Conventional Schemes Research Articles

Clavis: A New Selection and Gradation to Accelerate a Comprehensive Para-Tenses Mastery

This study delves into the effectiveness of the Clavis Selection and Gradation approach in teaching English as a Foreign Language (EFL). Grounded in the theories of Richards (2017) and Faravani & Zeraatpishe (2016), which underscore the significance of grammar selection and gradation, this research employs a mixed-methods approach to address its objectives comprehensively. Two distinct groups of English teacher trainees from Universitas Islam Negeri Mataram are strategically selected for the study, with one group undergoing the Clavis Selection approach. At the same time, the other follows the conventional scheme. Data collection encompasses Pre-Test and Post-Test assessments and open-ended interviews. The assessments cover various grammatical aspects, and both groups receive treatment through five sessions. By integrating quantitative and qualitative data analysis, this study aims to provide a nuanced understanding of the Clavis Selection approach's impact on EFL learners, contributing to the field of language education. Pre- and Post-Test assessments, coupled with open-ended interviews, reveal that the Clavis Selection approach significantly improves learners' grammar proficiency compared to conventional methods. This mixed-methods research advances our understanding of grammar instruction and underscores the relevance of systematic selection and gradation in EFL pedagogy.

Influence of product quality and digital marketing on the performance of SMEs

This research explores the intricate dynamics between product quality, digital marketing strategies, and Small and Medium Enterprises (SMEs) performance. The study focuses on the entire population of 43 SMEs affiliated with the Representative Office of Bank Indonesia in South Sumatra Province in 2022. These SMEs benefit from comprehensive guidance provided by Bank Indonesia consultants and actively participate in mentoring programs spanning both conventional and Sharia SME schemes, reflecting a census-based sample selection. The findings derived from multiple linear regression analysis underscore a noteworthy positive and significant impact of product quality and digital marketing on SME performance. In a marketplace saturated with similar products in South Sumatra Province, SMEs must cultivate distinctive attributes that resonate with the local community, thus enhancing their competitive edge. Additionally, the geographical remoteness of SMEs from the city center emerges as a pivotal factor influencing their performance. This remoteness not only affects production logistics but also poses challenges to sales, thereby shaping the overall performance landscape of these enterprises. In essence, this research contributes valuable insights into the multifaceted relationship between product quality, digital marketing strategies, and the performance of SMEs, particularly those aligned with Bank Indonesia in South Sumatra Province.

Adaptive fuzzy sliding mode control of magnetic levitation system based on Interval Type-2 Fuzzy Neural Network Identification with an Extended Kalman–Bucy filter

The electromagnet levitation control system (EMS) is the core component of the magnetic levitation train. However, its nature is characterized by an inherent instability and strongly nonlinear dynamic. Additionally, modeling uncertainties and numerous exogenous perturbations make the design of the controller even more difficult for this system. To overcome these limitations, a Fuzzy Sliding Mode Control based on Interval Type-2 Fuzzy Neural Network Identification (FSMCF2NN) is designed for the EMS system. The suggested controller has a unique feature that allows the sliding surface and controller effort to be designed by using model-free techniques. As a result, the drawbacks of the conventional SMC schemes, such as the chattering effect, requiring prior knowledge of the system’s uncertainties bounds, and selection of the appropriate control gains, are eliminated. Also, the FSMCF2NN method, since it is designed based on intelligence methods not only minimizes the accumulation of state errors, but also generates the optimum control efforts of the EMS system to ensure stability in different situations. Furthermore, since the measurement of all EMS states is not achievable in reality, a qualified observer is needed to estimate unmeasured states. For this purpose, the Extended Kalman-Bucy filter (EKBF) is selected because of its superiority in managing disturbances for nonlinear systems. Furthermore, to confirm the robustness of the FSMCF2NN scheme in different scenarios, the results of the controller based on Linear Matrix Inequality (LMI), Linear Quadratic Regulation (LQR) controller, and the conventional Sliding Mode Controller (SMC) are compared with the proposed controller. Analyzing the results of simulation demonstrates that maintaining the levitated object is achievable with the proposed control scheme, effectively. At the same time, it attempts to adequately compensate for the uncertainties and disturbances present in the EMS structure.

A New Artificial Staggered-Grid Central Difference Solution for Checkerboard Problem in Incompressible, Steady, Inviscid, and Quasi-One-Dimensional Flow through Convergent Nozzle

In this paper, a novel artificial staggered grid points and under-relaxation free solution for a checkerboard pattern problem in a quasi-one-dimensional, incompressible, steady, and inviscid flow is introduced. The purpose of this numerical development is to obtain a new numerical solution, which is under-relaxation factor free scheme, more accurate, and easier to implement than a conventional staggered grid scheme. The proposed numerical solution can be described as the non-staggered grid/collocated grid central difference scheme which is free of pressure checkerboard pattern or spurious oscillation. The accuracy and convergence speed of the proposed numerical scheme is benchmarked against a conventional SIMPLE-based finite volume scheme and the exact solution for the flow problem in a convergent nozzle. The numerical analysis shows that the proposed numerical scheme outperforms the SIMPLE-based finite volume scheme in terms of accuracy, computational resource, and convergence speed. Also, the proposed numerical scheme has consistent numbers of iteration over the different grid sizes in contrast to the SIMPLE-based scheme which is iteration-grid size dependent. The proposed numerical scheme can be implemented with both uniform and non-uniform grid points and shows good agreement with the exact solution for every grid size. However, the uniform grid approach produces significantly more accurate results than the non-uniform grid approach. Hence, the choice of grid distribution is still an important factor affecting the accuracy of the proposed numerical solution. The proposed numerical technique can be further extended to solve incompressible flow problem in the complex 2D-3D domain with unstructural grids.

Reflection-enabled HDOP-weighted underwater acoustic passive localization with a small aperture array

This paper addresses the localization problem of a noncooperative source in the multipath-rich environment. Unlike conventional schemes that only use the line-of-sight (LOS) and the once-surface-reflected (S1B0) path, the proposed scheme utilizes the complete spatial diversity of all multipaths by quantifying their positioning confidence. In the proposed scheme, all the measurement metrics (angle, relative delay and amplitude) extracted from multipath arrival structure, are combined to achieve localization with a small aperture array.Specifically, we first propose an algorithm for extracting multipath arrival structure based on spatial time-frequency analysis of underwater multipath signals. In this algorithm, each path is iteratively extracted, and the extraction error is close to the Cramér–Rao lower bound (CRLB). Then, the obtained CRLB is used to derive horizontal dilution of precision (HDOP) to quantify the positioning confidence of each path. Finally, the source location is estimated from an optimal HDOP-weighted multipath localization algorithm that assigns different weights to the LOS path and non-line-of-sight (NLOS) paths.Statistical-channel-model-based simulations and lake trial corroborate that the proposed scheme reduces the localization error by at least 128% compared with angle-only, relative-delay-only, and conventional hybrid metrics localization schemes.Index Terms--Underwater acoustic passive localization; Multipath arrival structure; Horizontal dilution of precision; Hybrid metrics.

Life cycle assessment of four different precision agriculture technologies and comparison with a conventional scheme

Precision farming technologies have the potential to enhance agricultural sustainability, but their exact environmental impact remains uncertain. This study aimed to (1) compare the life cycle assessment (LCA) of a conventional five-year crop rotation system with and without precision agriculture technologies (PATs) in Lower Austria; (2) to assess the emission hotspots and (3) to perform a sensitivity analysis on fertilization using the DeNitrification-DeComposition (DNDC) soil model to quantifying soil emission. Evaluated PATs included automatic steering systems, automatic section control (ASC), proximal sensors, and prescription maps from remote sensors. The crop rotation system included spring barley, soy, winter wheat, rapeseed, and winter barley. Assessed agricultural processes encompassed tillage, seeding, plant protection, fertilization, and harvesting. The impacts evaluated were climate change, fine particulate matter formation, freshwater eutrophication, freshwater ecotoxicity, terrestrial acidification, terrestrial ecotoxicity, and human carcinogenic toxicity. The sensor scheme scenario showed the highest reductions in climate change, followed by the prescription map, ASC, and autosteer scheme with reductions of −17.0, −8.9, −6.4, and −2.4%, respectively. This study emphasizes the potential of PATs to minimize environmental impacts in crop production while recognizing the influence of site and technology-specific factors. Future research should consider local variables for a comprehensive environmental assessment.

Consolidation of LVFRT capabilities of microgrids using energy storage devices

The performance and dependability of distribution networks may be enhanced by the incorporation of microgrids (MGs). However, it is necessary to enhance low voltage fault-ride-through (LVFRT), which has the capacity to prevent abrupt grid disconnections during LV occurrences under problematic circumstances. In this study, a control strategy for energy storage elements (ESDs) which includes batteries and supercapacitors is proposed to enhance LVFRT under balanced and unbalanced faults. The MG comprises wind farms and/or photovoltaic arrays. Based on the dynamic simulations using MATLAB/SIMULINK, the ESDs can enhance LVFRT capability. A comparison of the conventional crowbar scheme and ESDs is realized, and the latter has a better performance than the former in retaining the DC-link voltage within satisfactory bounds. For the purpose of maintaining the DC-link voltage at a reference level, the battery stores extra power in the DC-bus of three systems. LVFRT is improved by the crowbar circuit, however the resistance consumes the extra power. Super capacitors (SCs) prevent DC voltage fluctuations, reduce active power oscillations, and hasten system stabilization when present. At an advanced stage of this effort, the coot bird optimizer (CBO) is applied to generate the best gains of bi-directional converter PI-controller and the ESDs ratings to have minimum ripples in the DC-bus voltage and to boost the LVFRT capability of the MGs. The viability of the proposed method based on the CBO’s results is indicated with further validations under different operating scenarios.

A Low-Power SAR ADC with Capacitor-Splitting Energy-Efficient Switching Scheme for Wearable Biosensor Applications.

A low-power SAR ADC with capacitor-splitting energy-efficient switching scheme is proposed for wearable biosensor applications. Based on capacitor-splitting, additional reference voltage Vcm, and common-mode techniques, the proposed switching scheme achieves 93.76% less switching energy compared to the conventional scheme with common-mode voltage shift in one LSB. With the switching scheme, the proposed SAR ADC can lower the dependency on the accuracy of Vcm and the complexity of digital control logic and DAC driver circuits. Furthermore, the SAR ADC employs low-noise and low-power dynamic comparators utilizing multi-clock control, low sampling error sampling switches based on the bootstrap technique, and dynamic SAR logic. The simulation results demonstrate that the ADC achieves a 61.77 dB SNDR and a 78.06 dB SFDR and consumes 4.45 μW of power in a 180 nm process with a 1 V power supply, a full-swing input signal frequency of 93.33 kHz, and a sampling rate of 200 kS/s.

Efficient contingency analysis of power systems using linear power flow with generalized warm-start compensation

Contingency analysis (CA) is fundamental to power system planning and operation. The compensation method and linear power flow (LPF) models are frequently used in CA to boost efficiency. However, the conventional compensation scheme fails to adapt to modern LPF models with novel structures. To bridge this gap, this paper proposes a generalized warm-start compensation algorithm (GWSCA) for LPFs. To efficiently calculate the inversion of a perturbed coefficient matrix in LPF models, a generalized decomposition method is devised based on the matrix inverse lemma and full rank decomposition. A warm-start strategy is developed to improve the computational accuracy by using the precontingency operating point of a power grid. The proposed GWSCA is incorporated with an LPF model based on logarithmic transformation of voltage magnitudes to implement fast and accurate CA. Simulation results show that GWSCA outperforms the conventional algorithms in terms of computational efficiency and accuracy.

Novel partial punch-through-stopper scheme for substrate leakage optimization of nanosheet field-effect transistors

A novel and practicable partial punch-through-stopper (p-PTS) scheme beneath the gate area is proposed for the substrate leakage current suppression in the gate-all-around (GAA) nanosheet field-effect transistors (NSFETs). Thanks to the weakened electric field and widened tunneling length caused by the lightly doped substrate under the drain region, this p-PTS scheme can not only achieve a low PT current comparable to the conventional full-PTS (f-PTS) scheme, but also substantially reduce the BTBT current of drain–substrate junction by about two orders of magnitude. Moreover, the key parameters of the p-PTS scheme, such as p-PTS doping concentration (Np-PTS), thickness (Tp-PTS) and width (Wp-PTS), are systematically optimized and analyzed. As a result, compared to the conventional f-PTS scheme, p-PTS scheme exhibits a larger process window and better immunity of leakage current to process variations. The above results indicate that the proposed p-PTS scheme is one of the most promising methods for suppressing substrate leakage current in NSFET.

Scenario-based ultra-short-term rolling optimal operation of a photovoltaic-energy storage system under forecast uncertainty

The rapid development of renewable energy sources (RESs) facilitates the coordinated operation of different energy sources to hedge against the uncertain and non-dispatchable nature of RESs. In this paper, we propose an effective approach for ultra-short-term optimal operation of a photovoltaic-energy storage hybrid generation system (PV-ES HGS) under forecast uncertainty. First, a generic approach for modelling forecast uncertainty is designed to capture PV output characteristics in the form of scenarios. Then, stochastic model predictive control (SMPC) is utilized in the coordinated operation of PV-ES HGS for load shifting under forecast uncertainty. Finally, a PV-ES power station located in Northeast China is selected as a case study to validate the feasibility and effectiveness of the proposed method in detail. The results show that: (1) The forecast uncertainty modelling method, which incorporates adaptive kernel density estimation (KDE) and two-layer nested copula, could capture the characteristics of PV output effectively. (2) The proposed sampling procedure ensures the representativeness and temporal dependence of scenarios extracted from the joint predictive density, leading to stability and efficiency in solving the stochastic optimization problems. (3) The SMPC-based coordinated operation strategy exhibits significant superiority in load shifting performance and resistance to risks. The standard deviation of residual load (SDORL) is reduced by 17.5% on average compared to the conventional scheme. Thus, this work provides operators with guidance in the ultra-short-term optimal operation of a PV-ES HGS under forecast uncertainty.

Spectrum sensing for dynamic primary user with multiple transitions under Rayleigh distributed channel attenuation in additive Laplacian noise

We propose a real-time scenario of dynamic behavior of the primary user (PU) with multiple transitions under the Rayleigh distributed channel attenuation (RDCA) for spectrum sensing. We assume Multiple access interference (MAI) as an additive noise which is modeled using Laplacian noise model. Apart from this, we consider higher order modulation scheme such as Quadrature Amplitude Modulation (QAM) with its modulation order M. The Markov chain models the transitions of the PU using transition probabilities (TPs) which are functions of the Markov Chain parameters (MCPs) ψ and ξ. The MCPs are assumed to be known at the receiver. In improved absolute value cumulation detection (i-AVCD) scheme, decision statistic is obtained when the absolute value of received observation at the cognitive radio (CR) is raised to an exponent P with P∈(0,2]. The AVCD and ED (energy detection) are special cases of i-AVCD at P=1 and P=2, respectively. The TPs are used with i-AVCD to get a modified detection scheme, referred to as Mr: i-AVCD. The Mr refers to the term ‘modified’ under the effect of MCPs. Special cases, referred to as Mr: AVCD and Mr: ED are formed for the Mr: i-AVCD scheme at P=1 and P=2, respectively. Further, we consider the case of a multiple antenna system at the receiver. We derive closed-form expressions of the detection probability (PD) and false alarm probability (PF). Finally, we present the results using receiver operating characteristics (ROC) and PD vs. average SNR (γ). Our analytical findings are corroborated using a close match between simulations and analytical results. Besides this, the modified schemes have been compared with the conventional schemes. In conventional schemes, no information on MCPs is available at the receiver a priori. We find that the modified detection schemes (MDS) outperform conventional schemes. Further, we observe that performance of MDS degrades as we increase the value of M. We also observe that the spatial diversity improves the performance of the MDS.

A DDPG-based energy efficient federated learning algorithm with SWIPT and MC-NOMA

Federated learning (FL) has emerged as a promising distributed machine learning technique. It has the potential to play a key role in future Internet of Things (IoT) networks by ensuring the security and privacy of user data combined with efficient utilization of communication resources. This paper addresses the challenge of maximizing energy efficiency in FL systems. We employed simultaneous wireless information and power transfer (SWIPT) and multi-carrier non-orthogonal multiple access (MC-NOMA) techniques. Also, we jointly optimized power allocation and central processing unit (CPU) resource allocation to minimize latency-constrained energy consumption. We formulated an optimization problem using a Markov decision process (MDP) and utilized a deep deterministic policy gradient (DDPG) reinforcement learning algorithm to solve our MDP problem. We tested the proposed algorithm through extensive simulations and confirmed it converges in a stable manner and provides enhanced energy efficiency compared to conventional schemes.

Inverse design of optical cages by using a fully connected neural network and time-reversed dipole radiation

In the conventional scheme, the focal field is designed by selecting appropriate dipole parameters based on theory of the time-revered dipole radiation. The time-revered method relies on empirical judgment and iterative parameter testing to create only a few special optical cages, involving vast time-consuming global parameter scanning and prescreening. In this work, a combination of a time-reversed dipole radiation model and a fully connected neural networks (FCNN) is introduced as the inverse design of optical cages. Flexibility and little time consumption in the design of the light cage are the two pivotal advantages. The dual light needle focusing fields with varying lengths and the synthesis of light cages featuring bubble focusing fields with distinct characteristics are attained, which are prescribed focal structures with freedom. With the help of the FCNN, the required dipole parameters for generating the expected focal fields are obtained quickly. This approach opens up possibilities for the utilization of neural networks in the design and modulation of more structured focusing fields. The achieved optical cage holds great potential for diverse applications, such as multiparticle trapping, manipulation, assembly, and enhanced nanoscale optical operations.

Efficient Hartree–Fock exchange algorithm with Coulomb range separation and long-range density fitting

Separating the Coulomb potential into short-range and long-range components enables the use of different electron repulsion integral algorithms for each component. The short-range part can be efficiently computed using the analytical algorithm due to the locality in both the Gaussian-type orbital basis and the short-range Coulomb potentials. The integrals for the long-range Coulomb potential can be approximated with the density fitting method. A very small auxiliary basis is sufficient for the density fitting method to accurately approximate the long-range integrals. This feature significantly reduces the computational efforts associated with the N4 scaling in density fitting algorithms. For large molecules, the range separation and long-range density fitting method outperforms the conventional analytical integral evaluation scheme employed in Hartree–Fock calculations and provides more than twice the overall performance. In addition, this method offers a higher accuracy compared to conventional density fitting methods. The error in the Hartree–Fock energy can be easily reduced to 0.1 μEh per atom or smaller.

Comprehensive and quantitative evaluation for selecting a suitable scheme of central air-conditioning during the design phase

As for routinely selecting the number and size of chillers in central air-conditioning system, the conventional scheme in which the total cooling capacity is allocated in an equal or empirical way is generally suboptimal. A few factors are brought into consideration, and the time domain of evaluation is too short. The low suitability between the cooling load of building and the scheme selected results in an inefficient state of system during the most of operation time. Some novel methods provide long-term evaluations for selecting an efficient scheme by simulating the cooling loads then calculating the cost and performance of the scheme. However, the schemes are formed without correlating actual plants which is difficult to be applied to an actual project, and the long-term environmental impact is rarely considered. The evaluation method with a high engineering value is required. But the more complicated the method is, the more work is required. The relationship between the benefits and the costs is unknown. Therefore, this study proposes three evaluation methods at different levels. From simple to complex, the three methods are corresponding the cooling load curve of building calculated through EnergyPlus to the performance curves of chillers, system simulation using TRNSYS and co-simulation based on BCVTB respectively. A case study using a hospital building located in Zhejiang province, China combined with equipment list was conducted to demonstrate the evaluation process. The results calculated by different methods and the various indexes of different schemes were compared to illustrate how to optimize the scheme selection during the design phase in order to select a suitable scheme for a certain building reducing the energy consumption and carbon emission.

A Kalman Filter-Based Distributed Cyber-Attack Mitigation Strategy for Distributed Generator Units in Meshed DC Microgrids

To ensure fast dynamics and the stability of multiple distributed generator units (DGUs) in DC microgrids, communication links among the controllers of DGUs are generally adopted. However, those communication channels are vulnerable to cyber-attacks. To alleviate this hassle, a Kalman Filter (KF)-based distributed cyber-attack mitigation strategy, which is highly involved in both primary and secondary control, is proposed in this paper. The KF, as a robust state estimator, is utilized to accurately estimate the authentic terminal voltages and currents of the DGUs. Based on the discrepancies between the estimated and measured parameters of the systems under cyber-attacks, the proposed control can adaptively compensate the attack signals via an adaptive proportional integral (API) controller and a fractional API (FAPI) controller in cyber-attack-mitigation layers. The main advantage of using the proposed control scheme compared to conventional schemes is the fast dynamic response. The simulation results verify this merit by comparing the adopted KF and comparing it with conventional artificial neural networks (ANN), while the experimental results validate that effectiveness of the proposed control and showcase the superiority of the FAPI control in terms of its perfect compensation for different types of cyber-attacks.

Generation of a Flat Optical Frequency Comb via a Cascaded Dual-Parallel Mach–Zehnder Modulator and Phase Modulator without Using the Fundamental Tone

Under the conventional scheme to generate an optical frequency comb (OFC) using an electro-optic modulator (EOM), the frequency interval of the OFC is determined via the frequency of the fundamental tone of the radio frequency (RF) driving signals. In this work, we use two harmonics without the fundamental tone to drive two EOMs, where the frequency interval of the generated flat OFC is the frequency of the fundamental tone. The orders of the two harmonics are coprime. Specifically, one harmonic drives the first branch of the dual-parallel Mach–Zehnder modulator (DPMZM) only, and the other harmonic drives the phase modulator (PM). The flatness of the OFC is achieved by adjusting the amplitude and phase of the RF driving harmonics as well as the bias of the EOM. Both a simulation and an experiment were carried out to verify the effectiveness of the proposed scheme. When the second harmonic drives the DPMZM and the third harmonic drives the PM, an 11-comb line OFC is generated, where the flatness of the OFC was 0.63 dB and 0.65 dB under the simulation and experiment, respectively. When the third harmonic drives the DPMZM and the second harmonic drives the PM, a 13-comb line OFC is generated, where the flatness of the OFC was 0.62 dB and 0.95 dB under the simulation and experiment, respectively. We also investigate the performance of the generated OFC when one harmonic drives two branches of the DPMZM and the other harmonic drives the PM. The comparison of the OFCs’ performance demonstrates the effectiveness of the proposed scheme.

Adaptive Precoding for Aeronautical Communication Systems in Public Channels

The family of aeronautical communication systems is considered as one of the core technologies for the beyond-the-fifth-generation (B5G) networks, thus attracting rapidly increasing attention from both industry and academia. In this paper, a new multiple-input multiple-output (MIMO) precoding scheme is proposed for aeronautical communication systems, where the transmit power for the aerial user equipment (UE) approaching the target cell is maximized based on the direction information. Specifically, we first transform the precoding optimization problem into a linear programming problem, and then develop two algorithms to derive the precoders for two transmission modes, namely the multi-stream and single-stream transmissions. For the multi-stream case, an algorithm based on manifold optimization is proposed, which guarantees the equal power allocation for each antenna. For the single-stream case, we derive a precoder by a numerically stable algorithm that extends the Newton-Raphson method. Simulation results show that the proposed precoding schemes can improve the link performance of the UEs with known directions, while ensuring that the performance of the UEs with unknown directions can still be close to that achievable by conventional schemes.

Failure Probability Prediction for Offshore Floating Structures Using Machine Learning

Summary Accurately estimating the failure probability is crucial in designing civil infrastructure systems, such as floating offshore platforms for oil and gas processing/production, to ensure their safe operation throughout their service periods. However, as a system becomes complex, the evaluation of a limit state function may involve the use of an external computer solver, resulting in a significant computational burden to perform Monte Carlo simulations (MCS). Moreover, the high-dimensionality of the limit state function may limit efficient sampling of input variables due to the “curse of dimensionality.” To address these issues, an efficient machine learning framework is proposed, combining polynomial chaos expansion (PCE) and active subspace. This will enable the accurate and efficient evaluation of the failure probability of an offshore structure, which typically involves a large number of uncertain parameters. Unlike conventional PCE schemes that use the original random variable space or the auxiliary variable space for building a surrogate model, the proposed method utilizes a reduced-dimension space to circumvent the “curse of dimensionality.” An appropriate coordinate transformation is first sought so that most of the variability of a limit state function can be accounted for. Next, a PCE surrogate limit state function is constructed on the derived low-dimensional “active subspace.” The Gram-Schmidt orthogonalization process is used for making basis polynomial functions, which is particularly effective when input random parameters do not follow the Askey scheme and/or when a dependence structure between the input parameters exists. Therefore, a nonlinear iso-probabilistic transformation, which makes the convergence of a surrogate to the true model difficult, is not required, unlike traditional PCE. Numerical examples, including limit state functions related to structural dynamics problems, are presented to illustrate the advantages of the proposed method in estimating failure probabilities for complex structural systems. Specifically, the method exhibits significantly improved efficiency in estimating the failure probability of an offshore floating structure without compromising accuracy as compared to traditional PCE and MCS.