Multiform Informed Machine Learning Based on Piecewise and Weibull for Engine Remaining Useful Life Prediction

Informed machine learning (IML), which strengthens machine learning (ML) models by incorporating external knowledge, can get around issues like prediction outputs that do not follow natural laws and models, hitting optimization limits. It is therefore of significant importance to investigate how domain knowledge of equipment degradation or failure can be incorporated into machine learning models to achieve more accurate and more interpretable predictions of the remaining useful life (RUL) of equipment. Based on the informed machine learning process, the model proposed in this paper is divided into the following three steps: (1) determine the sources of the two types of knowledge based on the device domain knowledge, (2) express the two forms of knowledge formally in Piecewise and Weibull, respectively, and (3) select different ways of integrating them into the machine learning pipeline based on the results of the formal expression of the two types of knowledge in the previous step. The experimental results show that the model has a simpler and more general structure than existing machine learning models and that it has higher accuracy and more stable performance in most datasets, particularly those with complex operational conditions, which demonstrates the effectiveness of the method in this paper on the C-MAPSS dataset and assists scholars in properly using domain knowledge to deal with the problem of insufficient training data.

School Influences on Adolescent Depression: A 6-Year Longitudinal Study Amongst Catholic, Government and Independent Schools, in Victoria, Australia

This study examined associations between school sector (Government, Catholic or Independent) and depressive symptomology over the secondary school years. Six waves of data collected annually from a representative Australian sample were examined. Multilevel piecewise linear and logistic regression controlling for a variety of demographic variables and protective factors was undertaken. In all sectors, depressive symptomology decreased between 10 and 13 years of age, but significantly increased for girls at age 13. Adolescents in Catholic schools reported significantly fewer symptoms of depression compared to those in Government and Independent schools. Adolescents in Catholic schools were less likely to report clinical levels of depressed mood compared to adolescents in Government schools.

Is our breathing optimal? Solving a piecewise linear model with constraints

This paper is motivated by a question related to the control of amplitude and frequency of breathing. We present a simplified mathematical model, consisting of two piecewise linear ordinary differential equations, that could represent gas exchange in the lungs. We then define and solve an optimal control problem with unknown durations of inhalation and exhalation, subject to several constraints. The durations are divided such that one of the state variables is strictly increasing during the first phase and decreasing during the second phase. The optimal control problem can be solved analytically. One analytical solution is found when the forcing is a given sinusoidal function with unknown period and amplitude. Other analytical solutions are found when the forcing function, the period and the duration of the first phase are unknown but the amplitude is given. Our results show that different cost functions can produce different optimal forcing functions. We also show that the shape of these functions does not affect the average levels of oxygen in the lungs-the average level of oxygen is only dependent on the amplitude and period of breathing in the model we present.

Numerical calculation for coupling vibration system by Piecewise-Laplace method

To improve the reliability and accuracy of dynamic machine in design process, high precision and efficiency of numerical computation is essential means to identify dynamic characteristics of mechanical system. In this paper, a new computation approach is introduced to improve accuracy and efficiency of computation for coupling vibrating system. The proposed method is a combination of piecewise constant method and Laplace transformation, which is simply called as Piecewise-Laplace method. In the solving process of the proposed method, the dynamic system is first sliced by a series of continuous segments to reserve physical attribute of the original system; Laplace transformation is employed to separate coupling variables in segment system, and solutions of system in complex domain can be determined; then, considering reverse Laplace transformation and residues theorem, solution in time domain can be obtained; finally, semi-analytical solution of system is given based on continuity condition. Through comparison of numerical computation, it can be found that precision and efficiency of numerical results with the Piecewise-Laplace method is better than Runge-Kutta method within same time step. If a high-accuracy solution is required, the Piecewise-Laplace method is more suitable than Runge-Kutta method.

Rapid analysis of soluble solid content in navel orange based on visible-near infrared spectroscopy combined with a swarm intelligence optimization method

Navel orange is a very popular fruit which is rich in nutrition necessary to human health. Nowadays, rapid, nondestructive and pollution-free analysis of internal organic compounds of fruit is an important and promising technology. The purpose of this paper is to present a swarm intelligence optimization method to extract the feature information of visible-near infrared (Vis-NIR) spectra of navel orange for rapid and nondestructive analysis of soluble solid content (SSC) in navel orange. This method was developed on particle swarm optimization (PSO) and named as piecewise particle swarm optimization (PPSO). The experimental results showed that the PPSO algorithm proposed in this paper overcame the disadvantage of PSO's premature convergence. The PLS model based on variables selected by PPSO for nondestructively detecting SSC of navel orange yield promising results, as the standard deviation of prediction (SEP) was 0.427°Brix while the standard error of laboratory (SEL) was 0.22°Brix. It indicated that the application of near infrared spectroscopy (NIRS) technology combined with PPSO for rapid analysis of soluble solid content in navel orange was feasible.

Piecewise Mixed Effects Model to Compare the Weight-gain Patter ns Before and After Diagnosis of Asthma in Children Younger than 5 Years

Asthma and obesity are two significant public health problems that both originate in early childhood and have shared risk factors and manifestations. Studies suggest a strong association between asthma development and subsequent accelerated weight gain. Children are diagnosed with asthma in early childhood and are often exposed to factors associated with rapid weight gain. This article intends to demonstrate an innovative application of the piecewise mixed effects model to characterize the difference in the temporal rate of change in BMIz, the standardized scores of body mass index and weight-for-length that measure weight status, before and after asthma diagnosis in children younger than 5 years. The data consist of unique sequences from 1194 children's clinic visits during the first 5 years of life. We used a knot at the time of diagnosis and detected a differential weight-gain pattern before and after asthma diagnosis. The pre- and post-asthma-diagnosis weight-gain patterns further differ by sex and race-ethnicity. After asthma diagnosis, female children showed a higher increase in the rate of change in BMIz than males. Non-Hispanic African Americans and Hispanics had higher post-diagnosis rates of change in BMIz than Caucasians. The differential weight-gain patterns between male and female children were mainly contributed by Caucasian children. These findings could have important implications in the clinical care of children after asthma diagnosis.