Multi-Factor Modeling Method of the Load Sharing Ratio under Moving Train Loads

In railway engineering, the load sharing ratio (LSR) is the ratio of the rail seat load (RSL) to the axle load, which is affected by many factors. The LSR can be used in the design and analysis of railway track structures as well as in the research of predicting the dynamic influence of railway tunnels and the environment. The “static loading method” commonly used to study the LSR does not conform to reality; using it, it is difficult to obtain a complete LSR curve, limiting its application. Besides, there is currently a lack of LSR prediction methods considering the impact of multiple factors. Therefore, this paper proposes a “moving loading method” for investigating the LSR under moving train excitation, verified to be rational by comparing with the experimental results. At the same time, a procedure for establishing the LSR multi-factor prediction model is put forward, namely, we (1) determine the LSR function form and the fitting algorithm; (2) perform parameter sensitivity analysis to determine the main influencing parameters of the LSR function; and (3) design a quadratic regression orthogonal test to obtain the prediction formula of the LSR function coefficients. Once establishing the prediction model for a type of train-track system, the LSR of similar systems can be calculated by adjusting the main parameters of the model. Shijiazhuang Metro Line 1 using the A-type vehicle and the monolithic trackbed is taken as a case study to develop a corresponding LSR multi-factor prediction model by the moving loading method and the procedure mentioned above. The results indicate that the proposed method performs well and can be adopted to enhance the accuracy of track design or tunnel and environmental vibration prediction.

Power spectral density analysis for nonlinear systems based on Volterra series

A consequence of nonlinearities is a multi-harmonic response via a mono-harmonic excitation. A similar phenomenon also exists in random vibration. The power spectral density (PSD) analysis of random vibration for nonlinear systems is studied in this paper. The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function (GFRF). For a class of nonlinear systems, the growing exponential method is used to determine the first 3rd-order GFRFs. The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input. The relationship between the peak of PSD and the parameters of the nonlinear system is discussed. By using the proposed method, the nonlinear characteristics of multi-band output via single-band input can be well predicted. The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD. This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Intelligent Model for Predicting Downhole Vibrations Using Surface Drilling Data During Horizontal Drilling

Drillstring vibration is a major concern during drilling wellbore and it can be split into three types axial, torsional, and lateral. Many problems associate with the high drillstring vibrations as tear and wear in downhole tools, inefficient drilling performance, loss of mechanical energy, and hole wash-out. The high cost for the downhole measurement of the drillstring vibrations encourages machine learning applications toward downhole vibration prediction during drilling. Consequently, the objective of this paper is to develop an artificial neural network (ANN) model for predicting the drillstring vibration while drilling a horizontal section. The ANN model uses the surface drilling parameters as model inputs to predict the three types of drillstring vibrations. These surface drilling parameters are flow rate, mud pumping pressure, surface rotating speed, top drive torque, weight on bit, and rate of penetration. The study utilized a dataset of 13,927 measurements from a horizontal well that was used to train the ANN model. In addition, a different data set (9,284 measurements) was employed to validate the developed ANN model. Correlation coefficient (R) and average absolute percentage error (AAPE) are statistical metrics that are used to evaluate the model accuracy based on the difference between the actual and predicted values for the axial, torsional, and lateral vibrations. The results of the optimized parameters for the developed model showed a high correlation coefficient between the predicted and the actual drillstring vibrations that showed R higher than 0.95 and AAPE below 3.5% for all phases of model training, testing, and validation. The developed model proposed a model-based equation for real-time estimation for the downhole vibrations.

TREND FORECAST FOR SHORT-TERM OF SHOCK-VIBRATION PREDICTION

The short-term forecasting of vibration is considered, in which the trend of the gravitational constant is used as the initial data for forecasting. The trend is recorded throughout the entire period of maturation of the vibration at points on the earth's surface far from its epicenter.

Vehicle interior noise and vibration prediction by combination analyses of Component and Operational TPA

In this study, we propose an analytical method consisting of Operational TPA (OTPA) and Component TPA (CTPA) to predict the vehicle interior noise and vibration without the vehicle operational test in case the noise source such as engine was modified. In the proposed method, the blocked force of the noise source was obtained at a test bench and the vibration at the source attachment point on the vehicle was calculated by CTPA. After then, the response point signal (interior noise / vibration) is estimated from several reference point signals including the calculated vibration by OTPA. For the verification of this method, a simple vehicle model which is composed of four tires and a motor was prepared in addition to a test bench. OTPA was firstly applied to the vehicle model to analyze the contribution from tires and a motor to the body vibration (response point). The blocked force of a modified motor was obtained by CTPA at the test bench and the force was used to predict the response point by OTPA. Finally, the estimated interior vibration was compared with the actual measured response point vibration when the motor was replaced on the vehicle model and the accuracy was verified.