A New Approach for Capturing the Probability Density Function of the Maximum Value of a Markov Process

In the present paper a method to determine the probability distribution of the maximum value process (MVP) of a Markov process is proposed. In this method, an augmented vector process of a physical process and its MVP is constructed. The joint probability density function is then calculated by the path integral solution (PIS), and further the probability density function of the MVP can be obtained as the marginal probability density. A numerical example is shown to validate the proposed method.Financial supports from the National Natural Science Foundation of China (NSFC Grant Nos. 11672209, 51538010 and the National Distinguished Youth Fund of NSFC with Grant No.51725804), the NSFC-DFG joint program (11761131014) and the International Joint Research Program of Shanghai Municipal Government (Grant No. 18160712800) are highly appreciated

Equation governing the probability density evolution of multi-dimensional linear fractional differential systems subject to Gaussian white noise

Stochastic fractional differential systems are important and useful in the mathematics, physics, and engineering fields. However, the determination of their probabilistic responses is difficult due to their non-Markovian property. The recently developed globally-evolving-based generalized density evolution equation (GE-GDEE), which is a unified partial differential equation (PDE) governing the transient probability density function (PDF) of a generic path-continuous process, including non-Markovian ones, provides a feasible tool to solve this problem. In the paper, the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established. In particular, it is proved that in the GE-GDEE corresponding to the state-quantities of interest, the intrinsic drift coefficient is a time-varying linear function, and can be analytically determined. In this sense, an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original high-dimensional linear fractional differential system can be constructed such that their transient PDFs are identical. Specifically, for a multi-dimensional linear fractional differential system, if only one or two quantities are of interest, GE-GDEE is only in one or two dimensions, and the surrogate system would be a one- or two-dimensional linear integer-order system. Several examples are studied to assess the merit of the proposed method. Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems, the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian, and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems

A full‐probabilistic cloud analysis for structural seismic fragility via decoupled M‐PDEM

AbstractPerformance‐based earthquake engineering (PBEE) is essential for ensuring engineering safety. Conducting seismic fragility analysis within this framework is imperative. Existing methods for seismic fragility analysis often rely heavily on double loop reanalysis and empirical data fitting, leading to challenges in obtaining high‐precision results with a limited number of representative structural analysis instances. In this context, a new methodology for seismic fragility based on a full‐probabilistic cloud analysis is proposed via the decoupled multi‐probability density evolution method (M‐PDEM). In the proposed method, the assumption of a log‐normal distribution is not required. According to the random event description of the principle of preservation of probability, the transient probability density functions (PDFs) of intensity measure (IM) and engineering demand parameter (EDP), as key response quantities of the seismic‐structural system, are governed by one‐dimensional Li‐Chen equations, where the physics‐driven forces are determined by representative analysis data of the stochastic dynamic system. By generating ground motions based on representative points of basic random variables and performing structural dynamic analysis, the decoupled M‐PDEM is employed to solve the one‐dimensional Li‐Chen equations. This yields the joint PDF of IM and EDP, as well as the conditional PDF of EDP given IM, resulting in seismic fragility analysis outcomes. The numerical implementation procedure is elaborated in detail, and validation is performed using a six‐story nonlinear reinforced concrete (RC) frame subjected to non‐stationary stochastic ground motions. Comparative analysis against Monte Carlo simulation (MCS) and traditional cloud analysis based on least squares regression (LSR) reveals that the proposed method achieves higher computational precision at comparable structural analysis costs. By directly solving the physics‐driven Li‐Chen equations, the method provides the full‐probabilistic joint information of IM and EDP required for cloud analysis, surpassing the accuracy achieved by traditional methods based on statistical moment fitting and empirical distribution assumptions.</jats:p

Failure probability estimation of dynamic systems employing relaxed power spectral density functions with dependent frequency modeling and sampling

This work addresses the critical task of accurately estimating failure probabilities in dynamic systems by utilizing a probabilistic load model based on a set of data with similar characteristics, namely the relaxed power spectral density (PSD) function. A major drawback of the relaxed PSD function is the lack of dependency between frequencies, which leads to unrealistic PSD functions being sampled, resulting in an unfavorable effect on the failure probability estimation. In this work, this limitation is addressed by various methods of modeling the dependency, including the incorporation of statistical quantities such as the correlation present in the data set. Specifically, a novel technique is proposed, incorporating probabilistic dependencies between different frequencies for sampling representative PSD functions, thereby enhancing the realism of load representation. By accounting for the dependencies between frequencies, the relaxed PSD function enhances the precision of failure probability estimates, opening the opportunity for a more robust and accurate reliability assessment under uncertainty. The effectiveness and accuracy of the proposed approach is demonstrated through numerical examples, showcasing its ability to provide reliable failure probability estimates in dynamic systems

Clinical value of ultrasonography in the evaluation of multiple organs in patients with hyperuricemia

Objective To explore and evaluate the clinical value of color Doppler ultrasound in the evaluation of multiple organs in patients with hyperuricemia. Methods The research included 50 patients with newly diagnosed hyperuricemia who were admitted to Peking Union Medical College Hospital from July 2015 to May 2017. Serum uric acid (sUA) was recorded and color Doppler ultrasound was used to examine the bilateral first metatarsophalangeal joint, knee joint, kidney, carotid artery and liver in each patient. The potential correlation between sUA level and organ lesions were searched. The subjects were further divided into gouty arthritis (GA) group and asymptomatic chyperuricemia (AH) group. The multiple organ diseases were analyzed and compared. Statistical methods used in cluded chi-square test and Spearman correlation analysis. Results In the 50 patients with newly diagnosed hyperuricemia, the rate of joint lesions diagnosed by ultrasound was 56.0%; the rate of renal morphological changes was 72.0%; the rate of nonalcoholic fatty liver disease (NAFLD) was 64.0%, of which 59.4% was moderate to severe fatty liver, and the sUA level was positively correlated with the detection rate of NAFLD(P＜0.05),the detection rate of carotid atherosclerosis was 36.0%, and the level of sUA was positively correlated with the thickness of the common carotid artery (P＜0.05).The detection rate of two or more organ lesions in joint, kidney, liver and carotid artery was 80.0%, and the level of sUA was positively correlated with the detection rate of multiple organ lesions (P＜0.05). There was a significant difference in the detection rate of joint lesions and carotid atherosclerosis between the GA group and the AH group (P＜0.05). Conclusions Color Doppler ultrasound has certain clinical application value for early diagnosis, comprehensive evaluation of lesion progression and follow-up treatment of multiple organ lesions such as joint lesions and renal damage, nonalcoholic fatty liver and carotid atherosclerosis in patients with hyperuricemia

CEPC Technical Design Report -- Accelerator

International audienceThe Circular Electron Positron Collider (CEPC) is a large scientific project initiated and hosted by China, fostered through extensive collaboration with international partners. The complex comprises four accelerators: a 30 GeV Linac, a 1.1 GeV Damping Ring, a Booster capable of achieving energies up to 180 GeV, and a Collider operating at varying energy modes (Z, W, H, and ttbar). The Linac and Damping Ring are situated on the surface, while the Booster and Collider are housed in a 100 km circumference underground tunnel, strategically accommodating future expansion with provisions for a Super Proton Proton Collider (SPPC). The CEPC primarily serves as a Higgs factory. In its baseline design with synchrotron radiation (SR) power of 30 MW per beam, it can achieve a luminosity of 5e34 /cm^2/s^1, resulting in an integrated luminosity of 13 /ab for two interaction points over a decade, producing 2.6 million Higgs bosons. Increasing the SR power to 50 MW per beam expands the CEPC's capability to generate 4.3 million Higgs bosons, facilitating precise measurements of Higgs coupling at sub-percent levels, exceeding the precision expected from the HL-LHC by an order of magnitude. This Technical Design Report (TDR) follows the Preliminary Conceptual Design Report (Pre-CDR, 2015) and the Conceptual Design Report (CDR, 2018), comprehensively detailing the machine's layout and performance, physical design and analysis, technical systems design, R&D and prototyping efforts, and associated civil engineering aspects. Additionally, it includes a cost estimate and a preliminary construction timeline, establishing a framework for forthcoming engineering design phase and site selection procedures. Construction is anticipated to begin around 2027-2028, pending government approval, with an estimated duration of 8 years. The commencement of experiments could potentially initiate in the mid-2030s

CEPC Technical Design Report -- Accelerator

International audienceThe Circular Electron Positron Collider (CEPC) is a large scientific project initiated and hosted by China, fostered through extensive collaboration with international partners. The complex comprises four accelerators: a 30 GeV Linac, a 1.1 GeV Damping Ring, a Booster capable of achieving energies up to 180 GeV, and a Collider operating at varying energy modes (Z, W, H, and ttbar). The Linac and Damping Ring are situated on the surface, while the Booster and Collider are housed in a 100 km circumference underground tunnel, strategically accommodating future expansion with provisions for a Super Proton Proton Collider (SPPC). The CEPC primarily serves as a Higgs factory. In its baseline design with synchrotron radiation (SR) power of 30 MW per beam, it can achieve a luminosity of 5e34 /cm^2/s^1, resulting in an integrated luminosity of 13 /ab for two interaction points over a decade, producing 2.6 million Higgs bosons. Increasing the SR power to 50 MW per beam expands the CEPC's capability to generate 4.3 million Higgs bosons, facilitating precise measurements of Higgs coupling at sub-percent levels, exceeding the precision expected from the HL-LHC by an order of magnitude. This Technical Design Report (TDR) follows the Preliminary Conceptual Design Report (Pre-CDR, 2015) and the Conceptual Design Report (CDR, 2018), comprehensively detailing the machine's layout and performance, physical design and analysis, technical systems design, R&D and prototyping efforts, and associated civil engineering aspects. Additionally, it includes a cost estimate and a preliminary construction timeline, establishing a framework for forthcoming engineering design phase and site selection procedures. Construction is anticipated to begin around 2027-2028, pending government approval, with an estimated duration of 8 years. The commencement of experiments could potentially initiate in the mid-2030s

CEPC Technical Design Report -- Accelerator

The Circular Electron Positron Collider (CEPC) is a large scientific project initiated and hosted by China, fostered through extensive collaboration with international partners. The complex comprises four accelerators: a 30 GeV Linac, a 1.1 GeV Damping Ring, a Booster capable of achieving energies up to 180 GeV, and a Collider operating at varying energy modes (Z, W, H, and ttbar). The Linac and Damping Ring are situated on the surface, while the Booster and Collider are housed in a 100 km circumference underground tunnel, strategically accommodating future expansion with provisions for a Super Proton Proton Collider (SPPC). The CEPC primarily serves as a Higgs factory. In its baseline design with synchrotron radiation (SR) power of 30 MW per beam, it can achieve a luminosity of 5e34 /cm^2/s^1, resulting in an integrated luminosity of 13 /ab for two interaction points over a decade, producing 2.6 million Higgs bosons. Increasing the SR power to 50 MW per beam expands the CEPC's capability to generate 4.3 million Higgs bosons, facilitating precise measurements of Higgs coupling at sub-percent levels, exceeding the precision expected from the HL-LHC by an order of magnitude. This Technical Design Report (TDR) follows the Preliminary Conceptual Design Report (Pre-CDR, 2015) and the Conceptual Design Report (CDR, 2018), comprehensively detailing the machine's layout and performance, physical design and analysis, technical systems design, R&D and prototyping efforts, and associated civil engineering aspects. Additionally, it includes a cost estimate and a preliminary construction timeline, establishing a framework for forthcoming engineering design phase and site selection procedures. Construction is anticipated to begin around 2027-2028, pending government approval, with an estimated duration of 8 years. The commencement of experiments could potentially initiate in the mid-2030s