CHAOTIC BEHAVIOR IN THE ROTATIONAL SPEED OF INTERNAL COMBUSTION ENGINES

Instantaneous rotational speed measurement of the engine is crucial in routine inspection and maintenance of an automobile engine. Since the contact measurement of rotational speed is not always available, the vibration measurement has been used for noncontact rotational speed estimation methods. Unfortunately, the accuracy of the noncontact estimation methods by analyzing engine vibration frequency is not satisfactory due to the influence of noise and the strong nonstationary characteristic of the vibration signal. To overcome these problems, based on the multiple matching synchrosqueezing transform (MSST) (MMSST, improved MSST with multiple squeeze operations), a novel noncontact method is proposed to accurately estimate the instantaneous rotational speed of automobile engine in this paper. Firstly, a MMSST is proposed to process the vibration signal to obtain a concentrated time‐frequency (TF) representation. Secondly, the instantaneous frequency (IF) detection algorithm is employed to extract the fundamental frequency from the TF result. Finally, the rotational speed of the engine is calculated according to the relationship between the fundamental frequency and rotational speed. Results from numerical simulations and test on real engine have proven that the proposed method can obtain much higher frequency resolution and more precise IF estimation of the engine vibration signal and more accurate rotational speed estimation result compared with the MSST method. Furthermore, the proposed method is verified to have a stronger noise robustness and can provide satisfactory estimation results for engine vibration signal containing nonlinear frequency‐modulated components.

Research concerning the development of diagnostic methods of the state of the vehicle driving systems basic elements — have been carried on for many years. Modern diagnostic systems, regardless of being technically highly advanced or small degree only, concern about assessments of basic mechanical subsystems such as toothed gears or suspension elements. The information on state changes of mechanical systems can be obtained by an analysis of changes of nonlinear effects in such systems operations. Since the nonlinearity increase accompanies the system destruction, the separation of nonlinear parts of signals creates the possibility of the increase of an accuracy, reliability and application range of diagnostic methods. Technical state diagnostics for vehicles is much more difficult than for machines operating in stationary conditions. the main excitation source is an internal combustion engine, in which a rotational speed changes from an idle running (approximately 800 rpm) to a maximum rotational speed (e.g. above 5000 rpm). Thus, an application of classic analytical methods is not possible. the only solution is the transformation of the analysed signals into the “pseudostationary” ones, by taking into account changes in the engine rotational speed. One of the methods applied now a days is resampling (adaptation change of a signal time resolution in a digital form) performed on the basis of information concerning changes in an engine rotational speed. the signal from the sensor of the engine crankshaft location was used for the above application.

Blade tip‐timing (BTT) is a promising method of online monitoring rotating blade vibrations. Since BTT‐based vibration signals are typically undersampled, how to reconstruct characteristic vibrations from BTT signals is a big challenge. Existing reconstruction methods are mainly based on the assumption of constant rotation speeds. However, rotating speed fluctuation is inevitable in many engineering applications. In this case, the BTT sampling process should be nonuniform, which will cause existing reconstruction methods to be unavailable. In order to solve this problem, this paper proposes a new reconstruction method based on nonlinear time transformation (NTT). Firstly, the effects of rotating speed fluctuation on BTT vibration reconstruction are analyzed. Next, the NTT of BTT sampling times under rotating speed fluctuation is presented. Then, two NTT‐based reconstruction algorithms are derived for uniform and nonuniform BTT sensor configurations, respectively. Also several evaluation metrics of BTT vibration reconstruction under rotating speed fluctuation are defined. Finally, numerical simulations are done to verify the proposed algorithms. The results testify that the proposed NTT‐based reconstruction method can reduce effectively the influence of rotating speed fluctuation and decrease the reconstruction error. In addition, rotating speed fluctuation has more bad effects on the reconstruction method under nonuniform sensor configuration than under uniform sensor configuration. For nonuniform BTT signal reconstruction under rotating speed fluctuation, more attentions should be paid on selecting proper angles between BTT sensors. In summary, the proposed method will benefit for detecting early blade damages by reducing frequency aliasing.

To evaluate the relationship between Proximal Ulnar Dorsal Angulation (PUDA) and Olecranodiaphyseal Angle (ODA) in healthy elbows using both linear regression and advanced chaos theory approaches, analyzing the effects of age, sex, and side parameters. In this cross-sectional study, 295 healthy elbows (178 male, 117 female; 130 right, 165 left) were evaluated with standard radiographs. PUDA, Varus Angle (VA), and ODA measurements were performed by two independent observers. Linear regression analysis and chaos theory-based nonlinear modeling were used to establish mathematical relationships between PUDA and ODA. Phase space reconstruction, fractal dimension analysis, Lyapunov exponent calculation, and strange attractor identification were performed to characterize the underlying dynamical system. Linear analysis revealed an inverse relationship between PUDA and ODA (regression coefficient β = -0.340, significance level p < 0.001). However, chaos theory analysis uncovered complex nonlinear dynamics with a fractal attractor structure (correlation dimension D2 = 2.34 ± 0.12, indicating non-integer dimensional geometry) and positive Lyapunov exponent (λ1 = 0.127 ± 0.043, confirming sensitive dependence on initial conditions characteristic of chaotic behavior). The chaos-based local linear model achieved superior prediction accuracy (R2 = 0.758, RMSE = 2.53) compared to linear regression (R2 = 0.210, RMSE = 4.63), representing a 3.6-fold improvement. Bifurcation analysis identified critical PUDA threshold values where system behavior changed dramatically. Males exhibited higher dimensional complexity (correlation dimension D2 = 2.51 ± 0.18) compared to females (D2 = 2.14 ± 0.21, significance level p = 0.032), indicating that male proximal ulnar geometry is governed by more complex dynamical interactions. The chaotic dynamics underlying PUDA-ODA relationships provide superior predictive capability compared to traditional linear models. This chaos theory-based approach offers clinicians dramatically improved accuracy for estimating normal ODA values in complex elbow injuries, with precise predictions (± 2°) improving from 34.2 to 67.8% of cases. The identification of strange attractors and bifurcation points reveals that small variations in PUDA measurements can lead to dramatically different ODA predictions, emphasizing the critical importance of measurement precision in surgical planning.

Characterization of Iran electricity market indices with pay-as-bid payment mechanism

The order multi-scale morphology demodulation approach is proposed to extract the fault characteristic frequency from the vibration signal of a fault gearbox with rotating speed fluctuation. The chirplet path pursuit algorithm is used to obtain the rotation speed signal of the gearbox. According to the rotation speed signal,the time domain vibration signal of the gearbox is resampled at constant angle increments. An algorithm based on the information of local peaks of the signal is used to figure out the structuring elements for multiscale morphology analysis. The structuring elements are used to carry out morphology operations on the resampled signal. Spectral analysis on the average value of the operation results is carried out,so as to accomplish the order multi-scale morphology demodulation. Since the noise components do not correlate with the chirplet functions closely,the chirplet path pursuit algorithm can extract the rotation speed effectively even if the signal-to-noise ratio of the vibration signal is very low. By averaging the results of each scale morphology analysis,the multi-scale morphology demodulation can restrain the noise effectively. The proposed approach has good anti-noise ability,and is suitable for analyzing the actual vibration signal of a gearbox with rotating speed fluctuation. Simulation and practical application examples prove the validity and superiority of the proposed method.

&lt;div class="htmlview paragraph"&gt;There arm two kinds of rotational speed changes in running of internal combustion engines - rotational speed fluctuation within each working cycle and rotational speed change of successive cycles. Application of transient rotational speed nφ of each crank angle and average rotational speed n&lt;sub&gt;c&lt;/sub&gt; of any working cycle can rationally demonstrate the change of the rotational speed of I.C.E..&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;Conventional speed-measure instruments may not be used to measure nφ and n&lt;sub&gt;c&lt;/sub&gt;. Therefore authors take work on this measuring technique. This paper introduces the measuring principle and instrument and analyses the accuracy of measure.&lt;/div&gt; &lt;div class="htmlview paragraph"&gt;The developed instrument has been used on 5 types of diesel engines, such as 6135, 6130Q, R4100, etc. Measured results at steady condition, low speed radomrunning, sudden loading, free acceleration and starting process are given in this paper.&lt;/div&gt;

Chemical sensor drift shows a chaotic behavior and unpredictability in long-term observation, such that constructing an appropriate sensor drift treatment is difficult. This chapter introduces a new methodology for chaotic time series modeling of chemical sensor observations in embedded phase space. This method realizes a long-term prediction of sensor baseline and drift based on phase space reconstruction (PSR) and radial basis function (RBF) neural network. PSR can memory all of the properties of a chaotic attractor and clearly show the motion trace of a time series; thus, PSR makes the long-term drift prediction using RBF neural network become possible. Experimental observation data of three metal oxide semiconductor sensors in a year demonstrates the obvious chaotic behavior through the Lyapunov exponents. Results demonstrate that the proposed model can make long-term and accurate prediction of time series chemical sensor baseline and drift.

The Umbi teki skin peeling machine is a machine used to assist in the process of making chips. Umbi teki, which will be processed into chips, will go through several processing processes, such as soaking the material with clean water first and then peeling the fiber and skin until it is clean, then roasting until the texture of the seeds starts to soften and then pounded using a hammer, after which it is dried in the sun until it is scorched. One of these production processes is carried out using this peeling machine to peel the skin of the Umbi teki. Factors affecting peeling include engine rotation speed (rpm), while some researchers state that the best average rotation speed on a peeling machine is 250-500 rpm. This study aims to determine the effect of engine rotation speed on stripping results and find the best rotation speed on an Umbi teki peeling machine with a load of 121 grams/minute. The method used in this research is an experimental study conducted with ten rotation speed variations. Data were analyzed using ANOVA to determine the best variation treatment. Results show that using engine rotation speed variables affects the average difference in skin stripping. The best engine rotation speed of 626 rpm produces the best percentage of stripping results, with a value for TB (Well Peeled) and TS (Not Perfectly Peeled) being 87.3% and 9.3%, respectively.

To solve the display distortion caused by the motor rotational speed changes in the long-term operation of the rotating LED multi-sector display system, the model for LED multi-sector stable display (MSSD) in variable rotational speed is proposed based on the principle of visual persistence. The stepping motor subdivision driving technology is applied to the rotating LED multi-sector display, and the equal precision frequency measurement method is used for accurate rotational speed measurement. Then the innovation adaptive kalman filter (IAKF) is researched to further enhance the robustness to eliminate noise pollution, and the relationship between the modification value caused by rotational speed and the LED linear array minimum refresh time is analysed. The rotating LED MSSD system based on LED linear array rotated by stepping motor is provided. The test results reveal the relationship between rotational speed and the LED linear array minimum refresh time, and show that the lighting position of the LED can be synchronized with the lighting state during the rotational speed fluctuation, and the error can be controlled to a low level via LED linear array minimum refresh time correction. The designed model can effectively eliminate the distortion of the rotating LED multi-sector display screen caused by the changes of the motor rotational speed, and has a very stable display effect.

Effect of rotation speed fluctuation on rotor noise generation: A numerical and experimental study

Vortex beam (VB) is a structured light beam with a helical wavefront and carrying orbital angular momentum (OAM). Compared with Gaussian beam, the VB possesses the rotational Doppler effect (RDE), which is anticipated to compensate for the shortcoming of traditional detection methods in the spin motion of the target object. However, in practical applications, the rotational speed measurement technology based on the VB is facing some challenges, such as weak echo signal intensity due to low vortex beam light power and OAM spectrum expansion caused by off-axis incidence of the vortex beam. These above-mentioned problems directly limit the accuracy and application range of rotational speed measurement. To expand the application range of detection scheme based on the VB, we study the measurement scheme of the target rotational speed based on the combined vortex beam (CVB), which is on the basis of the experimental device for rotational speed measurement with CVB generated by fibre laser arrays. Firstly, the OAM spectra of the off-axis incidence situation are simulated. According to the simulation results, we derive a general model of the peak distribution of echo signals under the off-axis incidence, and propose a rotational speed measurement scheme based on the frequency interval between adjacent spectral peaks. Secondly, we carry out the target rotational speed measurement experiment in off-axis incidence case, and the difference in frequency between two adjacent spectral peaks is obtained from the spectrum map of the echo signal to measure the rotational speed of the target object. The results show that the target rotational speed can be accurately measured regardless of the lateral displacement and angular deflection in the case of off-axis incidence, which confirms the validity of the universal model for rotational speed measurement. The rotational speed measurement scheme proposed in this study takes into consideration the off-axis incidence prevalent in practical application, thereby improving the applicability in the target object rotational speed measurement, and providing technical reference for remote sensing detection application based on the VB.

The aero-thermodynamic effects of water ingestion on an axial flow compressor performance are presented in this article. Under adverse weather conditions, gas turbine engine performance deteriorates and in extreme cases, this performance deterioration may result in flameout or shutdown of the engine, which means that serious incidents or possibly accidents may occur. When the water droplets enter into the engine they break up into smaller droplets which may bounce, coalesce or splash onto the compressor blades. They also form a liquid film whose motion is influenced by inertia forces, blade friction, aerodynamic drag and pressure gradient. The water liquid film has considerable effects on blade’s geometric characteristics. Apart from the change in its profile due to thickness increase, air shear force and water droplets momentum cause waves in water film’s surface introducing a kind of ‘roughness’ on blade’s surface. The current work focuses on the aero-thermodynamic effects. Its methodology is based on computational fluid dynamics, which is used to solve the flow field of the computational domain. The model consists of an extended inlet, an inlet guide vane, a rotor and a stator blade. Several cases with water ingestion are solved, varying the parameter of water mass and engine rotational speed, simulating adverse weather conditions. On the rotor blade, the water film height and speed are calculated at the equilibrium condition. This condition is achieved when the water mass which flows out of the blade surface equals with this which impacts on it. Taking into account the film thickness at each computational node of the blade surface, the blade’s geometry is changed. Furthermore, an equivalent roughness is introduced and the effects on compressor’s performance are calculated. It is found that deterioration is more pronounced in low rotational speed. For 4% water/air, compressor’s isentropic efficiency deteriorates 8.5% for idle speed and 1.6% for full speed. For the same water mass, mass flow capacity deteriorates 2.4% at idle speed while the change is small for full speed.

Chaotic time series prediction of E-nose sensor drift in embedded phase space

A new wind power prediction method based on chaotic theory and Bernstein Neural Network