Academic literature on the topic 'Magnitude-Frequency Curve'

Abstract. This study developed a comprehensive method to quantify streamflow drought severity and magnitude based on a traditional frequency analysis. Two types of curve were developed: the streamflow drought severity-duration-frequency (SDF) curve and the streamflow drought magnitude-duration-frequency (MDF) curve (e.g., a rainfall intensity-duration-frequency curve). Severity was represented as the total water deficit volume for the specific drought duration, and magnitude was defined as the daily average water deficit. The variable threshold level method was introduced to set the target instream flow requirement, which can significantly affect the streamflow drought severity and magnitude. The four threshold levels utilized were fixed, monthly, daily, and desired yield for water use. The threshold levels for the desired yield differed considerably from the other levels and represented more realistic conditions because real water demands were considered. The streamflow drought severities and magnitudes from the four threshold methods could be derived at any frequency and duration from the generated SDF and MDF curves. These SDF and MDF curves are useful in designing water resources systems for streamflow drought and water supply management.

Abstract. The aim of this paper is to illustrate the effects of selected catchment storage thresholds upon runoff behaviour, and specifically their impact upon flood frequency. The analysis is carried out with the use of a stochastic rainfall model, incorporating rainfall variability at intra-event, inter-event and seasonal timescales, as well as infrequent summer tropical cyclones, coupled with deterministic rainfall-runoff models that incorporate runoff generation by both saturation excess and subsurface stormflow mechanisms. Changing runoff generation mechanisms (i.e. from subsurface flow to surface runoff) associated with a given threshold (i.e. saturation storage capacity) are shown to be manifested in the flood frequency curve as a break in slope. It is observed that the inclusion of infrequent summer storm events increases the temporal frequency occurrence and magnitude of surface runoff events, in this way contributing to steeper flood frequency curves, and an additional break in the slope of the flood frequency curve. The results of this study highlight the importance of thresholds on flood frequency, and provide insights into the complex interactions between rainfall variability and threshold nonlinearities in the rainfall-runoff process, which are shown to have a significant impact on the resulting flood frequency curves.

Abstract. The aim of this paper is to illustrate the effects of selected catchment storage thresholds upon runoff behaviour, and specifically their impact upon flood frequency. The analysis is carried out with the use of a stochastic rainfall model, incorporating rainfall variability at intra-event, inter-event and seasonal timescales, as well as infrequent summer tropical cyclones, coupled with deterministic rainfall-runoff models that incorporate runoff generation by both saturation excess and subsurface stormflow mechanisms. Changing runoff generation mechanisms (i.e. from subsurface flow to surface runoff) associated with a given threshold (i.e. saturation storage capacity) is shown to be manifested in the flood frequency curve as a break in slope. It is observed that the inclusion of infrequent summer storm events increases the temporal frequency occurrence and magnitude of surface runoff events, in this way contributing to steeper flood frequency curves, and an additional break in the slope of the flood frequency curve. The results of this study highlight the importance of thresholds on flood frequency, and provide insights into the complex interactions between rainfall variability and threshold nonlinearities in the rainfall-runoff process, which are shown to have a significant impact on the resulting flood frequency curves.

Centrifugal compressor is exposed to pulsating backpressure due to the movement of intake valves in internal combustion engine. The performance of compressor deviates from the steady performance map, which affects the matching between turbocharger and engine. The behavior of compressor system at pulsation conditions are investigated via an in-house developed 1D unsteady code validated by experimental results. The influence of pulse frequency, magnitude and compressor characteristic curve on the compressor transient responses, including filling-emptying effect and wave dynamics, are analyzed. Results show that the strength of wave dynamics grows stronger with the increasing of pulse frequency, while the strength of filling-emptying effect increases first then decreases. The rise of pulse magnitude results in an almost linearly increasing of filling-emptying effect, while it can hardly affect the wave dynamics. Furthermore, the influence of pulsation magnitude and frequency represents the influence of local pressure gradient, and a correlation as quadratic curve can be evaluated between the pressure gradient and compressor unsteadiness. On the other hand, the influence of operating point, including the average mass flow rate and the slope of characteristic curve, is confirmed to be evidently smaller, comparing to the influence of pulsation frequency and magnitude. This study is helpful to estimate the behavior of compressor and the discrepancy of performance when operating at unsteady environment or matched with engine.

Errors was generate when use integral methods to calculate pyrolysis kinetic. It was analyzed by considered the effects of methods and reaction orders. A α-T curve was established for the error discussion depending on basic kenotic theory. For analysis methods, both single curve and multiple curve methods can obtain reliable activation energy values (≤3%), but the error of frequency factor was significant (up to 40%). Frequency factor is sensitive to intercept changing and is also to reaction order. Magnitude error could show if reaction order deviates to true value.

It is generally believed that the micromechanics of active cochlear transduction mature later than passive elements among altricial mammals. One consequence of this developmental order is the loss of transduction linearity, because an active, physiologically vulnerable process is superimposed on the passive elements of transduction. A triad of sensory advantage is gained as a consequence of acquiring active mechanics; sensitivity and frequency selectivity (frequency tuning) are enhanced and dynamic operating range increases. Evidence supporting this view is provided in this study by tracking the development of tuning curves in BALB/c mice. Active transduction, commonly known as cochlear amplification, enhances sensitivity in a narrow frequency band associated with the “tip” of the tuning curve. Passive aspects of transduction were assessed by considering the thresholds of responses elicited from the tuning curve “tail,” a frequency region that lies below the active transduction zone. The magnitude of cochlear amplification was considered by computing tuning curve tip-to-tail ratios, a commonly used index of active transduction gain. Tuning curve tip thresholds, frequency selectivity and tip-to-tail ratios, all indices of the functional status of active biomechanics, matured between 2 and 7 days after tail thresholds achieved adultlike values. Additionally, two-tone suppression, another product of active cochlear transduction, was first observed in association with the earliest appearance of tuning curve tips and matured along an equivalent time course. These findings support a traditional view of development in which the maturation of passive transduction precedes the maturation of active mechanics in the most sensitive region of the mouse cochlea.

The aim of the method in this paper is to achieve desired gain and phase specifications for robustness and performance of first order plus time delay plants. The previously proposed method “frequency frame”, implemented for tuning fractional order proportional integral controllers, is applied on such plants controlled with a fractional order proportional derivative controller. Four specifications of gain and phase are considered in the Bode plot inspired from an ideal system. The frame is drawn enclosing the magnitude and phase curves limited by gain and phase crossover frequencies. Then, the size of the frame is tuned to provide loop-shaping of the curves to meet desired properties. The iso-damping property is achieved by shaping the phase curve. Similarly, numerous studies in the literature work on robustness achievement by loop shaping the phase curve of the Bode plot. However, the “frequency frame” approach is a new perspective in controller tuning. Two examples are illustratively given to prove the proposed method. Plants in the examples are also considered to be due to load disturbances. Simulation results and effects of the method are clearly explained.

Abstract. One hundred and one landslides were documented across 370km2 following a rainstorm that swept the British Columbia coastline on 18 November 2001. Despite the regional nature of the storm, the landslides were spaced close together, even within the study area. Landslide clustering is attributed to high intensity storm cells too small to be recorded by the general hydrometric network. The evidence nicely corroborates previous historical studies that reached similar conclusions, but against which there was no modern analog analyzed for coastal British Columbia. Magnitude-cumulative frequency data plotted well on a power law curve for landslides greater than 10000m2, however, below that size several curves would fit. The rollover effect, a point where the data is no longer represented by the power law, therefore occurs at about 1.5 orders of magnitude higher than the smallest landslide. Additional work on Vancouver Island has provided evidence for rollovers at similar values. We propose that the rollover is a manifestation of the physical conditions of landslide occurrence and process uniformity. The data was fit to a double Pareto distribution and P-P plots were generated for several data sets to examine the fit of that model. The double Pareto model describes the bulk of the data well, however, less well at the tails. For small landslides (<650m2) this may still be a product of censoring. Landscape denudation from the storm was averaged over the study area and equal to 2mm of erosion. This is more than an order of magnitude larger than the annual rate of denudation reported by other authors for coastal British Columbia, but substantially less than New Zealand. The number is somewhat affected by the rather arbitrary choice of a study area boundary.

A compact and low-profile curve-feed complementary split-ring resonator (CSRR) microwave sensor for solid material detection is presented in this article. The curve-feed CSRR sensor was developed based on the CSRR configuration with triple rings (TRs) designed together, utilizing a high-frequency structure simulator (HFSS) microwave studio. The designed curve-feed CSRR sensor resonates at 2.5 GHz, performs in transmission mode, and senses shift in frequency. Four varieties of the sample under tests (SUTs) were simulated and measured. These SUTs are Air (without SUT), Roger 5880, Roger 4350, FR4, and detailed sensitivity analysis is being performed for the resonant band at 2.5 GHz. The finalized CSRR curve-feed sensor was integrated with defective ground structure (DGS) to deliver high-performance characteristics in microstrip circuits, which leads to a high Q-factor magnitude. The presented curve-feed sensor has a Q-factor of 520 at 2.5 GHz, with high sensitivity of about 1.072. The relationship between loss tangent, permittivity, and Q-factor at the resonant frequency has been compared and discussed. These disseminated outcomes make the suggested sensor ideal for characterizing solid materials.

Transfer functions in the linear dynamic system theory are applied to characterize dynamic mechanical properties of viscoelastic materials. Correlation between transfer functions and typical rheological models and fractional derivative ones are briefly introduced. The transfer function of a rheological model may be expressed in terms of multiplication of factored polynomials. The frequency–response data are presented in the form of a Bode plot of magnitude, from which a transfer function can be established. The characteristic times can be conveniently identified via the corner frequencies of asymptotes of the magnitude curve. Dynamic frequency sweep results for a typical viscoelastic solid are presented to illustrate the use of the Bode diagram method for parameter identification.

Gli eventi sismici sono riconosciuti come una delle maggiori cause per l’innesco di frane (Keefer, 1984). Le frane sismo-indotte sono documentate sin dal IV secolo (Seed, 1968). È stata condotta un’analisi sulla distribuzione spaziale delle frane sismo-indotte nell’area circostante la sorgente sismogenetica per meglio comprendere il loro innesco in aree sismiche e per delimitare la massima distanza alla quale un sisma con data magnitudo possa indurre frane. Tuttavia, quando si applicano tali approcci a eventi storici si pone un problema legato al sottocampionamento delle frane più piccole, che possono essere obliterate dall'erosione e dall'evoluzione del paesaggio. Per questo motivo è importante caratterizzare accuratamente la distribuzione delle frane, in termini di dimensione, in funzione della distanza dalla sorgente sismica. Sono stati analizzati sei terremoti in tutto il mondo che hanno innescato un significativo numero di frane (Finisterre 1993, Northridge 1994, Niigata 2004, Wenchuan 2008, Iwate 2008 and Tohoku 2011) per meglio comprendere le relazioni esistenti tra la distribuzione spaziale delle frane, l’accelerazione di picco al suolo (PGA), la distanza dalla sorgente, il relief e le litologie presenti nell’area. Si è osservata una forte relazione tra la PGA e la dimensione delle frane, mentre una la relazione tra la loro dimensione e la distanza dalla sorgente non è altrettanto chiara, ciò legato all’interazione tra diversi fattori quali ad esempio il relief e la litologia. Sono state realizzate e analizzate le curve magnitudo-frequenza (MFC) per differenti distanze dall’area sorgente attraverso varie metodologie: stimatore di massima verosimiglianza per distribuzioni di tipo potenza cumulate (Clauset et al, 2009), stimatore di massima verosimiglianza per distribuzioni di tipo potenza non cumulate, regressione ai minimi quadrati per funzioni di tipo potenza non cumulate in scala logaritmica e stimatore di massima verosimiglianza per la distribuzione Double Pareto. Dalle analisi si è potuto osservare un decrescere della densità spaziale delle frane con la distanza, ma un basso impatto della dimensione delle frane. Inoltre la funzione Double Pareto è stata scelta come miglior strumento per il fittaggio dei dati (Valagussa et al, 2014). Allo scopo di definire il rischio legato alle frane sismo-indotte è stata sviluppata una metodologia per la zonazione probabilistica quantitativa del rischio da frane da crollo (Valagussa et al, 2014). Il metodo è stato applicato e dimostrato nell’area del Friuli (Apli orientali) colpita da un terremoto di magnitudo 6.4 nel 1976. Quattro inventari sono stati realizzati sia tramite attività di terreno che da dati storici. La metodologia si basa sul vettore di rischio tridimensionale (RHVmod) le cui componenti includo l’energia cinetica, l’altezza di volo e la frequenza annua. I primi due valori sono calcolati per ogni cella del versante per mezzo del programma Hy-STONE. La frequenza annua è invece determinata moltiplicando la frequenza d’innesco annua per il numero di transiti simulati in ogni cella. La frequenza d’innesco annua è calcolata combinando l’area instabile, calcolata per 10 differenti scenari con differente frequenza annua di occorrenza sulla base di caratteristiche morfometriche e sismiche, e la curva magnitudo-frequenza relativa dei blocchi identificati da attività di terreno. Una serie di analisi discriminanti sono state condotte per determinare le variabili che controllano l’area in frana, sulla base degli inventari redatti e di DEMs a differenti risoluzioni (1 e 10m). L’analisi ha dimostrato il ruolo rilevante della curvatura nella definizione dell’area instabile. Per verificare la validità della mappa di PGA utilizzata nelle analisi, una nuova mappa è stata redatta sulla base delle Precarious Balanced Rocks identificate sul terreno.
Earthquakes have been recognized as a major cause of landsliding (Keefer, 1984), and landslides triggered by earthquakes have been documented since the IV century (Seed, 1968). The spatial distribution of earthquake-induced landslides around the seismogenetic source has been analysed to better understand the triggering of landslides in seismic areas and to forecast the maximum distance at which an earthquake, with a certain magnitude, can trigger landslides. However, when applying such approaches to old earthquakes one should be concerned about the undersampling of smaller landslides, which can be cancelled, by erosion and landscape evolution. For this reason, it is important to characterize carefully the size distribution of landslides as a function of distance from the earthquake source. I analysed six earthquakes in the world that triggered significant amount of landslides (Finisterre 1993, Northridge 1994, Niigata 2004, Wenchuan 2008, Iwate 2008 and Tohoku 2011) to better understand the relation between the spatial distribution of the landslides, the peak ground acceleration (PGA), the distance from the sources, the relief and the lithologies of the area. I observed a strong relationship between landslides size and PGA, while the relationship between the distance from the source and the landslide size distribution is not clear, due to the interaction of different factors such as relief and lithology. I also developed magnitude frequency curves (MFC) for different distances from the source area by using different methods, such as: the maximum likelihood estimator of cumulative power-law distribution (Clauset et al, 2009); the maximum likelihood estimator of non-cumulative power-law function; the least square regression of non-cumulative log power-law function and the maximum likelihood estimator of Double Pareto distribution. I observed a decrease of the spatial density of landslides with distance, with a small effect of the size of these landslides. I also identify the Double Pareto function as the best tool for the fitting of the data (Valagussa et al., 2014a). In order to define the hazard due to earthquake-induced landslides, I developed a methodology for quantitative probabilistic hazard zonation for rockfalls (Valagussa et al., 2014b). I applied and demonstrated the method in the area of Friuli (Eastern Italian Alps) that was affected by the 1976 Mw 6.5 earthquake. Four rockfall datasets have been prepared from both historical data and field surveys. The methodology relies on a three-dimensional hazard vector (RHVmod), whose components include the rockfall kinetic energy, the fly height, and the annual frequency. The values of the first two components are calculated for each location along the slope using the 3D rockfall runout simulator Hy-STONE. The rockfall annual frequency is assessed by multiplying the annual onset frequency by the simulated transit frequency. The annual onset frequency is calculated 2 through a procedure that combines the extent of unstable areas, calculated for 10 different seismichazard scenarios with different annual frequencies of occurrence, and the magnitude relativefrequency relationship of blocks as derived from the collected field data. For each annual frequency of occurrence, the unstable area is calculated as a function of morphometric and earthquake characteristics. A series of discriminant-analysis models, using the rockfall datasets and DEMs of different resolution (1 and 10 m), identified the controlling variables and verified the model robustness. In contrast with previously published research, I show that the slope curvature plays a relevant role in the computation of the unstable area. To ensure the validity of the peak ground acceleration used as seismic parameter in the discriminant function, I also try to define a map of PGA based on the precarious balanced rocks surveyed on the field.

AbstractIn order to explore the external prestress effect of the curved tendons on the stiffness and natural vibration characteristics of the steel beam, this paper deduced the calculation equation of the natural frequency on the external prestressed simply supported steel beam of the curved arrangement, which was based on the Hamilton principle. The natural frequency is calculated by combining the example of I-shaped simply supported steel beam, which was analyzed and verified by establishing the finite element model. The results show that: the calculation of the equation is well demonstrated by the finite element results, and the validity of model equation was verified. When the applied prestress increases, the natural vibration frequency decreases and the change range is not large, which indicates that the magnitude of the prestress has little effect on the natural frequency of simply supported steel beams.

When magnetic bearings are employed in a pump, compressor, turbine or other rotating machine, measurement of the current in the bearing coils provides knowledge of the forces imposed on the bearings. This can be a significant indicator of machine problems. Additionally, magnetic bearings can be utilized as a load cell for measuring impeller forces in test rigs. The forces supported by magnetic bearings are directly related to the currents, air gaps and other parameters in the bearings. This paper discusses the current/force relation for magnetic thrust bearings. Force vs. current measurements were made on a particular magnetic bearing in a test rig as the bearing coil currents were cycled at various time rates of change. The quasi-static force vs. current relations were measured for a variety of air gaps and currents. The thrust bearing exhibits a hysteresis effect which creates a significant difference between the measured force when the current is increasing as compared to that when the current is decreasing. For design current loops, 0.95 A to 2.55 A, at the time rate of change of 0.1 A/sec, the difference between increasing and decreasing current curves due to hysteresis ranged from 4% to 8%. If the bearing is operated in small trajectories about a fixed (non-zero) operation point on the F/I (force/current) curve, the scatter in the measurement error could be expected to be on the order of 4 percent. A quasi-static non-linear current/force equation was developed to model the data and curve Fit parameters established for the measured data. The effect of coercive force and iron reluctance, obtained from conventional magnetic materials tests, were included to improve the model but theoretically calculated values from simple magnetic circuit theory do not produce accurate results. Magnetic fringing, leakage and other effects must be included. A sinusoidal perturbation current was also imposed on the thrust bearing. Force/current magnitude and phase angle values vs. frequency were obtained for the bearing. The magnitude was relatively constant up to 2 Hz but then decreased with frequency. The phase lag was determined to increase with frequency with value of 16 degrees at 40 Hz. This effect is due to eddy currents which are induced in the solid thrust bearing components.

Piezoelectric impedance-based damage detection approach has been recognized to be sensitive to small-sized damage, as the impedance information can be measured at relatively high frequency range. To enhance this approach, recently an innovative scheme is developed by integrating the inductive circuitry serially with the piezoelectric transducer. With the resonant effect due to such inductive circuitry integration, the measurement amplitude is greatly amplified. It has been identified that the change of admittance measurement before and after damage occurrence is increased by an order-of-magnitude, which yields much increased detection sensitivity. In this research, we first attempt to enhance this inductive circuitry scheme by integrating the negative capacitance element. With the peak magnitude of the curve of the admittance change remaining high, the magnitude of the admittance change away from the resonances is greatly increased, which means the amplification effect of the inductive circuitry becomes effective in a wider frequency range. Then we make further improvement by connecting the resistor (used to facilitate the admittance measurement) parallel with the inductor. This results in the amplification of the voltage across the resistor, and thus further increases the signal-to-ratio of admittance measurement. Extensive numerical and experimental studies are carried out to demonstrate the effectiveness of the proposed enhancements.

This paper proposes a measurement method of cubic non-linear elasticity. The measurement system consists of a vibrator and a control circuit. We apply a nonlinear feedback to actuate the vibrator for inducing van der Pol type self-excited oscillation, so that the response amplitude of the oscillation can be arbitrarily set by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity causes a natural frequency shift related to the vibration amplitude of the object. We can set the response amplitude various values by changing the nonlinear feedback gain and measure the shift of the response frequency depending on the magnitude of the response amplitude. As a result, the bend of the backbone curve reflecting the nonlinear elasticity of the object is obtained.

This study examines the upgrade of two forward-curved centrifugal induced draft fans, to support fuel blends with greater fractions of PRB coal for a 160 MWe generating unit. After a post installation event, an audible periodic low frequency vibration in the breeching was noticed at loads ranging from 75–95 MWe. A detailed investigation was conducted which included fluid dynamic and vibration analyses of the fan and system, as well as an assessment of the fan and motor performance characteristics. Results of the analyses revealed system resistances which generated operating points in the stall region on the fan performance curve. Non-uniform fan inlet flow distributions were characterized by axial and transverse distortion parameters. Data showed relatively high transverse distortion parameters over the affected load range with the maximum of 20.5% distortion occurring at 95 MWe; with a corresponding breeching vibration frequency approximately four-thirds shaft speed. Based on the data obtained and observed system behavior, it was determined the phenomenon responsible for the flow-induced vibration was the onset of rotating stall. The magnitude of the pressure pulses associated with this low frequency vibration is capable of causing fatigue damage to large ductwork and producing unwanted acoustic emissions. In light of the large number of similar conversions performed throughout industry and increases in partial-load operation, the accurate diagnosis of such phenomenon is vital for reliable plant operations. This work summarizes an effective and practical methodology for making such evaluations, while addressing issues of fan performance and system effects.

Abstract Among various models for estimating interfacial thermal conductance (ITC) across different material interfaces, the diffuse mismatch model (DMM) has been generally evaluated as a reliable approach for material interfaces at high temperatures. The previous works by DMM have indicated the correct order of magnitude of ITC in isotropic material interfaces. However, it cannot accurately reproduce the ITC for low-dimensional anisotropic layered materials that are desired for many potential applications. Also, the inappropriate mode matching process approximation of the phonon dispersion curve tends to overestimate the ITC. In this paper, we revisited and updated the numerical method in our previous work that utilizes a mode-to-mode comparison within the DMM framework to predict ITC with the first-principles accuracy. We employed this model to calculate ITCs between layered materials such as MoS2 and graphite and metals such as Al, Au, and Cr. We then compared our values with previous literature data from calculations of phonon dispersion curve and experimental data from time-domain thermoreflectance measurements. With a better mode matching algorithm, the updated numerical method can predict the ITCs with improved accuracy. Further analysis also confirmed that counting only the three acoustic modes and neglecting the low-frequency optical modes lead to significant underestimation of the ITC using DMM.

The embrittlement of steel in the presence of water and hydrogen sulfide is a well known phenomenon. For the resulting degradation in fatigue performance, the industry today applies a knock-down factor onto in-air S-N endurance curve that relates the sour-service life to the in-air performance. Several published results are available, and most of these, although rigorous in test approach, report knock-down factors that include unspecified levels of conservatism, consistent with that particular author’s engineering intuition. (For example, typically a lower bound S-N curve in sour-service testing is related to a mean S-N curve in-air). This paper summarizes all of the published small scale sour service testing results, and applies a consistent knock-down factor calculation. Analyses of the data show that sour degradation is highly correlated to H2S concentration and solution pH value. In practice frequency scanning test is highly recommended since sour fatigue test results are highly dependent on loading frequency. Although the database is small, some trends are discernable. In particular, observations indicate that sour service exposure may act as an equalizer, removing the initiation life associated with the time for initial micro-defects at the weld toes to become macro-cracks and leaving only aggravated propagation due to sour service. In this paper, we use initiation life (for welds) to describe the life for the micro-defects (∼0.1mm height) to become macro-cracks (∼1.0 mm height), and a postulation is made that associates the fatigue performance of girth welds (F2, E, D, etc.) with the size and magnitude presence of these micro-defects. The metal surface attack of the sour environment is postulated to provide pitting-like initiation sites for the macro-crack for fatigue propagation. As a base we can use the F2 level performance as the performance due to presence of macro-cracks, and any margin for the D and E level fatigue performances then is associated with more benign initial micro-defects. Once we remove the differences in initiation life; all of the sour performance converges on a single lower performance curve. In this scenario, the knockdown factor is more consistently computed from a standard performance S-N curve rather than the same girth weld’s in-air performance since the in-air data may include significant initiation life. Furthermore, if project sour condition is less severe than NACE TM0177, Solution B with pH = 3.5 and H2S partial pressure = 70mbar, a knock down factor of 45 indexed to BS7608 E design curve is supported from the current database. This provides a design recommendation which can be used for preliminary design in sour environments.

When major pipeline incidents occur there is always a question as to how applicable the learnings from that incident are across the industry. To address this question for the San Bruno pipeline failure in 2010, an analysis of historical transmission pipeline industry events was conducted to determine if San Bruno was consistent with past industry performance or whether it was an outlier event. This paper draws on Power Law analysis to generate a characteristic curve of past transmission pipeline accidents in the US. Power Law, or Pareto, behavior has been observed for a wide variety of phenomenon, such as fire damage, earthquake damage and terrorist attacks. The size of these events is seen to follow not the typical normal distribution but the Power Law distribution, where low probability - high consequence (LPHC) events play a more significant role in the overall risk picture. Analysis shows that the consequences of pipeline incidents in a variety of pipeline industries (gas distribution, gas transmission, gas gathering and hazardous liquid pipelines) are seen to exhibit Power Law behavior. The Power Law model is seen to capture the distribution of the size of consequences from pipeline incidents and defines the relationship between the size of an incident and its frequency. Through characterization of these distributions, it is possible to project the likelihood or expected frequency of events of a given magnitude and to assess if a given incident fits within historical industry patterns; i.e. whether the incident is consistent with past observations or is an outlier. The Power Law analysis shows that the San Bruno incident, which caused eight fatalities and an estimated $380 million in property damage in 2010, is not an outlier. Rather, this incident lies on the Power Law curve for historical transmission pipeline incidents, with an estimated frequency of once every 40 years. The event is consistent with the history of gas transmission pipeline consequences in the US. This paper argues that the San Bruno incident, therefore, provides lessons relevant to the industry as whole.

Many important diagnostic techniques yield the magnitude, but not the phase, of the Fourier transform of a response, and hence, may not determine the response uniquely. Even when a specific model function is known to approximate the response well, determining the parameters of the model uniquely may not be possible. Consider, for example, the commonly used temporal response, the sum of two exponentials: h α (t) = θ(t){A exp(−t/τ f ) + B exp(−t/τ s )}, where θ(t) is the unit step function, τ f and τ s are fast and slow time scales, A ≡ α/τ f , B = (1 − α)/τs, and α is the relative weight. Knowledge of only the magnitude of the Fourier transform of hα(t) allows two distinct values of α to result from a curve fit (even in the absence of noise). We have seen this ambiguity in frequency domain experiments measuring the ultrafast optical Kerr transient of carbon disulfide using a nonlinear optical technique. The ambiguity can be removed by reconfiguring the experiment to allow some coherent, quadrature phase background to add to the Fourier transform of hα(t) before the magnitude is taken. Only one scan is necessary. For more general impulse responses consisting of sums of two arbitrary functions, we have derived expressions for (1) the condition in which relative weight ambiguity occurs and (2) the spurious solution that results. A corollary to these results reveals a general condition for determining whether coherent background removes a relative weight ambiguity. We also consider the sum of N exponentials, where we show that as many as 2N−1 solutions for the relative weights can exist, depending on whether real or complex weights are assumed. Finally, we derive expressions for the amount of quadrature phase background necessary to definitively remove relative weight ambiguities (that is, remove even local minima in the fitting function) in sum-of-two-exponential impulse responses.

Abstract In the previous work by the authors (Oh et al. (1998)), it was shown that in order for the model of an interacting spur gear pair to conserve energy, the dependence of the mesh stiffness on the mean rotation must be included in deriving the equations of motion. A quadratic nonlinearity arises from the dependence of the mesh stiffness on the mean rotation, even under the assumption of small deflection. This nonlinearity ensures conservation of energy. In this study, the stability of the steady-state response of interacting spur gears, both for the new equation of motion (EOM) and the classical EOM, is investigated. The map for periodic orbits is determined and a linearized stability analysis is performed. Once the stability is determined, the comparison between the classical and the new EOM is made for a primary, a secondary sub-harmonic, and super-harmonic resonances. The frequency-amplitude curve from direct simulation is compared to the stability analysis. The effect on the stability by the nonlinear jump term is shown, as well as by the variable time. The effect of damping and the magnitude of the applied torque on the stability is shown.

The purpose of the present work consists on improving the understanding of the energy dissipation mechanism in the structure of a gas foil bearing. The analysis is based on an analytical model capable of predicting bumps deformation due to a load on the top coupled with dry friction forces at the top and bump ends. Models of mass-individual bump and mass-bump foil subject to a harmonic force are predicted numerically. The nonlinear behavior due to dry friction results in the possibility of stick-slip conditions over the surfaces in contact. The Variation of parameters such as excitation amplitude, mass magnitude, coefficient of friction, and bump geometry were considered. Equivalent dynamic coefficients of stiffness and damping are estimated through a least squares curve fitting, which constitutes a linearization of the system with dry friction. A computer program was developed in order to consider the effect of stick-slip. As a final product of this research the nonlinear model of the structure support was used to obtain a linear and simplified equivalent model. In most studied cases it is possible to represent the system with a linearized model of constant stiffness and viscous damping which is a variable function of the studied parameters and the frequency.

Review question / Objective: The aim of this systematic review is to explore the magnitude of the placebo effect in randomized controlled trials for diarrhea-type irritable bowel syndrome and to understand possible relevant factors that affect the placebo effect. Condition being studied: Irritable bowel syndrome is a chronic functional gastrointestinal disorder characterized by abdominal pain related to defecation and a change in frequency and form of stool. Epidemiological study indicates that the prevalence of irritable bowel syndrome in different countries is high. It is estimated conservatively that direct costs related to irritable bowel syndrome causes a huge economic burden in the United States. In the latest Rome IV criteria, irritable bowel syndrome is divided into 4 subtypes based on abnormal bowel habits: irritable bowel syndrome with predominant constipation, irritable bowel syndrome with predominant diarrhea, irritable bowel syndrome with mixed bowel habits, and irritable bowel syndrome unclassified. Regarding treatment for irritable bowel syndrome, there is no cure or curative treatment. Any agent should be compared with placebo to identify its efficacy. In fact, the placebo response rate of irritable bowel syndrome is high. However, the placebo response rate of IBS-D and the moderators of the magnitude of the placebo response rate are not clear.

Review question / Objective: The aim of this systematic review is to explore the magnitude of the placebo effect in randomized controlled trials for diarrhea-type irritable bowel syndrome and to understand possible relevant factors that affect the placebo effect. Condition being studied: Irritable bowel syndrome is a chronic functional gastrointestinal disorder characterized by abdominal pain related to defecation and a change in frequency and form of stool. Epidemiological study indicates that the prevalence of irritable bowel syndrome in different countries is high. It is estimated conservatively that direct costs related to irritable bowel syndrome causes a huge economic burden in the United States. In the latest Rome IV criteria, irritable bowel syndrome is divided into 4 subtypes based on abnormal bowel habits: irritable bowel syndrome with predominant constipation, irritable bowel syndrome with predominant diarrhea, irritable bowel syndrome with mixed bowel habits, and irritable bowel syndrome unclassified. Regarding treatment for irritable bowel syndrome, there is no cure or curative treatment. Any agent should be compared with placebo to identify its efficacy. In fact, the placebo response rate of irritable bowel syndrome is high. However, the placebo response rate of IBS-D and the moderators of the magnitude of the placebo response rate are not clear.