Input Energy Spectra Research Articles

Novel approach for energy-spectrum-based probabilistic seismic hazard analysis in regions with limited strong earthquake data

With the rapid development of energy-based seismic design, probabilistic seismic hazard analysis (PSHA) in terms of the input energy spectrum, E I, has become increasingly important. Generally, implementing E I-based PSHA requires a ground-motion prediction equation (GMPE) for E I. However, although a GMPE for E I can be constructed in regions with abundant earthquake data based on regression analyses, it is difficult to obtain in regions lacking strong ground-motion records. Therefore, this study proposes a new approach for performing E I-based PSHA in regions with limited earthquake data. Instead of using a GMPE for E I directly, a model of Fourier amplitude spectrum (FAS) is adopted, which can be determined using a small number of earthquake data with small-to-moderate magnitudes. Then, the E I of the ground motion is obtained from FAS based on the relationship between E I and FAS. Furthermore, to calculate the annual intensity exceedance rate within the proposed framework of adopting the FAS model, a highly efficient method, namely, the moment method, is applied. Several numerical examples indicate that the proposed approach not only is suitable for regions lacking strong ground-motion records but also performs very efficiently in calculating the annual intensity exceedance rate.

A Deep-Neural-Network-Based Prediction Model for Elastic Input Energy Spectra of Horizontal and Vertical Ground Motions

ABSTRACT Intensity measures based on energy have proven to be robust indicators of damage for a variety of structural types. This article presents a modified ground-motion model (GMM) incorporating a deep neural network to predict elastic input energy spectra for both horizontal and vertical ground motions, considering the pulselike ground motions. The newly developed model employs six predictor variables, that is, moment magnitude Mw, fault mechanism F, rupture distance Rrup, logarithmic rupture distance ln(Rrup), rupture directivity term Idir, and logarithmic shear-wave velocity ln(VS30) as inputs. A subset of records, sourced from the recently updated Next Generation Attenuation-West2 Project database constituted by 2745 ground motions from 97 earthquakes, have been employed in the development of the model. The performance of the developed model remains within the prescribed error range. In addition, the proposed model is compared against currently used GMMs. The predicted spectra obtained from the present study are in good agreement with those given by other literature, and the standard deviations of residuals have been reduced by ∼20% and are more stable. Observations from these results indicate that the newly proposed model generates improved predictions.

A prolegomenon to Design Input Energy Spectra for the Himalayan region

Energy-based design is becoming progressively significant as a new age of earthquake-resistant design unfolds. Thitherto, very little is known about energy-based design in India despite the fact that the Himalayan region is one of the most seismically active regions in the world. Therefore, the current work provides a preliminary analysis of the elastic input energy and equivalent velocity (Vea) spectra for the active regions in the Himalayas. In this regard, the ground motions of Himalayan databases are blended with NGA WEST2 to estimate the Vea spectra, an inertia-independent representation of the input energy spectra. Incipiently, an Artificial Neural Network-based ground motion model (GMM) is developed for Vea spectra based on the predictor variables as magnitude, distance, hypocentral depth and site conditions. Consequently, a Probabilistic Seismic Hazard analysis is performed to obtain the uniform hazard energy spectra for a 2475-year return period. In addition, a Design Input Energy Spectra is proposed for the active regions in the Indian Himalayas. In addition, the relationship between the Vea and pseudo-spectral velocity (PSV) is analyzed to develop a Vea-informed GMM for PSV. Furthermore, the PSA estimated from the Vea-PSV model is compared with the design spectra recommended by the Indian Standard Code of Practice (IS1893-1:2016).

Comparison of Various Input Energy Spectra for the February 6th, 2023, Kahramanmaraş Earthquake Sequence

ABSTRACT This study aims to evaluate the success of various seismic input energy spectra equations in capturing the energy content of the ground motion records of the Türkiye earthquakes since the acceleration response spectra of some records exceeded the design spectra. Although most existing spectra had limited success, especially near the corner period, some recent equations yielded accurate results. Based on the obtained results, it is envisaged that the energy-based seismic design concept will have the maturity to be included in the next-generation seismic design codes as a reliable alternative to the current approaches.

Optimal selection and scaling of ground motion records compatible with input energy and acceleration spectra

AbstractNonlinear response history analysis is the primary tool for risk‐targeted design and seismic performance evaluation of structures. These analyses require the selection of a set of ground motions that satisfy predetermined conditions such as spectral acceleration. Numerous efforts have been made so far to obtain ground motion records which are expected to represent possible earthquakes. Even though spectral acceleration‐based ground motion scaling is a common procedure, recent studies showed that structural response can be better represented through the energy content of the records. To this end, this study aims to develop an energy and acceleration spectra‐compatible record selection and scaling methodology to achieve higher efficiency and lower bias in the predicted structural response. The efficiency of the proposed method is evaluated through the standard deviations of the computed story drifts of benchmark structures resulting from the records processed by either the proposed or commonly used methods. The results demonstrated that considering input energy together with spectral acceleration for the selection and scaling of the records can considerably reduce the bias in structural response, especially for structures located on stiff soils.

Pulse pileup model for spectral resolved X-ray photon-counting detectors with dead time and retrigger capability

We developed an analytical model to evaluate the effect of signal pileup on the recorded energy spectrum in X-ray photon-counting detectors affected by dead time and equipped with retrigger capability. The retrigger function allows the system to work in a specific non-paralyzable counting mode by counting the time-over-threshold of piled-up signals in multiples of a predefined and selectable retrigger time. The model, designed for rectangle-like-shaped signals, allows for arbitrary input energy spectra and can significantly help understand and optimize the behavior of counting detectors with spectral capabilities and retrigger mechanisms in applications involving polychromatic beams, e.g., spectral X-ray imaging and computed tomography (CT), in a time-efficient way. Dedicated numerical simulations were used to validate the model under several conditions of incoming flux and threshold energy, with excellent results.

Simulation-based study of noise, vibration, and harness of BLDC motor for energy level variation with frequency

The energy spectrum measurements in noise, vibration, and harness analysis with power spectrum response is a very ancient concept. The work and energy approaches for analyzing Noise, Vibration, and Harmonics (NVH) features are increasing rapidly in recent years. The primary focus is on evaluating imparted energy due to the NVH using an FFT spectrum against the input energy in motors. The simulation depicts the input energy spectra of the kinetic energy, absorbed energy, and dissipated energy very clearly. Earlier the smoothed Fourier amplitude spectrum approach was used for plotting the energy dissipation due to the NVH effect. However, most of the part of accountable energy goes to waste with noise, vibration, and harmonics generated due to harness in motor design. This experiment is conducted in support of Sir Nikola Tesla’s statement “If you wish to understand the universe think in terms of energy, frequency, and vibration”. The ripples an induced in phase current because of the step change of the speed. The predominant frequency in phase current waveform creates the collapsing vibratory waves that create the sound. Sound frequencies above 20 dB are considered unwanted sound known as noise. The energy level variation with NVH influence in BLDCM is measurable for its performance analysis. This research can be further enhanced by designing NVH-free BLDC motors.

Bayesian analysis-based ground motion prediction equations for earthquake input energy

Earthquake energy-based procedures offer a promising alternative for seismic evaluation and earthquake-resistant design of structures. Accurate determination of earthquake energy demand and the provision of an adequate energy supply to the structural system are crucial for this approach. This is where the utilization of ground motion prediction equations (GMPEs) becomes essential in achieving accurate assessment of seismic demands on structures. However, most GMPEs primarily focus on determining spectral accelerations. This study proposes a methodology to derive GMPEs by combining the Fourier amplitude spectrum, the elastic input energy spectrum, and Bayesian regression analysis. These GMPEs estimate energy-based spectral values for interplate and intraslab earthquakes recorded in the firm ground of Mexico City. Furthermore, a mathematical expression is devised to determine correlation coefficients between energy-based spectral values for interplate and intraslab earthquakes, expanding the GMPEs' applicability. Finally, a probabilistic seismic hazard analysis is conducted using the proposed GMPEs and the correlation model.

Optimal Acceleration and Energy-Based Record Selection Using Artificial Intelligence Approaches and NP

ABSTRACT The new trend toward modern earthquake-resistant design of buildings based on nonlinear dynamic analysis accounting for peak and energy demands requires efficient ground motion record selection procedures. For this reason, in the present work, two record selection strategies based on acceleration and input energy spectrum considering the spectral shape via Np are presented. Furthermore, both record selection strategies are optimized by means of four artificial intelligence (AI) techniques: Genetic Algorithms (GA), Harmony Search (HS), Particle Swarm Optimization (PSO) and Vibrating Particle System (VPS). In particular, the effectiveness of each AI approach toward the best set of ground motion records for nonlinear dynamic analysis is compared. For this aim, spectral acceleration and input energy design spectra were considered, as well as 1024 seismic records obtained from the Pacific Earthquake Engineering Research Center. For all the AI or meta-heuristic approaches, the fitness function used is focused on minimizing the difference between the average spectrum of eleven ground motion records and the design spectrum using the well-known parameter Np, which represents the spectral shape in a range of periods. In addition, a penalization is included for those spectra with very large or low demands. Thus, 24 sets of eleven seismic records that can be used for nonlinear dynamic analysis of structures with a fundamental period of vibration of 0.6, 1.2 and 1.8 seconds were obtained and purposes. The results demonstrate the ability of the two records selection strategies analyzed and the four meta-heuristic procedures, achieving results quickly and simply regardless of the type of demands, intensities and periods considered. Finally, it is concluded that the VPS algorithm is better in comparison with GA, HS, and PSO since it obtains superior results in almost all the selected cases.

Relationship between SDOF-Input-Energy and Fourier Amplitude Spectral Amplification Ratios

ABSTRACT This article presents the theoretical relationship between the site amplification ratio of the input energy spectrum for a single-degree-of-freedom system (SDOF) and that of the Fourier amplitude spectrum (FAS). The relationship indicates that the input energy spectral ratio is the result of smoothing the square of the Fourier amplitude spectral ratio. The spectral window for smoothing is determined by the bedrock-motion FAS and the oscillator transfer function for the relative velocity. The characteristics of the input energy spectral ratio were derived based on the idea of smoothing and confirmed based on real seismic records. The findings of this study contribute to a better understanding of site effects on the input energy spectrum.

Estimation of input energy spectrum from pseudo-velocity response spectrum incorporating the influences of magnitude, distance, and site conditions

The input energy spectrum is useful information for determining the hysteretic energy demand in energy-based seismic design. The input energy spectrum commonly expressed in terms of the energy equivalent velocity spectrum, Veq, can be easily established from the code-specified response spectra (RS) based on the relationship between Veq and RS. Several formulations for the Veq-RS relationship have been developed; however, all of them ignore the influences of magnitude, distance, and site conditions. The aim of this study is to propose a practical formulation for the relationship between Veq and the pseudo-velocity response spectrum, RSpv, incorporating the influences of magnitude, distance, and site conditions. Firstly, to explore the influences of magnitude, distance, and site conditions on the Veq-RSpv relationship, an approach for estimating Veq/RSpv is proposed based upon random vibration theory and verified by comparison with the values calculated by traditional time-series analysis. It is found that the magnitude influences Veq/RSpv the most among these parameters by changing the frequency content of the ground motion, and the Veq/RSpv values at long oscillator periods decrease significantly with an increasing magnitude. Then, based on these conclusions, a practical Veq/RSpv formulation incorporating the influences of magnitude, distance, and site conditions was developed using 16,660 real seismic ground motions in Japan.

A new radionuclide identification method for low-count energy spectra with multiple radionuclides

Radionuclide identification is to recognize the radionuclides in the environment by analyzing the energy spectrum. Rapid and accurate identification is important for nuclear security. Current radionuclide identification methods based on traditional peak search require background subtraction. As a result, they have difficulties to deal with complex situations in practical applications such as low-count energy spectrum and mixed nuclides. In this paper, we propose a new radionuclide identification method with a feature enhancer and a one-dimensional neural network. The training dataset in this method is from simulated data generated by Geant4. By preprocessing the input energy spectrum data through the feature enhancer and extracting the nonlinear information through the neural network, this approach performs well on experimental energy spectra even at low count. The method also shows a high recognition accuracy and little misjudgments when dealing with mixed radionuclides spectra. Due to its good performance in identifying mixed nuclides and low-count spectra, the method has been deployed in portable instrument for radionuclide identification in real-time measurement.

GMPEs for elastic input energy spectra of horizontal and vertical offshore ground motions based on the ETMC database in Japan

In this study, the characteristics of offshore ground motions related to elastic relative and absolute input energy are investigated, and ground-motion prediction equations (GMPEs) for elastic input energy of offshore ground motions are proposed. The GMPEs are developed using mixed-effects models calibrated through regression analysis of elastic responses which are derived from dynamic analyses of single-degree-of-freedom (SDOF) systems subjected to offshore ground motions. To compare the differences between offshore and onshore ground motions with regard to input energy, an onshore GMPE is derived from the onshore database. The ground motion database includes 892 offshore records and 4033 onshore records; the offshore and onshore records are collected from the same set of 273 earthquakes. To quantitatively analyze the elastic input energy of offshore ground motions, the moment magnitude, tectonic source type, focal depth, hypocentral distance and site condition are considered in the proposed equations. A comparison and analysis of the relative and absolute input energy of offshore and onshore ground motions manifest that the horizontal input energy spectra of the entire period band and the vertical input energy spectra of moderate and long period band of offshore ground motions are larger than those of onshore motions of all site classes, except that the vertical input energy of offshore motions is slightly smaller than that of onshore motions for short periods due to the combined effects of water layer and soft sediments under seafloor. The differences between the relative and absolute input energy of offshore ground motions and comparisons of the proposed GMPEs with others from the literature are also discussed in this study. The comparisons show that the proposal of the GMPE for elastic input energy of the offshore ground motion is necessary due to the offshore ground motion being considerably different from the onshore motion and the proposed onshore GMPEs. • The prediction equations for elastic input energy of offshore ground motions are proposed, providing the seismic demand for the energy-based seismic design of offshore structures. • The site condition of offshore ground motions is significantly different from those of onshore motions. • The offshore ground motions are larger than those of onshore ones for long period due to the effect of thick soft sediments.

Inelastic input energy spectra of far-fault ground motions: influence of hysteresis model

Inelastic input energy spectra of far-fault ground motions: influence of hysteresis model

Estimation of the input energy of beam bridges by using near-fault input energy design spectra

In Chinese seismic design codes, soils are divided into four sites (I ~ IV), and each site is divided into three groups (G1 ~ G3) according to the design characteristic period (Tg) again. The current studies only present the near-fault inelastic input energy (SEI) spectra corresponding to each site, while those corresponding to G1 ~ G3 of each site have not been reported. Therefore, in this study, 210 near-fault ground motion (GM) records were selected and classified according to G1 ~ G3 of Sites I ~ IV. By inputting the records into the BISPEC software, the effects of the characteristics of near-fault GMs and the parameters of hysteretic models on the near-fault SEI spectra were studied, and then the near-fault SEI design spectra corresponding to G1 ~ G3 of Sites I ~ IV were established. Moreover, by improving the previous procedure and using the near-fault SEI design spectra, an energy-based procedure for estimating the near-fault input energy of beam bridges was proposed, and its feasibility and safety were verified through a case study.

Damping effect on seismic input energy and its verification by shake table tests

Seismic input energy per unit mass ( EI/m) imparted into a structure is a function of earthquake (duration, frequency content, amplitude etc.), soil (shear velocity, dominant period etc.) and the structural (vibrational periods etc.) characteristics. Generally, the damping properties of the structure is assumed negligible for seismic input energy. Most of the existing spectral equations derived for SDOF systems generally use a constant damping ratio of 5%. In this study, the damping effect on EI/m is investigated experimentally and numerically on SDOF systems with distinct damping ratios. Experimental investigation and numerical computations proved that seismic input energy is very sensitive to variation of damping within the vicinity of fundamental frequencies. Specifically, up to 50% increment was observed in the plateau region of the input energy spectrum, where maximum EI/m values occur, by variation of damping from 2% to 10%. Hence, a novel damping modification factor ( DMF), which could be utilized for existing energy spectra, is proposed in this paper. Validation studies of the proposed DMF are achieved through the various energy spectra found in the literature.

Seismic isolation design for simply-supported beam bridges based on the energy balance method under near-fault ground motions

The seismically isolated simply-supported beam bridge (SISBB) with the seismic isolation bearing (SIB) is converted into an equivalent bilinear single-degree-of-freedom system. Then, by inputting the 139 near-fault ground motion (GM) records into the equivalent system, the parametric study on the near-fault seismic input energy spectra (SEI) of the SISBB is conducted by considering the equivalent system parameters and the near-fault GM characteristics. So, it can be found that: the increase of post-yield stiffness ratio (ηe) can slightly increase the peak values of the near-fault SEI, and ηe = 0.2 can be used to calculate the near-fault SEI design spectra of the SISBB; with the increase of the damping ratio (ξe) (or ductility ratio (μe)), the spectral values of the near-fault SEI increases, the hysteretic energy dissipation capacity of the SIB decreases, and the damping energy dissipation capacity of the equivalent system increases; when μe ≥ 10, the effect of μe on the near-fault SEI can be ignored; the softer the site soil or the smaller the Joyner-Boore distance to rupture plane (Rjb) is, the greater the near-fault SEI is; if the near-fault SEI with a standard peak ground acceleration (PGA) is known, the near-fault SEI with other PGAs can be obtained by multiplying the (PGAOther/PGAStandard)2 by the spectral values of the near-fault SEI with a standard PGA. Finally, the near-fault SEI design spectra of the SISBB are obtained, and the seismic isolation design for SISBB based on the energy balance method is proposed, the feasibility of which is verified by a case study.

Estimation of inelastic seismic input energy

The more accurate prediction of the seismic input energy spectrum contributes to a more efficient energy-based design and seismic assessment. This study presents a model to estimate the inelastic seismic input energy imposed on structures, employing a wide range of ground shaking and structural features. In this regard, the pseudo-velocity spectrum and the proposed Scaled Energy Index (SEI) are utilized to present a versatile estimation equation for input energy spectrum of bilinear Single-Degree-of-Freedom (SDOF) systems. The method takes advantage of the input energy scaling rule and the adaptability of pseudo-velocity spectrum to acquire estimations with improved accuracy. The precision of the model is evaluated comparing with similar existing methods by a novel procedure, which indicates its advantages.

A compatible energy demand estimate considering code-specified design spectra

To make the energy demand estimate in the energy-based seismic design (EBSD) approach consistent with current seismic design framework, compatible design energy spectra consisting of input energy spectra and hysteretic-to-input energy ratio spectra are proposed. A direct relation between the input energy spectrum and the pseudo-acceleration spectrum is theoretically established by the frequency-domain earthquake response of a single-degree-of-freedom (SDOF) system. The code-specified site classification in the design pseudo acceleration spectra can be directly addressed in the proposed input energy spectra. The strength reduction factor is used to account for the degree of plasticity in the hysteretic-to-input ratio energy spectra. The feasibility and accuracy of the proposed spectra are verified on single-story reinforced concrete frames. The ground motions for verification are selected by the rules that both the pseudo-acceleration spectrum and the input energy spectrum are fitted with the design spectra, proposing a new selection method from the perspective of energy.

Energy Spectrum Study and Optimal Design of an Inerter-Based Structure Considering the Underlying Soil

As a classic inerter system, the tuned viscous mass damper (TVMD) has been proven to be efficient for vibration control. It is characterized by an amplification effect, where the deformation of the dashpot in the TVMD can be larger than that of a single dashpot, providing enhanced energy dissipation. However, the contribution of this system to the enhancement of the energy dissipation quantity and vibration control remains unclear. To deal with this, and considering the underlying soil, this study proposes a systematic energy spectrum analysis framework for the single-degree-of-freedom (SDOF) element controlled by a tuned viscous mass damper (TVMD) in order to reveal the energy characteristics of the TVMD and develop an optimal energy dissipation enhancement-based design. The proposed energy spectrum analysis includes ground motion propagation and energy balance analysis. Considering the underlying soil, energy balance analysis is performed for a series of SDOF elements connected to the TVMD, which yields a fitted input energy spectrum for optimal design of the TVMD. Extensive parametric analysis reveals energy characteristics of the TVMD compared with a single dashpot, yielding an optimal energy dissipation enhancement-based design. The findings of this study show that by considering the soil underneath the inerter-based structure, the developed energy spectrum analysis quantifies the degree of energy dissipation enhancement effect of the TVMD. The proposed design is effective in guaranteeing the target of displacement control, which optimizes the efficiency and quantity of the TVMD for energy dissipation, relieving the energy-dissipation burden on the primary element.