist an internationally recognized primary standard for dynamic pressure. At the moment traceability is achieved by reference to static pressure standards. Because dynamic and static pressure characteristics of transducers may differ significantly from each other, it is vital that these transducers are calibrated against dynamic pressure standards.

In this paper we present the development of a primary standard for dynamic pressures based on the dropping weight method. In this method, a weight is dropped on a piston which compresses glycerol inside the measurement chamber of the piston cylinder assembly generating a pressure pulse. Traceability to SI- units is realized through interferometric measurement of the acceleration of the dropping weight during impact, the effective area of the piston-cylinder assembly and the mass of the accelerating weight.

Based on experimental validation and uncertainty evaluation of the generated pressure, the developed primary standard is able to provide traceability for dynamic pressures measurements in the range from 20 MPa to 500 MPa with a typical expanded uncertainty (k = 2) of approx. 1,5 %. The operation of the measurement standard is demonstrated by calibrating two types of commercial dynamic pressure sensors. As a final step, an inter-comparison of dynamic pressure standards will be arranged in order to achieve international recognition as a primary standard for dynamic pressure.
A dynamic state-estimation method for LV and MV electrical grids
Guosong Lin, Physikalisch-Technische Bundesanstalt
Due to the increasing number of decentralized generation units on the distribution level, the problem of dissymmetrical loads and knowing the exact status of the grid has become of more interest during the past few years.

On the transmission grid level of symmetrical electric power systems, state estimation is well established in practice. Many methods proposed aim at adapting the static state estimation methods used on the transmission grid level to the circumstances on the distribution level (three-phase models, unbalanced conditions, radial topologies) and to replace in one way or another the missing measurements by forecasts based on historical data or knowledge about controller set points in the grid. To these forecasts, also called pseudo-measurements, then a large uncertainty is assigned, while real measurements in comparison have a rather low uncertainty. Another method for determining the grid state of a medium voltage electrical power grid with incomplete measurements is proposed. It is based on estimating the vector of active and reactive power through voltage magnitude and angle measurements with an Iterated Extended Kalman Filter using a dynamic model of the grid. Through rough forecasts of load and generation data, it is then possible to get a voltage magnitude and angle estimate even for buses without any measurement. In contrast to previous approaches, the here proposed method does not rely on voltage angle measurements. Instead, the estimation method estimates nodal active and reactive power at all nodes from measurements of nodal power, power-from and to nodes, and nodal voltage magnitude measurements. The proposed dynamic estimation method is shown to work for single phase networks as well as three- phase networks under unbalanced load.
Study on sensitivity to leakage currents of the voltage divider with autocalibration
Jerzy Nabielec, AGH-University of Science and Technology, Kraków , Poland
The problem of high voltage measurements in power grid will be discussed. The range of measured voltage is up to several hundred kV. In such a system voltage reduction is evident. Voltage transformers or capacitive, resistive or inductive dividers usually do this. Their metrological parameters, and in particular the k division ratio, are sensitive to environmental factors, ageing, the load type and its value. Otherwise, the use of increasing numbers of power electronics devices causes noises in the power grid. There are numerous harmonics in the measured voltage, that why the ratio k should be defined as a complex number whose value depends on the frequency of the harmonics it refers to. Without a doubt, the ratio k, in general is not a real number. In the nearest future voltage measurement will need not only the effective voltage value, but also the analysis of the harmonics of the measured voltage, including the relationship between their phase angles. Unfortunately, contemporary measurement methods and regulations refer only to measuring the True RMS of the measured voltage and the ratio k is treated as a real number. Presented problem, voltage measurement is performed by measurement method called 'blind method'. This method gives the possibility of determining the ratio k as the complex value. Moreover, the main advantage of the method is autocallibrations. It refers to the ability of a measurement system to identify its parameters where and when it is operating ("in situ"), using an unknown measured signal as the only excitation of the identification procedure. This method can be implemented in the measurement system with different structures. These structures have been investigated in theory and through simulation studies as well as verified in laboratory for several years . They are indyvidual idea of author (J.N) and are protected by number of patents (e.g. US 9,331,663 B2, EP 2745121 B1) . One structure of the conditioning circuit has a specific property and it is therefore under intensive investigation. It has been turned out that result of autocallibration is insensitive to the harmful influence of leakage currents in one node of the circuit. The reaserch results are the basis for determining the easier method of shielding the other nodes of the conditioning circuit, protecting them from leakage currents that may flow between the components forced by a high voltage occurring between these components. Presented measurement method and a system implementing it can be a basis for setting a new standard defines a way to carry out the measurement of high and medium voltage containing numerous harmonics, the result of which takes into account both amplitude and phase angles.
Applications and calibration of pencil probes
Oğuzhan Küçük, TUBITAK / SAGE
Pencil type probe sensors are designed and manufactured in order to measure air blast and shock waves caused by explosions. Basically, most of explosions are observed in defense area. In our institute pencil type probes are used in research and development activities in on-site tests in different projects. As a result of frequent usage of pencil probes, test engineers want to be sure if probes are in good condition and operate in a correct way and produce accurate results. For such purpose, for the check and calibration of pencil probes a homemade method was improved. This study presents a research study and measurement results on the applications of pencil type probe sensors. Additionally, the study reveals calibration facility of such sensors by using newly home developed method.
Main classes of electromechanical transducers – Electrodynamical vs. Electromagnetical
Dan Stefanescu, Romanian Measurement Society
Among the 12 measuring methods of mechanic quantities by electric means we make an attempt to compare electrodynamic with electromagnetic ones, starting from a particular example, such as Magnetic or Electrodynamic Force, that US Patent subclass 335/195 places together under the same title.

Certain authors use interchangeably the two words having the same “root”, but their fundamental difference is given by the way of inducing voltages: by moving or, respectively, by transformation.

A current flow in a magnetic field generates a force F, which is proportional to the magnetic induction B, the current I and the path length l (F = B I l). In electromagnetic weighing systems an applied mass generates a force under the influence of gravity. The conversion from a force to a current is not achievable. This leads to a compensation principle where the force due to the mass is compensated by a counter force so that the difference between the two forces is zero. The current used to achieve the equilibrium is proportional to the force. This is a dynamic system and the principle is often called electrodynamic force compensation
Evaluation of uncertainty of the results of dynamic measurements, conditioned the limited properties used the measuring instrument
Aleksander Vasilewskyi, Vinnytsia National Technical University
Proposed the spectral of method to assessing the dynamic uncertainty of measurement devices which allows to investigate the accuracy of changes in the dynamic operation conditions in the frequency domain, estimate the amplitude dynamic uncertainty based on frequency characteristic and the spectral function of the input signal.
Uncertainty of identification parameters of the dynamic object by Monte Carlo method
Zygmunt Warsza, PIAP
On the example of dynamic object the accuracy of identification of internal parameters of the model using two Monte Carlo (MC) methods is considered. The identification is based on the results of measurements of available externally, dependent on frequency or time, parameters of this object. The measured parameters and identified parameters are usually linked by a system of nonlinear relationships and their analytical solution is either very troublesome or even non-existent. As an example, parameters of the 4-element equivalent RC circuits has been identified. Identification is based on of simulated measurements of components of equivalent input impedance AC or transmittance at several frequencies. The identification was carried out using single and multiple iterative MC method. With both MC methods the distributions of identified parameters are received. From the received distributions of searched parameters accuracy of their identification is estimated. The accuracy of identification of each internal parameter depends on their level of observability from object terminals. The single MC method gives not enough satisfactory results. Analysis of the results of the identified parameters of above model of AC circuit has shown that the MC iterative method is sufficiently fast and accurate enough to be recommended for the wider use in practice, but there are also some limitations for second order objects with low damping.

In continuation of our work we would like to consider together the measurement uncertainties and identification errors.
Primary complex-valued hydrophone calibration using broadband pulse excitation
Martin Weber, Physikalisch-Technische BundesanstaltN
Membrane hydrophones are used as a transfer standard for the ultrasonic pressure in water. They require regular primary calibration against an acoustical field with a known pressure. In the discussed realization the surface displacement under excitation of the ultrasonic field is characterized with a high frequency laser vibrometer to determine the acoustic pressure. The use of this vibrometer enables the application of short nonlinearly distorted pulses with broad frequency spectra to perform the calibration under dynamic conditions.

By comparing the hydrophone output signal against the ultrasonic pressure, the frequency response of the hydrophone is calculated as a complex-valued function, usually expressed by amplitude and phase responses. Accordingly, the associated uncertainties need to be determined as uncertainties for complex quantities. In this contribution the calibration procedure including the different necessary correction factors as well as the uncertainty budget for a typical calibration example will be presented.
Research on dynamic compensation technology of thermocouple sensor
Zhijie Zhang, North University of China
In the field of temperature measurement, thermocouple sensor is widely applied. Because of the thermal inertia of thermocouple, there is the dynamic measurement error in transient temperature measurement. At present, there are two main methods to improve the dynamic characteristics of thermocouple. One method is to reduce the volume and thermal capacity of the thermocouple junction; another method is to establish the dynamic compensation filter which is used to widen the working frequency bandwidth. In this paper, the inverse modeling method based on quantum-behaved particle swarm optimization (QPSO) algorithm was proposed to establish the compensation filter model.