Search

The paper presents a stochastic gamma process model to account for both population (i.e., sampling) and temporal variability associated with a degradation process that typically increases the probability of failure with the aging of a structure. The proposed method is more versatile than the random-variable degradation rate model commonly used in the structural reliability literature. The reason being that the random rate model cannot capture temporal variability associated with evolution of degradation. The paper also describes two methods for estimating parameters of the gamma process to facilitate its practical engineering applications.

Condition monitoring data are routinely collected from various nuclear plant systems to ensure they are operating within an acceptable envelope, and to detect any potential onset of degradation in the system condition. The condition monitoring includes periodic monitoring of not only physical variables, such as temperature and vibration, but also chemical properties of lubricants, oils, and other control fluids. The time series of such monitoring data tend to exhibit non-stationary nature and complex correlation structure, as they consist of fluctuations of different time scales and noise. Since standard text-book methods of stationary time series analysis are not applicable to such data sets, the paper presents an advanced method of Empirical Mode Decomposition (EMD) to filter out the noise and identify the long-term trend, i.e., a likely indicator of degradation, in condition monitoring data. The proposed method is verified by a simulation example and then applied to a real data set obtained from an operating nuclear plant.

In the life-cycle cost analysis of a structure, the total cost of damage caused by external hazards like earthquakes, wind storms and flood is an important but highly uncertain component. In the literature, the expected damage cost is typically analyzed under the assumption of either the homogeneous Poisson process or the renewal process in an infinite time horizon (i.e., asymptotic solution). The paper reformulates the damage cost estimation problem as a compound renewal process and derives general solutions for the mean and variance of total cost, with and without discounting, over the life cycle of the structure. The paper highlights a fundamental property of the renewal process, referred to as renewal decomposition, which is a key to solving a wide range of life cycle analysis problems. The proposed formulation generalizes the results given in the literature, and it can be used to optimize the design and life cycle performance of structures.

The rise of Performance Based Design methodologies for fire safety engineering has increased the interest of the fire safety community in the concepts of risk and reliability. Practical applications have however been severely hampered by the lack of an efficient unbiased calculation methodology. This is because on the one hand, the distribution types of model output variables in fire safety engineering are not known and traditional distribution types as for example the normal and lognormal distribution may result in unsafe approximations. Therefore unbiased methods must be applied which make no (implicit) assumptions on the PDF type. Traditionally these unbiased methods are based on Monte Carlo simulations. On the other hand, Monte Carlo simulations require a large number of model evaluations and are therefore too computationally expensive when large and nonlinear calculation models are applied, as is common in fire safety engineering. The methodology presented in this paper avoids this deadlock by making an unbiased estimate of the PDF based on only a very limited number of model evaluations. The methodology is known as the Maximum Entropy Multiplicative Dimensional Reduction Method (ME-MDRM) and results in a mathematical formula for the probability density function (PDF) describing the uncertain output variable. The method can be applied with existing models and calculation tools and allows for a parallelization of model evaluations. The example applications given in the paper stem from the field of structural fire safety and illustrate the excellent performance of the method for probabilistic structural fire safety engineering. The ME-MDRM can however be considered applicable to other types of engineering models as well.

Sheshanath V. Bhoslae received his PhD from Freie University Berlin (Germany) in supramolecular chemistry under the supervision of Prof. J. H. Fuhrhop in 2004. He then pursued his postdoctoral studies with Prof. S. Matile at University of Geneva (Switzerland) under the auspices of a Roche Foundation Fellowship. This was followed by a stay at Monash University (Australia) for 5 years as an ARC‐APD Fellow. He worked at RMIT University, Melbourne (Australia) for 6 years as ARC‐Future Fellowship. Currently, Prof. Bhosale is working at the Department of Chemistry, Goa University (India) as a UGC‐FRP Professor, His research interests lie in the design and synthesis of π‐functional materials, especially small molecules, for sensing, biomaterials, and supramolecular chemistry applications. So far, Prof. Bhosale has produced 185 research articles and his work has been cited more than 4400 times, giving him an h‐index of 32. He currently serves as an active Editorial Board member for ChemistryOpen.

The main function of the concrete containment structures is to prevent radioactive leakage to the environment in case of a loss of coolant accident (LOCA). The Canadian Standard CSA N287.6 (2011) proposes periodic inspections, i.e., pressure testing, in order to assess the strength and design criteria of the containment (proof test) and the leak tightness of the containment boundary (leakage rate test). During these tests, the concrete strains are measured and are expected to have a distribution due to several uncertainties. Therefore, this study aims to propose a probabilistic finite element analysis framework. Then, investigates the relationship between the concrete strains and the prestressing loss, in order to examine the possibility of estimating the average prestressing loss during pressure testing inspections. The results indicate that the concrete strain measurements during the leakage rate test may provide information with respect to the prestressing loss of the bonded system. In addition, the demonstrated framework can be further used for the probabilistic finite element analysis of real scale containments.

This paper proposes two algorithms to generate spectrum-compatible time histories based on two approaches recommended by USNRC Standard Review Plan 3.7.1. Hilbert–Huang Transform technique is used to analyze frequency contents and amplitudes of seed motions. Through adjusting the frequency contents and amplitudes of seed motions, spectrum-compatible time histories are obtained. The first algorithm is to generate tri-directional time histories compatible with multi-damping target design spectra (ground response spectra or floor response spectra). The second algorithm is to generate tri-directional time histories compatible with single-damping target design spectra. Examples are presented to demonstrate versatility of these two proposed algorithms to generate spectra-compatible time histories.

Newmark design spectra have been implemented in many building codes, especially in building codes for critical structures. Previous studies show that Newmark design spectra exhibit lower amplitudes at high frequencies and larger amplitudes at low frequencies in comparison with spectra developed by statistical methods. To resolve this problem, this study considers three suites of ground motions recorded at three types of sites. Using these ground motions, influences of the shear-wave velocity, earthquake magnitudes, source-to-site distances on the ratios of ground motion parameters are studied, and spectrum amplification factors are statistically calculated. Spectral bounds for combinations of three site categories and two cases of earthquake magnitudes are estimated. Site design spectrum coefficients for the three site categories considering earthquake magnitudes are established. The problems of Newmark design spectra could be resolved by using the site design spectrum coefficients to modify the spectral values of Newmark design spectra in the acceleration sensitive, velocity sensitive, and displacement sensitive regions.

Ultraso nic testing is a non-destructive and non-invasive method which has been used for internal condition assessment of wood poles in electric transmission and distribution lines. The reliability of this method of evaluation relies on a good understanding of propagation of ultrasonic waves in wood. However, a full-waveform analysis in ultrasonic testing is rarely performed in practice because of difficulties in establishing realistic values for the elastic parameters, modeling the material damping and characterizing the dynamic response of an ultrasonic transmitter. In this paper, a calibrated orthotropic finite element model for numerical simulations of ultrasonic testing of a sound red pine pole is presented. In the calibrated model, the dynamic modulus of elasticity in the radial and tangential directions, Poisson’s ratio and damping ratios are estimated from ultrasonic testing; whereas the dynamic modulus of elasticity in the longitudinal direction is estimated from transverse-vibration testing. The measured response of an ultrasonic transmitter to a one-cycle sinusoidal pulse of 50 kHz is used as dynamic excitation and introduced in the numerical model as displacement-time history. Results of the first arrival of compression waves and the frequency response magnitude computed at three receiver locations are in good agreement with the obtained ones from ultrasonic testing. The calibrated orthotropic finite element model will be used for a better understanding of propagation of surface and compression waves in ultrasonic testing for the detection of early stages of decay in wood poles.

This paper presents the development of a simplified regression approach for modelling the diametral creep over time in Zr-2.5 wt% Nb pressure tubes used in CANDU reactors. The model is based on a large dataset of in-service inspection data of 328 different pressure tubes from eight different CANDU reactor units. The proposed weighted least squares (WLS) regression model is linear in time as a function of flux and temperature, with a temperature-dependent variance function. The model predicts the shape of the observed diametral creep profiles very well, and is useful not merely for prediction, but also for assessing tube-to-tube variability and manufacturing properties among the inspected tubes.

Since the disastrous earthquake and tsunami on March 11, 2011, Japanese people have discussed the question of “How safe is safe enough?” The risk of spills from nuclear power plants is one of the major issues, and the government has shut down almost all nuclear power plants to re-evaluate the risk from each one. However, even after the re-evaluation, the nuclear power plants remain closed because many people do not agree with the evaluation, and they prefer to avoid as much risk as possible without fully understanding the cost of their demands. Currently, to sustain the electric demand with thermal power plants, Japan must import more fossil fuel at great cost. This study provides uncomplicated criteria for decision makers to use when describing the need to the general public to balance risks and costs. These criteria are known as Societal Capacity to Commit Resources (SCCR), and have been developed as comprehensible cost-benefit criteria for enhancing life safety. With the criteria, the acceptable risk is calculated based on the cost of prohibiting the nuclear power plants from operating. This suggested risk could be used as a basis to form the Japanese energy policy.

When generating floor response spectra (FRS) using the direct spectra-to-spectra method developed in the companion paper, probability distribution of t-response spectrum (tRS), which deals with equipment-structure resonance or tuning, corresponding to a specified ground response spectrum (GRS) is required. In this paper, simulation results using a large number of horizontal and vertical ground motions are employed to establish statistical relationships between tRS and GRS. It is observed that the influence of site conditions on horizontal statistical relationships is negligible, whereas the effect of site conditions on vertical statistical relationships cannot be ignored. Considering the influence of site conditions, horizontal statistical relationship suitable for all site conditions and vertical statistical relationships suitable for hard sites and soft sites, respectively, are established. The horizontal and vertical statistical relationships are suitable to estimate tRS for design spectra in USNRC R.G. 1.60 and NUREG/CR-0098, Uniform Hazard Spectra (UHS) in Western North America (WNA), or any GRS falling inside the valid coverage of the statistical relationship. For UHS with significant high frequency spectral accelerations, such as UHS in Central and Eastern North America (CENA), an amplification ratio method is proposed to estimate tRS. Numerical examples demonstrate that the statistical relationships and the amplification ratio method are acceptable to estimate tRS for given GRS and to generate FRS using the direct method in different practical situations.

In this paper, probabilistic finite element analysis (FEA) is applied using the Monte Carlo simulation (MCS) and the multiplicative dimensional reduction method (M-DRM). M-DRM is proposed for stochastic FEA of large scale and/or complex problems, as it provides the probability distribution of the structural response, apart the statistical moments, and requires fairly small computational time. MCS and M-DRM results are compared, indicating that both are in a good agreement. In addition, sensitivity analysis is also performed using the M-DRM, which does not require any extra analytical effort. The probabilistic FEA is applied with the use of the ABAQUS software, where the development of the FEA model and the updating of each input random variable for the required simulations, are both implemented with the use of the Python programing language. Two previously tested reinforced concrete flat slabs, with and without shear reinforcement, are examined. The concrete damaged plasticity model is used for the modeling of the concrete, which is offered in ABAQUS. The results of the deterministic FEA simulation show reasonable response compared to the behavior of the test specimens in terms of ultimate load, deflection and cracking propagation. For the probabilistic analysis, only the material uncertainty is taken into account, in order to examine the accuracy and efficiency of the proposed M-DRM framework and the contribution of the material uncertainty to the output response. Finally, design codes (ACI 318-11 and EC2 2004) for punching shear and the critical shear crack theory (CSCT 2008, 2009) are examined, considering the same input uncertainties. Useful outcomes are presented indicating the predictive capability of the proposed probabilistic FEA for future studies.

A direct spectra-to-spectra method is developed for generating floor response spectra (FRS), which are used as input for seismic design and assessment of secondary systems in nuclear facilities. Only ground response spectra (GRS) and basic modal information of primary structures, including natural frequencies, modal damping, participation factors, and mode shapes, which can be readily obtained from a modal analysis, are needed. In tuning cases, when equipment is resonant with the primary structure, the concept of t-response spectrum (tRS) is proposed, and statistical relationships between tRS and GRS developed in the companion paper are employed to determine FRS. Furthermore, a new modal combination rule (called FRS-CQC), which considers the correlation between modal responses of a structure and correlation between responses of equipment and its supporting structure, is derived based on random vibration theory. Numerical examples of a typical service building in nuclear power plants indicate that results from the proposed method agree extremely well with the numerically “exact” FRS obtained from a large number of sets of time history analyses. It is observed that FRS from time history analyses have large variabilities, particularly in tuning cases. Numerical examples demonstrate that the modal combination rules have a significantly effect on the accuracy of FRS by the direct spectra-to-spectra method. The proposed direct spectra-to-spectra method, which avoids the deficiencies of time history methods, is of excellent accuracy, efficiency, and simplicity; it is convenient to implement in practice for generating FRS.

The paper presents a stochastic approach to analyze instantaneous unavailability of standby safety equipment caused by latent failures. The problem of unavailability analysis is formulated as a stochastic alternating renewal process without any restrictions on the form of the probability distribution assigned to time to failure and repair duration. An integral equation for point unavailability is derived and numerically solved for a given maintenance policy. The paper also incorporates an age-based preventive maintenance policy with random repair time. In case of aging equipment, the asymptotic limit or average unavailability should be used with a caution, because it cannot model an increasing trend in unavailability as a result of increasing hazard rate (i.e. aging) of the time to failure distribution.

The non-invasive detection of debonding conditions and cavities beneath the wall of a steel tank are common applications in a variety of engineering and construction fields. Compressional ultrasonic waves have been used for the evaluation of steel plate thicknesses; however, they lack energy for penetrating a Portland cement grout in contact with a steel wall to detect debonding conditions. In this work, a joint analysis of surface waves and Lamb waves (high and low frequency) is used for the detection of debonding conditions in a scale model grouting steel tank. The propagation of high frequency ultrasonic waves generated by a 50-kHz transmitter along the side of the tank model is analyzed in the time domain and the frequency domain. In addition, using instrumented hammers with plastic or aluminum tips (low frequency sources) and a 50-kHz transmitter, three different configurations are used for the analysis of surface waves. The low-frequency Rayleigh waves generated by the hammer are used for void detection. Fourier spectra of the measured signals indicate that the effect of a void on the waves propagating through the medium is reduced when there is debonding. The comparisons of theoretical (high frequency) dispersion curves with experimental ones, computed from frequency wavenumber (FK) spectra, show that Lamb waves dominate the surface response in the wall of the steel tank. High frequency Lamb waves are successfully used in the detection of debonding between the tank wall and the grout because of the lower attenuation measured on top of the void.

The effect of Mn doping on Fe3O4 nanocrystalline spinel particles is studied. Two doping concentrations of 10 and 15% Mn were employed. The nanoparticles synthesis was carried out by wet chemical reduction technique. The energy dispersive analysis of X-ray confirmed the stoichiometry of the samples. The X-ray diffraction technique was used to determine the crystal structure and particles size of the synthesized nanoparticles. The electron microscopy revealed that both the synthesized nanoparticles surfaces have flower-like patterns and the particles are spherical. The optical absorption study showed that the absorption is more in case of 10% Mn doped compared to 15% Mn doped Fe3O4 nanoparticles. The Fourier transform infra-red spectroscopy revealed that both the samples contain characteristics bands. The magnetization variation with temperature with zero field cooled and field cooling conditions for two different applied magnetic fields of 500 Oe and 1000 Oe as well as the hysteresis study was carried out by vibrating sample magnetometer technique. The obtained results are discussed in details.

A highly efficient and accurate I-HPDIM algorithm is proposed.An absolute-response-oriented scheme of PEM is derived.A scheme in modelling tridirectional non-uniform nonstationary spatial motions is presented.The proposed stochastic analysis scheme is implemented in general FE platform.The proposed analysis scheme is demonstrated in bridge seismic pounding analysis. This paper proposes an improved high precision direct integration method (I-HPDIM) and an absolute-response-oriented scheme of pseudo-excitation method (PEM) for nonstationary stochastic seismic analysis of large structures under tridirectional nonuniformly modulated spatial ground motions. The proposed approaches resolve the bottle-neck problem of conventional HPDIM and significantly improve computational efficiency of both PEM and HPDIM, making the proposed nonstationary stochastic analysis scheme more attractive for engineering purposes. Hence, it has been implemented in general finite element platforms, having powerful and versatile modelling and analysis capabilities, for stochastic seismic analysis of large and complex structures under tridirectional nonstationary spatial seismic motions.

The degradation process of Alloy 800 under simulated steam generator (SG) secondary-side crevice-chemistry conditions containing chloride and thiosulphate was investigated. The SG chemical excursions were simulated by applying a series of square wave potential, followed by various periods of recovery. The results indicated that the damage to the passive film on Alloy 800 tubing material, caused by the excursions, was cumulative if the recovery time was no more than 900 s. The damage to the passive film of Alloy 800 was recoverable if the chemical excursions were shorter than a threshold value even after initiation of pitting/localized corrosion.

The objectives of this paper are to integrate the structural health monitoring (SHM) technique with the structural seismic analysis, and to make the SHM technique serve, benefit and promote the structural seismic analysis integrally. Therefore, considering a concrete-filled steel tubular arch bridge structure, the SHM technique is used to calibrate the finite element (FE) model through the model-updating scheme to minimise the structural response differences caused by FE model errors. Effects of model updating on structural seismic responses are investigated using the stochastic vibration analysis approach. It is observed that effects of model updating are significant on structural seismic responses, and these effects may become more evident in structural nonlinear dynamic analysis. Hence, it is of prime importance to calibrate the FE models through the SHM technique for seismic evaluations of some operational critical structures.

This paper presents a theoretical nonstationary stochastic analysis scheme using pseudo-excitation method (PEM) for seismic analysis of long-span structures under tridirectional spatially varying ground motions, based on which the local site effects on structural seismic response are studied for a high-pier railway bridge. An absolute-response-oriented scheme of PEM in nonstationary stochastic analysis of structure under tridirectional spatial seismic motions, in conjunction with the derived mathematical scheme in modeling tridirectional nonstationary spatially correlated ground motions, is proposed to resolve the drawbacks of conventional indirect approach. To apply the proposed theoretical approach readily in stochastic seismic analysis of complex and significant structures, this scheme is implemented and verified in a general finite element platform, and is then applied to a high-pier railway bridge under spatially varying ground motions considering the local site effect and the effect of ground motion nonstationarity. Conclusions are drawn and can be applied in the actual seismic design and analysis of high-pier railway bridges under tridirectional nonstationary multiple excitations.

This paper presents a comprehensive theoretical analysis of a concrete-filled steel tubular (CFST) arch bridge under tridirectional spatial seismic motions using the pseudo-excitation method. Formulations for modelling tridirectional spatial ground motions at varying site conditions are first derived. A site response analysis is presented for the tridirectional motions based on deterministic wave propagation theory, assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the multiple layered site with an assumed incident angle. Integration between the structural health monitoring (SHM) technique and the structural seismic analysis is proposed and conducted for the finite element (FE) model calibration of the CFST arch bridge through the model updating approach. Using the calibrated FE model, stochastic seismic analysis of the CFST arch bridge is conducted in a comprehensive and systematic way, by considering the dimensionality, incoherence effect, wave-path effect of ground motions, and local site effects with different and irregular site conditions. Critical conclusions are drawn and can be applied in the actual seismic design of the half-through CFST arch bridges under tridirectional multiple excitations.

An accurate estimation of the degradation growth rate is necessary for reliability analysis and fitness-for-service assessment of engineering components and structures. The growth rate analysis is based on repeated measurements of flaw sizes created by a degradation process over time in a component population. The flaw size measurements by inspection tools invariably include noise or sizing error, which complicates the estimation of growth rate. Most engineering models dealing with this issue do not properly account for the probabilistic structure of noisy data. Furthermore, the fact that the prediction of future degradation should be consistent with the model of underlying degradation process is often overlooked. This paper presents a comprehensive two-stage hierarchical model of noisy degradation measurement data, and formulates the associated maximum likelihood function. The parameter estimation is subsequently carried out in the spirit of well-known empirical Bayes method. The analysis is further extended to the prediction of the distributions of future degradation, remaining lifetime and reliability of components in both inspected and un-inspected component populations.

Utility wood poles are extensively used to support electrical-transmission and distribution lines in North America. Wood poles are exposed to extreme weather conditions, making them vulnerable to internal deterioration resulting in loss of pole strength, which can compromise the reliability of energy supply to customers. Ultrasonic testing is a nondestructive method that has been used for evaluation of the internal condition of in-service wood poles. However, the current assessment criterion is mostly based only on the first arrival of compression waves. This paper presents experimental and numerical methods for the detection of voids in wood poles using ultrasonic waves; the wood is considered as an orthotropic material. This investigation involves ultrasonic testing of a red-pine pole without and with a void. Changes in both compression wave velocity and wave attenuation are used to identify the presence of a void. An orthotropic finite-element model, calibrated with experimental results, is use...

The stochastic gamma process model is widely used in modeling a variety of degradation phenomena in engineering structures and components. If degradation in a component population can be accurately measured over time, the statistical estimation of gamma process parameters is a relatively straight-forward task. However, in most practical situations, degradation data are collected through in-service and non-destructive inspection methods, which invariably contaminate the data by adding random noises (or sizing errors) to the data. Therefore, a proper estimation method is needed to filter out the effect of sizing errors from the measured degradation data. This article presents an efficient method for estimating the parameters of the gamma process model based on a novel use of the Genz transform and quasi-Monte Carlo method in the maximum likelihood estimation. Examples presented show that the proposed method is very efficient compared with the Monte Carlo method currently used for this purpose in the literature.

Probabilistic seismic risk analysis (SRA) is often used for accurately quantifying seismic risk of critical engineering structures. It combines the probabilistic model of the behavior of structural response given a ground motion parameter (GMP) (e.g., seismic fragility model) and the probabilistic seismic hazard analysis (PSHA) for the GMP in a mathematically rigorous manner. In current engineering practice, SRA is performed based on a single GMP. For structures whose responses can be better predicted using multiple GMPs, a vector-valued SRA (VSRA) gives more accurate estimates of risk. However, due to the extensive computational efforts required for the multiple-dimensional cases, VSRA has not been widely applied in engineering practice. This paper presents a simplified approach to VSRA, which can substantially improve computational efficiency without losing accuracy. A new seismic hazard deaggregation procedure is proposed to determine a set of controlling earthquakes in terms of magnitude, sour...

The National Bureau of Standards (NBS) had undertaken a comprehensive study of underground soil corrosion of iron pipes and plates. The maximum pit depth data for different types of wrought iron and carbon steel pipes have been widely analyzed and utilized in the corrosion literature. There is another important but relatively obscure data set about the testing of pipes with bituminous coating that NBS carried out in collaboration with the American Petroleum Institute (API). This program tested dozens of coatings on operating line pipes as well as short sections of pipes at 15 soil sites over a 10 year period (1930–1940). This paper presents an overview of this data and presents statistical analysis of protection offered by coatings.

Nuclear power plants and many other industries are required to periodically inspect their buried piping to determine its fitness-for-continued service (FFS). The FFS process requires that both the general corrosion rate and the rate of maximum penetration for localized corrosion (e.g., pitting) be estimated so that the remaining lifetime and/or time until the next inspection can be determined. Revision 1 to ASME Code Case N-806, “Evaluation of Metal Loss in Class 2 and 3 Metallic Piping Buried in a Back-Filled Trench” [1] provides 4 options for estimating the corrosion rates: a. Wall thickness measurements from the current examination and from one or more previous examinations of the same metal loss region. b. Repeat measurements at two or more times from another location that has a predicted metal loss rate greater than or equal to the rate of the metal loss region under evaluation. c. Repeat measurements using corrosion coupons, linear polarization probes, or electrical resistance probes d. Generic historical data Each of these methods has its uses and limitations, and it is generally preferable to consider results from 2 or more of the methods. This paper examines historical data gathered by the National Bureau of Standards (NBS, renamed in 1988 as the National Institute of Standards & Technology - NIST) at ∼ 70 locations around the US in the 1930s – 1950s. Maximum penetration and weight loss (general corrosion) data from each site were placed in one of four soil texture groups for both carbon steel and cast iron. A regression analysis was performed to determine the median rates and 80% and 95% probabilistic values. It was found that results within each soil texture group were relatively similar and that the corrosion rates in the first 3 years after burial tended to be much higher than rates in years 5–18. The coefficients of determination were determined to quantify differences within each soil texture group. It is proposed that the steady state rates provided herein are an option to be used as the Historical Rates for FFS evaluations as described in [1].

The stochastic gamma process has been widely used to model uncertain degradation in engineering systems and structures. The optimization of the condition-based maintenance (CBM) policy is typically based on the minimization of the asymptotic cost rate. In the financial planning of a maintenance program, however, a more accurate prediction interval for the cost is needed for prudent decision making. The prediction interval cannot be estimated unless the probability distribution of cost is known. In this context, the asymptotic cost rate has a limited utility. This paper presents the derivation of the probability distribution of maintenance cost, when the system degradation is modelled as a stochastic gamma process. A renewal equation is formulated to derive the characteristic function, then the discrete Fourier transform of the characteristic function leads to the complete probability distribution of cost in a finite time setting. The proposed approach is useful for a precise estimation of prediction limits and optimization of the maintenance cost.

Uniform hazard spectra (UHS) have been used as design earthquakes in several design codes. However, as the results from scalar probabilistic seismic hazard analysis (PSHA), UHS do not provide knowledge about the simultaneous occurrence of spectral accelerations at multiple vibration periods. The concept of a single “design earthquake” is then lost on a UHS. In this study, a vector-valued PSHA combined with scalar PSHA is applied to establish an alternative design spectrum, named vector-valued UHS (VUHS). Vector-valued seismic hazard deaggregation (SHD) is also performed to determine the design earthquake in terms of magnitude, distance, and occurrence rate for the VUHS. The proposed VUHS preserves the essence of the UHS and can also be interpreted as a single design earthquake. To simplify the procedure for generating the VUHS, so that they can be easily incorporated into performance-based seismic design, an approximate method is also developed.

This paper aims to describe an alternative fire growth model that allows prediction of fire development, including time to flashover. The unpredictable nature of real fire development is incorporated into the model through use of probability distributions which can be defined using appropriate fire test data, when available. By assuming that the fire goes through five different stages starting from ignition and progressing to flashover, the total time to flashover may also be estimated. The model considers potential variability in the times at which the fire will undergo transitions between the various stages of development, using a state transition method called the semi-Markov process model. Different fire data may be incorporated into the model by defining appropriate statistical distributions for the transition descriptors, making the model flexible enough for use in a variety of applications important to both product design engineers and fire safety regulators.

The lack of fixed spatial referencing in inspection data is a confounding factor in the assessment of wall thinning due to flow-accelerated corrosion (FAC). Because of the loss of wall thickness over time, it is impossible to match any two unreferenced points precisely between inspection outages, making the use of point-to-point comparison methods highly uncertain. In this study, we develop a new methodology for estimating the FAC rate and component lifetime from spatially unreferenced inspection data. The method is based on a small circular patch that represents the minimum wall thickness as a random variable. This allows the predictions to be performed in a probabilistic setting, hence providing valuable risk information for long-term replacement planning and life-cycle management. The uncertainty and errors introduced by inspection and grid coverage are minimized in the analysis by fitting a continuous surface through the inspection data using the method of kriging. The developed methodology is applied to the assessment of carbon steel feeder piping in CANDU reactors, where the economic and safety consequences of FAC can be highly significant. Based on the analysis of a large industry dataset, FAC in feeder piping appears to be a relatively uniform and stationary process. The results of the study demonstrate the key advantages of the developed methodology and how it can be used to support risk-informed decision making with respect to FAC at power plants.

In the CANDU pressurized heavy water reactor (PHWR), the nuclear fuel is contained in hundreds of Zr–2.5 Nb alloy pressure tubes. The corrosion of zirconium alloy produces deuterium that is absorbed by the body of the pressure tube. The presence of this deuterium causes hydrogen embrittlement of zirconium alloy with an adverse effect on the integrity of the pressure tube. An accurate prediction of deuterium accumulation over time is an important step for ensuring the fitness-for-service of pressure tubes. Deuterium ingress data collected from in-service inspection of pressure tubes exhibit heteroscedasticity, i.e., the variance of deuterium concentration is dependent on operating time (or exposure) and temperature. The currently used model by the nuclear industry involves a logarithmic regression of deuterium content over time and temperature. Since this approach does not deal with heteroscedasticity precisely, it results in a conservative prediction of the deuterium ingress. The paper presents a new approach for predicting deuterium ingress based on a weighted least-squares (WLS) regression that overcomes the limitations of the existing model, and it provides realistic prediction bounds of deuterium ingress.

The gamma process is a stochastic cumulative process with gamma distributed increments. Professor van Noortwijk's research work played a key role in modelling uncertain and time-dependent degradation of structures as a gamma process, making it popular in the engineering community (van Noortwijk, J.M. and van Gelder, P.H.A.J.M., 1996. Optimal maintenance decisions for berm breakwaters. Structural Safety, 18 (4), 293–309). The maintenance optimisation models mostly use the renewal theorem to evaluate the asymptotic cost rate and use it to optimise the maintenance policy. However, many engineering structures have a relatively short and finite time horizon in which the application of the asymptotic formula becomes questionable. This article presents a finite time model for computing the expected cost of a condition-based maintenance program considering degradation as the gamma process. The article investigates the suitability of the asymptotic cost rate formula and provides a rich discussion about the qualita...

A new approach for generating a set of tri-directional earthquake time-histories compatible with the target seismic design spectra for nuclear energy facilities based on multiple sets of actual earthquake records is presented. The tri-directional spectrum-compatible earthquake time-histories are generated using the Hilbert–Huang transform (HHT) and solving optimization problems. Three orthogonal components of generated earthquake ground motion are statistically independent from the point of view of practical engineering. The two horizontal components have the same frequency–time–amplitude distribution. The generation procedure can preserve the nonstationary characteristics of the seed actual earthquake records.

The paper presents an analytical formulation for evaluating the maintenance cost of engineering systems that are damaged by shocks arriving randomly in time. The damage process is nonlinear in a sense that damage increments form an increasing sequence (i.e., accelerated damage) or a decreasing sequence (saturated damage) of random increments. Such processes are motivated from damage data collected from nuclear reactor components. To model the nonlinear nature of damage process, the paper proposes the use of non-homogeneous Poisson process for damage increments, which is in contrast with the common use of a renewal process for modeling the damage. The paper presents a conceptually clear and comprehensive derivation of formulas for computing the expected cost rate associated with a periodic inspection and preventive maintenance policy. Distinctions between the analysis of self-announced and latent failures are highlighted. The analytical model presented in this paper is quite generic and versatile, and it can be applied to optimize other types of maintenance policies.

The pulse velocity test (PVT) is an ASTM standard for the dynamic characterisation of geomaterials such as stiff clays, cemented sands, rooks and concrete. The PVT is based on the first arrival of the compressional wave. The analysis of full waveforms in ultrasonic testing is important in evaluating the variation with frequency of the dynamic properties of materials (phase velocity and material damping). Reliable full waveforms are also required to calibrate numerical simulations for the interpretation of ultrasonic wave propagation in viscoelastic materials. However, the analysis of full waveforms is rarely performed in practice because of the difficulties involved in the characterisation of ultrasonic transducers and their coupling with the medium. This paper presents a new methodology for measurement of the frequency response and impulse response functions of ultrasonic transducers. The proposed methodology uses the complex exponential method to extract dynamic properties from impulse response functions. Ultrasonic tests and numerical simulations are conducted on a calibration aluminium bar and a cemented sand specimen to demonstrate the applicability of the new methodology. The results show that this methodology can be successfully used for dynamic characterisation of ultrasonic transducers for evaluation of the wave velocity and damping ratio of stiff geomaterials.

The performance and reliability of engineering systems and structures are usually affected by uncertain degradation that occurs in service as a result of various physical and environmental processes, such as corrosion, erosion, fatigue, and creep. To maintain reliability of degrading systems, periodic inspection and preventive maintenance programmes are adopted. In the literature, the optimization of a maintenance programme is typically based on the minimization of the asymptotic cost rate. However, many engineering systems operate in a relatively short and finite time horizon in which the application of the asymptotic approximation becomes questionable. This paper presents an accurate formulation for computing the expected value and variance of the cost of a condition-based maintenance programme over a defined time horizon. A stochastic gamma process is used to model uncertain degradation. This paper emphasizes that the consideration of variance of the cost is of utmost importance in maintenance optimization, because it helps to identify a more robust (less uncertain) solution in a set of competing optimum solutions based on expected cost.

A reliability analysis of nuclear component cooling water (NCCW) system is carried out. Semi-Markov process model is used in the analysis because it has potential to solve a reliability block diagram with a mixture of repairable and non-repairable components. With Markov models it is only possible to assume an exponential profile for component failure times. An advantage of the proposed model is the ability to assume Weibull distribution for the failure time of components. In an attempt to reduce the number of states in the model, it is shown that usage of poly-Weibull distribution arises. The objective of the paper is to determine system failure probability under these assumptions. Monte Carlo simulation is used to validate the model result. This result can be utilized as an initiating event probability in probabilistic safety assessment projects.

In this paper, we stress upon rapid synthesis of irregular shape gold nanoparticles from a biological base. Treatment of macerated extracellular aqueous dried clove buds (Syzygium aromaticum) solution with the aqueous gold salt solution yielded irregular shaped stable gold nanoparticles in the range of 5-100 nm. The synthesis and morphology of these gold nanoparticles are understood by UV (UV-vis spectroscopy), FESEM (field emission scanning electron microscopy), TEM (transmission electron microscopy) and AFM (atomic force microscopy) techniques. The formation of these bio-adsorbed gold nanoparticles is rapid as the reaction process completes within few minutes. The XRD (X-ray diffraction studies) and EDAX (energy dispersive X-ray analysis) show that the particles are crystalline in nature. This clean-green method of synthesis is performed under ambient conditions. Probable biochemical pathway of the synthesis is studied using FTIR (Fourier transformed infrared spectroscopy). It is observed that the freely water soluble flavonoids of clove buds are responsible for bioreduction. The possible applications viz., catalysis, sensor, diagnostics, biomedical imaging and photo thermal therapy of these functionalized noble metal nanoparticles are envisaged.

Recently, blind source separation (BSS) methods have gained significant attention in the area of signal processing. Independent component analysis (ICA) and second-order blind identification (SOBI) are two popular BSS methods that have been applied to modal identification of mechanical and structural systems. Published results by several researchers have shown that ICA performs satisfactorily for systems with very low levels of structural damping, for example, for damping ratios of the order of 1% critical. For practical structural applications with higher levels of damping, methods based on SOBI have shown significant improvement over ICA methods. However, traditional SOBI methods suffer when nonstationary sources are present, such as those that occur during earthquakes and other transient excitations. In this paper, a new technique based on SOBI, called the modified cross-correlation method, is proposed to address these shortcomings. The conditions in which the problem of structural system identification can be posed as a BSS problem is also discussed. The results of simulation described in terms of identified natural frequencies, mode shapes, and damping ratios are presented for the cases of synthetic wind and recorded earthquake excitations. The results of identification show that the proposed method achieves better performance over traditional ICA and SOBI methods. Both experimental and large-scale structural simulation results are included to demonstrate the applicability of the newly proposed method to structural identification problems.

This paper presents methods to evaluate the reliability and optimize the maintenance of engineering systems that are damaged by shocks or transients arriving randomly in time and overall degradation is modeled as a cumulative stochastic point process. The paper presents a conceptually clear and comprehensive derivation of formulas for computing the discounted cost associated with a maintenance policy combining both condition-based and age-based criteria for preventive maintenance. The proposed discounted cost model provides a more realistic basis for optimizing the maintenance policies than those based on the asymptotic, non-discounted cost rate criterion.

The delayed hydride cracking (DHC) of flaws and cracks in pressure tubes is a serious form of degradation in the reactor core. CSA standard N285.8 (2005) recommends deterministic and probabilistic procedures for assessing the potential of DHC initiation from flaws that are generated by fretting or any other mechanism. Although the deterministic method is simple, it lacks a quantitative risk-informed basis for the assessment. On the other hand, a full probabilistic method based on simulation is tedious to implement. This paper presents an efficient, reliability-based approach that bridges the gap between a simple deterministic analysis and full Monte Carlo simulations. In the proposed method, a deterministic DHC initiation criterion is calibrated to specified target probability levels. The main advantage of the proposed approach is that it provides a practical, risk-informed basis for DHC initiation assessment while retaining the simplicity of the deterministic method.

Steam generators in nuclear power plants have experienced varying degrees of under-deposit pitting corrosion. A probabilistic model to accurately predict pitting damage is necessary for effective life-cycle management of steam generators. This paper presents an advanced probabilistic model of pitting corrosion characterizing the inherent randomness of the pitting process and measurement uncertainties of the in-service inspection (ISI) data obtained from eddy current (EC) inspections. A Markov chain Monte Carlo simulation-based Bayesian method, enhanced by a data augmentation technique, is developed for estimating the model parameters. The proposed model is able to predict the actual pit number, the actual pit depth as well as the maximum pit depth, which is the main interest of the pitting corrosion model. The study also reveals the significance of inspection uncertainties in the modeling of pitting flaws using the ISI data: Without considering the probability-of-detection issues and measurement errors, the leakage risk resulted from the pitting corrosion would be under-estimated, despite the fact that the actual pit depth would usually be over-estimated.

Alloy 800 has been used for steam generator (SG) tubing for more than 30 years, primarily in CANDU reactors worldwide and in reactors in Germany. Extensive laboratory testing and in-service experience suggest that the Alloy 800 tubing has excellent resistance to corrosion-related degradation under appropriate operating conditions. In planning refurbishment of nuclear plants stations, a key concern is the longevity of existing SGs up to the 60-year lifetime of the refurbished plant. The paper reviews an existing methodology based on the concept of the improvement factor, and refines its estimation based on data specific to CANDU operating conditions. The paper presents a more advanced Bayesian probabilistic approach to estimate the degradation free lifetime distribution of Alloy 800 tubing, which is used to quantify the probability of degradation during the service life and to evaluate the impact of potential occurrences of degradation on reliability of SG tubing.

In the life-cycle management of infrastructure systems, the decisions regarding the time and frequency of inspection, maintenance and replacement are confounded by sampling and temporal uncertainties associated with deterioration of the structural resistance. To account for these uncertainties, probabilistic models of deterioration have been developed under two broad categories, namely the random variable model and the stochastic process model. This paper presents a conceptual exposition of these two models and highlights their profound implications on age-based and condition-based preventive maintenance policies. The stochastic gamma process model of deterioration proposed here is more versatile than the random rate model commonly used in structural reliability literature.

Monitoring of degradation and predicting its progression using periodic inspection data are important to ensure safety and reliability of engineering systems. Traditional regression models are inadequate in modeling the periodic inspection data, as it ignores units specific random effects and potential correlation among repeated measurements. This paper presents an advanced nonlinear mixed-effects (NLME) model, generally adopted in bio-statistical literature, for modeling and predicting degradation in nuclear piping system. The proposed model offers considerable improvement by reducing the variance associated with degradation of a specific unit, which leads to more realistic estimates of risk.

This paper presents results from multi-channel analysis surface waves (MASW) tests conducted to locate buried timber trestles in two different sections (A and B) of an earth embankment. For section A, the location of the trestles is known as well as the soil properties; thus, it is used for calibration purposes. Conversely, the location of the timber trestles is unknown for section B. A seismic array of 24 geophones with a spacing of 0.5 m is used for surface-wave measurements. Different signal processing techniques are used for data analysis: dispersion curves, power spectral functions, frequency-spectra contour plots, two-dimensional-Fourier transform, and the wavelet transform. A new procedure is proposed for the surface location of buried trestles, which is based on the use of the normalized average power energy plot. Finite-element numerical simulations of MASW tests on layered and homogeneous media with and without buried trestles are performed to support experimental results and to explain the wave–trestle interaction. The numerical simulations show that a buried trestle induces vibration amplifications at the surface in front of its location but vibration attenuation immediately after. These effects, however, are observed only if the embedment depth of timber trestle is smaller than one third of the wavelength. Experimental and numerical results show that the results from MASW tests can be successfully used to define the surface location of decayed buried trestles.

This paper describes a standard of practice for optimizing engineered safety. The objective in managing risk is to ensure that significant risks are identified and appropriate actions taken to minimize these risks to a reasonably low level. Engineered safety is always determined on the basis of a balance between the cost effectiveness of risk control and the benefits arising from the mitigation of risk. For the net benefit to be positive, whether it accrues to the organization or to society at large, the management of risk entails a process of priority setting, as there are limits on available resources. The net benefit is measured by the consequent increment to the Life Quality Index (LQI). With this approach, enterprises, both public and private, have a more confident and rigorous basis for decision-making and planning engineering projects when life safety is a concern. The evaluation process, the requirements for data to support the analysis, and the major components of the LQI model are illustrated by...