Trapezoidal Distribution Research Articles

Dynamic fuzzy comprehensive evaluation of wet friction components performance degradation based on G1-CRITIC

High power density wet friction components are crucial in heavy equipment transmission systems, directly influencing equipment reliability. This paper proposes a fuzzy comprehensive evaluation method with combined weighting, which dynamically divides the performance degradation of wet friction components into three stages. It constructs a multi-indicator, multi-level evaluation system, in which the performance degradation data is obtained from the wet clutch accelerated life test. Additionally, we utilize the combined weighting method to dynamically allocate weights for evaluation indicators at different stages and introduce the trapezoidal distribution membership function. The accuracy of the fuzzy comprehensive evaluation model is then verified by using two prediction models as a comparison method. The results indicate that the model achieves an average relative error of 14.79% and a correlation coefficient R2 of 0.9580, indicating higher usability and accuracy than the prediction models. Furthermore, the evaluation indicator weights are more sensitive to pressure variations.

Chance-constrained programming for drinking water quality management under fuzziness and randomness

ABSTRACT In this paper, an inexact fuzzy random chance-constrained programming (IFRCCP) model was proposed to deal with the randomness and fuzziness in the optimization of booster cost for the water distribution system (WDS). The IFRCCP model was applied to a WDS to analyze the effects of randomness and fuzziness on the booster costs. The booster cost intervals were obtained under various violation levels and confidence levels. The results indicated that the lower and upper booster costs increased with the confidence levels of the lower limits and decreased with the violation levels of the lower limits for both normal and log-normal distribution fuzzy random variables (FRVs). Moreover, the increased magnitude of lower and upper booster costs under normal distribution FRV is a little less than that under log-normal distribution FRV, while the decreased magnitude of lower and upper booster costs under normal distribution FRV is larger than that under log-normal distribution FRV. The same regulation can be found for the FVR with both triangular and trapezoidal distribution FRVs. With the increase of booster number, the increased magnitude of the lower and upper booster costs decreased for both normal and log-normal distribution FRVs.

Customized and Optimized Treatment of Extended-Spectrum-Beta-Lactamase Bacteria for Individual Patients

This paper discusses the optimization of customized intravenous-drip therapy regimens for individual patients infected with antibiotic-resistant bacteria, namely Extended-Spectrum-Beta-Lactamase (ESBL) bacteria. By utilizing Ordinary Differential Equations (ODE) to model the system’s dynamics, evaluated the efficiencies of the four most typical types of pulse functions, namely Dirac delta, sine, trapezoid, and normal distribution functions, as well as the time required for each treatment to suppress the pathogen population. The results revealed that a trapezoid pulse function for intravenous delivery of antibiotics is most favorable. Subsequently, infection severity was randomized by altering the bacterial and Beta-Lactamase population. The efficiency of each randomized regimen was evaluated using a predetermined score matrix that assessed the dosing length, dosing interval, maximum rate of antibiotic infusion, net consumption of antibiotics, and the total number of required treatments. Radar charts and box plot models were employed to present the findings. It was discovered that for more severely infected patients with a higher initial population and growth rate, it is important to decrease the time interval between subsequent doses and increase the time of maximum infusion rate. Conversely, for mild infections, the time interval between doses should be increased, and the time of maximum infusion rate should be decreased. It should be noted that maximizing the infusion rate does not enhance treatment efficiency. Furthermore, in comparison to the initial infected bacteria population size, the growth rate, and Bla production rate play more important roles in impacting treatment efficacy.

Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions

Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions

Influence of geogrid arrangement on the bearing capacity of a granular soil on physical models and its comparison to theoretical equations

This study presents an analysis of the influence of geogrid distribution on the bearing capacity of granular soils. For this purpose, the bearing capacity is compared based on 3 arrangements, uniform, trapezoidal, and inverted trapezoidal, with 2 types of geogrids, biaxial and multiaxial, under the application of an axial load. The tests performed were analyzed in three forms in which the trapezoidal distribution was the best arrangement for biaxial and multiaxial geogrids. The first analysis considers the peaks for each stress–strain curve, the trapezoidal distribution increases the bearing capacity by 36% and 33% for biaxial and multiaxial geogrids, respectively. The second analysis considers a settlement ratio (s/B) of 10%, which had an average increment of 30.5% for the two types of geogrids. The third analysis considers a 20% of s/B ratio, which showed a 56% and 81% of bearing capacity ratio (BCR) increase for biaxial and multiaxial geogrids respectively. From an economical and environmental analysis, the trapezoidal distribution saves 7% of material compared to the traditional uniform distribution. The comparison between physical and numerical models with theoretical equations is presented.

An improved band design framework for atmospheric pollutant detection and its application to the design of satellites for CO2 observation

High-precision atmospheric remote sensing observation is one of the most challenging tasks in the key fields of earth observation. The accurate accounting for technical indicators such as the working spectral band, spectral resolution, and signal-to-noise ratio (SNR) of high-precision atmospheric observation satellites is an urgent research task. To address this need, this paper proposes a band design framework (BDF) that can replace airborne detection experiments to some extent and reduce the workload of satellite design. First, based on the HITRAN database, the absorption spectra of gases in the target gas absorption window are extracted as a band dataset. Then, membership functions are designed based on a trapezoid distribution, the monitoring factor α is introduced according to the importance of strong and weak absorption channels to obtain the improved fuzzy comprehensive evaluation (IFCE) model. Subsequently, the IFCE model is used to screen the band dataset. Finally, the bands are optimized based on the SCIATRAN model, sensitivity analysis and optimal inversion algorithm, and the BDF-IFCE band design method for remote sensing detection of gaseous atmospheric pollutants is established based on the improved fuzzy synthetic evaluation model. The BDF-IFCE method is applied to design the CO2 sensor detection band and two absorption windows are successfully identified (6170–6270 cm−1 and 6290–6380 cm−1). With a restricted range of aerosol AODs, detection accuracy of 3–4 ppm can be achieved with a signal-to-noise ratio of ∼300. The test results are the same as the band setting of existing atmospheric sensors, indicating that this method is effective and feasible in designing the CO2 remote sensor detection band.

Linear analysis of the gravitational beam–plasma instability

We investigate the well-known phenomenon of the beam–plasma instability in the gravitational sector when a fast population of particles interacts with the massive scalar mode of a Horndeski theory of gravity, resulting in linear growth of the latter amplitude. Following the approach used in the standard electromagnetic case, we start from the dielectric representation of the gravitational plasma, as introduced in a previous analysis of the Landau damping for the scalar Horndeski mode. We then set up the modified Vlasov–Einstein equation, using a Dirac delta function to describe the fast beam distribution. We thus provide an analytical expression for the dispersion relation, and we demonstrate the existence of a nonzero growth rate for the linear evolution of the Horndeski scalar mode. A numerical investigation is then performed with a trapezoidal beam distribution function, which confirms the analytical results and allows us to demonstrate how the growth rate decreases as the beam spread increases.

How do tall buildings affect seismic earth pressures on their basement walls?

The construction of tall buildings has recently undergone exponential growth in major cities, creating new challenges in earthquake engineering and design. For instance, existing analytical procedures for evaluating seismic lateral earth pressures on basement walls connected to these buildings typically ignore the inertia and dynamic properties of the superstructure. The inertial forces from a tall superstructure may cause additional displacements and rotations in its basement, affecting the distribution and magnitude of seismic lateral earth pressures. These additional soil-basement-structure-interaction (SBSI) effects are currently not well understood. Hence, the applicability and reliability of existing procedures to the basements of tall buildings remain questionable. In this paper, we use an experimental-numerical approach to provide insight into how the lateral resisting system of tall superstructures may impact the magnitude and distribution of seismic earth pressures on basement walls buried in dry sand and gravel. Numerical simulations are first validated in 3D using a prior centrifuge experiment that included a simplified model of a 42-story, high-rise structure in medium-dense, dry sand. Then, the numerical tool is used to perform 156 2D, nonlinear simulations of more realistic buildings and basements, ground motion characteristics, and sandy and gravely soil profiles. Nonlinear numerical simulations successfully capture the building's inertial and kinematic seismic interactions with the basement and an adjacent underground structure. The subsequent numerical sensitivity study showed that inertial forces from the dynamic lateral movements of the tall superstructure increase the total lateral earth pressures on the basement walls. This increase is particularly notable in the top two-thirds of the basement wall, and it can be approximated by a trapezoidal distribution. These effects and reliability of existing analytical procedures are shown to be highly sensitive to the building's modal frequencies in relation to the frequency content of the input motion as well as the stiffness of the structure-basement system with regard to the underlying soil. The results highlight the importance of considering the building's dynamic properties and inertia in evaluating seismic earth pressures on basement walls to avoid unsafe estimations or the need for overdesign.

Can neurological soft signs and neurocognitive deficits serve as a combined endophenotype for Han Chinese with bipolar disorder?

Bipolar disorder's (BD) potential endophenotypes include neurological soft signs (NSS) and neurocognitive disorders (ND). Few research, meanwhile, has coupled NSS and ND as combined endophenotypes of BD. This study intends to investigate NSS and ND and compare their differences in euthymic patients with bipolar disorder (EBP), their unaffected first-degree relatives (FDR), and healthy controls (HC). Additionally, search for potential endophenotypic subprojects of NSS and ND and construct and verify a composite endophenotypic. The subjects were all Han Chinese and consisted of 86 EBP, 81 FDR, and 81HC. Cambridge Neurological Inventory and MATRICSTM Consensus Cognitive Battery tested NSS and ND independently. All three groups displayed a trapezoidal distribution of NSS levels and cognitive abnormalities, with EBP having the most severe NSS levels and cognitive deficits, followed by FDR and HC. Among them, motor coordination in NSS and Information processing speed (IPS), Verbal learning (VL), and Working memory (WM) in neurocognitive function are consistent with the traits of the endophenotype of BD. The accuracy in differentiating EBP and HC or FDRs and HC was higher when these items were combined as predictor factors than in differentiating EBP and FDR. These results provide more evidence that motor coordination, IPS, VL, and WM may be internal characteristics of bipolar disease. When these characteristics are combined into a complex endophenotype, it may be possible to distinguish BD patients and high-risk groups from normal populations.

A Distributionally Robust Fuzzy Optimization Method for Single-Period Inventory Management Problems

This paper investigates single-period inventory management problems with uncertain market demand, where the exact possibility distribution of demand is unavailable. In this condition, it is important to order a reliable quantity which can immunize against distribution uncertainty. To model this type of single-period inventory management problem, this paper characterizes the uncertain demand by generalized interval-valued possibility distributions. We present a novel concept about an uncertain distribution set to describe distribution perturbation characterization. First, we introduce a lambda selection of the interval-valued fuzzy variable, and the uncertain distribution set is a collection of all generalized possibility distributions of lambda selection variables. According to the uncertain distribution set, a new distributionally robust fuzzy optimization method is developed for single-period inventory management problems. Under mild assumptions, the robust counterpart of the proposed fuzzy single-period inventory management model is formulated, which is an optimization program with certain linear objectives and infinitely many integral constraints. We discuss the computational issue of integral constraints and reformulate equivalently the robust counterpart as three deterministic inventory submodels under generalized interval-valued trapezoidal possibility distributions. According to the characteristics of three submodels, a domain decomposition method is designed to find the robust optimal solution that can immunize against uncertainty in our single-period inventory management problem. Finally, some computational results demonstrate the efficiency of the proposed distributionally robust fuzzy optimization method.

NOX EMISSION ON RECIPROCAL FILTRATION COMBUSTION OF BIOGAS: A CASE STUDY

Filtration combustion is an effective technique for dealing with low-calorific value fuels, such as derivative fuels from biomass, and simultaneously reducing pollutant emissions. In this study, combustion of biogas (22% of CO2) was investigated theoretically and experimentally by utilizing a reciprocal flow porous burner with heat exchangers inserted in the porous medium. Combustion of lean biogas-air mixtures is stabilized in a naturally transient process, in which a lean equivalence ratio range (0.1 ≤ Φ ≤ 0.9) and gas flow velocities of 0.2 and 0.3 m/s were employed, periodically switching gas flow direction. Reciprocal flow combustion has been compared with unidirectional combustion, using technical methane as reference gas. In this context, predicted temperature profiles inside the burner, as well as experimental results, have shown that the reciprocating system plays an important role in the combustion process, significantly improving flammability limits, efficiency, and emissions. As result, trapezoidal temperature distribution profiles have been obtained with peaks between 1200 and 1600 K, reaching high efficiency up to 90% and ultra-low emission of nitrogen oxides (≤ 2ppm).

Effect of vortex generator spanwise height distribution pattern on aerodynamic characteristics of a straight wing

Vortex generator (VG) is a passive flow control technology, which can effectively inhibit flow separation. Recently, significant research efforts have been devoted to the study on the application of VG in airfoil, wing/blade and aircraft flow separation inhibition. However, the research on the variable height distribution of VG along the wingspan still lacks. This study focuses on the experimental investigation of the influence of variable height distribution of ramp VG on aerodynamic characteristics. First, VG was designed, such that it was composed of two parts, one fixed region and one deformed region, which allowed for height modification. The height of VGs along the wingspan presented equal-height, triangular and trapezoidal distribution, forming a total of 15 VG layouts. Then, the connection mode of the model, the change of angle of attack and the collection and processing of aerodynamic data were introduced. Finally, a wind tunnel experiment was performed to investigate the influence of height distribution of VG on aerodynamic characteristics of wing. The experimental results show that: (1) the height distribution of the three types of VGs could inhibit the stall flow and improve the aerodynamic performance of the wing; (2) “Triangular translation 3” and “Trapezoidal translation 2” were the best layouts, both of which could increase the maximum lift coefficient, delay stall, and significantly increase the lift-to-drag ratio at high angle of attack; (3) the influence of VG height and position factors on wing stall characteristics was analyzed by using the rough set theory, and the key position information of VG arrangement was provided. This study indicates that the variable height distribution is obviously better than the equal height distribution, which can provide ideas and references for the active control of variable height distribution of VGs.

Distributed square root fuzzy cubature information filter for object tracking on the possibilistic framework

AbstractIn this study, a distributed fuzzy filter is proposed for a non‐linear state estimation problem on the possibilistic framework. Firstly, instead of Gaussian distribution on the probability framework, the process and observation noises are modelled as fuzzy random variables with trapezoidal possibility distributions. Secondly, a novel square root fuzzy cubature information filtering (SRFCIF) algorithm is proposed to deal with non‐linear state estimation with fuzzy noise; a fuzzy variable fusion (FVF) algorithm is used for fuzzy random variables fusion. Consequently, a distributed square root fuzzy cubature information filter (DSRFCIF) is proposed by embedding SRFCF and FVF into the consensus frame. Finally, consistency analysis and simulation demonstration are executed for the proposed filter.

Uncertainty analysis of water quality in water distribution system

Abstract Water quality simulation is affected by uncertain parameters such as pipe roughness coefficients, chlorine bulk decay coefficients, and chlorine wall decay coefficients, which are usually considered to be fuzzy variables. The minimum and maximum nodal chlorine concentrations and water ages at each α-cut level were obtained by the genetic algorithm (GA) based on EPANET hydraulic and water quality simulation toolkit. The fuzziness of nodal chlorine concentrations and water ages were measured using the fuzziness measure (FM) proposed in this paper. The method was applied to four networks to analyze the fuzziness of nodal chlorine concentrations and water ages. The results indicated that the distribution of nodal chlorine concentrations does not follow typical trapezoid distribution, while the distribution of nodal water ages follows typical trapezoid distribution. In addition, the chlorine concentration and water ages of nodes farther from the source are affected by uncertain parameters to a greater extent. The greater demands of nodes lead to less effects of uncertain parameters on chlorine concentration, and greater effects of uncertain parameters on water ages. This study would help in analyzing the fuzziness of hydraulic and water quality simulation results in WDS under uncertain conditions.

Mechanical Analysis of Frozen Wall with Trapezoidal Temperature Field Distribution Based on Unified Strength Theory

In order to study the elastic–plastic stress field distribution of a double-row-pipe frozen wall, the temperature field of the double-row-pipe frozen wall is equivalent to a trapezoidal distribution, and the frozen wall is regarded as an elastic–plastic thick-walled cylinder with functionally gradient material (FGM) characteristics in the radial direction. Considering that the elastic modulus and cohesion of the frozen wall material change linearly with the radius, the elastic–plastic analysis of the frozen wall is carried out based on unified strength theory. The analytical solutions of the elastic–plastic stress field distribution, the elastic ultimate bearing capacity, the plastic ultimate bearing capacity, and the relative radius of the plastic zone of the frozen wall are derived. The analytical solution is calculated based on the engineering case and compared with the numerical solution obtained based on COMSOL. At the same time, the influence of strength theory parameters on the mechanical properties of heterogeneous and homogeneous frozen walls is analyzed. The results show that the analytical solution and the numerical solution are in good agreement, and their accuracy is mutually verified. The external load on the frozen wall of the selected layer is greater than its elastic ultimate bearing capacity and less than its plastic ultimate bearing capacity, which indicates that the frozen wall is in a safe state of stress. The radial stress increases with the increase in the strength theoretical parameter b and the relative radius r, the tangential stress increases with the increase in the strength theoretical parameter b, and first increases and then decreases with the increase in the relative radius r. The larger the strength theoretical parameter b, the smaller the relative radius of the plastic zone of the frozen wall. The strength theoretical parameter b increases from 0 to 1, the elastic ultimate bearing capacity and plastic ultimate bearing capacity of the heterogeneous frozen wall increase by 33.3% and 40.8%, respectively, and the elastic ultimate bearing capacity and plastic ultimate bearing capacity of the homogeneous frozen wall increase by 33.3% and 41.0%, respectively. Therefore, considering the influence of intermediate principal stress, the potential of materials can be fully exerted and the ultimate bearing capacity of frozen walls can be improved. This study can provide theoretical reference for the design and construction of frozen wall.

A mixed integer fuzzy-interval credibility-constrained programming for booster optimization in water distribution system under uncertainty

Generally, boosters should be placed in water distribution system (WDS) to preserve the required residual disinfectant concentration at the far-ends. To cope with the fuzzy and interval uncertainties in the optimization of boosters, a mixed integer fuzzy-interval credibility-constrained programming (MIFICCP) model was formulated for disinfection booster design, location, and operation, which is solved by transforming the model into two linear sub-models. The results indicated that: The booster injection rates, operational injection costs (BCI), and booster capital costs (BCD) increased with the credibility levels; The lower and upper booster costs under fuzzy-interval set (FIS) with trapezoidal distribution are higher than FIS with triangular distribution for various credibility levels except for the credibility level of 0.5; With the increase of maximum booster number, the values of BCI decreased, the value of BCD increased, and the total costs may increase or decrease, which depend on the relative magnitude of BCI to the total costs. The results obtained can give more information for managers to make decisions on the booster strategies to uniform chlorine distribution along WDS scientifically and reasonably, especially under dual uncertainties of fuzzy and interval.

A fuzzy-interval nonlinear programming for boosters under uncertainty

Abstract In this paper, an integration of a fuzzy-interval credibility-constrained (FIC) model expressed by fuzzy interval sets (FIS) and interval nonlinear programming (INP), termed an FIC-INP model, was proposed and applied to two cases. After formulating the FIC-INP model, upper and lower disinfection booster costs can be obtained for two cases under various combinations of credibility levels of upper and lower limits. The results indicated that the upper and lower booster costs increased with the credibility levels of the lower limits. The upper as well as the lower booster costs increased with the booster numbers. For credibility levels of lower limit constraints ranging from 0.6 to 0.9, the upper and lower booster costs increased under enlarging/widening trapezoidal distributions, and the intervals of booster costs increased with interval uncertainty. For a lower limit constraint credibility level of 0.5, the upper and lower booster costs decreased under shrinking/narrowing trapezoidal distributions, and the booster cost intervals increased under larger interval trapezoidal distributions. The degrees of effect of the interval uncertainty are higher than the fuzzy uncertainty. The results obtained can provide more information for managers to make booster schemes under fuzzy and interval uncertainties.

Quantifying the impact load of rapid dry granular flows exerted on rigid slit structures using centrifuge experiments and DEM simulation

Granular flows are typical hazard in mountainous terrains. Slit structure has been shown to be a successful mitigating strategy. However, the interaction mechanism between granular flows and slit structure has not been completely elucidated, and the impact load and impact pressure distribution pattern of granular flow on slit structures also has not been fully discussed. Therefore, a novel centrifuge flume experiment and DEM simulation were designed. The centrifugal acceleration field and Coriolis field accounting for the Coriolis effect were also implemented in the DEM model. Results reveal that, the grain size almost has no effect on normal impact forces when the granular flows act as continuous characteristic, and the initial volume and impact force do not show a simple linear relationship. Furthermore, the impact pressure profiles indicate a trapezoidal distribution with a peak impact pressure at the bottom and a decline from the bottom to the top. In addition, the impact forces also showed a decreasing trend from the slit to the flume channel sidewall, making the inner part vulnerable. This study might contribute to the study of flow-slit structure interaction and provide scientific support for slit structure engineering design.

Research of the design of a solar radiation concentrator for autonomous photoenergy installation

Significant increase in power due to the use of concentrators of solar radiation confirms the feasibility of using concentrated radiation, and the development of concentrators makes a separate task of optical physics. Hubs deserve special attention to obtain a high degree of radiation concentration, their development requires a number of innovative technical solutions. The complex researches on optimization of concentrators of solar radiation for use as a part of high-concentration photovoltaic systems by research of optical properties and features of degradation of facet, vacuum and segment concentrators are carried out in the work. According to the results of field testing of the experimental sample of the facet concentrator, it was found that the procedure of adjusting the concentrator is associated with individual adjustment of the position of each of the 400 mirrors, which is extremely difficult. And due to the insufficient rigidity of the structure, the concentrator needs to be adjusted in the settings after the operations of moving or assembling-disassembling the experimental sample of the concentrator. As the concentrator needs regular cleaning due to natural pollution from dust, rain and other natural factors, this operation is associated with mechanical impact on the mirrors, which leads to a violation of their settings. According to the results of testing the vacuum type concentrator, it was found that such concentrators are very sensitive to the quality of the base because due to design features cannot be adjusted after manufacture and they had too large a focal spot larger than the heat sink. According to the results of field testing, it is established that the design of a segment-type concentrator is promising for use in the high-concentration photovoltaic systems, which is a circular array of segments made of mirror material, the integrated reflection coefficient of which reaches 95% and made an experimental sample with an area of 3.6 m2, which allows to obtain a focal spot with a diameter of 120 mm with a trapezoidal light distribution with a radiation concentration factor of 360 units.

Solving geometric programming problems with triangular and trapezoidal uncertainty distributions

The geometric programming problem is an important optimization technique that is often used to solve different nonlinear optimization problems and engineering problems. The geometric programming models that are commonly used are generally based on deterministic and accurate parameters. However, it is observed that in real-world geometric programming problems, the parameters are frequently inaccurate and ambiguous. In this paper, we consider chance-constrained geometric programming problems with uncertain coefficients and with geometric programming techniques in the uncertain-based framework. We show that the associated chance-constrained uncertain geometric programming problem can be converted into a crisp geometric programming problem by using triangular and trapezoidal uncertainty distributions for the uncertain variables. The main aim of this paper is to provide the solution procedures for geometric programming problems under triangular and trapezoidal uncertainty distributions. To show how well the procedures and algorithms work, two numerical examples and an application in the inventory model are given.