Lognormal Research Articles

Gait rhythm analysis as a new continuous scale for cerebellar ataxia: Power law and lognormal components represent the ataxic gait quantity

We estimated the severity of cerebellar ataxia by analyzing gait rhythm. We measured the step times in patients with pure cerebellar ataxia and healthy controls and then analyzed the distribution of the ratios of adjacent times. Gait rhythm displayed the best adaptation when expressed as the sum of the power law and lognormal distributions in both groups, and the groups could be distinguished by the exponent of the power law distribution, reflecting the fractal property of gait rhythm. Gait rhythm might reflect different features of impairment in patients with cerebellar ataxia, making it a useful continuous scale for cerebellar ataxia.

Assessment of random dynamic behavior for EMUs high-speed train based on Monte Carlo simulation

A novel statistical method was developed to obtain a dynamic response with irregular line excitations and independent uncertain parameters. The proposed approach combines a three-dimensional vehicle-track coupling dynamics model and uncertainty parameters. Moreover, a new method is used to treat the dynamic indices: derailment coefficient, vertical/lateral wheel/rail force, vertical/lateral car body acceleration, and wheel reduction ratio. The model is validated by comparing simulations (deterministic) results with field measurements, which provide excellent agreement with limited data. According to the findings, the results reveal that the high vibration effect arises when the uncertainty parameter in the dynamic system exists. The total fit effects, the consistency of the vehicle safety, and the tail fit effects are determined for selecting the best method. Therefore, regarding the approach, the lognormal and extreme maximum distribution values may be the appropriate assumed distribution for dynamic safety under limited data.

Maintenance of Lognormal-Like Skewed Dendritic Spine Size Distributions in Dentate Granule Cells of TNF, TNF-R1, TNF-R2, and TNF-R1/2-Deficient Mice.

Dendritic spines are sites of synaptic plasticity and their head size correlates with the strength of the corresponding synapse. We recently showed that the distribution of spine head sizes follows a lognormal-like distribution even after blockage of activity or plasticity induction. As the cytokine tumor necrosis factor (TNF) influences synaptic transmission and constitutive TNF and receptor (TNF-R)-deficiencies cause changes in spine head size distributions, we tested whether these genetic alterations disrupt the lognormality of spine head sizes. Furthermore, we distinguished between spines containing the actin-modulating protein synaptopodin (SP-positive), which is present in large, strong and stable spines and those lacking it (SP-negative). Our analysis revealed that neither TNF-deficiency nor the absence of TNF-R1, TNF-R2 or TNF-R 1 and 2 (TNF-R1/R2) degrades the general lognormal-like, skewed distribution of spine head sizes (all spines, SP-positive spines, SP-negative spines). However, TNF, TNF-R1 and TNF-R2-deficiency affected the width of the lognormal distribution, and TNF-R1/2-deficiency shifted the distribution to the left. Our findings demonstrate the robustness of the lognormal-like, skewed distribution, which is maintained even in the face of genetic manipulations that alter the distribution of spine head sizes. Our observations are in line with homeostatic adaptation mechanisms of neurons regulating the distribution of spines and their head sizes.

Large-deformation study of T-bar penetration in spatially variable sediments

The T-bar penetrometer is extensively used in offshore field investigation and laboratory testing to evaluate the undrained shear strength of soft clay because of its reliability and repeatability in measurements. However, most previous studies on T-bar penetration have adopted a deterministic approach and focused solely on homogeneous soils, neglecting the geological uncertainty caused by the spatial variability of soil. To remedy this situation, this study aimed to investigate the effect of soil spatial variation on the T-bar penetration process in soft clay by employing large deformation random finite element modeling. The findings indicate that the variability in soil strength substantially modifies the flow pattern and failure mechanism of the soil, consequently influencing the penetration resistance factor of the T-bar. It was observed that the resistance factors follow the log-normal distribution. A relationship between the probability of failure as well as the factor of safety was determined, allowing for a clear assessment of the reliability level associated with varying factors of safety. To allow for this effect, a practical framework is developed to correct T-bar penetration data to estimate soil strength.

Probabilistic evaluation of spectral acceleration demands on light secondary systems supported by partially self-centering structures

Partially self-centering structures are promising seismic resilient structural systems by reducing residual inter-story drifts with low initial construction costs. Comprehensive studies focused on structural design and performance evaluation, but no research was conducted to investigate the design of nonstructural components in partially self-centering structures. This research focuses on developing the probabilistic spectral acceleration demands for the nonstructural design in partial self-centering structures. 320 near-fault recorded ground motions were adopted for considering the uncertainties of seismic excitations. The spectral accelerations of the light nonstructural component were obtained through comprehensive dynamic analyses. The logarithmic normal distribution can be used for describing the probabilistic distribution of floor spectra for partially self-centering structures under earthquakes, validating through the Anderson-Darling test. The influences of design parameters (including structural period, hysteretic parameters, structural damping, the ratio of the structural period to the nonstructural period, and nonstructural damping) on the probabilistic distribution of floor spectra were investigated through parametric dynamic analysis results. Artificial neural network (ANN) models were developed for predicting the probabilistic floor spectra for partially self-centering structures. The analysis results indicate that ANN models can achieve excellent accuracy with a coefficient of determination larger than 0.99. Comparative analysis results reveal that the ASCE method may underestimate the acceleration demand of light secondary systems supported by partially self-centering structures. The developed ANN models were interpreted using the shapely additive explanations. It has been found that the fundamental periods of the main structure and nonstructural components and the response modification factor show significant effects on the median and deviation of the probabilistic floor spectra for partially self-centering structures. The software FloorSpecPS was established to predict the probabilistic floor spectra for partially self-centering structures using the developed ANN models in practical application.

Non-parametric fragility curves for probabilistic risk assessment of rainfall-triggered landslides

Fragility analysis of slopes under rainfall condition express the conditional probabilities of exceeding prescribed slope limit states under a range of rainfall intensities, which is the basic and pivotal procedure in rainfall-triggered landslide risk assessment. Classical fragility analysis methods of slopes always develop fragility curves with the assumption of lognormal distribution. The validation of assuming the shape of fragility curves as lognormal distribution remains a open question in practice. In addition, the existing fragility analysis of slopes under rainfall condition have not dealt with the effect of spatially-variable geo-material parameters. In the present study, a novel fragility analysis methodology is proposed for the construction of non-parametric fragility curves of slopes under rainfall condition, in which the spatially-variable soil properties are taken into account. The non-parametric fragility curves are developed by the calculated slope failure probabilities under various rainfall intensities on the basis of probability density evolution theory, without restricting fragility functions to some assumed distribution models. With the proposed method and a set of probabilistic slope rainfall seepage and stability analyses, non-parametric fragility curves, fragility surface using two rainfall intensity measures and time-dependent fragility curves of a slope subjected to various rainfall scenarios are obtained for rainfall-triggered landslides risk assessment.

Secrecy performance analysis of a IRS-assisted underwater optical wireless communication system

In response to the dearth of radio frequency (RF) equivalents, there has been a recent surge in interest in optical wireless communication in underwater environments. To ensure a strong line-of-sight (LOS) connection, the intelligent reflecting surface (IRS) is installed to create a virtual LOS. Then, the first part of this study looks into the security of underwater optical wireless communication (UOWC) in relation to a number of real-world phenomena, including oceanic propagation loss, oceanic turbulence, and IRS-induced geometric loss. Then, a wiretap channel with three authorized users - a reputable broadcaster named Alice (the submarine), a law-abiding user named Bob, and an eavesdropper named Eve - is examined over turbulent channels that exhibit the Log-normal distribution. Furthermore, our study derives the closed-form formulas for the secrecy performance measures, secrecy outage probability, and secrecy throughput. Finally, the numerical results show how the impact of oceanic turbulence-induced fading and distance between Bob’s and Eve’s positions on the secrecy system performance.

Influence of Foundation Stiffness on the Fragility Curves of a Concrete Gravity Dam Subjected to Near-Field Ground Motions Using Finite Element Method

A concrete gravity dam is being investigated to determine the fragility curves during near-field ground motions under various foundation stiffness conditions. This is accomplished using the finite element method for modeling the Latyan dam and its dam-reservoir-bed complex interaction system. The nonlinear constitutive model of concrete, plastic damage, is used to simulate the cyclic behavior of tensile and compressive failures in concrete. An acoustic element is used to model the propagation of compressive waves in the reservoir to account for the hydrodynamic effects of the lake reservoir. A total of 100 real and scaled accelerograms are used to simulate near-filed seismic loading in eight different concrete-to-foundation stiffness ratios. Based on the peak ground acceleration (PGA) of the earthquake, numerical models are applied to obtain the probability density function (PDF) and cumulative distribution function (CDF) for lognormal distributions and to determine and analyze the fragility curves of the dam. According to the findings, the seismic performance of the dam is improved for stiffness ratios of 0.75, 1, and 1.5, and the best seismic performance is determined for stiffness ratios of 1. Concrete dams with stiffness ratios of 0.75, however, perform better when the peak ground acceleration is greater than 0.74g compared to those with stiffness ratios of 1. DOI: https://doi.org/10.52783/pst.502

The pH paradox

This paper highlights the critical role of pH or proton activity measurements in environmental studies and emphasises the importance of applying proper statistical approaches when handling pH data. This allows for more informed decisions to effectively manage environmental data such as from mining influenced water. Both the pH and {H+} of the same system display different distributions, with pH mostly displaying a normal or bimodal distribution and {H+} showing a lognormal distribution. It is therefore a challenge of whether to use pH or {H+} to compute the mean or measures of central tendency for further environmental statistical analyses. In this study, different statistical techniques were applied to understand the distribution of pH and {H+} from four different mine sites, Metsämonttu in Finland, Felsendome Rabenstein in Germany, Eastrand and Westrand mine water treatment plants in South Africa. Based on the statistical results, the geometric mean can be used to calculate the average of pH if the distribution is unimodal. For a multimodal pH data distribution, peak identifying methods can be applied to extract the mean for each data population and use them for further statistical analyses.

Extension of the Eeigenvalue-Based Selection Index Method for Fixation of Multiple Trait-Transgressive Segregates in Mungbeans (Vigna radiata L. Wilczek)

The selection of the early generation is a viable strategy for the rapid development of new plant varieties. In mungbeans (Vigna radiata L. Wilczek), the selection process is carried out to obtain high seed yield, early maturity, and sufficiently large seed size. To enhance this process, the extension of the combined-eigenanalysis selection index method (CESIM) with transgressive segregation variables can be used to fix multiple-trait transgressive segregates. Therefore, this research aimed to (1) develop an eigenvalue-based selection index method in information from relatives analysis capable of fixing multiple-trait transgressive segregates in the early generation, (2) predict expected and realized multiple-trait selection responses, and (3) verify the presence of multiple-trait transgressive segregates in the early generation of mungbeans. The material used consisted of the F3 generation population and its selection outcomes in F4, originating from the crossbreeding of mungbean varieties Gelatik × Lasafu Lere Butsiw. The empirical breeding values (EBV) between and within families were obtained using the BLUP values of the F3 generation from the mixed linear model with a nested design and log-normal distribution. The EBV values between families and dummy variables of transgressive segregate families were used in the selection process with CESIM. Furthermore, analysis of variance in EBV values within families in the F4 generation was applied to verify the presence of multiple-trait transgressive segregates. The results showed that the selection from the best CESIM equation yielded index scores with a determination coefficient R2 = 97.76% and an expected selection response of 136.62. The verification process confirmed the presence of 9 families as multiple-trait transgressive segregate families in the early generation.

Simulation of rice grain breakage process based on Tavares UFRJ model

Understanding the breakage characteristics of rice grains is an important means to reduce rice breakage rate. However, the dynamic breakage mechanism of rice grain is unclear due to the lack of a reasonable breakage model. In this study, the uniaxial compression test and drop weight test of single rice were carried out, the breakage model of rice grain was constructed, the reliability of rice model was verified by the experiment and simulation results. The results showed that the fracture energy distribution of rice can be obtained by uniaxial compression test, the specific fracture energy of rice accords with a lognormal distribution, and the median specific fracture energy of rice is 479.75 J/kg. The damage accumulation coefficient and fragment size distribution of rice can be acquired by drop test, the result of damage accumulation coefficient of rice was 4.3. Rice grain breakage mainly occurs in the milling section of the vertical circulation rice mill.

Domain adaptation via gamma, Weibull, and lognormal distributions for fault detection in chemical and energy processes

AbstractThe burgeoning development of supervised machine learning (ML) has led to its widespread applications in chemical and energy processes, such as fault detection. However, in some scenarios, collecting labelled data can be costly, hazardous, or impossible. Moreover, data of the same process can follow varying distributions due to changes in, for example, devices and environment, causing ML models to be ineffective. These challenges pose a domain adaptation task, necessitating the refinement of existing ML models to tackle issues from related applications. This study proposes a domain adaptation approach to address label scarcity and data distribution variation. The method has three stages: data distribution modelling (knowledge discovery), adaptation of target domain samples to source domains (knowledge transformation), and classifier ensemble for fault detection (knowledge fusion). Gamma, Weibull, and lognormal distributions are applied for data modelling and domain adaptation. The effectiveness of the method is validated on synthetic datasets and then applied to identify anomalies in coal mine pressure data and detect faults in the Tennessee Eastman (TE) process.

Parameter Estimation and Testing for the Doubly Geometric Process with Lognormal Distribution: Application to Bladder Cancer Patients’ Data

The geometric process (GP) has been widely utilized as a stochastic monotone model in the fields of probability and statistics. However, its practical application is often limited by certain assumptions. To address this, [Wu (2018). Doubly geometric process and applications. Journal of the Operational Research Society, 69(1), 66–67] introduced the doubly geometric process (DGP) as an extension of the GP model, relaxing some of its assumptions. Due to its ability to overcome the limitations of the GP model, the DGP has gained significant popularity in recent times. This study focuses on the parameter estimation problem for the DGP when the distribution of the first interarrival time follows a lognormal distribution with parameters [Formula: see text] and [Formula: see text]. We employ the maximum likelihood method to obtain estimates for both the model parameters and the distribution parameters. Additionally, we investigate the asymptotic joint distribution and statistical properties such as asymptotic unbiasedness and consistency of the estimators. Furthermore, we propose a novel test procedure to distinguish between the GP and DGP models. To assess the performance of the estimators and the proposed test procedure, we conduct a simulation study involving various sample sizes and parameter values. Finally, we present an application of the developed methods in fitting data from bladder cancer patients.

Similarity analysis of randomness in instantaneous chloride diffusion coefficient of concrete under different environmental exposures

This study addresses the temporal variability and randomness of concrete's chloride diffusion coefficient by proposing an analysis using stochastic measures for the instantaneous chloride diffusion coefficient (Dins) alongside Kullback-Leibler (K-L) divergence and Hamming distance for similarity assessment. Examination of diverse concrete specimens subjected to both natural tidal environments (NE) and simulated environments (SE) indicated that the environmental factors, primarily exposure setting and duration, substantially influence the diffusion coefficient's temporal behavior. SE with elevated temperature and salinity accelerated chloride penetration, leading to higher diffusion rate means than those in NE. Concrete in NE exhibited a log-normal distribution for Dins, while under SE, a normal distribution was observed. Variability was mainly driven by the exposure environment, with minor contributions from material components. Similarity analysis suggested that the stochastic character of Dins in SE after 120 days resembled those in NE at 600 days, as per K-L divergence, whereas Hamming distance showed the closest resemblance at 240 days in SE. The Material make-up showed negligible impact on distribution similarity, and the extending simulation exposure time had a limited effect on enhancing similarity of stochastic diffusion behavior across environments.

Simplified and Detailed Evaluations of the Uncertainty of the Measurement of Microbiological Contamination of Pharmaceutical Products.

The control of the microbial contamination of pharmaceutical products (PP) is crucial to ensure their safety and efficacy. The validity of the monitoring of such contamination depends on the uncertainty of this quantification. Highly uncertain quantifications due to the variability of determinations or the magnitude of systematic effects affecting microbial growth or other analytical operations make analysis unfit for the intended use. The quantification of the measurement uncertainty expressing the combined effects of all random and systematic effects affecting the analysis allows for a sound decision about quantification adequacy for their intended use. The complexity of the quantification of microbial analysis uncertainty led to the development of simplified ways of performing this evaluation. This work assesses the adequacy of the simplified quantification of the uncertainty of the determination of the microbial contamination of PP by log transforming microbial count and dilution factor of the test sample whose uncertainty is combined in a log scale using the uncertainty propagation law. This assessment is performed by a parallel novel bottom-up and accurate evaluation of microbial analysis uncertainty involving the Monte Carlo method simulation of the Poisson log-normal distribution of counts and of the normally distributed measured volumes involved in the analysis. Systematic effects are assessed and corrected on results to compensate for their impact on the determinations. Poisson regression is used to predict precision affecting determinations on unknown test samples. Simplified and detailed models of the uncertainty of the measurement of the microbial contamination of PP are provided, allowing objective comparisons of several determinations and those with a maximum contamination level. This work concludes that triplicate determinations are required to produce results with adequately low uncertainty and that simplified uncertainty quantification underevaluates or overevaluates the uncertainty from determinations based on low or high colony numbers, respectively. Therefore, detailed uncertainty evaluations are advised for determinations between 50 and 200% of PP's maximum admissible contamination value. User-friendly tools for detailed and simplified evaluations of the uncertainty of the measurement of microbial contamination of PP are provided together with the understanding of when simplifications are adequate.

Stochastic modelling of material variability in structural dynamics: A threefold comparison of Monte Carlo, polynomial chaos, and random sampling techniques

This article investigates the influence of random elastic modulus on beam eigenfrequencies using multiple simulation techniques: Monte Carlo simulations (employing Cholesky decomposition (MCS-CD) and Kosambi-Karhunen-Loève expansion (MCS-KKL)), Polynomial Chaos expansion (PCE), and a proposed Random Sampling method (RSM). Anomalies in Monte Carlo simulations, where normally distributed elastic modulus led to negative values and imaginary eigenfrequencies, were effectively addressed by adopting a log-normal distribution. Comparative analyses focused on covariance variation of the first three eigenfrequencies with correlation length and standard deviation of the random field, highlighting nuanced differences between normal and log-normal distributions. PCE exhibited distinct responses, showcasing variations in covariance with different distributions. The study culminates in eigenfrequency estimation using the proposed RSM, wherein the beam is discretised into n elements with randomly assigned elastic moduli. The mean and variance of eigenfrequencies are compared with existing methods, which represent an alternative method for achieving similar outcomes.These comparative studies provide a comprehensive understanding of how different statistical treatments and simulation methods impact the reliability and accuracy of eigenfrequency predictions in beams with random elastic properties, thus contributing valuable insights for structural analysis and design under uncertainty.

Cracking characteristics and axial capacity degradation of precast segmental bridge piers connected with corroded tapered sleeve locking-type splicing

The tapered sleeve locking-type splicing (TSLTS) reinforcement joint is a new method of steel mechanical connection. When applying the TSLTS reinforcement joints to precast segmental bridge (PSB) piers in coastal environments, the durability need to be taken into account. After the TSLTS reinforcement joint is corroded, the connection performance of the TSLTS reinforcement joint is degraded. Therefore, the mechanical properties of PSB piers decrease due to the corrosion of the joints, which brings some potential hazards. In this paper, the durability of PSB piers with TSLTS reinforcement joints in coastal environments was studied. The corrosion-induced cracking characteristics, failure mode and axial capacity of PSB piers with TSLTS reinforcement joints were investigated by means of accelerated corrosion test and axial loading failure test. The results indicated that, with increasing corrosion time, the total length of the corrosion-induced cracks on the surface of the pier specimens increased, but the increasing rate of the total length decreased. The mass loss of TSLTS reinforcement joints increased linearly with the maximum width of longitudinal corrosion-induced cracks on the concrete cover of the self-compacting concrete (SCC) segment, and the critical mass loss of TSLTS reinforcement joints was approximately 4.0 % when longitudinal corrosion-induced cracks appeared. The probability distribution type of the width of longitudinal corrosion-induced cracks on the surface of pier specimens was mainly a lognormal distribution. When the mass loss of TSLTS reinforcement joints was less than 7.2 %, the damaged area of the pier specimens was mainly concentrated in the SCC segment, while when the mass loss of TSLTS reinforcement joints was higher than 8.8 %, the damaged area was located in the ordinary Portland concrete segment near the top of the pier specimens, and the corroded TSLTS reinforcement joints could still maintain their connection performance. With an increase in the corrosion degree of the steel bars, the axial capacity of the pier specimens decreased, and the equivalent stiffness also degraded. The degradation rate of the axial capacity of the pier specimens increased linearly with the mass loss of the TSLTS reinforcement joints, and the degradation of the axial capacity occurred only when the mass loss of the TSLTS reinforcement joints was greater than 4.6 %. The research results can provide a theoretical reference for the application of TSLTS reinforcement joints in PSB piers.

Joint monitoring of mean and variance using Max-EWMA control chart under lognormal process with application to engine oil data

The control charts are frequently employed in process monitoring to assess the average and variability of a process, assuming a normal distribution. However, it is worth noting that some process distributions tend to exhibit a positively skewed distribution, such as the lognormal distribution. This article proposed a maximum exponential weighted moving average control chart for joint monitoring of mean and variance under a lognormal process. The proposed control chart is evaluated by using the run length profile such as ARL and SDRL. The Monte Carlo simulation is conducted by using the R language to find the run length profile. An application is presented to demonstrate the design of the proposed control chart.

Constraining primordial black holes as dark matter using AMS-02 data

Primordial black holes (PBHs) are the plausible candidates for the cosmological dark matter. Theoretically, PBHs with masses MPBH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\ extrm{PBH}}$$\\end{document} in the range of 4×1014∼1017g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\ imes 10^{14}\\sim 10^{17}\\,\ extrm{g}$$\\end{document} can emit sub-GeV electrons and positrons through Hawking radiation. Some of these particles could undergo diffusive reacceleration during propagation in the Milky Way, potentially reaching energies up to the GeV level observed by AMS-02. In this work, we utilize AMS-02 data to constrain the PBH abundance fPBH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{\ extrm{PBH}}$$\\end{document} by employing the reacceleration mechanism. Under the assumption of a monochromatic PBH mass distribution, our findings reveal that the limit is stricter than that derived from Voyager 1 data. This difference is particularly pronounced when MPBH≲1015g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\ extrm{PBH}}\\lesssim 10^{15}\\,\ extrm{g}$$\\end{document}, exceeding an order of magnitude. The constraints are even more robust in a more realistic scenario involving a log-normal mass distribution of PBHs. Moreover, we explore the impact of varying propagation parameters and solar modulation potential within reasonable ranges, and find that such variations have minimal effects on the final results.

Underwater Wireless Optical Communication for IOT using Coding MIMO Diversity

The present study examined and simulated the coding or no coding performance for different configurations of multi-input, multioutput underwater wireless optical communication systems. MIMO diversity and channel coding were used to reduce the power transmitter, assuming lognormal distribution random for weak ocean turbulence. The simulation tested for a link range of 30 m in low ocean turbulence and 500 Mbps on–off-keying was also presented using Monte-Carlo. The results showed improvement in power transmitted (gain) for 2x5 compared to Uncoded SISO, which was about 33.60db using the concatenated code. So that the underwater wireless optical communications (UWOC) even now will also be significantly impacted by the Internet of Underwater Things (IoUT) and ultimate mobile technologies five generation communication systems because of their extraordinarily high demand for data safety, bit rate, energy consumption, so it is used in combined data transfer between underwater communication devices. The UWOC system based on coded MIMO may successfully be used in IoUT due to its high robustness and power qualification.