Publications & talks

Modeling the dynamics of the flow rate system is challenged by the nonlinear behavior and the noisy measurement data. Accurate models require a comprehensive understanding of fluid mechanics, as well as knowledge of all instruments in the measurement chain. This study presents a black-box optimization approach to develop a nominal Fractional-Order (FO) model of a laboratory-scale flow system. The model was constructed by repeatedly solving an optimization problem using preprocessed experimental data and averaging the resulting optimal parameters. The nominal FO model was then validated against unseen, unprocessed measurement data to assess its robustness. The parameter sensitivity of the proposed model was analyzed by introducing +10% and +20% perturbations in each parameter individually. Error analysis evidences that root mean squared, mean absolute, and mean absolute percentage errors with the proposed model have reduced to 9.3%, 5.1%, and 5.3%, respectively, compared to those integer-order models. Furthermore, residual-based distribution analysis confirms the robustness of the approach, with residuals tightly concentrated around the lowest values. Although the FO model incurs a higher computational cost during optimization, it was significantly reduced using an online optimizer. The proposed model demonstrates superior robustness and accuracy, making it a compelling choice for precise modeling.

Accurately characterising datasets is crucial for effective statistical modelling, particularly when analysing Global Navigation Satellite System (GNSS) data. While traditional approaches often assume a Gaussian distribution, real-world GNSS datasets frequently exhibit heavy-tailed and skewed properties, prompting the need to explore alternative statistical models. The study examines the suitability of non-Gaussian distributions, specifically the Laplace, skew-normal, skew-t, and generalised hyperbolic (GH) distributions, for modelling GNSS data obtained from a stationary receiver. Using empirical GNSS datasets, we estimate parameters within confidence intervals (CIs) through weighted maximum likelihood estimation (WMLE). Model performance is assessed using log-likelihood analysis, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and root mean squared error (RMSE). Our comparative analysis shows that heavy-tailed and skewed distributions, particularly those offering greater flexibility in capturing extreme deviations, consistently outperform the conventional normal distribution. Among the non-Gaussian models considered, the GH distribution provides the best overall performance. These results emphasise the importance of selecting appropriate statistical models to improve uncertainty quantification in GNSS-based measurements.

Air quality measurements conducted using unmanned aerial vehicles offer researchers opportunities that were previously difficult to achieve. An increasing number of publications on this topic are appearing in the literature. However, the popularity of low-cost sensors is often associated with their limited accuracy and sensitivity to environmental changes. This work demonstrates that CO2 sensors can accurately indicate the actual concentration of this gas in the air, provided that the influence of temperature is considered.

Regulated flow systems exhibit a variable dynamic behavior when subjected to distinct inputs. The significant non-linear behavior of the system at low inputs and the difference in the output pattern for the increase and decrease in flow pose challenges in modeling. One way is to identify separate sets of parameters for each input-output data set and develop distinct models. However, this approach is computationally expensive when designing a single controller covering the whole input range. To overcome the said limitation, we used a Principal Component Analysis (PCA) based estimation technique. The developed Linear Parameter Varying (LPV) dynamic model describes real measurement values of a laboratory flow system. The data treatment consists of (1) an automated input-output data acquisition, (2) 3rd-order model estimation from measured data, (3) the reduction of the dynamic parameters using PCA, and (4) the development of a reduced LPV model for the entire input range. The LPV model presents its output response comparable to the experimentally taken flow rates. The proposed modeling technique can help design a single controller sufficient to achieve the desired output applicable in the whole measuring range. The effectiveness of our approach suggests its use for synthesizing an LPV controller for flow systems.

Accurate positioning obtained from the Global Navigation Satellite System (GNSS) is crucial for many applications; however, environmental and instrumental factors, such as satellite geometry, signal multipath, and atmospheric delays, often degrade its accuracy. Traditional uncertainty quantification and filtering methods, such as the Kalman Filter (KF), assume that the measurement noise follows a Gaussian distribution. In practice, real-world GNSS data often violate this assumption, showing skewness, heavy tails, and outliers that distort the estimates and reduce the accuracy. This study systematically evaluates the impact of non-Gaussian noise on GNSS positioning accuracy and introduces a unified framework that integrates robust statistical methods and nonlinear filtering. Specifically, we compared the performance of the KF, Median Absolute Deviation (MAD), and Particle Filter (PF) on stationary GNSS data. The evaluation used comprehensive accuracy and uncertainty diagnostics, including the root mean square error (RMSE), probable circular error (CEP), estimated position error at 95% (R95), covariance analysis, and nonparametric bootstrapping. The results demonstrate that Gaussian-based models fail under heavy-tailed noise, whereas MAD and PF achieve superior reliability by suppressing outlier influence and capturing complex error distributions. The proposed framework advances GNSS uncertainty quantification by bridging robust statistics and nonlinear filtering. It offers a statistically sound and practical approach for real-world environments in which non-Gaussian noise is prevalent.

In statistical analysis, evaluating the normality of large datasets is crucial for validating parametric tests, particularly in areas such as Global Navigation Satellite System (GNSS) measurements, where data often exhibit non-normal characteristics resulting from their variability and errors. This research aims to transform the measured GNSS data and to assess the effectiveness of transformation methods in achieving normality. Techniques like logarithmic, quantile and rank-based Inverse Normal Transformation (INT) were evaluated using visual methods (histograms, Q-Q plots), descriptive statistics (skewness, kurtosis) and statistical tests, including Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Lilliefors (LF), D’Agostino K-squared (DA), Shapiro-Wilk (SW), Jarque-Bera (JB), Cramérvon Mises (CM), and Pearson Chi-square (Chi2) tests. The sensitivity of these tests to deviations from normality was assessed through the Receiver Operating Characteristic (ROC) analysis and the Area Under the Curve (AUC) values at a significance level of 0.1, using Monte Carlo (MC) simulations across the varying sample sizes. The results showed that untransformed latitude data consistently failed normality tests, while transformed data displayed normal characteristics. The rank-based INT showed superior effectiveness, influenced by the original distribution and characteristics of the dataset. The findings underscore the importance of tailored transformations in large-scale data applications, enhancing the accuracy and applicability of parametric statistical methods in geospatial and other industrial domains.

Due to additional parameters and similar structure with PID, fraction-order (FO) PID controllers offer tuning flexibility for better performance. More degree of freedom poses challenges in applying simple tuning rules for FO-PID controllers. The dilemma of practical realization of the FO controllers further limits their benefits. This work proposes simple tuning rules for the parameters of the FO-PI controllers by following the frequency-domain methods. We apply three different approximation approaches to realize the controller implementation and validate its performance on a simulation example. Comparison with a FO-PID controller evidences the effectiveness of the proposed approach

Electromyography (EMG) signals, crucial for neuromuscular assessment, are frequently corrupted by noise, impairing signal fidelity and subsequent analysis across diverse applications. Conventional filters often inadequately address non-stationary noise or introduce signal distortion. This paper introduces an advanced deep learning framework for EMG denoising, centred on a U-Net-inspired convolutional autoencoder with integrated residual blocks and skip connections. Training utilised synthetic EMG data, closely emulating physiological frequency bands and burst dynamics, subsequently corrupted by a comprehensive noise model encompassing electrode, crosstalk, electronic, drift, and contact artefacts. Training was guided by a custom loss function that combined weighted mean squared error (MSE) with signal-to-noise ratio (SNR). The proposed autoencoder achieved substantial improvements, SNR increased from -0.95 dB (noisy) to 14.64 dB (denoised), and MSE was drastically reduced from 0.001493 V2 to 0.000041 V2 on the test dataset. Qualitative analysis confirmed effective noise suppression while retaining crucial EMG burst characteristics. This advanced framework offers a promising solution for robust restoration of EMG signals in practical settings.

Recent review articles highlight an exponential rise in publications on Digital Twin (DT) technology. Despite its recognised potential, DTs have yet to achieve widespread practical use. Following a presentation of the state of the art and an original conceptual diagram illustrating the technology, this work presents the key factors contributing to the gap between conception and implementation. Using experimental data from a laboratory water system and a reliability-based perspective, this analysis examines the practical limitations of DT application. The findings indicate that broader use of DTs depends on the technological maturity and reliability of all system components, which still require further development.

This study presents the application of an Internet of Things (IoT)-based system for environmental data acquisition in a scientific research setting. The system comprises a network of 12 sensor nodes and a central server. Each node is built around a D1 Mini module, which collects data from an attached sensor and transmits the measurements to the server via web requests. A server-side script processes these requests and stores the data in structured text files. The collected data can be analysed either in real time during the experiment or retrospectively. To ensure durability and reliability in outdoor conditions, all sensor nodes are enclosed in protective housings. This work highlights the practicality, cost-effectiveness, and efficiency of a custom-designed, application-specific IoT measurement system, demonstrating its suitability for rapid deployment in environmental monitoring applications.

Train on-board system calculates its speed based on values provided by several sensors. This work deals with a hypothetical case where the speed is estimated throughout 60 seconds during braking. Information from five sensors characterized by different error models is fused in three ways: mean, median, and the weighted method. Although the weighted method is the most complex, it exhibits the best fit to the reference value.

Understanding dataset characterisation is fundamental to achieving accurate statis- tical modelling, particularly in the context of Global Navigation Satellite System (GNSS) data analysis. GNSS data exhibit heavy-tailed and skewed distributions, prompting this study to eval- uate non-Gaussian models (Cauchy, Student’s t, lognormal, skew-normal) in modelling GNSS data collected from a stationary receiver. This study uses maximum likelihood estimation for parameter estimation with a confidence i nterval. I t evaluates t he m odel’s p erformance using log-likelihood analysis, the Akaike Information Criterion, the Bayesian Information Criterion, and the Root Mean Squared Error. The comparative assessment of these models highlights that lognormal and skew-normal outperform in capturing extreme deviations and provide a better fit than the normal distribution. These findings underscore the importance of selecting appropriate statistical models to enhance uncertainty quantification in GNSS-based measurements.

The availability of two additional tunable parameters compared with Proportional Integral Derivative (PID) controllers makes it possible to incorporate fractional-order (FO) integral/derivative actions. The selection of the optimization algorithm and objective function is important for tuning the fractional-order PID controller. This paper presents the formulation of the FOPID controller design as an optimization problem and its solution using four built-in algorithms in MATLAB. Each algorithm solves the optimization by minimizing two cost functions resulting eight sets of controller parameters. To overcome the sensitivity of algorithms to the initial and boundary values of the parameters, we considered nine different initial and boundary conditions. The proposed method considers the minimum of the optimal values obtained in each case. This provides globally-optimal FOPID controllers. To validate its efficiency, the proposed method uses a Twin Rotor Aerodynamic System (TRAS) as an example. Comparison with a nonlinear approach shows that the proposed approach ensures tracking with minimal and smooth control efforts.

Particulate matter (PM) suspended in the air significantly impacts human health. Those of anthropogenic origin are particularly hazardous. Poland is one of the countries where the air quality during the heating season is the worst in Europe. Air quality in small towns and villages far from state monitoring stations is often much worse than in larger cities where they are located. Their residents inhale the air containing smoke produced mainly by coal-fired stoves. In the frame of this project, an air quality monitoring network was built. It comprises low-cost PMS7003 PM sensors and ESP8266 microcontrollers with integrated Wi-Fi communication modules. This article presents research results on the influence of the PM sensor location on their indications. It has been shown that the indications from sensors several dozen meters away from each other can differ by up to tenfold, depending on weather conditions and the source of smoke. Therefore, measurements performed by a network of sensors, even of worse quality, are much more representative than those conducted in one spot. The results also indicated the method of detecting a sudden increase in air pollutants. In the case of smokiness, the difference between the mean and median indications of the PM sensor increases even up to 400 µg/m3 over a 5 min time window. Information from this comparison suggests a sudden deterioration in air quality and can allow for quick intervention to protect people’s health. This method can be used in protection systems where fast detection of anomalies is necessary.

In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object.

We know that least Lp-norm filters, processing a one-dimensional signal within a time window, are suitable for attenuation of impulses. This article proposes a new analogue filter with exponentially weighted old samples, which is a generalization of the first-order low-pass filter. The obtained formula describing the output signal is presented in an implicit form. A simple but always convergent algorithm facilitates the approximation of the signal. Conducted simulations show properties of a set of the analogue filters with different values of p in the range of 1 to 2, covering step, ramp, and sinusoidal responses, as well as the ability to attenuate random noises, including stable distributions. The results prove that the elaborated filters achieve steady states faster than the typical low-pass filter and are particularly useful in the suppression of impulses. This property makes it possible that such a filter is perfectly adequate as an input filter of measurement transducers.

The growing popularity of ESP boards has led to the development of several programming platforms. They allow users to develop applications for ESP modules in different programming languages, such as C++, C, Lua, MicroPython, or using AT Commands. Each of them is very specific and has different advantages. The programming style, efficiency, speed of execution, level of advancement, or memory usage will differ from one language to another. Users mostly base their choice depending on their programming skills and goals of the planned projects. The aim of this work is to determine, which language is the best suitable for a particular user for a particular type of project. We have described and compared the mentioned languages. We have prepared test tasks to indicate quantified values. There is no common rule because each of the languages is intended for a different kind of user. While one of the languages is slower but simpler in usage for a beginner, the other one requires broad knowledge but offers availability to develop very complex applications.

Fractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approximation. This article shows that the chosen model influences the dynamic properties of signals. First, we calculated symbolically the steady-state values of an FO inertia using three variants of the Oustaloup filter approximation. Then, we showed how the models influence the Nyquist plots in the frequency domain. The unit step responses calculated using different models also have different plots. An example of FO control system evidenced different trajectories dependent on applied models. We concluded that publicized parameters of FO models should also consist of the name of the model used in calculations in order to correctly reproduce described phenomena. For this reason, the inappropriate use of FO models may lead to drawing incorrect conclusions about the described system.

The purpose of an automatic control is to provide the best quality of the output signal of a controlled object. This quality is dependent on the type and tuning parameters of the used controller and on the properties of a transducer measuring the output signal. In this work, it was considered how the imperfections of the transducer propagate by the fractional-order (FO) control system. It was revealed that the assumed approximation method of FO derivation changes the trajectory of the output signal and also has an influence on the steady-state value. In turn, the measurement uncertainty estimation should take into account the analysis of the occurrence of oscillations, arising from drifts of imperfect components, that may exceed the permissible errors of the measuring transducer.

Glass pH electrodes are still successfully applied in the chemical and environmental industry. During their long-term use, periodic calibration is required to maintain the required accuracy of measurements because the parameters of the electrodes change over time. This work presents an aging of 11 pH electrodes within approximately 600 days in tap water. During this period, potentials of all electrodes in five buffer solutions were measured 44 times. This allowed determining the aging models of the electrodes. Models in other mediums might be different. Changes in slope, standard potential, hysteresis, and linearity of the characteristics were the objects of observations. A method for predicting electrode parameters is proposed. Furthermore, the procedure for estimating the uncertainty of pH measurements considering the aging of the electrodes is described. As a result of this work, a model of the aging process of pH electrodes in tap water can be constructed and subsequently, the measurement accuracy in the periods between calibrations can be improved.

Evaluation of measurement uncertainties covers uncertainty propagation from sources to a measured quantity. Phenomena taking place inside measuring transducers are typically considered applying Type B evaluation. It is evidenced in this work, that transducers included in a closed-loop control system should be treated in a different way because their uncertainty sources propagate through the dynamic system and change their limits of variabilities. Depending on frequencies, the limits may be either similar or lower or even higher. An especially dangerous case takes place when the variability at the output of the plant is greater than at the output of the transducer. In this work, such cases are presented and discussed.

An assessment of measurement uncertainty is a task, which has to be the final step of every chemical assay. Apart from a commonly applied typical assessment method, Monte Carlo (MC) simulations may be used. The simulations are frequently performed by a computer program, which has to be written, and therefore some programming skills are required. It is also possible to use a commonly known spreadsheet and perform such simulations without writing any code. Commercial programs dedicated for the purpose are also available. In order to show the advantages and disadvantages of the ways of uncertainty evaluation, i.e., the typical method, the MC method implemented in a program and in a spreadsheet, and commercial programs, a case of pH measurement after two-point calibration is considered in this article. The ways differ in the required mathematical transformations, degrees of software usage, the time spent for the uncertainty calculations, and cost of software. Since analysts may have different mathematical and coding skills and practice, it is impossible to point out the best way of uncertainty assessment—all of them are just as good and give comparable assessments.

In this article, a project of an unmanned aerial vehicle (UAV) equipped with a measurement head designed for monitoring of air pollution is presented. The head contains modern sensors selective to the most important components of air in view of environmental pollution. Measurement data are acquired locally as well as transmitted wirelessly to a ground station. The UAV may be programmed to a particular measurement missions. The ground station dispose of a software for flight control and for visualisation of measurement results on-line.

This paper describes a way of determining selected water parameters using a prototype of a remote-controlled catamaran. The remote controlling allows to steer the boat and to manage the measurement process from the shore. It is possible to monitor the water parameters online as well as to store them and analyze them afterwards. The measured parameters are determined mainly using potentiometric methods and include several ion concentrations. The system is orientated towards monitoring breeding ponds or other similar surface waters. The mechanical construction of the catamaran, its electronic circuits and implemented software are described in detail in the paper. Conclusions obtained from preliminary tests are also included. The described construction allows analysts to perform simple and inexpensive remote measurements or assessments of water quality and reduces the time of such analysis in comparison to traditional sampling.

Acoustic insulation of a device from the environment can be enhanced by appropriate control of its casing vibrations. The level of noise reduction obtained in such way is considered as the main point for evaluating the performance of the active control system, hence its appropriate measurement constitutes a vital issue. In this study, measurement uncertainty evaluation of the sound pressure level difference is presented. Three independent components of the Type A evaluated uncertainties are derived. Many sets of conducted experiments allow to estimate the components, while information read from the calibration certificate of the employed sound level meter allow to estimate the Type B components. Prepared uncertainty budgets show that the most contributing source is the location dependency. Recommendations for appropriate performance measurement of an active control system are stated basing on the obtained results.

The term “Internet of things,” despite the lack of commonly acceptable definition, is now often used, mainly for marketing purposes, by manufacturers of various types of equipment. This article shows how to understand this term based on the recommendations of the International Telecommunication Union (ITU), and gives properties of the discussed technology. Implementation of the technology to a pH measurement transmitter is also described and results of laboratory tests are presented.

According to recent findings, it is possible to computationally determine a measurement result (value and uncertainty), using a special measurement method, in which this uncertainty is less than that assessed directly from experiments using Type B evaluation. The method works well only if the quantity is additive and its uncertainty is constant, i.e. independent of the measurement value. In the paper, a generalisation is made that also allows for the application of similar reasoning to quantities with variable uncertainties. The generalisation is obtained thanks to the replacement of the least squares optimisation, used in the derivation of the first method, with the weighted least squares. Examples with models of quantities that have variable uncertainties are described to show circumstances where improvements are significant. It can be said that the method described always improves uncertainties of additive quantities, but the improvement is not always significant. Suggestions to obtain the best improvement are given according to the analysis performed. A real laboratory experiment of a resistance measurement, with its uncertainty dominated by current measurement, was conducted to show how the method works.

Parameters of a model describing a measurement process obtained during a calibration experiment allow one to calculate a measurement result, but a simple estimation of measurement uncertainties of the parameters is not sufficient to assess the uncertainty of the result. In this paper, an example of a pH measurement conducted using an ion-selective electrode is presented, in which the uncertainty is evaluated taking into consideration the existing correlation between the parameters of the electrode. The calculations apply either covariances or correlation coefficients that have to be computed additionally. The example presented in this paper illustrates that there are some problems with rounding of variables which, because of the existing very strong correlations, significantly changes the sought uncertainty. This approach is compared with other approaches, that is, usage of uncorrelated variables and Monte Carlo simulations that are described in an earlier work. It is concluded that the approach of uncertainty evaluation, in which covariances or correlation coefficients are explicitly calculated, is work-consuming and may cause significant discrepancies between correct and obtained assessments if some roundings or approximations are done, or if the correlation coefficient is obtained experimentally based on data including random errors.

The paper deals with the problem of ion activity determination for a mixture by means of ion-selective electrodes. Mathematical model of the analysed phenomenon is described by the Nicolsky-Eisenman equation, which relates activities of ions and ion-selective electrode potentials. The equation is strongly nonlinear and, especially in the case of multi-compound assays, the calculation of ion activities becomes a complex task. Application of multilayer perceptron artificial neural networks, which are known as universal approximators, can help to solve this problem. A new proposition of such network has been presented in the paper. The main difference in comparison with the previously proposed networks consists in the input set, which includes not only electrode potentials but also electrode parameters. The good network performance obtained during training has been confirmed by additional tests using measurement results and finally compared with the original as well as the simplified analytical model.

Determination of pH using a typical glass electrode requires prior calibration in order to determine the electrode parameters. Knowledge about uncertainties of the parameters is insufficient to calculate the uncertainty of measured pH because of existing correlation. In the paper, an example illustrating the problem is presented. Two ways of proper uncertainty assessment are suggested: (1) analytical with removing the correlated variables and (2) numerical using Monte Carlo simulations. The second one seems to be much less time-consuming and allows easier investigations of the uncertainty properties.

The paper deals with the problem of ion activity determination for a mixture by means of ion-selective electrodes. Mathematical model of the analysed phenomenon is described by the Nicolsky-Eisenman equation, which relates activities of ions and ion-selective electrode potentials. The equation is strongly nonlinear and, especially in the case of multi-compound assays, the calculation of ion activities becomes a complex task. Application of multilayer perceptron artificial neural networks, which are known as universal approximators, can help to solve this problem. A new proposition of such network has been presented in the paper. The main difference in comparison with the previously proposed networks consists in the input set, which includes not only electrode potentials but also electrode parameters. The good network performance obtained during training has been confirmed by additional tests using measurement results and finally compared with the original as well as the simplified analytical model.

Determination of pH using a typical glass electrode requires prior calibration in order to determine the electrode parameters. Knowledge about uncertainties of the parameters is insufficient to calculate the uncertainty of measured pH because of existing correlation. In the paper, an example illustrating the problem is presented. Two ways of proper uncertainty assessment are suggested: (1) analytical with removing the correlated variables and (2) numerical using Monte Carlo simulations. The second one seems to be much less time-consuming and allows easier investigations of the uncertainty properties.

A common technique applied during an assay is averaging several repeated measurements in order to obtain a more accurate result. This approach is suitable for most applications. However, in the case of impulsive disturbances which affect the measured object, averaging is not optimal. In the paper, the properties of impulsive disturbances are described and it is explained why averaging is suitable for Gaussian disturbances and unsuitable for impulse ones. The iteratively reweighted least squares method, popular among researchers dealing with signal processing, has been simplified, allowing analysts to use it easily, and it has been adopted to calculate a weighted mean which is more reliable. The properties of the weighted mean have been determined based on Monte Carlo simulations and an analytical signal obtained from an ion-selective electrode. The results shown that the most reliable results are obtained when the average is replaced by such weighted mean, which reduces to the median filtration---then, the obtained results are in some cases a bit worse but far less sensitive to impulses.

The commented article has introduced to metrology a new way of lowering the uncertainty assessed using Type B evaluation. The proposed method operates properly under some assumptions but unfortunately, the idea has been presented with some understatements and mistakes. The weak points are shown and discussed in this article.

This paper presents a research installation for developing flow measurements in open channel. A tracer technique is used where sodium chloride is applied as a tracer and a conductometric cell as a tracer sensor. Properties of the applied electrical measuring circuit, the ways of determining tracer transit time, flow rate and flow velocity are described. From conducted experiments, the expanded measurement uncertainty of flow rate is assessed as less then 6%.

In this paper a novel calibration procedure for the parameter determination of ion-selective electrodes used in an array is described. Commonly used procedures require a large number of standards to determine the parameters based on the Nicolsky–Eisenman model. The elaborated procedure reduces the number of standards to a minimum by using a standard containing a mixture of ions instead of a couple of pure standards. This paper presents a complete calibration procedure, which consists of designing the composition of the standards, parameter determination and verification of the calibration results. Comparison of the results obtained by the procedure presented with results obtained by the Two-Point Calibration and Separate Solution methods proves that the accuracies of both procedures are comparable. The outlined procedure can be applied in multicomponent analysers.

The response time of ion-selective electrodes (ISEs) is especially essential when measurements are performed for diluted solutions. The time needed to archive the steady-state E2 can be measured in minutes. The developed algorithm shorten the time significantly by using the estimated value of E2. The dynamic error is then reduced 2-6 times, depending on model applied to describe the dynamic properties of ISE, on disturbances and on correctness of choice of the dynamic parameters. Real measuring data used in tests prove that the best model applied to the prediction of E2 value is Rechnitz-Hameka model.

In the paper, the evaluation of uncertainty in concentration measurement based on the cause and effect diagram is presented. Two methods of evaluating the uncertainty of calibration parameters of ion-selective electrode are compared: the GUM method and the Monte Carlo method. Values obtained in examples are very similar. Small differences are visible for larger values of input data uncertainties. It is caused by the change of the probability distribution shape when the function is non-linear. The comparison covers the possibility of determination the final value and its uncertainty, the necessity of derivation of the parameters and sensitivity coefficients formulae, the possibility of analyzing the contributions, of making histograms and of taking into considerations nonlinearities. Using the Monte Carlo method, the concentration uncertainties are evaluated for example data.

Measured values of dynamic parameters of ion-selective electrodes are dependent i.a. on the research methods applied due to difficulties in the proper realization of the ion activity change at the electrode membrane. In the paper, the new measuring set-up, realizing the activity step, is presented. Two jets, controlled by the electric valves, through those solutions having different activities are flowed, are applied in the set-up. Basing on the results obtained experimentally, it can be stated that the activity change is enough rapid. Furthermore, the electric circuit is not opened during the change of the activities what is a drawback of some methods.

The relationship between the potential E of the ion-selective electrode and ion concentration c are presented in the paper – eqs. (1) – (5). The operations needed to prepare an activity standard, basing on eqs. (7) – (10), are listed and an example is given, haw to make it. Basing on eq. (11), linking concentration c, mass of salt m* and volume of solution V, the relative concentration uncertainty ur(c) is derived – eq. (12), and using a scale and non-ideal salt not having 100% content (cont) of substance of interest, the eq. (14) is obtained. After dilutions – eq. (15), concentration uncertainty changes – eq. (17). The next example is placed illustrating the change. The concentration uncertainties of standards obtained using multiple dilution method implemented on the automatic system SAWCEJS [5] are calculated in sec. 4.

The plot of ion-selective electrode's potential vs. ion concentration in a solution is non-linear and very complex. In the paper, a set-up is described which allows to determine the plot using multiple dilution method in an automatic way. The set-up is not expensive and the presence of experimenter in the laboratory is not necessary during the test of the electrode. Additionally, the system allows for simultaneous investigation of several electrodes.

Dynamic models of an ion-selective electrode are analysed in this article taking into account the independence of values of its dynamic parameters from the value and direction of activity change. Unfortunately, a complicated mathematical representation of a new model makes the model difficult to be applied in practice. Therefore, some simplifications are made constructing two semi-empirical models: 1) a model with the k parameter and 2) a model basing on two other models well-known from the literature. Verifications of the new models have been performed using the measuring set-up built in the Division of Measurement Systems at the Silesian University of Technology. Obtained results proved that the model with the k parameter completely fulfils the goal of the article − its dynamic parameters are dependent on the slightest degree of the kind of activity step.