Equal Area Method Research Articles

A global urban heat island intensity dataset: Generation, comparison, and analysis

The urban heat island (UHI) effect, a phenomenon of local warming over urban areas, is the most well-known impact of urbanization on climate. Globally consistent estimates of the UHI intensity (UHII) are crucial for examining this phenomenon across time and space. However, publicly available UHII datasets are limited and have several constraints: (1) they are for clear-sky surface UHII, not all-sky surface UHII and canopy (air temperature) UHII; (2) the estimation methods often neglect anthropogenic disturbance, introducing uncertainties in the estimated UHII. To address these issues, this study proposes a new dynamic equal-area (DEA) method that can minimize the influence of various confounding factors on UHII estimates through a dynamic cyclic process. Utilizing the DEA method and leveraging various gridded temperature data, we develop a global-scale (>10,000 cities), long-term (over 20 years by month), and multi-faceted (clear-sky surface, all-sky surface, and canopy) UHII dataset. Based on these estimates, we provide a comprehensive analysis of the UHII and its trends in global cities. The UHII is found to be greater than zero in >80% of cities, with global annual average magnitudes around 1.0 °C (day) and 0.8 °C (night) for surface UHII, and close to 0.5 °C for canopy UHII. Furthermore, an interannual upward trend in UHII is observed in >60% of cities, with global annual average trends exceeding 0.1 °C/decade (day) and over 0.06 °C/decade (night) for surface UHII, and slightly surpassing 0.03 °C/decade for canopy UHII. Notably, there exists a positive correlation between the magnitude and trend of UHII, suggesting that cities with stronger UHII tend to experience faster growth in UHII. Additionally, discrepancies in UHII are found between different temperature data, stemming not only from distinctions in data types (surface or air temperature) but also from differences in data acquisition times (Terra or Aqua), weather conditions (clear-sky or all-sky), and processing methodologies (with or without gap filling). Overall, our proposed method, dataset, and analysis results have the potential to provide valuable insights for future urban climate studies. The UHII dataset is publicly available at https://doi.org/10.6084/m9.figshare.24821538.

Transient Synchronization Stability of Grid-Forming Converter During Grid Fault Considering Transient Switched Operation Mode

With the increasing penetration of renewable energy generation, grid-forming (GFM) converters that simulate the dynamics of synchronous generator (SG) and actively participate in grid voltage and frequency regulation are increasingly employed. In GFM converter dominated power system, similar transient synchronization stability that is common in conventional power system also exists, which is closely related with the control dynamics of GFM converters. In this paper, the transient synchronization stability of GFM converters with virtual synchronous generator (VSG) control is focused on, with the influence of transient switched operation mode (TSOM) introduced by current saturation limitation considered especially. First, a novel transient equivalent motion model of VSG is developed. The model is a switched system and TSOM significantly changes the power angle characteristics. Based on power angle curve analysis and equal area method, the transient stability analysis is carried out from non-existence of equilibrium point and non-matching of accelerating-decelerating area. Analysis indicates that TSOM imposes another constraint to equilibrium point and reduces deceleration area, which worsens the transient stability. Further, employing the stability region theory of nonlinear dynamic systems, the stability region of VSG is visually displayed in phase plane. It is identified that the TSOM reduces the stability region and worsens the stability. Finally, the influence factors including power reference, grid voltage sag and grid impedance are discussed.

Constructing outlier-free histograms with variable bin-width based on distance minimization

We propose a new method of constructing a variable bin width histogram that can accommodate the unbalanced distribution of the samples yet retaining, as a whole, the good aspect of both equal width (EW) and equal-area (EA) histograms that are being used popularly for data visualization and analysis. We formulate this as an optimal change point detection problem in which the bin boundaries are determined by minimizing the sum of the absolute error or the squared error in each bin. The former is based on Distance Minimization (DM) and new, and the latter is based on Variance Minimization (VM) and is considered the state-of-the-art. The constructed histograms can effectively be used to detect and visualize hidden outliers/anomalies by applying the interquartile range method in each bin. The final histograms are obtained by adjusting bin boundaries and heights accordingly after removing the detected outliers/anomalies. We further propose a method to annotate the constructed bins if the data for annotation is given for each sample as a set of nominal variables, using z-score with respect to their distribution within each bin. We applied our method to both real vinyl greenhouse datasets and two different sets of three synthetic datasets, and confirmed that both DM and VM methods work as intended, both can represent the sample distribution with a smaller number of bins than those by EW and EA methods, The use of interquartile range method can detect anomalies as well as outliers, and the terms selected for annotation are interpretable and reasonable. EW and EA methods have contrasting properties. DM and VM methods lie in between, but the former is closer to EA method and the latter to EW method. DM method runs substantially faster than VM method and performs slightly better than VM method in outlier detection and annotation tasks.

Using buffer analysis to determine urban park cooling intensity: Five estimation methods for Nanjing, China

Urban parks are part of the blue-green infrastructure of urban ecosystems. Although the cooling effect of urban parks has been widely recognized, the understanding of park cooling intensity (PCI) and its mechanisms remains incomplete. Applicable and accurate quantification could facilitate better design and management of urban parks. We used five methods (equal area method [EAM], equal radius method [ERM], fixed radius method [FRM], turning point method-maximum perspective [TPM-M], and turning point method-accumulation perspective [TPM-A]) to estimate PCI, and established the method selection mechanism, which we evaluated in terms of PCI amplitudes, spatial heterogeneity, and interactions with park landscape features. Using Nanjing as a case study, we employed spatial and statistical analyses to further assess the autocorrelation of PCI and its relationship with park landscape features. The results indicate the following: (1) 62.38 % of Nanjing's urban parks are located above the 90 % confidence level in cold spot areas. (2) Different methods had significant effects on the estimated PCI, were positively correlated, and had similar spatial heterogeneity. (3) All methods revealed that park area (PA), water area proportion (WAP), and the normalized difference vegetation index (NDVI) of the vegetated area (NDVIveg) were the three dominant factors that influenced PCI; WAP and NDVIveg that achieved more effective cooling. (4) The quantification of PCI using the ERM and TPM is recommended over other methods. These findings are essential for landscape planners to understand the formation of PCI and design cooler parks to mitigate the urban heat island (UHI) effect more systematically.

Study on the Influence of Roadway Structural Morphology on the Mechanical Properties of Weakly Cemented Soft Rock Roadways

We used the 11,303 return air roadway of the Hongqingliang coal mine as the engineering background for a study exploring the impact of the structural morphology of the roadway on the stress distribution characteristics and the stability of a weakly cemented soft-rock mine roadway. This work studies the evolution law of stress and deformation, and the plastic zone of weakly cemented soft-rock roadways with retaining the top or bottom coal seams. The results show that when retaining the top coal is replaced by the bottom coal, the high-stress zone of the vertical stress is reduced, the peak stress is decreased, and the stress concentration coefficient is slightly reduced from 1.67 to 1.64. The peak value of the vertical displacement of the roof of the shaft which was 78.4% of that of the top coal also decreases significantly, while the peak value of the vertical displacement of the floor, which was 1.37 times that of the top coal, increases. The equal area method was used to change the aspect ratio of the roadway. When the aspect ratio decreased from 1.38 to 0.88, the high-stress zone of the vertical stress was reduced, the stress peak decreased, and the stress concentration coefficient decreased from 1.8 to 1.75. The vertical displacement of the roof increased by 27.7% from 10.91 mm to 13.93 mm, and the vertical displacement of the floor increased by 15.2% from 6.60 mm to 7.60 mm. The plastic failure range was significantly reduced, particularly at the bottom corners. These findings show that structural morphology has a great influence on the floor heave of weakly cemented soft rock. Reasonable retention of the top or bottom coal and the aspect ratio of the roadway can prevent the deformation and failure of the roadway in weakly cemented soft rock.

Improved transient stability of virtual synchronous generators for grid voltage cascading faults

• The basis of the investigation is a cascading fault of a grid-connected inverter in both low and high voltage power grids. • Pay attention to the fault with equilibrium point and the fault without equilibrium point while dealing with low-voltage faults, and utilize the phase portrait to assess stability. Finally, a control technique is given to ensure that the two defects are well controlled. • The equal area method is utilized to assess the fault in high voltage faults, and it is inferred that there must be an equilibrium point in high voltage faults. Finally, a control technique for active power transient overshoot mitigation and PCC voltage support during faults is provided. The topic of VSG grid voltage fault ride through has drawn increasing attention as virtual synchronous generator (VSG) technology has been widely applied in the field of renewable energy power generation. Due to the delay of the reactive power compensation device after the low-voltage fault recovery, the high-voltage fault will happen immediately after the grid's low-voltage fault is resolved. This phenomenon is known as low and high voltage cascading faults. There is not enough research on this specific voltage fault right now. For specific investigation, the low and high voltage cascading faults in this paper are separated into low-voltage fault stages and high-voltage fault stages. The equal area criterion (EAC) is used to analyze the specific process at the low-voltage fault stage. In addition, the dynamic damping control (DDC) is utilized to resolve the problem of low-voltage fault stability. Under low voltage fault, the phase portrait studies the single-period stability with an equilibrium point in a single-period and the multi-period stability without an equilibrium point in a single-period, respectively. Using a phase portrait to analyze system performance during a high voltage fault, and a virtual capacitor feedback control (VCFC) is offered to effectively reduce active power overshoot due to high voltage fault. The EAC is used to analyze the specific process of the high voltage stage, it is concluded that there is always an equilibrium point in the high-voltage fault where IGBT limitations are ignored. Finally, the correctness and feasibility of the theory are verified by simulation, and the specific analysis results are given.

Research on Filling Strategy of Pipeline Multi-Layer Welding for Compound Narrow Gap Groove.

With the increase in transmission pressure and pipe diameter of long-distance oil and gas pipelines, automatic welding of the pipeline has become the mainstream welding method. The multi-layer and multi-pass welding path planning of large-diameter pipelines with typical narrow gap grooves are studied, and a welding strategy for pipeline external welding robot is proposed. By analyzing the shape of the weld bead section of the narrow gap groove and comparing the advantages and disadvantages of the equal-height method and the equal-area method, the mathematical model of the filling layer is established. Through the test and analysis in the workshop, the predicted lifting value meets the actual welding requirements. The microstructure of the weld was analyzed by SEM. The main structure of the weld was fine acicular ferrite, which could improve the mechanical properties of the welded joint. After multi-layer filling, the filling layer is flush with the edge of the groove. The establishment of this model lays a foundation for the formulation of welding process parameters for large-diameter pipes and the off-line programming of welding procedures.

Analysis and Comparison of Two Permanent-Magnet Width-Modulation Arrays for Permanent Magnet Linear Synchronous Motor

Permanent-magnet (PM) width-modulation array is designed to solve the issues resulting from big pole-pitches of PMLSMs in high-speed and high-precision systems. PM width-modulation array provided in this paper is a kind of segmented magnetic-pole structure, featuring low PM eddy currents and low thrust ripples. First, the magnetomotive force (MMF) excited by the PM width-modulation array is analyzed to prove its feasibility, the PM eddy current of the novel array is studied to show its advantage in high-speed applications, and the electromagnetic models of two PM width-modulation arrays are established, which are designed by the equal area method and the triangular modulation method, respectively. Then, the thrust features and the PM usage amounts of the two PM width-modulation arrays are analyzed by the finite element method (FEM) and the performance comparisons are presented. The prototype is manufactured and tested to verify the analytical results. The experimental data agree well with the simulations and analyses.

A Method for Calculating Grounding Resistance of Reinforced Concrete Foundation Grounding Systems

Tower foundations have been used as grounding electrodes to reduce the area of the grounding devices. However, it is difficult to calculate the grounding resistance due to the complex structure of the reinforced concrete foundation. A method for calculating grounding resistance of reinforced concrete foundations is proposed in this paper. The method equates the complex foundation structure into a cylindrical conductor and then calculates the grounding resistance with the help of the method of moments, which simplifies establishment of the simulation model and reduces the extensive computation. In addition, the applicability of the equal cross-sectional area method and the equal cross-sectional perimeter method is analyzed. It shows that both methods are applicable only when the concrete resistivity is close to the soil resistivity. The equal cross-sectional area method is applicable when the concrete resistivity is within twice the soil resistivity, while the equal cross-sectional perimeter method is applicable when the concrete resistivity is approximately same or less than the resistivity of the soil.

Material R-factors of buildings with irregularity

R-factor (Response reduction factor) is an important design consideration in seismic design of structures, which is assumed to consider energy dissipation of structures by means of ductility. So, proper estimation of R-factor is required for seismic design of structures which will account for ductile deformation so that suitable detailing of reinforcement can be done. In case of irregular structures, where the torsion effect is the predominant factor, accurate estimation of R-factor is even more difficult. Therefore, in the present study, an attempt has been taken to determine R-factor for plan irregular buildings. A G +7 storied building is considered and irregularity effect has been incorporated by C and L-shaped configuration. The design of the buildings has been done following Indian Standards. Modeling and analysis have been done using SAP2000. Plastic hinges have been considered to represent material nonlinearity. Mander’s confinement model has been considered. Nonlinear Static (Pushover) following FEMA 440 methods with uniform lateral load variations has been done. Initial tangent stiffness has been followed in equal area method during bi-linearization of pushover curve. It can be stated that apart from material strength and geometrical configuration, performance requirement of the buildings is the most important factor for selection of R-factor.

The effect of nanopores geometry on desalination of single-layer graphene-based membranes: A molecular dynamics study

The water desalination process using nanoporous single-layer graphene membranes is simulated through classical molecular dynamics. The effect of nanopores shapes on the capacity of the membrane for filtration of water is investigated. According to the results, the geometry of the nanopores considerably affects the performance of the membrane and can completely change the water flow rate and salt rejection. The results reveal that the effective area of the nanopores plays a critical role and for a better understanding of the impact of this parameter, aspect ratio and the equal diameter of noncircular pores based on different methods such as equal area, equal perimeter, and hydraulic diameter for each case are calculated. In the case of noncircular nanopores, the results indicate that aspect ratio and hydraulic diameter, as well as equal area method, can adequately capture the associated trends, while the equal perimeter method is unable to correctly predict them.

A simple and easy method to quantify the cool island intensity of urban greenspace

Accurately and easily quantifying the greenspace cool island intensity (GCII) is important to understand the cooling effect of urban greenspace for better urban greenspace planning and management. This study proposed two new methods (i.e., equal area method and equal radius method) to estimate GCII and compared them with two old methods (i.e., turning point method and fixed radius method) in terms of the GCII magnitudes, spatial variations, relationships with greenspace size, and the estimation of optimal greenspace size in cooling the environment (i.e., threshold value of efficiency (TVoE)). We performed the analysis based on Landsat derived land surface temperature (LST) in seven Chinese cities with varied climate background and geographic variations. The results showed that: (1) Different methods significantly impacted the estimated GCIIs with higher values by the turning point method and lower values by the equal area method. (2) GCIIs by different methods were positively and significantly correlated with each other and characterized similar spatial heterogeneities. (3) GCIIs by all methods showed significantly positive logarithmic relationships with greenspace area with higher R2 observed by the equal area method. (4) The four methods estimated close TVoEs with no significant difference among them. We recommend the equal radius method to quantify GCII for its equal effectiveness but easier calculation compared to other methods.

Efficacy of R-factors in the performance based evaluation of RCC buildings

The main characteristic of prescriptive building design codes is that they adopt force-based seismic design procedure for evaluating seismic force demand. The actual seismic force demand is reduced by the introduction of response reduction factor (R) to obtain design lateral seismic force. This diminution in real seismic force implicitly accounts for the energy dissipating capability of the structures when building is expected to undergo inelastic deformation during strong earthquakes. The code is silent about ductility value of the structures designed for a given value of R. Also, irrespective of the structures geometrical configuration and strength, the assigned R-values as per codal provisions are same in most of the cases. Hence, proper estimation of R-factor is of great importance to rightly design the structures with proper assessment of ductile deformation supplemented by correct reinforcement detailing. In the present study, effect of geometrical configuration on R-factor has been considered. The R-factor has been determined for buildings with and without plan irregularities. G + 3, G + 7 and G + 11 story square shaped and G + 7 story L-shaped and C-shaped buildings have been considered for the study purpose. All the buildings have been designed as per IS codal provisions. Material nonlinearity has been considered using plastic hinge model. Confinement effect in RC beam and column section has been considered using Mander’s model. Pushover analysis of the buildings has been done using FEMA440 equivalent linearization and displacement modification methods. The bi-linearization of pushover curve has been done using equal area method with initial tangent stiffness. It has been observed that the R-factor values for various performance levels are different and judgment of considering an R-factor for a building depends upon specific performance objectives. Also, it has been observed that the R factor is sensitive to both geometrical configuration and material strength of structures.

An adaptive sampling method for accurate measurement of aeroengine blades

The surface of aeroengine blades has geometrical complexity and its measurement accuracy directly affect the assessment correction of the different machining processes. A NURBS based parametric model was employed to represent the geometry of blade surface for evaluating deviation between ideal model and measurement model. In view of the various curvature at the different blade region, an adaptive surface sampling strategy with bending moment theory is proposed. The distribution and number of the check points can be determined adaptively and accurately in accordance with geometrical feature altering. The accuracy and effectiveness of the proposed method were validated through simulations. Case studies involving comparing with bidirectional isoparametric method, equal area method and hammersley sequence method showed that the deviation between the measured blade surface and its reconstructed model using the developed method is the least among all the methods while the numbers of the selected check points are the same.

Mid-scale and full-scale experiments of cavity-insulated gypsum and calcium-silicate sheathed CFS walls under different fire exposures

Most previous fire experiments of cold-formed steel (CFS) walls were conducted under ISO834 fire exposure, for which the results can not reflect the fire performance in some special scenarios. Meanwhile, full-scale fire experiments of CFS walls are time-consuming and suffer from high equipment requirements and cost. In this paper, two 1.1 m×1.1 m mid-scale non-load-bearing fire experiments and three 3 m×3 m full-scale load-bearing fire experiments of CFS walls were carried out. The specimens used gypsum plaster (GP) board and calcium-silicate (CS) board as the sheathing boards, and rock wool as the cavity insulation. In addition, the experiments involved four different fire exposures. The results show that the time-temperature profiles between the mid-scale and full-scale specimens, which had the identical dimensions and configuration of wall cross-section, tend to be consistent under the same fire condition. Therefore, a simplified experimental method was proposed to determine the fire resistance time for the structural failure of CFS walls with different load ratios through only one non-load-bearing fire experiment of mid-scale specimen, which avoided the current complex implementation that the fire resistance time of CFS walls with different load ratios was determined by carrying out multiple full-scale load-bearing fire experiments. In addition, the horizontal board joints were identified as the weak parts for the fire resistance of CFS walls under different fire exposures, which would cause stud buckling near the horizontal joints during the fire experiments. Moreover, the experiments under different fire exposures shows extended fire resistance time by substituting GP board with CS board as the base-layer sheathing, and the critical temperatures of stud hot flanges, which corresponded to the structural failure of present cavity-insulated GP-CS sheathed CFS walls and the load ratio of 0.27, were close to each other with the average of 693.8 °C. Finally, it was verified that the equal area method can give a rational prediction of the fire resistance time equivalency after correction by reference temperatures.

ОПРЕДЕЛЕНИЕ ОБЪЁМА ДЫХАТЕЛЬНЫХ МЁРТВЫХ ПРОСТРАНСТВ МЕТОДОМ КАПНОВОЛЮМЕТРИИ

The article provides information on the lung dead space – a part of the respiratory volume that does not participate in gas exchange. The anatomical and alveolar dead spaces jointly together form the physiological dead space. The article describes methods for determining the volume of dead spaces using the capnovolumetry. The volume of physiological dead space is calculated using the C. Bohr equation. The volume of anatomical dead space can be determined using the equal area method proposed by W.S. Fowler. The volume of the alveolar dead space is the difference of volumes of the physiological and anatomical dead spaces. In pathology, the volume of the alveolar space and, consequently, physiological dead space can increase significantly. Determination of the volume of dead space is the significant criterion for diagnostic and predicting the outcome of a number of diseases. Keywords: Physiological dead space , anatomical dead space , alveolar dead space , capnovolumetry, volumetric capnography.

Full-scale experiments of gypsum-sheathed cavity-insulated cold-formed steel walls under different fire conditions

Most previous fire experiments of cold-formed steel (CFS) walls focused on ISO 834 fire. The corresponding results may not represent the actual fire performance of CFS walls in some special circumstances. This paper presents a full-scale experimental investigation of gypsum-sheathed cavity-insulated CFS walls under four different fire conditions. The results show that the axial load has an insignificant effect on the heat transfer of such walls in fire. This realization provides a basis for the indirect coupling method of thermal-mechanical analysis of CFS walls, in which the time-temperature profiles of non-load-bearing CFS walls are adopted in the thermal-mechanical analysis of load-bearing walls. In addition, for CFS walls with the same configuration and load level, different fire conditions do not change the failure mode of steel studs; in particular, the stud hot flanges exhibit almost the same temperature when the structural failure of CFS walls occurs. Hence, a new time equivalency method of CFS walls is proposed, which uses the same temperature of hot flange as the principle of equivalency. Meanwhile, both the equal area method and energy-based method are modified by using reference temperatures, and give a good prediction of the fire resistance time equivalency of CFS walls. Moreover, significant opening of gypsum board joints is observed during the fire exposure; however, this phenomenon is an inherent characteristic of heated gypsum boards and has insignificant correlation with the out-of-plane deflection of CFS walls. Furthermore, staggered board joints are recommended as an important and effective fire resistance configuration of CFS walls.

Large Signal Synchronizing Instability of PLL-Based VSC Connected to Weak AC Grid

Similar large signal synchronizing instability that is common in traditional power system also exists in voltage source converter (VSC) dominated power system, which is increasingly reported and investigated. In this paper, the large signal instability of phase locked loop (PLL) synchronized VSC connected to weak ac grid is investigated. First, the influence of high grid impedance on PLL's dynamics is explored and an additional feedback loop is found to be introduced, which deteriorates the performance of PLL. Then an analysis model that is similar as the rotor motion model of synchronous generator (SG) is developed. Based on the developed model, equal-area method is employed to carry out the large-signal stability analysis. The large signal instability is found to be mainly resulted by the following two factors. One is the nonexistence of equilibrium point, which is similar as that there does not exist intersection between the mechanical power input curve and electromagnetic restoring force curve in SG grid connected system. The other is related with the transition process resulted by insufficient decelerating area, which leads to that the system cannot stably go through the transition from initial point to the existing equilibrium point. The proposed analysis not only contributes to revealing the physical mechanism but also provides guidance for the future improvement measures.

Thermal performance of non-load-bearing cold-formed steel walls under different design fire conditions

Most previous fire experiments of cold-formed steel (CFS) walls focused on the ISO 834 or the E119 fire curve. Although the fire performance of CFS walls under ISO 834 or E119 curve can be theoretically converted to that under other fire curves, the corresponding time equivalency methods have not been experimentally examined. This paper presents an experimental investigation of non-load-bearing CFS walls under four different fire conditions. It is proved by the experiments that the maximum temperature of the design fire curve is one of the most important indexes for representing the severity of fire exposure. Especially, the maximum temperature of 680 °C for external fire was not severe to the present non-load-bearing CFS walls. Two specimens were subjected to 285 min of external fire but demonstrated an almost steady-state heat transfer process. Meanwhile, the hydrocarbon fire and realistic design fire demonstrated much more severe damage. It is also proved for the first time that neither the equal area method nor the energy-based method was suitable for the fire-resistance time equivalency of CFS walls. Based on post fire observation, significant local crushing of studs was identified, especially after the fall off of fire-side sheathing. Additionally, it was found that replacing the fire-side base-layer gypsum plasterboard with low-bulk-density calcium-silicate board extends the insulation and structure performance of CFS walls under fire conditions. Moreover, a simplified temperature distribution model and the critical temperature on the fall off of fire-side gypsum plasterboard were recommended for the numerical modeling of CFS walls.

Transient stability enhancement by series braking resistor control using local measurements

Series braking resistors (SeBR) offer an effective way to enhance transient stability for severe near-to-generator faults cleared with a delay. The SeBR is switched on for a short time, already during the fault. The SeBR should switch on as quickly as possible after identifying the risk of losing transient stability. Then, the SeBR is switched off, and it is the decision-making algorithm that chooses the switch-off time. This paper presents an algorithm to choose the moment the SeBR switches off. The algorithm identifies the direction of a rotor motion based on changes in the square of the current and real power of the synchronous machine. The proposed algorithm is characterized by its simplicity, and is easy to implement because it uses local measurements. To develop the control algorithm, the effect of the SeBR on power angle characteristics for a fault state and post-fault states were determined. In addition, the effect of the SeBR on transient stability is explained using the equal area method. The conducted simulation tests have confirmed that the proposed SeBR control algorithm leads to longer critical clearing times, and thus it contributes to enhanced transient stability.