Structural Reliability Evaluation Research Articles

Simulation of multivariate ergodic stochastic processes using adaptive spectral sampling and non-uniform fast Fourier transform

The simulation of multivariate ergodic stochastic processes is critical for structural dynamic analysis and reliability evaluation. Although the traditional spectral representation method (SRM) has a wide application in many areas, it is highly inefficient in simulating stochastic processes with many simulation points or long durations due to the significant computational cost associated with matrix factorizations concerning frequency. To address the encountered challenge, this paper presents an efficient approach for simulating ergodic stochastic processes with limited frequencies. Central to this approach is a fusion of the adaptive spectral sampling and the non-uniform fast Fourier transform (NUFFT) techniques. The adaptive spectral sampling of the envelope spectrum enables the determination of limited non-equispaced frequencies, which are randomly sampled according to a uniform distribution. Thus, the Cholesky decomposition is only required at limited specific frequencies, which dramatically reduces the computational cost of matrix factorizations. Since the randomly sampled frequencies are not equispaced, utilizing FFT to accelerate the summation of trigonometric functions becomes impractical. Then, the NUFFT that adapts the non-equispaced sampling points is employed instead to expedite this process with the non-uniform increment approximated through reduced interpolation. By taking the wind field simulation of a long-span suspension bridge as an example, a parametric analysis is conducted to investigate the effect of random frequencies on the simulation error of the developed approach and the convergence of spectra. Finally, the developed approach is further validated by focusing on the spectra and probabilistic density functions of the simulated wind samples, and the simulation performance is compared with that of the traditional approach. The analytical results demonstrate the efficiency and accuracy of the developed approach in simulating ergodic stochastic processes.

Probability Analysis of Duration of Stochastic Process Exceeding Fixed Threshold and Its Application on Structural Cumulative Damage and Fatigue Reliability Evaluation

Probability Analysis of Duration of Stochastic Process Exceeding Fixed Threshold and Its Application on Structural Cumulative Damage and Fatigue Reliability Evaluation

Adaptive directed support vector machine method for the reliability evaluation of aeroengine structure

Machine learning methods have been widely applied to structural reliability analysis, due to the excellent performance in modeling precision and efficiency. In this paper, an adaptive directed support vector machine model (ADSVM) is proposed by integrating the adaptive sampling technology (AST) and the developed directed support vector machine (DSVM), to improve the efficiency and accuracy of turbine blade reliability analysis. In the developed method, the AST is adopted to extract high quality samples, in respect of distributed probability density and the distances between sample values and response values. The DSVM was developed by introducing the penalty coefficients for all the slack variables, to improve the modeling accuracy of SVM approach. One numerical example and the reliability analysis of aeroengine high-pressure turbine blade were performed to validate the developed methods. As illustrated in this numerical investigation, the modeling precision of DSVM is improved by alleviating the lag effect of support vector regression. From the comparison of methods, it is demonstrated that the ADSVM has higher accuracy, efficiency and stability in reliability simulations, which are improved by ∼20 % and ∼46.2 %, respectively. The main efforts of this study are to propose a promising approach, ADSVM, for the reliability analysis of complex structures besides turbine blades, which hold the academical significance in enriching and developing mechanical reliability theory.

Design of UHPC prestressed girders for shear

AbstractBreakthrough technology of ultra‐high‐performance concrete (UHPC) introduced in the 1990s exhibits several exceptional mechanical properties that are advantageous in elements of bridge applications. Extensive research has aimed to industrialize UHPC and develop design models. This paper investigates several design models for shear, including a unified approach with that of conventional concrete based on the modified compression field theory (MCFT). An experimental database of UHPC prestressed concrete girders subjected to shear failure is compiled to evaluate model accuracy and a reliability study is conducted to establish appropriate safety factors. The analysis demonstrates that the proposed MCFT‐based model aligns well with experimental results, exhibiting a suitable level of conservatism for design. A reliability assessment of a typical prestressed girder designed according to Canadian Standards Association building and bridge loadings is performed, resulting in a structural reliability evaluation against a target reliability index. The study recommends specific strength reduction and safety factors for design approaches using UHPC.

Extreme state prediction of long-span bridges using extended ACER method

An accurate prediction of the future service state of long-span bridges is crucial for the structural reliability evaluation, maintenance planning, and further life-cycle cost analysis. By extending the average conditional exceedance rate (ACER) statistical model and applying input–output data collected through a structural health monitoring (SHM) system, this paper proposes a novel methodology for predicting the future service state of long-span bridges. The advantages lie in the consideration of the main excitation load as the structural input and the strain response of the bridge as the output. Therefore, a mapping relationship between the extreme excitation load and extreme strain could be established, and the future service state of long-span bridges could be predicted. The proposed method comprises three steps: (1) extraction of the ambient temperature-induced strain and vehicle-induced strain from the measured strain series through the SHM system using the baseline estimation and denoising with sparsity (BEADS) method, (2) establishing statistical models of the extreme values of different excitations (input) and structural strains (output) using a cascade of conditioning approximations and the ACER to obtain the tail trend of the data and extrapolating it, and (3) establishing a functional relationship between the input and output extreme values based on the same conditions of the regression period at the target prediction level, after which the future service state of long-span bridges can be predicted. The proposed method is applied to a case study of the Jinchao Bridge in Guangdong Province, China, and the results are expected to provide a scientific reference for the design of new bridges and in the maintenance of existing ones in service.

Development, Reliability, and Structural Validity of the Scale for Knowledge, Attitude, and Practice in Ethics Implementation Among AI Researchers: Cross-Sectional Study.

Medical artificial intelligence (AI) has significantly contributed to decision support for disease screening, diagnosis, and management. With the growing number of medical AI developments and applications, incorporating ethics is considered essential to avoiding harm and ensuring broad benefits in the lifecycle of medical AI. One of the premises for effectively implementing ethics in Medical AI research necessitates researchers' comprehensive knowledge, enthusiastic attitude, and practical experience. However, there is currently a lack of an available instrument to measure these aspects. The aim of this study was to develop a comprehensive scale for measuring the knowledge, attitude, and practice of ethics implementation among medical AI researchers, and to evaluate its measurement properties. The construct of the Knowledge-Attitude-Practice in Ethics Implementation (KAP-EI) scale was based on the Knowledge-Attitude-Practice (KAP) model, and the evaluation of its measurement properties was in compliance with the COnsensus-based Standards for the selection of health status Measurement INstruments (COSMIN) reporting guidelines for studies on measurement instruments. The study was conducted in 2 phases. The first phase involved scale development through a systematic literature review, qualitative interviews, and item analysis based on a cross-sectional survey. The second phase involved evaluation of structural validity and reliability through another cross-sectional study. The KAP-EI scale had 3 dimensions including knowledge (10 items), attitude (6 items), and practice (7 items). The Cronbach α for the whole scale reached .934. Confirmatory factor analysis showed that the goodness-of-fit indices of the scale were satisfactory (χ2/df ratio:=2.338, comparative fit index=0.949, Tucker Lewis index=0.941, root-mean-square error of approximation=0.064, and standardized root-mean-square residual=0.052). The results show that the scale has good reliability and structural validity; hence, it could be considered an effective instrument. This is the first instrument developed for this purpose.

LCF Lifetime Reliability Prediction of Turbine Blisks Using Marine Predators Algorithm-Based Kriging Method

To achieve the low-cycle fatigue (LCF) lifetime prediction and reliability estimation of turbine blisks, a Marine Predators Algorithm (MPA)-based Kriging (MPA-Kriging) method is developed by introducing the MPA into the Kriging model. To obtain the optimum hyperparameters of the Kriging surrogate model, the developed MPA-Kriging method replaces the gradient descent method with MPA and improves the modeling accuracy of Kriging modeling and simulation precision in reliability analysis. With respect to the MPA-Kriging model, the Kriging model is structured by matching the relation between the LCF lifetime and the relevant parameters to implement the reliability-based LCF lifetime prediction of an aeroengine high-pressure turbine blisk by considering the effect of fluid–thermal–structural interaction. According to the forecast, when the allowable value of LCF lifetime is 2957 cycles, allowing for engineering experience, the turbine degree of reliability is 0.9979. Through the comparison of methods, the proposed MPA-Kriging method is demonstrated to have high precision and efficiency in modeling and simulation for LCF lifetime reliability prediction of turbine blisks, which, in addition to the turbine blisk, provides a promising method for reliability evaluation of complicated structures. The work done in this study aims to expand and refine mechanical reliability theory.

A Dynamic Reliability Prognosis Method for Reusable Spacecraft Mission Planning Based on Digital Twin Framework

Abstract Reusable spacecraft has great potential in reducing space launch cost. Structural reliability evaluation is critical for mission planning of reusable spacecraft. A dynamic reliability prognosis method based on digital twin framework is proposed for mission planning in the paper. In this method, Uncertainties integration and dynamic model updating are implemented through a dynamic Bayesian network. A maintenance point is set when the predicted structural reliability level is lower than a threshold or unexpected conditions such as landing impact occur. Then, inspected data can be assimilated by the framework to dynamically update the structural reliability. Thus, it supports dynamic adjustment of maintenance interval, early warning of structure failure, and mission planning with quantified risk. A numerical example considering single point crack growth under fatigue load and landing impact of a simplified spacecraft structure is used for demonstration. Results show that the crack size predictions can be calibrated by inspected data and its uncertainties can be reduced. The proper selection of landing impact probability in reliability prediction is helpful to control the maintenance interval. The reliability of the spacecraft can be increased through model updating with new inspected data, representing a potential lifetime extension can be realized by the proposed method.

Structural Reliability Analysis of Large Planar Steam Solid Oxide Electrolysis Cells

Solid oxide electrolysis cells (SOEC) have been receiving significant attention recently because of their high energy efficiency and fast hydrogen production. In our previous study, a multi-physics modeling framework to simulate the SOEC performance and structural reliability of planar SOEC design was developed and demonstrated. The electrochemical reactions, fluid dynamics, species transport, electron transfer, and heat transfer were modeled in the commercial computational fluid dynamics (CFD) software STAR-CCM+. The thermomechanical analysis and the associated structural reliability evaluations were conducted using the commercial finite element analysis software ANSYS. The electrochemistry model was validated by using the experimentally obtained current-voltage (I-V) characteristics of the electrode-supported SOECs. In this study, this framework was applied on a large 300 cm2 steam planar SOEC design, and systematically studied the structural reliability under combinations of cell operating conditions, with cell voltage 1-1.5 V, steam fraction in fuel inlet 0.7-0.9, air inlet flow rate 0-10 L/min, fuel inlet flow rate 2.5-12.5 L/min, and inlet temperature 600-900 C. In the modeling framework, all the cells were investigated under the adiabatic thermal conditions, which is equivalent to packing the cell in an insulated container. This induced the relatively larger temperature variation than in the smaller cell designs. This cell internal temperature non-uniformity may further enhance the spatial variations of open circuit voltage, activation loss, and ionic conductivity in the cell, which all influence the overall cell performance. This situation is more obvious when the cell voltage is higher than 1.35V, under which the cell is significantly heated along the steam flow direction. Traditionally, it is assumed that the cell internal temperature spatial variation plays an important role on cell structural reliability. However, because it was assumed that all the components in cell are stress free at 850 , the cell temperature deviation from 850 is more critical to the stress distribution and structural reliability in the cell. For the investigated cells in the practical conditions, like 750 C inlet temperature and varying voltage from 1.05 to 1.5 V, the highest first principal stress is always in the air side electrode, which is around 45 MPa. This is explained by the higher coefficient of thermal expansion of LSCF-GDC with respect to the other layers. This may indicate that the failure would possibly occur in the air side electrode, but at low risk due to the relatively higher Weibull characteristic strength.

Active learning-based structural reliability evaluation Kriging model and sequential importance sampling

The efficient analysis of structural system reliability with multiple failure modes and small failure probabilities presents significant challenges for active Kriging methods. This paper proposes a novel method, PAK-SEIS, which combines the Parallel Active learning Kriging model and the Sequential Importance Sampling method to overcome these challenges. The proposed method includes a new sequential importance sampling method that integrates the sequential Monte Carlo simulation (MCS) and kernel density estimation to construct the optimal importance density. Additionally, the proposed parallel learning strategy allows for the selection of multiple new training samples, reducing performance function calls and refining iterations of Kriging models. The PAK-SEIS method gradually approximates the optimal importance density by updating multiple new training samples and failure modes in parallel at each iteration based on a small number of candidate samples. Candidate samples generated in the final sequence can cover all limit state surfaces, and all Kriging models are accurately constructed. The PAK-SEIS method can effectively address system reliability problems with small failure probability, multiple failure regions, and implicit functions. Two examples demonstrate the efficiency and accuracy of the proposed PAK-SEIS method.

Applying an Artificial Neural network- Developed Collective Animal Behavior Algorithm for seismic reliability evaluation of structure

The seismic design contains considerable uncertainties, which originate from the structural geometries, earthquake motions, analytical models, and material properties. By considering all main uncertainties, reliability analysis is applied estimating the possibility of failure in each of a set of performance requirements. Structural failure localization, quantification, and failure possibility evaluation are principal outputs in the structures reliability evaluation. In this paper, an Artificial Neural Network- Developed Collective Animal Behavior Algorithm is used for reducing the problem complexity needed for reliability investigation and failure detect. In this way, a definite structure is modeled and some failure case are determined. These cases are recognized as train databases for organizing the ANN-DCABA. Therefore, the correlation among structure's response as input and structure's stiffness as output is provided utilizing Artificial Neural Network- Developed Collective Animal Behavior Algorithm. The provided method is so efficient and produces advisable precision in structural failure discovery under a series of ground motions. Besides, for assessing the structure reliability, 5 accidental variables are determined. These are columns’ state of the 1st, 2nd, and 3rd floor, gravity loads, and elasticity modulus. Finally, the Artificial Neural Network- Developed Collective Animal Behavior Algorithm specifies the failure probability of the proposed structure and it can reduce the computational effort required for reliability analysis and damage detection. However, MCS could indicate the failure probability for a given structure; the Artificial Neural Network- Developed Collective Animal Behavior Algorithm helps simulation techniques for receiving an acceptable precision and decrease computational effort.

An efficient time-variant reliability analysis strategy embedding the NARX neural network of response characteristics prediction into probability density evolution method

Stochastic response analysis and first-passage reliability evaluation of multi-degree of freedom nonlinear systems subject to non-stationary seismic excitation have been a critical issue in the field of compound random vibrations, yet remain unsolved. This study extends the time-varying reliability analysis method based on the probability density evolution method, making it applicable to the problem of stochastic response analysis and first-passage reliability evaluation of complex engineering structures. To efficiently represent the response of representative samples, a nonlinear autoregressive with exogenous inputs neural network model is introduced in this study. After comparing three different optimization methods, the neural network model based on the Bayesian regularization algorithm is selected as the predictor for the response of complex nonlinear systems, enabling efficient stochastic response analysis and time-varying reliability evaluation. To this end, leveraging the high efficiency of the probability density evolution method, the analysis of time-varying reliability of large-scale structures has been successfully conducted. Furthermore, the proposed method can be easily expanded to dynamic reliability evaluation problems represented by extreme value theory. Three numerical examples are quoted to demonstrate the applicability and advantages of the proposed method in the field of first-passage and extreme-value problems of systems, which are also compared with PCE, SVR, and Kriging. The results from these numerical examples indicate that the proposed method can effectively reduce the required calculational cost for the reliability analysis of complex structures while maintaining high analytical accuracy.

Reliability Evaluation of a Nonlinear Frame Structure under Explosive Ground Motions Generated by Dimension-Reduction Method

In the present study, a stochastic model of explosive ground motions applying the dimension-reduction method is proposed, and the reliability evaluation of a nonlinear frame structure under such excitations is realized by means of the probability density evolution method and an equivalent extreme-value-based reliability evaluation strategy. Firstly, the evolutionary power spectrum density function of the explosive ground motions is modeled by respectively identifying the normalized total energy distribution function and the frequency total energy distribution function on the basis of the measured motion records. In addition, an exponential model is constructed to forecast the seismic characteristics of the explosive ground motions based on the given distance to the explosive source and the charge quantity. Then, the representative samples of the explosive ground motions are simulated using the dimension-reduction method. The simulation results show that the generated acceleration samples have significant seismic characteristics of the explosive ground motions, and the accuracy is verified by comparing the second-order statistics with the sample set and the corresponding targets. Due to the fact that the probabilities of the representative samples simulated by the dimension-reduction method can compose a comprehensive probability set, it contributes to the refined dynamic response analysis and reliability evaluation of complex structures combining with the probability density evolution method. The accurate dynamic response analysis and reliability evaluation of a nonlinear frame structure illustrates the effectiveness of the proposed model and the dimension-reduction method for simulating the explosive ground motions. The numerical results demonstrate that the explosive ground motions have a substantial effect on the nonlinear behavior and the security of engineering structures.

Applicability Analysis of Nickel Steel Plate Friction Coefficient Model Based on Fractal Theory

In the field of aerospace, weapons and other complex assembly, there are more than 50 factors affecting the performance degradation of joint structures, among which the friction coefficient is the main factor. Nickel steel is widely used in large complex equipment due to its advantages of high strength. Therefore, this paper first establishes a theoretical model of friction coefficient based on fractal theory. Secondly, the friction coefficient experiment was carried out to measure the friction coefficient of nickel steel plates with different roughness under different normal loads. Finally, the experimental results are compared with the theoretical results, and the accuracy and error analysis of the model is carried out. The results show that the friction coefficient increases with the increase in roughness. When the normal load is greater than 50 kg, the friction coefficient gradually tends to be stable. The error of identification results of correction factor a was all within 5%. The error between theoretical model prediction and experimental data is 6%–15%, which indicates that the calculation of the friction coefficient has high accuracy. The results of this study can provide data and theoretical support for the friction coefficient evaluation of nickel steel plate joint structures, and contribute to the health detection and reliability evaluation of nickel steel plate joint structures.

Multivariate ensembles-based hierarchical linkage strategy for system reliability evaluation of aeroengine cooling blades

To improve the computing accuracy and efficiency of system reliability evaluation for aeroengine cooling blades, by fusing the benefits of multivariate ensembles model (ME) into the hierarchical linkage technique (HL), a multivariate ensembles-based hierarchical linkage strategy (ME-HL) is proposed. In the ME-HL modeling, the complex evaluation system is first decomposed into multiple subsystems (i.e., frail site and failure mode) by the developed HL strategy, after that the multiple output responses of subsystems are synchronously mapped by proposing the ME model, and the multi-level system reliability framework is finally built with the Copula-based correlation quantification. The reliability evaluation of a typical aeroengine turbine cooling blade is regarded as a case, to verify the effectiveness of the proposed strategy. From the reliability evaluation results, we observe that the acquired reliability degree considering the failure correlation (i.e., 0.9547) is higher than that of without considering the failure correlation (i.e., 0.9356). From the methods comparison, we discover that the computing efficiency of the ME-HL method is 86.89%, 80.12%, 80.63%, and 18.85% greater than that of the ANN, BT, ME, and BT-HL methods, respectively; and the computing efficiency of the ME-HL method is 12.47%, 11.26%, 6.11%, and 0.93% higher than that of the ANN, BT, ME, and BT-HL methods, respectively. The evaluation and comparison results demonstrate that the proposed ME-HL holds significant advantages in computing accuracy and efficiency in system reliability evaluation problems. The current study can shed a light on the complex multi-level structural system reliability evaluation.

Modeling Multidimensional Multivariate Turbulent Wind Fields Using a Correlated Turbulence Wave Number–Frequency Spectral Representation Method

Accurate and efficient simulation of turbulent stochastic fields lays a solid foundation for dynamic response analysis and reliability evaluation of wind-sensitive structures. In this paper, a correlated-turbulence wave number–frequency spectral representation method (CT-WSRM) is proposed for simulating turbulent wind fields. Turbulent spectra that consider the correlation of turbulence are established using wind data measured during Typhoon Yanhua at the Ma’anshan Yangtze River (MYR) Bridge site in China. Using the established spectra, a customized turbulence wave number–frequency spectra density (WSD) matrix is defined and adopted in the proposed CT-WSRM. The proposed method can be utilized to simulate multidimensional multivariate two dimensional-three variate (2D-3V) spatial-temporal turbulent wind fields. In addition, a dimension-reduction model is introduced to describe turbulent wind fields in the probability density level within three random variables. The fast Fourier transform (FFT) algorithm is also embedded in the CT-WSRM to alleviate the computational burden. The stochastic turbulent wind fields for the MYR Bridge were simulated. Results demonstrated the effectiveness of the proposed method against the measured turbulent spectra. This method can be further utilized in the dynamic reliability analysis, providing structural reliability evaluation from the probabilistic view.

Proof testing to improve the reliability and lifetime of ceramic dental prostheses.

Ceramic dental prostheses exhibit increasing failure rates with service time. In particular, veneered crowns and bridges are susceptible to chipping and other fracture modes of failure. The purpose of this manuscript is to introduce a computational methodology and associated software that can predict the time-dependent probability of failure for ceramic prostheses and subsequently design proof test protocols to significantly enhance their reliabilities and lifetimes. Transient reliability and corresponding proof testing theories are introduced. These theories are coded in the Ceramic Analysis and Reliability Evaluation of Structures (CARES/Life) code. This software will be used to demonstrate the predictive capability of the theory as well as its use in designing proof test protocols to significantly improve the reliability (survival probability) and lifetime for dental prostheses. A three-unit fixed dental prosthesis (FDP) with zirconia core (ZirCAD) and veneering ceramic (ZirPress) are used to compare the predicted probabilities of failure to general clinical results. In addition, the capability to use proof testing to significantly improve the performance (reliability and lifetime) for this restoration is demonstrated. The probability of failure, Pf, after five years without proof testing is predicted to be 0.337. This compares to clinical studies showing the failure rate to be between 0.2 and 0.23 after 5 years. After 10 years, reference 18 found the clinical failure rate for similar bridges (but not the same) to be up to 0.28 compared to the predicted Pf of 0.38. The difference may be due to the analysis applying the load at an inclination of 75° which is more critical than vertical loading. In addition, clinical studies often report a simple survival rate instead of using Kaplan-Meier analysis to properly account for late enrollees. Therefore, true clinical failure rates may be higher than reported and may more closely match the predictions of this manuscript. The effectiveness of proof testing increases with selecting materials less susceptible to slow crack growth (higher SCG exponent, N). For example, proof testing the ZirPress glass-veneered bridges with N=43.4 analyzed in this manuscript at 400N bite force for 1s which induces a failure rate during proof testing of 0.31, reduces the Pf of bridges not proof tested from 0.45 to an attenuated-proof-tested probability of failure Pfa of 0.21 after 20 years of usage. If another material is selected with improved resistance to SCG of N=60 and the same loading conditions, the failure rate for the proof tested bridges after 20 years of service drops to 2 in 10,000 from 2.4 in 100 had they been not proof tested. The failure rate during proof testing for this material would be 5.1 in 100. Proof testing a material with absolutely no susceptibility to SCG at the same service load (in this case 285N, not even the 400N load used above) results in 0 % failure rate and is of course independent of time. The transient reliability and proof test theory presented in this paper and associated computational software CARES/Life were successful in predicting the performance of ceramic dental restorations when compared to clinical data. Well-designed proof test protocols combined with proper material selection can significantly enhance the reliabilities and lifetimes of ceramic prostheses. This proof test capability can be a translational technology if properly applied to dental restorations.

A quasi-brittle fracture investigation of concrete structures integrating random fields with the CSFEM-PFCZM

Design and maintenance of concrete structures require efficient methods for predicting quasi-brittle fracture while incorporating mesoscale-induced structural uncertainties. Toward this aim, a phase field cohesive zone model combined with the cell-based smoothed finite element method (CSFEM-PFCZM) is developed in the study, with mesoscale heterogeneity of concrete characterised by Weibull random fields. An automatic quadtree decomposition technique is presented to adaptively refine meshes around mesoscale areas, in which the hanging-node problem is tackled by treating hierarchical quadtree elements as CSFEM polygons. The crack driving forces are evaluated as history variables at the integration points of CSFEM subcells, and only the boundary geometry and Wachspress shape functions are needed to calculate strain matrices and stiffness matrices without the Jacobian inversion problems. The developed method is validated by extensive Monte Carlo simulations of typical nonlinear fracture benchmarks of concrete structures, demonstrating that the well-captured variability of crack paths and load–displacement curves can supplement the limited statistical results obtained from a small number of experiments. It is also found that larger correlation length and higher variance underline higher heterogeneity that leads to more dispersed responses. The developed method holds promise for the efficient evaluation of structural reliability taking into account stochastic mesoscale effects, due to the fast generation of random field samples in large quantities and flexible simulation of complicated fracture through the CSFEM-PFCZM.

浮体式洋上風車の風と波による応答および構造損傷発生確率評価に関する研究

An evaluation method of structural damage probability of floating offshore wind turbines under wind and wave actions is presented. The structural damage probability of the floating wind turbines is analyzed by using the first order reliability method in the structural reliability evaluation. In the evaluation of the probability, the response analysis results of the floating wind turbine for the wind and wave actions are used. The response for the action by the mean wind speed is analyzed by using the statically equation of equilibrium. On the other hand, the response for the dynamic actions by the variable wind speed and the wave is analyzed by using a mode superposition method and a stationary random vibration theory. Numerical model of the floating wind turbine is discretized by finite elements, whereas interface of the floating wind turbine and the sea water is discretized by boundary elements. Moreover, variation of the damage probability of the floating wind turbine for different wind speed is discussed by using the proposed method.

High signal-to-noise-ratio ultrasonic imaging of crack defects in particles filled composite explosives

<sec>Polymer bonded explosive (PBX) is a kind of composite material with highly filled molding explosive particles (normally more than 95%) and a small quantity of binders (less than 5%). The effective detection of internal cracks in PBX is of great significance in evaluating structural integrity and safety reliability.</sec><sec>Ultrasonic phased array detection and imaging methods show great advantages and potential in detecting crack defects. But acoustic test results indicate that the PBX has unique characteristics with low longitudinal wave velocity (～3000 m·s<sup>–1</sup>) and strong attenuation (attenuation coefficient ～400 dB·m<sup>–1</sup> for 2.5 MHz ultrasound). When the defect is imaged by traditional ultrasonic total focusing method (TFM), the structural noises at the boundaries between particles lead to low signal-to-noise ratio (SNR) in the FMC signals and strong background noise in reconstructed image, which will disturb the detection of cracks.</sec><sec>To realize the high SNR imaging of crack defects in PBX, an ultrasonic imaging algorithm based on baseband nonlinear synthetic focusing (BB-NSF) is proposed. By utilizing the spatial coherence of the received signals in full matrix capture (FMC) data, the pixel intensity at defect position can be enhanced while the background noise can be drastically weakened. The delay rule of the algorithm is modified according to the characteristics of PBX surface configuration. In this way, the high SNR imaging of crack defects with different orientations of PBX surface configuration is realized, and the quality of the reconstructed images is compared and evaluated quantitatively. Meanwhile, the base band transformation in calculation process optimization could significantly reduce calculation burden and increase imaging efficiency.</sec><sec>Experimental results show that the proposed algorithm can effectively suppress background noise and significantly improve the ability to detect the PBX cracks. The effective suppression to background noise makes the defect more highlighting and distinguished easily. For the BB-NSF algorithm, spatial coherence coefficient <i>p</i> is a crucial parameter used for dynamically regulating the SNR of reconstructed image. When <i>p</i> value is more than 2.0, the SNR of the ultrasonic reconstructed image of PBX crack defect is improved by more than 10 dB compared with that of the traditional linear synthetic focusing imaging. With the increase of <i>p</i> value, the SNR is further improved, while the calculation efficiency for a single image is almost kept stable. Moreover, the increase of SNR to some extent will improve the far-field detect capability.</sec><sec>Besides, with the BB-NSF algorithm, flexible transducer inhibits different imaging characteristics of for cracks with different orientations and depths in curved PBX specimens. For defects with large orientation angle and buried depth, the tip, root and shape of cracks can be completely present. For defects with small orientation angle and buried depth, part of shape and contour features will be lost.</sec><sec>In conclusion, the BB-NSF algorithm shows the advantage of high SNR and calculation efficiency in imaging PBX cracks, and exhibits great application prospect in imaging internal defects of other strongly attenuated composites.</sec>