Knowledge of the uncertainty of measurement of testing results is important when results have to be compared with limits and specifications. In the measurement of sound insulation following standards ISO 140-4 and 140-5 the uncertainty of the final magnitude is mainly associated to the average sound pressure levels L1 and L2 measured. However, the study of sound fields in enclosed spaces is very difficult: there are a wide variety of rooms with different sound fields depending on factors as volume, geometry and materials. A parameter what allows us to quantify the spatial variation of the sound pressure level is the standard deviation of the pressure levels measured at the different positions of the room. Based on the analysis of this parameter some results have been pointed out: we show examples on the influence of the microphone positions and the wall characteristics on the uncertainty of the final magnitudes mainly at the low frequencies regime. In this line, we propose a theoretical calculus of the standard deviation as a combined uncertainty of the standard deviation already proposed in the literature focused in the room geometry and the standard deviation associated to the wall vibrational field.
The object of the present study is to investigate the influence of damping uncertainty and statistical correlation on the dynamic response of structures with random damping parameters in the neighbourhood of a resonant frequency. A Non-Linear Statistical model (NLSM) is successfully demonstrated to predict the probabilistic response of an industrial building structure with correlated random damping. A practical computational technique to generate first and second-order sensitivity derivatives is presented and the validity of the predicted statistical moments is checked by traditional Monte Carlo simulation. Simulation results show the effectiveness of the NLSM to estimate uncertainty propagation in structural dynamics. In addition, it is demonstrated that the uncertainty in damping indeed influences the system response with the effects being more pronounced for lightly damped structures, higher variability and higher statistical correlation of damping parameters.
The objective of the submitted paper is to analyze the influence of the load on the calibration of micro-hardness and hardness testers. The results were validated by Measurement Systems Analysis (MSA), Analysis of Variance (ANOVA) and Z-score. The relationship between the load and micro-hardness in calibration of micro-hardness testers cannot be explained by Kick's Law (Meyer's index "n" is different from 2). The conditions of Kick's Law are satisfied at macro-hardness calibration, the values of "n" are close to 2, regardless of the applied load. The apparent micro-hardness increases with the increase of the load up to 30 g; the reverse indentation size effect (ISE) behavior is typical for this interval of the loads. The influence of the load on the measured micro-hardness is statistically significant for majority of calibrations.
The acoustic climate assessment needed for the selection of solutions (technical, legal and organisational), which will help to minimise the acoustic hazards in the analysed areas, is realised on the basis of acoustic maps. The reference computational algorithms, assigned to them, require very thorough preparation of input data for the considered noise source model representing - in the best possible way - the acoustic climate. These input data are burdened with certain uncertainties in this class of computational tasks. The uncertainties are related to the problem of selecting proper argument values (from the interval of their possible variability) for the modelled processes. This situation has a direct influence on the uncertainty of acoustic maps. The idea of applying the interval arithmetic for the assessment of acoustic models uncertainty is formulated in this paper. The computational formalism assigned to the interval arithmetic was discussed. The rules of interval estimations for the model solutions determining the sound level distribution around the analysed noise source - caused by possible errors in the input data - were presented. The application of this formalism was illustrated in uncertainty assessments of modelling acoustic influences of the railway noise linear source on the environment.
The multicriteria decision process consists of five main steps: definition of the optimisation problem, determination of the weight structure of the decision criteria, design of the evaluation matrix, selection of the optimal evaluation method and ranking of solutions. It is often difficult to obtain the optimal solution to a multicriterion problem. The main reason is the subjective element of the model – the weight functions of the decision criteria. Expert opinions are usually taken into account in their determination. The aim of this article is to present a novel method of minimizing the uncertainty of the weights of the decision criteria using Monte Carlo simulation and method of data reconciliation. The proposed method is illustrated by the example of multicriterion social effectiveness evaluation for electric power supply to a building using renewable energy sources.
This paper presents a robust control technique for small-scale unmanned helicopters to track predefined trajectories (velocities and heading) in the presence of bounded external disturbances. The controller design is based on the linearized state-space model of the helicopter. The multivariable dynamics of the helicopter is divided into two subsystems, longitudinallateral and heading-heave dynamics respectively. There is no strong coupling between these two subsystems and independent controllers are designed for each subsystem. The external disturbances and model mismatch in the longitudinal-lateral subsystem are present in all (matched and mismatched) channels. This model mismatch and external disturbances are estimated as lumped disturbances using extended disturbance observer and an extended disturbance observer based sliding mode controller is designed for it to counter the effect of these disturbances. In the case of heading-heave subsystem, external disturbances and model mismatch only occur in matched channels so a second order sliding mode controller is designed for it as it is insensitive to matched uncertainties. The control performance is successfully tested in Simulink.
The aim of the article is to present the issue of risk and related management methods, with a particular emphasis on the conditions of investment in energy infrastructure. The work consists of two main parts; the first one is the theoretical analysis of the issue, while the second discusses the application of analysis methods on the example of the investment in an agricultural biogas plant. The article presents the definitions related to the investment risk and its management, with a particular emphasis on the distinction between the risk and uncertainty. In addition, the main risk groups of the energy sector were subjected to an analysis. Then, the basic systematics and the division into particular risk groups were presented and the impact of the diversification of investments in the portfolio on the general level of risk was determined. The sources of uncertainty were discussed with particular attention to the categories of energy investments. The next part of the article presents risk mitigation methods that are part of the integrated risk management process and describes the basic methods supporting the quantification of the risk level and its effects – including the Monte Carlo (MC), Value at risk (VaR), and other methods. Finally, the paper presents the possible application of the methods presented in the theoretical part. The investment in agricultural biogas plant, due to the predictable operation accompanied by an extremely complicated and long-term investment process, was the subject of the analysis. An example of “large drawing analysis” was presented, followed by a Monte Carlo simulation and a VaR value determination. The presented study allows for determining the risk in the case of deviation of financial flows from the assumed values in particular periods and helps in determining the effects of such deviations. The conducted analysis indicates a low investment risk and suggests the ease of similar calculations for other investments.
Referring to the Guide to the Expression of Uncertainty in Measurement (GUM), the paper proposes a theoretical contribution to assess the uncertainty interval, with relative confidence level, in the case of n successive observations. The approach is based on the Chi-square and Fisher distributions and the validity is proved by a numerical example. For a more detailed study of the uncertainty evaluation, a model for the process variability has been also developed.
The issues connected with the complex design of various facilities, including up-to-date boiler equipment as well as the ways of organizing the space around them, are the reasons why there is often a lack of room for mounting a flowmeter in accordance with the recommendations of manufacturers. In most cases the problem is associated with ensuring sufficient lengths of straight pipe leading into and out of a flowmeter. When this condition cannot be fulfilled, the uncertainty of measurement increases above the value guaranteed by the manufacturer of the flowmeter. This sort of operation problem has encouraged the authors of this paper to undertake research aimed at the analysis of applicability of averaging Pitot tubes in the areas of flow disturbance.
The paper deals with the problem of bias randomization in evaluation of the measuring instrument capability. The bias plays a significant role in assessment of the measuring instrument quality. Because the measurement uncertainty is a comfortable parameter for evaluation in metrology, the bias may be treated as a component of the uncertainty associated with the measuring instrument. The basic method for calculation of the uncertainty in modern metrology is propagation of distributions. Any component of the uncertainty budget should be expressed as a distribution. Usually, in the case of a systematic effect being a bias, the rectangular distribution is assumed. In the paper an alternative randomization method using the Flatten-Gaussian distribution is proposed.
The main aim of the study was to determine the goodness of fit between the relaxation function described with a rheological model and the real (experimental) relaxation curves obtained for digital materials fabricated with a Connex 350 printer using the PolyJet additive manufacturing technology. The study involved estimating the uncertainty of approximation of the parameters of the theoretical relaxation curve. The knowledge of digital materials is not yet sufficient; their properties are not so well-known as those of metallic alloys or plastics used as structural materials. Intensive research is thus required to find out more about their behavior in various conditions. From the calculation results, i.e. the uncertainty of approximation of the relaxation function parameters, it is evident that the experimental curves coincide with the curves obtained by means of the solid model when the approximation uncertainty is taken into account. This suggests that the assumed solid model is well-suited to describe a real material.
The paper presents a new method for simultaneous tracking of varying grid impedance and its uncertainty bounds. Impedance tracking consists of two stages. In the first stage, the actual noise estimate is obtained from least squares (LS) residua. In the second stage, the noise covariance matrix is approximated with the use of residual information. Then weighted least squares (WLS) method is applied in order to estimate impedance and background voltage. Finally uncertainty bounds for impedance estimation are computed. The robustness of the method has been verified using simulated signals. The proposed method has been compared to sliding LS. The results have shown, that the method performs much better than the LS for all considered cases, even in the presence of significant background voltage variations.
The aim of this study was to estimate the measurement uncertainty for a material produced by additive manufacturing. The material investigated was FullCure 720 photocured resin, which was applied to fabricate tensile specimens with a Connex 350 3D printer based on PolyJet technology. The tensile strength of the specimens established through static tensile testing was used to determine the measurement uncertainty. There is a need for extensive research into the performance of model materials obtained via 3D printing as they have not been studied sufficiently like metal alloys or plastics, the most common structural materials. In this analysis, the measurement uncertainty was estimated using a larger number of samples than usual, i.e., thirty instead of typical ten. The results can be very useful to engineers who design models and finished products using this material. The investigations also show how wide the scatter of results is.
The paper concerns the problem of treatment of the systematic effect as a part of the coverage interval associated with the measurement result. In this case the known systematic effect is not corrected for but instead is treated as an uncertainty component. This effect is characterized by two components: systematic and random. The systematic component is estimated by the bias and the random component is estimated by the uncertainty associated with the bias. Taking into consideration these two components, a random variable can be created with zero expectation and standard deviation calculated by randomizing the systematic effect. The method of randomization of the systematic effect is based on a flatten-Gaussian distribution. The standard uncertainty, being the basic parameter of the systematic effect, may be calculated with a simple mathematical formula. The presented evaluation of uncertainty is more rational than those with the use of other methods. It is useful in practical metrological applications.
This paper proposes an inverse method to obtain accurate measurements of the transient temperature of fluid. A method for unit step and linear rise of temperature is presented. For this purpose, the thermometer housing is modelled as a full cylindrical element (with no inner hole), divided into four control volumes. Using the control volume method, the heat balance equations can be written for each of the nodes for each of the control volumes. Thus, for a known temperature in the middle of the cylindrical element, the distribution of temperature in three nodes and heat flux at the outer surface were obtained. For a known value of the heat transfer coefficient the temperature of the fluid can be calculated using the boundary condition. Additionally, results of experimental research are presented. The research was carried out during the start-up of an experimental installation, which comprises: a steam generator unit, an installation for boiler feed water treatment, a tray-type deaerator, a blow down flashvessel for heat recovery, a steam pressure reduction station, a boiler control system and a steam header made of martensitic high alloy P91 steel. Based on temperature measurements made in the steam header using the inverse method, accurate measurements of the transient temperature of the steam were obtained. The results of the calculations are compared with the real temperature of the steam, which can be determined for a known pressure and enthalpy.
The paper presents analysis of optimisation results of power system stabilizer (PSS) parameters when taking into account the uncertainty of mathematical model parameters of the power system (PS) elements. The Pareto optimisation was used for optimisation of the system stabilizer parameters. Parameters of five stabilizers of PSS3B type were determined in optimisation process with use of a genetic algorithm with tournament selection. The results obtained were assessed from the point of view of selecting the criterion function. The analysis of influence of the parameter uncertainty on the quality of the results obtained was performed.
In this paper precision of the system controlling delivery by a helicopter of a water capsule designed for extinguishing large scale fires is analysed. The analysis was performed using a numerical method of distribution propagation (the Monte Carlo method) supplemented with results of application of the uncertainty propagation method. In addition, the optimum conditions for the airdrop are determined to ensure achieving the maximum area covered by the water capsule with simultaneous preserving the precision level necessary for efficient fire extinguishing.
Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed conditions are compared with the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.
The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix inequalities for the Dstable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-lime linear systems with polytopic uncertainties.
High distribution system power-losses are predominantly due to lack of investments in R&D for improving the efficiency of the system and improper planning during installation. Outcomes of this are un-designed extensions of the distributing power lines, the burden on the system components like transformers and overhead (OH) lines/conductors and deficient reactive power supply leading to drop in a system voltage. Distributed generation affects the line power flow and voltage levels on the system equipment. These impacts of distributed generation (DG) may be to improve system efficiency or reduce it depending on the operating environment/conditions of the distribution system and allocation of capacitors. For this purpose, allocating of distributed generation optimally for a given radial distribution system can be useful for the system outlining and improve efficiency. In this paper, a new method is used for optimally allocating the DG units in the radial distribution system to curtail distribution system losses and improve voltage profile. Also, the variation in active power load in the system is considered for effective utilization of DG units. To evidence the effectiveness of the proposed algorithm, computer simulations are carried out in MATLAB software on the IEEE-33 bus system and Vastare practical 116 bus system.
Measurement of the perfusion coefficient and thermal parameters of skin tissue using dynamic thermography is presented in this paper. A novel approach based on cold provocation and thermal modelling of skin tissue is presented. The measurement was performed on a person’s forearm using a special cooling device equipped with the Peltier module. The proposed method first cools the skin, and then measures the changes of its temperature matching the measurement results with a heat transfer model to estimate the skin perfusion and other thermal parameters. In order to assess correctness of the proposed approach, the uncertainty analysis was performed.
When an artificial neural network is used to determine the value of a physical quantity its result is usually presented without an uncertainty. This is due to the difficulty in determining the uncertainties related to the neural model. However, the result of a measurement can be considered valid only with its respective measurement uncertainty. Therefore, this article proposes a method of obtaining reliable results by measuring systems that use artificial neural networks. For this, it considers the Monte Carlo Method (MCM) for propagation of uncertainty distributions during the training and use of the artificial neural networks.
The aim of this study was to assess the innovation risk for an additive manufacturing process. The analysis was based on the results of static tensile tests obtained for specimens made of photocured resin. The assessment involved analyzing the measurement uncertainty by applying the FMEA method. The structure of the causes and effects of the discrepancies was illustrated using the Ishikawa diagram. The risk priority numbers were calculated. The uncertainty of the tensile test measurement was determined for three printing orientations. The results suggest that the material used to fabricate the tensile specimens shows clear anisotropy of the properties in relation to the printing direction.
The paper addresses the problem of experimental studies of miniature tilt sensors based on low-range accelerometers belonging to Microelectromechanical Systems (MEMS). A custom computer controlled test rig is proposed, whose kinematics allows an arbitrary tilt angle to be applied (i.e. its two components: pitch and roll over the full angular range). The related geometrical relationships are presented along with the respective uncertainties resulting from their application. Metrological features of the test rig are carefully evaluated and briefly discussed. Accuracy of the test rig is expressed in terms of the respective uncertainties, as recommended by ISO; its scope of application as well as the related limitations are indicated. Even though the test rig is mostly composed of standard devices, like rotation stages and incremental angle encoder, its performance can be compared with specialized certified machines that are very expensive. Exemplary results of experimental studies of MEMS accelerometers realized by means of the test rig are presented and briefly discussed. Few ways of improving performance of the test rig are proposed.
The paper deals with the accuracy of measurements of strains (elongation and necking) and stresses (tensile strength) in static room-temperature tensile strength tests. We present methods for calculating measurement errors and uncertainties, and discuss the determination of the limiting errors of the quantities measured for circular and rectangular specimens, which is illustrated with examples.