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11399 results about "Method of undetermined coefficients" patented technology

In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations. It is closely related to the annihilator method, but instead of using a particular kind of differential operator (the annihilator) in order to find the best possible form of the particular solution, a "guess" is made as to the appropriate form, which is then tested by differentiating the resulting equation. For complex equations, the annihilator method or variation of parameters is less time consuming to perform.

Computational method and system to perform empirical induction

The present invention is an improved computational method and system of empirical induction that can be used to arrive at generalized conclusions and make predictions involving longitudinal associations between and among variables and events. Empirical induction is used to gain scientific knowledge, to develop and evaluate treatments and other interventions, and to help make predictions and decisions. The invention, which is distinct from and often complementary to the statistical method, is applied to repeated measures and multiple time-series data and can be used to quantify, discover, analyze, and describe longitudinal associations for individual real and conceptual entities. Major improvements include provisions to define Boolean independent events and Boolean dependent events and to apply analysis parameters such as episode length and episode criterion for both independent and dependent variables, persistence after independent events, and delay and persistence after Boolean independent events. These improvements are in addition to levels of independent and dependent variables, delay after independent events, and provision to quantify benefit and harm across two or more dependent variables. Additional improvements include provisions to quantify longitudinal associations as functions of period or time and to compute values of predictive indices when there are two or more independent variables. Major applications and uses of the invention include data mining, the conduct of clinical trials of treatments for the management or control of chronic disorders, health-effect monitoring, the quantification and analysis internal control in adaptive systems, analyses of serial functional images, analyses of behavior and behavior modification, and use to create computerized devices and systems whose behavior can be modified by experience. The present invention is best implemented on the Internet.
Owner:BAGNE MILLER ENTERPRISES INC

Separating motion from cardiac signals using second order derivative of the photo-plethysmogram and fast fourier transforms

The present invention is directed toward a pulse oximetry system for the determination of a physiological parameter capable of removing motion artifacts from physiological signals comprises a hardware subsystem and a software subsystem. The software subsystem is used in conjunction with the hardware subsystem to perform a method for removing a plurality of motion artifacts from the photo-plethysmographic data and for obtaining a measure of at least one physiological parameter from the data. The method comprises acquiring the raw photo-plethysmographic data, transforming the data into the frequency domain, analyzing the transformed data to locate a series of candidate cardiac spectral peaks (primary plus harmonics), reconstructing a photo-plethysmographic signal in the time domain with only the candidate cardiac spectral peaks (primary plus harmonics), computing the second order derivative of the reconstructed photo-plethysmographic signal, analyzing the candidate second order derivative photo-plethysmographic signal to determine the absence or presence of cardiac physiologic signal characteristics, and finally selecting the best physiologic candidate from the series of potential cardiac spectral peaks (primary plus harmonics) based upon a second derivative scoring system. This scoring system is preferentially based upon second derivative processing analysis, but can be equally applied using the first, third, fourth or other similar derivative processing analysis.
Owner:SPACELABS HEALTHCARE LLC

System and device for multi-scale analysis and representation of physiological data

System comprised of a medical device and method for analyzing physiological and health data and representing the most significant parameters at different levels of detail which are understandable to a lay person and a medical professional. Low, intermediate and high-resolution scales can exchange information between each other for improving the analyses; the scales can be defined according to the corresponding software and hardware resources. A low-resolution Scale I represents a small number of primary elements such as intervals between the heart beats, duration of electrocardiographic PQ, QRS, and QT-intervals, amplitudes of P-, Q-, R-, S-, and T-waves. This real-time analysis is implemented in a portable device that requires minimum computational resources. The set of primary elements and their search criteria can be adjusted using intermediate or high-resolution levels. At the intermediate-resolution Scale II, serial changes in each of the said elements can be determined using a mathematical decomposition into series of basis functions and their coefficients. This scale can be implemented using a specialized processor or a computer organizer. At the high-resolution Scale III, combined serial changes in all primary elements can be determined to provide complete information about the dynamics of the signal. This scale can be implemented using a powerful processor, a network of computers or the Internet. The system can be used for personal or group self-evaluation, emergency or routine ECG analysis, or continuous event, stress-test or bed-side monitoring.
Owner:SHUSTERMAN VLADIMIR

Method and Apparatus for Measuring a Structure on a Substrate, Computer Program Products for Implementing Such Methods and Apparatus

Diffraction models and scatterometry are used to reconstruct a model of a microscopic structure on a substrate. A plurality of candidate structures are defined, each represented by a plurality of parameters (p1, p2, etc.)). A plurality of model diffraction signals are calculated by simulating illumination of each of the candidate structures. The structure is reconstructed by fitting one or more of the model diffraction signals to a signal detected from the structure. In the generation of the candidate structures, a model recipe is used in which parameters are designated as either fixed or variable. Among the variable parameters, certain parameters are constrained to vary together in accordance with certain constraints, such as linear constraints. An optimized set of constraints, and therefore an optimized model recipe, is determined by reference to a user input designating one or more parameters of interest for a measurement, and by simulating the reconstruction process reconstruction. The optimized model recipe can be determined automatically by a parameter advisor process that simulates reconstruction of a set of reference structures, using a plurality of candidate model recipes. In the generation of the reference structures, restrictions can be applied to exclude unrealistic parameter combinations.
Owner:ASML NETHERLANDS BV

Rolling bearing fault diagnosis method in various working conditions based on feature transfer learning

The present invention provides a rolling bearing fault diagnosis method in various working conditions based on feature transfer learning, and relates to the field of fault diagnosis. The objective ofthe invention is to solve the problem that a rolling bearing, especially to various working conditions, is low in accuracy of diagnosis. The method comprise the steps of: employing a VMD (VariationalMode Decomposition) to perform decomposition of vibration signals of a rolling bearing in each state to obtain a series of intrinsic mode functions, performing singular value decomposition of a matrixformed by the intrinsic mode functions to solve a singular value or a singular value entropy, combining time domain features and frequency domain features of the vibration signals to construct a multi-feature set; introducing a semisupervised transfer component analysis method to perform multinuclear construction of a kernel function thereof, sample features of different working conditions are commonly mapped to a shared reproducing kernel Hilbert space so as to improve the data intra-class compactness and the inter-class differentiation; and employing the maximum mean discrepancy embedding to select more efficient data as a source domain, inputting source domain feature samples into a SVM (Support Vector Machine) for training, and testing target domain feature samples after mapping. Therolling bearing fault diagnosis method in various working conditions has higher accuracy in the rolling bearing multi-state classification in various working conditions.
Owner:HARBIN UNIV OF SCI & TECH

Extraction method for early failure sensitive characteristics based on ensemble empirical mode decomposition (EEMD) and wavelet packet transform

InactiveCN103091096AGuaranteed Adaptive Accurate PartitioningAdaptive Precise Partition PreciseMachine gearing/transmission testingMachine bearings testingNODALDecomposition
The invention relates to an extraction method for early failure sensitive characteristics based on ensemble empirical mode decomposition (EEMD) and wavelet packet transform. The extraction method for the early failure sensitive characteristics based on the EEMD and the wavelet packet transform includes the following steps: (1), collected original vibration signals of mechanical and electrical equipment are decomposed according to the EEMD, white noise is added, and intrinsic mode function (IMF) components are obtained through decomposition; (2), the sensitive IMF components closely related to failure are chosen, and other irrelative IMF components are ignored; (3), the sensitive IMF components chosen through step (2) are decomposed in an orthogonal wavelet packet mode, and a wavelet coefficient of each node is obtained; and (4), envelopes are extracted from the obtained wavelet packet coefficients by adoption of the Hilbert transform and the Fourier transform, power spectrums are calculated, the power spectrum corresponding to each wavelet packet coefficient is obtained and serves as the early failure sensitive characteristic , and the sensitive characteristics are automatically obtained. Self-adapting signals can be decomposed, the sensitive characteristics can be convenient to obtain automatically, diagnosis precision and speed are improved, and a mechanical and electrical system can be diagnosed quickly, accurately and stably. The extraction method for the early failure sensitive characteristics based on the EEMD and the wavelet packet transform can be applied to the field of mechanical and electrical equipment failure diagnosis.
Owner:BEIJING INFORMATION SCI & TECH UNIV

Cross-modal subject correlation modeling method based on deep learning

The invention belongs to the technical field of cross-media correlation learning, and particularly relates to a cross-modal subject correction modeling method based on deep learning.The method includes two main algorithms of multi-modal file expression based on deep vocabularies and correlation subject model modeling fusing cross-modal subjection correction learning.A deep learning technology is utilized for constructing deep semantic vocabularies and deep vision vocabularies to describe a semantic description part and an image part in a multi-modal file.Based on multi-modal file expression, a cross-modal correlation subject model is constructed to model a whole multi-modal file set, so that the generation process of the multi-modal file and the correlation between different modals are described.The accuracy is high, and adaptability is high.The cross-modal subject correction modeling method has important meaning for efficient cross-media information retrieval in consideration of multi-modal semantic information on the basis of the large-scale multi-modal file (a text and an image), can improve retrieval correlation and promote user experience, and has great application value in the field of cross-media information retrieval.
Owner:FUDAN UNIV
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