Linear Regression Estimation Methods for Inferring Standard Values of Snow Load in Small Sample Situations

The aim of this paper is to establish a new method for inferring standard values of snow load in small sample situations. Due to the incomplete meteorological data in some areas, it is often necessary to infer the standard values of snow load in the conditions of small samples in engineering, but the point estimation methods of classical statistics adopted till now do not take into account the influences of statistical uncertainty, and the inference results are always aggressive. In order to overcome the above shortcomings, according to the basic principle of optimal linear unbiased estimation and invariant estimation of the minimum type I distribution parameters and the tantile, using the least square method, the linear regression estimation methods for inferring standard values of snow load in small sample situations are proposed, which can take into account two cases such as parameter-free and known coefficient of variation, and the predicted formulas of snow load standard values are given, respectively. Through numerical integration and Monte Carlo numerical simulation, the numerical table of correlation coefficients is established, which is more convenient for the direct application of inferential formulas. According to the results of theoretical analysis and examples, when using the indirect point estimation methods to infer the standard values of snow load in the conditions of small samples, the inference results are always small. The linear regression estimation method is suitable for inferring standard values of snow load in the conditions of small samples, which can give more reasonable results. When using the linear regression estimation to infer standard values of snow load in practical application, even if the coefficient of variation is unknown, it can set the upper limit value of the coefficient of variation according to the experience; meanwhile, according to the parameter-free and known coefficient of variation, the estimation is carried out, respectively, and the smaller value of the two is taken as the final estimate. The method can be extended to the statistical inference of variable load standard values such as wind load and floor load

Approximate Calculation Method for Noncentral t-Distribution Quantile

In the process of structural design and structural performance evaluation, the inference of the reliable life of the structure and the representative value of the material strength is a necessary work. The determination of material strength is the presumption of the quantile of the normal distribution, and the determination of the confidence level of the quantile of the normal distribution involves the noncentral t-distribution function. However, the calculation of the quantile is very complicated and is often provided in the form of a numerical table, which often involves multiparameter interpolation calculation, so it is not convenient to apply. The existing approximate calculation methods for noncentral t-distribution quantiles have strict application conditions, and the calculation process is relatively cumbersome. It is still difficult to meet actual needs in terms of fitting accuracy, application range, and convenience. In this paper, a new calculation method for noncentral t-distribution quantiles is proposed by introducing new probability expressions and related approximate distributions, based on theoretical derivation and numerical fitting. The comparative analysis results show that the method not only is convenient for calculation but also has the advantages of higher accuracy and wider application range, and it is more in line with the actual needs of engineering

Bayesian Methods of Representative Values of Variable Actions

In engineering practice, it is sometimes necessary to infer the representative value of variable action under the condition that the test data is insufficient, but the classical statistics methods adopted now do not take into account the influences of statistical uncertainty, and the inferring results are always small, especially when characteristic and frequent values are inferred. Variable actions usually obey a type I maximum distribution, so the linear regression estimation of the tantile of type I minimum distribution can be employed to infer their characteristic and frequent values. However, it is inconvenient to apply and cannot totally meet the demands of characteristic and frequent values inference. Applying Jeffreys non-informative prior distribution, Bayesian methods for inferring characteristic and frequent values of variable actions are put forward, including that with known standard deviation, which could yield more advantageous results. The methods proposed are convenient and flexible, possessing good precision

Study on Partial Factor of Load for Reinforced Concrete Columns

At present, the design method of components is still a partial factor design method, and the partial factor value is related to the load value. Because the partial factor has a great influence on the safety of engineering structure, it has been adjusted many times in the process of organization of the code. In order to be basically equivalent to European and American reliability standards and to conform to China’s national conditions and national policies, the Unified standard for reliability design of building structures is revised (i.e., the partial factor of permanent action and variable action was adjusted). Although the concept of factor of safety is commonly used in structure design practice to cover all the unexpected risks, there are some disadvantages to its direct use in structural reliability analysis. For example, the eccentricity of compression members is random, which will lead to the change in resistance parameters of compression members, rather than the fixed value specified in the code. However, the random variation in eccentricity is not considered in the code. So, in this paper, the partial factors of eccentrically loaded members are studied by considering the statistical parameter information of members with random eccentricity. This paper studies the partial factors of different types of components in different ratios of live load effect to dead load effect, and some recommendations are proposed to obtain safer designs. Finally, Monte Carlo simulation method is used to analyze the reliability of the eccentric member. The research results show that the value of partial factors of structure proposed in this paper is reasonable

Numerical Analysis of Different Influencing Factors on the In-Plane Failure Mode of Unreinforced Masonry (URM) Structures

The research work herein presented is aimed at investigating the effects of different influencing factors on the in-plane failure mode of unreinforced masonry (URM) structures. Firstly, the in-plane stress failure criterion cited in this paper was introduced, and the corresponding judgment procedure was demonstrated. Then, various finite element models considering different influencing factors were established, which included the aspect ratio of pier (η), stiffness ratio of pier to spandrel (ρ) and vertical load (σ). Furthermore, the in-plane stress failure criterion that we introduced was used to evaluate the failure modes of each model. The main findings of the simulations were as follows: under the condition of (η ≤ 1.0), three failure modes emerged in all models, which included pier, mixed and spandrel failure modes, with the gradual increase in ρ. Once the value of η exceeded 1.0, all models exhibited the pier failure mode regardless of whether the value of ρ increased or decreased. Moreover, under the identical aspect ratio (η = 1.0), the failure modes of the models altered regularly with the increase in the value of σ (from 0.3 MPa to 0.6 MPa), which transferred from pier failure to mixed failure, and from mixed failure to spandrel failure. The research results not only provide theoretical reference for the design of new masonry buildings, but also provide technical guidance for the judgement and prediction of failure modes of existing masonry buildings

Method for Inferring the Design Value of the Resistance Based on Probabilistic Model

Methods for inferring the design value of the resistance based on test have long been studied extensively, but the existing methods have several limitations on unified guarantee rate ensurance and reliability control. Firstly, the rationales and deficiencies of the present methods in ISO 2394 : 2015 and EN 1990 : 2002 were generalized. Secondly, in view of the disadvantages, a new inferring method combining the probability model of resistance with statistical approach was put forward. The proposed method established a relationship among design resistance, probability characteristics of known factors, and statistical results of unknown factors and possessed a rigorous and sound theoretical basis on both conditions that the coefficient of variation of model uncertainty was unknown and full known. Lastly, a contrast work was carried out between the Eurocode method and the proposed method; the results showed that the latter method had a higher inferring value, which means a better inferring result

Sclerosing Adenosis of the Prostate—A Benign Lesion Similar to Prostate Cancer: A Case Report and Literature Review

Sclerosing adenosis of the prostate (SAP) is a rare benign non-neoplastic small acinar hyperplasia. Like sclerosing adenosis of the breast, which is confused with breast cancer, SAP is a trap in the pathological differential diagnosis of benign and malignant lesions of the prostate. We report such a case to help colleagues better distinguish and diagnose such diseases. A 75-year-old patient with SAP had a prostate specific antigen (PSA) level of 11.0 ng/mL, and he had been suffering from progressive dysuria for 3 years. The central glandular area and the right periphery of the prostate were found to have nodular low signals on magnetic resonance imaging (MRI). Prostate biopsy showed that basal cells were positive for P63 and P504s, few basal cells were positive for S-100, and the positive rate of Ki67 was approximately 2%. We consider that the possibility of SAP is high. The patient was treated conservatively and was discharged in good health, free of dysuria and other problems. SAP is a rare benign lesion that is easily misdiagnosed as prostate cancer. The prostatic gland tube has a complete basal cell layer surrounding it, as well as myoepithelial cell metaplasia of basal cells, which is a key trait in distinguishing it from prostate cancer. Although the latest research indicates that SAP does not require treatment, the question of whether it is a risk factor for prostate cancer remains unanswered