Small Error Research Articles

Automatic verification method of relay protection equipment setting value combining cell image gray enhancement and AI recognition

In order to solve the problems of tedious, insufficient manpower, low efficiency, and easy to cause human errors in the verification of relay protection equipment settings with the development of the power grid, an automatic verification method of relay protection equipment settings combining cell image gray enhancement and AI recognition is studied. In this method, Gaussian mixture and particle swarm algorithm are used to enhance the gray level of the original image captured, and the binary method is used to further denoise the image; The histogram is used to segment the cells in the denoised constant value image one by one; The OCR technology in AI technology uses the maximum width backtracking segmentation algorithm to segment a coherent text in a cell into multiple single words, and collects the 13 dimensional characteristics of the text to be detected to compare with the text in the database. The text with the smallest error is the detected text, which completes the text extraction in the cell; Store the extracted text data in the database, check the data in the notification constant value sheet and the device constant value sheet, and give an abnormal prompt of different data. The experimental results show that the image pre processed by this method is clear, the fixed value single cell segmentation is accurate, and the OCR text extraction efficiency is high. Through a large number of data experiments, the final verification accuracy can reach 99.8%.

The role of antisymmetric functions in nonlocal equations

We use a Hopf-type lemma for antisymmetric super-solutions to the Dirichlet problem for the fractional Laplacian with zero-th order terms, in combination with the method of moving planes, to prove symmetry for the semilinear fractional parallel surface problem. That is, we prove that non-negative solutions to semilinear Dirichlet problems for the fractional Laplacian in a bounded open set Ω ⊂ R n \Omega \subset \mathbb {R}^n must be radially symmetric if one of their level surfaces is parallel to the boundary of Ω \Omega ; in turn, Ω \Omega must be a ball. Furthermore, we discuss maximum principles and the Harnack inequality for antisymmetric functions in the fractional setting and provide counter-examples to these theorems when only ‘local’ assumptions are imposed on the solutions. The construction of these counter-examples relies on an approximation result that states that ‘all antisymmetric functions are locally antisymmetric and s s -harmonic up to a small error’.

Simulation and Evaluation of Runoff in Tributary of Weihe River Basin in Western China

Model simulation plays a significant role in the water resources cycle, and the simulation accuracy of models is the key to predicting regional water resources. In this research, the Qianhe tributary at the Weihe River basin in Western China was selected as the study area. The tributary was divided into 29 sub-basins and 308 hydrological response units according to the spatial raster data and attribute data of the hydrology, meteorology, topography, land use, and soil types. On this basis, a soil and water assessment tool (SWAT) model for runoff simulation and evaluation of this region was established. A sensitivity test and parameter calibration were then executed on 15 parameters involved with surface runoff, soil flow, and shallow underground runoff. The simulation results demonstrate a calibration and verification error of 3.06–10.08%, with very small uncertainties throughout the simulation, whereas they exhibit relatively large errors in the simulation of the dry period (winter) but, in contrast, quite small errors in the rainy period (summer). In addition, the simulated runoff with a low value is overestimated. When the annual, monthly, and daily runoff are 4–13.5 m3/s, 4–69.8 m3/s, and 40–189.3 m3/s, respectively, the relative error is smaller, and the simulation results are more accurate. The sensitive parameters predominantly affecting the runoff simulation of the basin include soil evaporation compensation, runoff curve coefficient, vegetation transpiration compensation, and saturated hydraulic conductivity in this region. In the case of hypothetical land use change scenarios, we observe a great reduction in simulated runoff in arable land, woodland, and grassland, while we observe an increment in construction and residential land and wasteland. The annual and monthly runoff are increased by above 54.5%. With the increase in cultivated land and forestland, the annual and monthly runoff decrease by 24.6% and 6.8%, respectively. In the case of hypothetical scenarios under 24 climate combinations, if the precipitation remains unchanged, the increase and decrease in temperature by 1 °C leads to a decline and increment of runoff by −0.72% and 5.91%, respectively. With regard to the simulation for the future under the RCP2.6 and RCP8.5 climate scenarios, downscaling was employed to predict the runoff trend of the future. In short, this study provides a method for runoff inversion and water resources prediction in small mountainous watersheds lacking hydrological and meteorological observation stations.

The reduction of ill-posedness of the inverse heat transfer problem in rotating disc cavities using the wall temperature characteristics as the priori knowledge

Solving the heat conduction equation using surface measurement temperature as boundary conditions to obtain surface heat flux is an ill-posed inverse heat transfer problem, in which small temperature errors can create large uncertainties in heat flux. This paper proposes a RBF (Radial Basis Function) + BP (Back Propagation) neural network approximation method that uses the wall temperature characteristics as priori knowledge to reduce the ill-posedness of the inverse heat transfer problem in rotating disc cavities of aero-engines. The wall temperature characteristics are described using first-order derivative, which are discussed and obtained through analytical solution and fluid-thermal coupling numerical simulation. Bayesian inference theory is used to construct neural network training objective function with regularization term and the RBF + BP neural network approximation method with uncertain regularization coefficient is proposed. Numerical experiments were conducted based on numerical simulation data to verify the effectiveness of the proposed method. The results show that the method can effectively suppress the ill-posed nature of the inverse heat transfer problem and can reduce the heat flux relative error level by 1 ∼ 2 orders of magnitude compared with several traditional data fitting methods commonly used in rotating disc cavities. The method of densifying measurement points combined with priori knowledge revision near the air impact point can effectively capture the local heat flux characteristics caused by airflow impact. The RBF + BP approximation method can reduce the demand for measurement points by approximately 44 ∼ 60 % under the error of 3σ = 0 K ∼ 0.9 K compared with Bayesian inference method.

Research on Time Series-Based Pipeline Ground Penetrating Radar Calibration Angle Prediction Algorithm.

The pipeline ground-penetrating radar stands as an indispensable detection device for ensuring underground space security. A wheeled pipeline robot is deployed to traverse the interior of urban underground drainage pipelines along their central axis. It is subject to influences such as resistance, speed, and human factors, leading to deviations in its posture. A guiding wheel is employed to rectify its roll angle and ensure the precise spatial positioning of defects both inside and outside the pipeline, as detected by the radar antenna. By analyzing its deflection factors and correction trajectories, the intelligent correction control of the pipeline ground-penetrating radar falls into the realm of nonlinear multi-constraint optimization. Consequently, a time-series-based correction angle prediction algorithm is proposed. The application of the long short-term memory (LSTM) deep learning model facilitates the prediction of correction angles and torque for the guiding wheel. This study compares the performance of LSTM with an autoregressive integrated moving average model under identical dataset conditions. The subsequent findings reveal a reduction of 4.11° and 8.25 N·m in mean absolute error, and a decrease of 10.66% and 7.27% in mean squared error for the predicted correction angles and torques, respectively. These outcomes are achieved utilizing the three-channel drainage pipeline ground-penetrating radar device with top antenna operating at 1.2 GHz and left/right antennas at 750 MHz. The LSTM prediction model intelligently corrects its posture. Experimental results demonstrate an average correction speed of 5 s and an average angular error of ±1°. It is verified that the model can correct its attitude in real-time with small errors, thereby enhancing the accuracy of ground-penetrating radar antennas in locating pipeline defects.

Effect of total heat input on coaxiality of rotor shaft in laser cladding

Abstract The total heat input by the laser directly affects the temperature distribution of the rotor shaft during the cladding process, and then affects its coaxiality. This article uses ANSYS for numerical simulation to study the effect of laser heat input on the deformation of the rotor shaft during laser cladding process. Simulate and analyze the temperature and stress fields inside the rotor shaft using thermal coupling. The results show that by changing the pitch, axial cladding width and laser irradiation duration to change the laser induced total heat input, a more uniform temperature distribution can be generated in the rotor shaft. The increase of temperature distribution uniformity can reduce the deformation of rotor shaft during cladding. Using a cladding equipment, iron based customized alloy powder was coated on the 45 steel rotor shaft for cladding experiments. And the mechanical properties and coaxiality of the rotor shaft after cladding were measured. The results showed that the hardness and wear resistance of the cladding layer were significantly improved compared to the substrate, and the changes in coaxiality of the rotor shaft were consistent with the simulation results, with relatively small errors. It is of great significance for repairing damaged rotor shafts.

A Novel Time-frequency Domain Reflectometry Method Based on S-transform for Power Cable Defect Localization

Background:: The large-scale aging of cross-linked polyethylene (XPLE) leads to an increase in the frequency of power cable accidents, which poses a threat to the safe operation of the power grid. Objective:: Traditional time-frequency domain reflectometry (TFDR) techniques for fault localization in power cables are susceptible to cross-terms interference, which makes it impossible to accurately locate defects. To overcome the limitation, this paper has proposed a novel cable fault localization method based on S-transform. Method:: The method employs S-transform to perform time-frequency analysis on the collected signals of TFDR, mapping the time-domain signals into time-frequency domain signals. Then, cross-correlation of the time-frequency domain signals is estimated, allowing for accurate positioning of cable defects. Results:: The results of the field experiments conducted on a 10 kV cross-linked polyethylene cable with artificially introduced defects have demonstrated that the proposed method could effectively locate the cable defects with small absolute error. Conclusion:: Compared to existing TFDR methods, the proposed method has been found to be free from interference of cross-terms, resulting in higher reliability and smaller blind spots for detecting cable defects.

Remaining Useful Life Estimation of Hollow Worn Railway Vehicle Wheels via On-Board Random Vibration-Based Wheel Tread Depth Estimation.

The problem of remaining useful life estimation (RULE) of hollow worn railway vehicle wheels in terms of remaining mileage via wheel tread depth estimation using on-board vibration signals from a single accelerometer on the bogie frame is presently investigated. This is achieved based on the introduction of a statistical time series method that employs: (i) advanced data-driven stochastic Functionally Pooled models for the modeling of the vehicle dynamics under different wheel tread depths in a range of interest until a critical limit, as well as tread depth estimation through a proper optimization procedure, and (ii) a wheel tread depth evolution function with respect to the vehicle running mileage that interconnects the estimated hollow wear with the remaining useful mileage. The method's RULE performance is investigated via hundreds of Simpack-based Monte Carlo simulations with an Attiko Metro S.A. vehicle and many hollow worn wheels scenarios which are not used for the method's training. The obtained results indicate the accurate estimation of the wheels tread depth with a mean absolute error of ∼0.07 mm that leads to a corresponding small error of ∼3% with respect to the wheels remaining useful mileage. In addition, the comparison with a recently introduced Multiple Model (MM)-based multi-health state classification method for RULE, demonstrates the better performance of the postulated method that achieves 81.17% True Positive Rate (TPR) which is significantly higher than the 45.44% of the MM method.

Four-dimensional variational data assimilation of a turbulent jet for super-temporal-resolution reconstruction

The super-temporal-resolution (STR) reconstruction of turbulent flows is an important data augmentation application for increasing the data reach in measurement techniques and understanding turbulence dynamics. This paper proposes a data assimilation (DA) strategy based on weak-constraint four-dimensional variation to conduct an STR reconstruction in a turbulent jet beyond the Nyquist limit from given low-sampling-rate observations. Highly resolved large-eddy simulation (LES) data are used to produce synthetic measurements, which are used as observations and for validation. A segregated assimilation procedure is realised to assimilate the initial condition, inflow boundary condition and model error separately. Different types of observational data are tested. The first type is down-sampled LES data containing many small-scale turbulence structures with or without synthetic noise. The DA results show that the temporal variation of the small-scale structures is well recovered even with noise in the observations. The spectra are resolved to a frequency approximately one order of magnitude higher than what can be captured within the Nyquist limit. The second type of observation is low-sampling-rate tomographic particle image velocimetry (tomo-PIV) data with or without the injection of small-scale structures. The modulation between the large-scale structures contained in the tomo-PIV fields and the small scales injected from the observations is improved. The resultant small scales in the STR reconstruction have the characteristics of authentic turbulence to a considerable extent. Additionally, DA yields much smaller errors in the prediction of particle positions when compared with the Wiener filter, demonstrating the great potential for Lagrangian particle tracking in measurement techniques.

Integrating ISPH simulations with machine learning for thermal radiation and exothermic chemical reaction on heat and mass transfer in spline/triangle star annulus

This work integrates incompressible smoothed particle hydrodynamics (ISPH) with machine learning (ML) to examine the uses of two different domain shapes, spline star-domain, and triangle star-domain, on double diffusion of nano-encapsulated phase change material (NEPCM). The effects of thermal radiation and exothermic chemical reactions are conducted in this work. The hexagonal-shaped is located inside the center of the star-shape carrying (Th&Ch). The left/right walls of the star shape are kept at (Tc&Cc) and the other walls have an adiabatic condition. It is recommended to examine the smoothness of closed curves in the heat and mass transfer by changing the triangle to spline curves. The present investigations of transmission of heat and mass of NEPCM within a complicated star shape can be employed in cooling systems of electronic/battery, heat exchangers, food processing, and chemical engineering. The ISPH simulations are executed for the pertinent parameters, Darcy number, Frank-Kamenetskii number, Rayleigh number, Dufour number, Soret number, and thermal radiation parameter. The performed simulations showed the significance of the spline star domain compared to the triangle star domain in smoothening the nanofluid flow and double-diffusive convection in an annulus. Frank-Kamenetskii number is a promising factor in the enhancement of heat transfer and controlling the phase change zone within an annulus. At a spline-star cavity, the maximum velocity rises by 32.32 % and 54.95 % when the Frank-Kamenetskii number grows from 0 to 5, and thermal radiation increases from 0 to 5. Soret number works effectively in enhancing the distribution of concentration at large temperature differences. Machine learning plays a vital role in many engineering applications. Hence, ML's powerful capabilities to predict the average Nu‾ and Sh‾. In the proposed ML model, the dimensionless time and thermal radiation parameter are used as input to the ML model, while their corresponding numeral estimated values of Nu‾ and Sh‾ are used as output targets for the ML model. The values of Nu‾ and Sh‾ are predicted by the suggested ML model with a comparatively small error less than 1 %.

Construction and Application of MOOC + Flipped Classroom Mixed Teaching Model in Volleyball Teaching in Colleges and Universities

MOOC+Flipped Classroom (MFC) is a new model that make the online learning and offline learning integrated. And it also shows a new way in developing the teaching reform. Based on MFC, a mixed teaching mode suitable for college volleyball was studied and established. And a reasonable evaluation index system was developed. It fosters educational fairness and improvements in volleyball learning performance. To be applicable to many kinds of problems, the support vector machine (SVM) is improved to obtain the DBT-SVM based quality evaluation model of college volleyball mixed teaching. The average score of students in the mixed teaching mode was higher than that in the traditional teaching mode. The comprehensive performance scores of the former and the latter after the experiment are 9.12 ± 0.75 and 7.63 ± 0.56 respectively. The mixed teaching mode results in higher student attendance. Among the prediction results of DBT-SVM, BT-SVM and SVM, DBT-SVM has higher accuracy, less training and testing time, and smaller error. This shows that DBT-SVM can accurately evaluate the teaching effect and quality.

Fuzzy adaptive control of coal gangue sorting parallel robot with variable load

ABSTRACT Delta parallel robot is widely used in the high-speed sorting industry with a light load and constant load. Its motion control is based on kinematic planning, without considering the influence of load and disturbance. The gangue sorting robot has the characteristics of a large load and random mass change, so traditional kinematics planning can not meet the control requirements. A fuzzy adaptive robust control algorithm is proposed to solve the problems of unstable motion and jitter in the coal gangue sorting robot. By establishing the mathematical model of the fuzzy system, the uncertain terms of the dynamic parameters caused by the random changes in the load are approximated. At the same time, to reduce the number of fuzzy rules and the amount of fuzzy calculation, the uncertain terms are decomposed into velocity terms and acceleration terms and then approximated, respectively. The Lyapunov analysis of the system is carried out, and the convergence of the system is proved. The simulation results show that the fuzzy adaptive robust control algorithm has a smaller error and faster convergence compared with the computational torque control algorithm when the system is sorting gangue within 8 kg, which improves the stability of gangue grasping.

Applying Bayesian optimization to predict parameters in a time-domain model for cross-flow vortex-induced vibrations

As the demand for harvesting offshore energy increases worldwide, the need for slender structures, such as marine risers and power cables, will increase. The dominating loads for deep water applications will primarily be caused by current-structure interactions, where vortex-induced vibrations (VIV) are known to be a challenging response type to handle correctly during design. Semi-empirical time-domain models are promising for VIV prediction, but uncertainties related to simplifications in the hydrodynamic load model and empirical parameters lead to over-conservative designs, where the parameters are estimated from model tests within a relatively low Reynolds number range. The aim of this paper is to present an efficient tool to estimate empirical hydrodynamic parameters directly from test data. To illustrate the method, the hydrodynamic parameters were estimated from pure cross-flow VIV model tests in a steady current with Reynolds numbers in the range of 40,000-120,000. The parameters were updated sequentially by using a Bayesian optimization framework, with the aim of minimizing an objective function that incorporates the response errors between time-domain VIV simulations and model test data. It is shown that three empirical parameters can be obtained simultaneously, resulting in small response errors but the optimal parameters were overly sensitive to variations in the flow velocity. The optimal parameters were used to reconstruct the drag amplification related to cross-flow VIV and in forced motion simulations to illustrate how the parameters in the load model would map into the traditional formulation in terms of the added mass and excitation coefficient.

Deep learning model based on multi-scale feature fusion for precipitation nowcasting

Abstract. Forecasting heavy precipitation accurately is a challenging task for most deep learning (DL)-based models. To address this, we present a novel DL architecture called “multi-scale feature fusion” (MFF) that can forecast precipitation with a lead time of up to 3 h. The MFF model uses convolution kernels with varying sizes to create multi-scale receptive fields. This helps to capture the movement features of precipitation systems, such as their shape, movement direction, and speed. Additionally, the architecture utilizes the mechanism of discrete probability to reduce uncertainties and forecast errors, enabling it to predict heavy precipitation even at longer lead times. For model training, we use 4 years of radar echo data from 2018 to 2021 and 1 year of data from 2022 for model testing. We compare the MFF model with three existing extrapolative models: time series residual convolution (TSRC), optical flow (OF), and UNet. The results show that MFF achieves superior forecast skills with high probability of detection (POD), low false alarm rate (FAR), small mean absolute error (MAE), and high structural similarity index (SSIM). Notably, MFF can predict high-intensity precipitation fields at 3 h lead time, while the other three models cannot. Furthermore, MFF shows improvement in the smoothing effect of the forecast field, as observed from the results of radially averaged power spectral (RAPS). Our future work will focus on incorporating multi-source meteorological variables, making structural adjustments to the network, and combining them with numerical models to further improve the forecast skills of heavy precipitations at longer lead times.

Development of Water Debit Measuring Instruments as Physics Learning Media Using a Flow Meter Sensor

Physics learning aims to ensure that students understand physics concepts completely. Understanding of the concept can be achieved through the help of learning media in the form of teaching aids from physics materials. This research aims to develop learning media for measuring water discharge using a flow meter sensor to improve students' conceptual understanding of dynamic fluid material. This research includes development research through the ADDIE model, carried out until the development stage. Data collection techniques are carried out through the calibration of measuring instruments. The technique for data analysis used is the descriptive analysis of proportions. The study results obtained the following results: 1) The calibration results show that the water discharge measuring instrument as a learning medium has a very small error rate, and 2) The results of the validity assessment obtained by the water discharge measuring instrument have high validity. The water debit measuring instruments can be used to increase understanding of the dynamic fluid material concept. Using this air discharge measuring instrument will help students understand the concept of fluid dynamics, especially in air discharge subjects.

Analysis of Students' Error in Working on Story Problems Based on Newman's Criteria in Class II MIA 3 Man 3 Padang

The background of this research is that there are still many students who are less interested and motivated in learning mathematics so that many students make mistakes in solving math word problems. The purpose of this research is to identify and identify the types of mistakes made students in working on word problems based on Newman's Error criteria and knowing the causes of students making mistakesIn doing story problems.The research method used is descriptive method with a qualitative approach . The sample of this study were 24 students of class XI MIA 3. The research instrument was tests and interviews. The test results were analyzed based on Newman's criteria, after which students were interviewed based on the types of mistakes made by students.The results of this study indicate that the types of errors made by students based on Newman's criterion analysis consist of 5 errors, namely Reading errors, Comprehension errors, Transformation errors, Process Skill errors and Endcoding errors. The biggest mistake was made at the stage of writing the final answer, namely as much as 46.67%, while the smallest error was made at the stage of understanding the questions, namely as much as 5.33%.

Solusi Eksak Sistem Imun Terhadap Virus Ebola

The Ebola virus is a deadly disease that causes blood clots in the body's organs and is spread through direct contact with the blood or body fluids of sufferers. Based on this, the immune system in the body will continue to decrease and cause Ebola Hemorrhagic Fever. The 2014-2016 Ebola outbreak in West Africa has accelerated the development of several preventive vaccines against the Ebola virus. The goal of the vaccination is to induce immunity against infectious diseases. And also to stimulate the immune system and its ability to store and remember information about specific pathogens, leading to long-term protective immunity. The model equation for the Ebola virus vaccine in this study involves the concentration of the antigen which is a variable , by means of which the vaccine is inserted into the patient's body where it will attach to B memory cells which are variable , which will then be stimulated by the cells short-lived antibodies are denoted by variables or long-lived cells are denoted by variables , while antibodies will prove efficacy denoted by variables on the patient's immune response. The simulation of the exact solution for the Ebola vaccine uses the integration factor method which will later be compared with numerical simulations according to the parameter values from the research of Irene Balelli et al (2020). The simulation obtained has a very small calculation error value for each variable, which means that the exact value of the Ebola virus vaccination model shows that there is no significant difference to the numerical solution using the order 45 Rungge Kutta method, the largest resulting numerical error is 2.29640283510782×〖10〗^9.

Going Deeper, Generalizing Better: An Information-Theoretic View for Deep Learning.

Deep learning has transformed computer vision, natural language processing, and speech recognition. However, two critical questions remain obscure: 1) why do deep neural networks (DNNs) generalize better than shallow networks and 2) does it always hold that a deeper network leads to better performance? In this article, we first show that the expected generalization error of neural networks (NNs) can be upper bounded by the mutual information between the learned features in the last hidden layer and the parameters of the output layer. This bound further implies that as the number of layers increases in the network, the expected generalization error will decrease under mild conditions. Layers with strict information loss, such as the convolutional or pooling layers, reduce the generalization error for the whole network; this answers the first question. However, algorithms with zero expected generalization error do not imply a small test error. This is because the expected training error is large when the information for fitting the data is lost as the number of layers increases. This suggests that the claim "the deeper the better" is conditioned on a small training error. Finally, we show that deep learning satisfies a weak notion of stability and provides some generalization error bounds for noisy stochastic gradient decent (SGD) and binary classification in DNNs.

Phase transition and higher order analysis of Lq regularization under dependence.

We study the problem of estimating a [Formula: see text]-sparse signal [Formula: see text] from a set of noisy observations [Formula: see text] under the model [Formula: see text], where [Formula: see text] is the measurement matrix the row of which is drawn from distribution [Formula: see text]. We consider the class of [Formula: see text]-regularized least squares (LQLS) given by the formulation [Formula: see text], where [Formula: see text] [Formula: see text] denotes the [Formula: see text]-norm. In the setting [Formula: see text] with fixed [Formula: see text] and [Formula: see text], we derive the asymptotic risk of [Formula: see text] for arbitrary covariance matrix [Formula: see text] that generalizes the existing results for standard Gaussian design, i.e. [Formula: see text]. The results were derived from the non-rigorous replica method. We perform a higher-order analysis for LQLS in the small-error regime in which the first dominant term can be used to determine the phase transition behavior of LQLS. Our results show that the first dominant term does not depend on the covariance structure of [Formula: see text] in the cases [Formula: see text] and [Formula: see text] which indicates that the correlations among predictors only affect the phase transition curve in the case [Formula: see text] a.k.a. LASSO. To study the influence of the covariance structure of [Formula: see text] on the performance of LQLS in the cases [Formula: see text] and [Formula: see text], we derive the explicit formulas for the second dominant term in the expansion of the asymptotic risk in terms of small error. Extensive computational experiments confirm that our analytical predictions are consistent with numerical results.

The Robustness of Favorable Propagation in Massive MIMO to Location and Phase Errors

The impact of random errors (implementation inaccuracies) in element locations and beamforming phases on favorable propagation (FP) in massive multiple-input multiple-output (MIMO) line-of-sight (LOS) channels is studied. For arbitrary array geometry and under independent (possibly non-Gaussian) errors, the FP property is shown to hold for the perturbed array as long as it holds for the unperturbed one. This means that small errors do not have catastrophic impact on the FP, even for a large number of antennas. The negative impact of random errors is to slow down the convergence to the asymptotic value so that more antennas are needed under random errors to achieve the same low inter-user interference as without errors. For large but finite number of antennas, the distribution and an analytically-tractable approximation of the inter-user interference power are obtained. Practical design guidelines are given that quantify the accuracy level needed to make the impact of random errors negligible. The analytical results are validated via numerical simulations and are in agreement with measurement-based studies.