45 results about "Nonlinear manifold" patented technology

A fault diagnosis method based on OLPP feature reduction in rotary machine fault diagnosis field includes that a vibration signal is performed with EMD to construct Shannon entropy to obtain high-dimensional feature vectors, and then OLPP is adopted reduce the high-dimensional vectors to low-dimensional feature vectors which are inputted to a Morlet MWSVM for fault recognition. The OLPP preserving local and overall structure retains the low-dimensional internal features of the nonlinear manifold structure, and the MWSVM has self-adaptive decisive power and can be used as a terminal classifier. The invention sufficiently excels the advantages of EMD, OLPP and MWSVM respectively in fault feature extraction, information compression and pattern recognition, not only realizes the full automatic process from fault feature extraction to fault diagnosis, but also has high fault diagnosis accuracy and self-adaptive diagnosis capacity.

The invention relates to an electromechanical device nonlinear failure prediction method, comprising the following steps: 1, obtain data which can represent the running state of a device and select a section continuous vibration signal which has a long course and is sensitive to the failure to analyze; 2, respectively carry out exceptional value elimination and missing data filling to the vibration data by a 3 sigma method and an interpolation method; 3, carry out noise reduction to the vibration signal by a lifting wavelet method; 4, decompose the vibration signal after the noise reduction to corresponding characteristic bandwidths; 5, obtain a low dimension manifold character by utilizing a typical predicted characteristic bandwidth and adopting a nonlinear manifold learning method through decoupling of topological mapping and non-failure energy information; 6, carry out intelligent failure prediction with long course trend in a time domain by utilizing a recurrent neural network which has the dynamic self-adaptive characteristic and a first dimension of the low dimension manifold character as a neural network input. The lifting wavelet method is adopted in the invention, the algorithm is simple, the arithmetic speed is high, and the used memory is less, thereby being suitable for the characteristic bandwidth abstraction of failure character. The electromechanical device nonlinear failure prediction method can be widely applied to the failure prediction of all kinds of electromechanical devices.

The invention provides a nuclear power device fault diagnosis method based on local linear embedding and a K-nearest neighbor classifier. The method comprises steps of (1) acquiring operation data of a nuclear power device in steady-state operation and typical accident states as training data; (2) using the mean-variance standardization method, carrying out dimensionless standardization processing on the training data to obtain high-dimension sample data; (3) using the local linear embedding algorithm, extracting low-dimension manifold structures of the high-dimension sample data so as to obtain low-dimension characteristic vectors; (4) inputting the low-dimension characteristic vectors into a K-nearest neighbor classifier to carry out classification training; (5), acquiring real-time operation data of the nuclear power device, and repeating the steps of (2) and (3); and (6) using the trained K-nearest neighbor classifier to make decisions for classification of the characteristic vectors. According to the invention, by taking advantages of the nonlinear manifold learning method in the aspects of characteristic dimension reduction extraction, the provided method is suitable for fault diagnosis of nonlinear data high-dimension systems, and has quite high fault diagnosis accuracy.

The invention discloses a wind power plant short-term wind power prediction modeling method based on wavelet analysis and a multi-model AdaBoost deep network. On the basis of analyzing the relationship between wind power and meteorological factors, wavelet multi-scale analysis and entropy and nonparametric estimation methods are firstly used for respectively inspecting time-frequency domain feature distribution, uncertainty and randomness of wind power data, and the wavelet multi-scale analysis, entropy and nonparametric estimation methods are used for reasonably dividing subsets so as to ensure that training samples fully excite all modes of a system. Secondly, nonlinear manifold learning is adopted to extract nonlinear features of the wind power data, and dimensionality reduction is achieved so as to reduce calculation complexity; and finally, a short-term wind power combined prediction model is created with high prediction precision, low calculation complexity and strong robustnessin combination with a long-term and short-term memory neural network with an optimized structure. Accurate and reliable wind power prediction can be provided for a wind power plant, and guarantee is provided for coordination control and power grid dispatching of large-scale wind power grid connection.

The invention provides a k-means nonlinear manifold clustering and representative point selecting method based on a graph theory. Specifically, the method comprises following steps: constructing a graph model; calculating a graph distance matrix and an infinite random walk probability matrix between various sample points; and alternately iterating various clustering centers and clustering members on the graph model until convergence. A fatigue random walk model provided in the invention may fast achieve nonlinear manifold clustering and select a representative point for each cluster so as to overcome a defect that conventional k-means just achieves a good effect when samples comply with Gaussian distribution. The method has a good clustering effect on high-dimensional data with lower-dimensional manifold distribution, such as images, texts, and videos, and may assign a most representative point to each cluster. The method is easy to implement and manipulate.

The invention discloses an ISOMAP-based lithium battery (LIB) thermal-technology space-time modeling method. The method comprises: step 1, constructing a lithium battery recharging-discharging controlplatform; step 2, obtaining time-space data of temperature distribution which is of a lithium battery under a cyclic recharging-discharging condition and changes with time; and step 3, using an ISOMAP algorithm by a host computer to learn an orthogonal mapping function, which characterizes space nonlinear-features, on the time-space data collected in the step 2. An ISOMAP method is global nonlinear technology, can use local geometry structures of high-dimensional data to reveal internal nonlinear manifold structures thereof, and preserves topology structures of the original data in low-dimensional space. From a view of inherent configurations, ISOMAP can reduce a model of nonlinear DPS more effectively than a PCA method, and model accuracy is high.

The invention discloses a combined method and system for extracting and classifying features of images. The combined method comprises the following steps: firstly, constructing a neighbor graph according to the similarity of training samples and calculating and reconstructing a coefficient matrix; introducing nonlinear manifold learning with minimum neighbor reconstructing error measured on the basis of nuclear norm measurement, performing low-dimension manifold feature learning on a training image sample, thereby acquiring a linear projection matrix capable of extracting the low-dimension manifold feature of the sample; utilizing the low-dimension manifold feature of the training sample to minimize L2,1-norm regularization classifying error, completing robust sparse classifier learning and outputting the optimal classifier, thereby extracting and classifying the features of the tested sample. Compared with the prior art, the method has the advantage that the combination of nuclear norm measurement and L2,1-norm regularization is adopted for effectively increasing the descriptiveness of feature extraction and classification accuracy.

The invention relates to a surge monitoring method based on incremental nonlinear manifold learning, high-dimensional characteristic information is constructed according to multipath dynamic characteristics expressed in the operating process of a compressor, a one-dimensional main manifold is extracted by utilizing a local tangent space algorithm, the one-dimensional main manifold is updated in real time by an incremental manifold learning method, and whether a surge occurs or not under the varying duty condition of the compressor is judged by monitoring the change of a geometrical structure of a main manifold time sequence. The monitoring method extracts a concealed nonlinear change rule from complete high-dimensional characteristic data in the self operation of compressor equipment, thereby avoiding a phenomenon of missing report; meanwhile, the main manifold has the characteristic of enlarging diversity, and on the basis of ensuring real-time performance, an incremental algorithm simplifies the setting of a warning line and achieves low false alarm rate, and lays a foundation for effectively realizing surge early warning.

The present invention discloses a method for synthesizing three-dimensional human body movement based on non-linearity manifold study, so as to make three-dimensional human body movement animations, characterized in that firstly a set of sparse three-dimensional human body movement samples is mapped in movement semantic parameter space builded on a low-dimentsion manifold; then implementing uniformly distributed coarctation resample to the low dimensional movement semantic parameter space, and applying resample coefficient set to movement samples distributed in an original movement space sparsely to obtain dense and well distributed movement samples of a high dimensional space; then remapping the newly sampled high dimensional movement samples to obtain a final low dimensional movement semantic parameter space; finally, by means of interacting the movement semantic parameters synthezed selectively in the low dimensional semantic parameter space by users, the system maps the movement semantic parameter to a high dimensional movement space to obtain a new movement sequence. The invention is not only capable of controlling precisively movement physical parameters, e.g. movement position, physical movement characteristics of special arthrosis, and also used to synthesize novel movement data having high-rise movement semantion such as movement styles.

The invention discloses a nonlinear manifold learning dimension reduction method based on adaptive density clustering. The method comprises the following steps: 1) after the adaptive density clustering algorithm is used for clustering, ICA (Independent Component Analysis) is used for carrying out dimension reduction on each cluster to form a linear model plane; 2) the minimum spanning tree (MST) between local linear models is built; 3) manifold global MSTs are transversed; and 4) through operating the ICA on a global hyperplane, low dimensional implantation is found out. According to the nonlinear manifold learning dimension reduction method based on adaptive density clustering, the parallel mapping of the plane is used for overcoming the distortion generated by dimension reduction of the original data set, the accuracy is high, and the credibility is good.

The invention discloses a vibration equipment fault diagnosis method and system, and relates to the field of equipment fault diagnosis. Vibration equipment vibrates non-periodically and / or is asymmetric in the aspect of appearance. The method comprises the following steps of: arranging two groups of vibration sensors on a vibration equipment shell at two sides of a centroid plane, wherein each group of vibration sensors comprises a plurality of vibration sensors, each vibration sensor is used for acquiring dynamic vibration signal of the equipment, and the centroid plane is parallel to a planewhere a vibration equipment base is located; analyzing the dynamic vibration signal acquired by each vibration sensor to obtain a feature weighting signal, and generating a contour feature signal ofthe vibration equipment according to all the feature weighting signals; carrying out dimensionality reduction on the contour feature signal on the basis of a nonlinear manifold learning method so as to obtain low-dimensional feature descriptions of the vibration equipment; and classifying the low-dimensional feature descriptions by adoption of a classifier so as to obtain a fault diagnosis result.The method and system are capable of effectively reducing minor and interference information in original vibration data so as to obtain stable and correct fault diagnosis results.

The invention discloses a manifold learning and Hilbert-Huang transformation combined structural modal parameter identification method. The method comprises the following steps of: 1, acquiring time domain response data of a measure point in a structure; 2, processing the time domain response data acquired in the step 1 by adoption of a manifold learning algorithm so as to obtain a vibration modeand a fixed frequency of the structure; and 3, processing the time domain response data acquired in the step 1 by adoption of a Hilbert-Huang transformation method so as to obtain a damping ratio of the structure. Compared with the prior art, the method has the beneficial effects as follows: 1, when modal parameter extraction is carried out by utilizing the manifold learning and Hilbert-Huang transformation combined method, vibration modes, fixed frequencies and damping ratios with relatively high precision can be obtained through response data when material parameters and experiment conditions of structures are unknown; and 2, the method can be used for processing nonlinear data and retaining nonlinear manifolds of the structures.

The invention discloses an image super resolution reconstruction method based on maximum linear block neighborhood embedding. The method mainly comprises steps: a training sample set is constructed, a hierarchical division clustering method is adopted for clustering, a nonlinear manifold is approximately divided into multiple maximum linear blocks, and after clustering, medium and high frequency features are used for constructing the maximum linear blocks; a low resolution test image is classified to be divided into edge blocks and non edge blocks, and by adopting two different neighborhood selection modes, the reconstruction result is more accurate; neighborhood selection is carried out; neighborhood embedding is carried out; and image reconstruction is carried out, de-blurring is carried out on the initial reconstructed image, and a complete and clear high resolution reconstructed image is obtained. The maximum linear blocks are approximately obtained from the nonlinear manifold of the training samples through the clustering method, local linear neighborhood embedding is realized in combination with feature representation and neighborhood selection, more accurate high frequency information is reconstructed, the time complexity is greatly reduced, super resolution reconstruction on a natural image is realized, and clearer edge details can be recovered.

The invention discloses UHV equipment monitoring system and a UHV equipment monitoring method. The UHV equipment monitoring system comprises a platform resource layer, a basic service layer, a servicesupport layer and an application service layer, wherein the platform resource layer is configured to provide data and resource support, and the platform resource layer comprises a data base storing data generated during the operation and maintenance of UHV equipment, a knowledge base storing knowledge of the UHV equipment, a model library storing algorithm models and diagnostic rules, and an index library; the service support layer is configured to perform fault diagnosis and state monitoring on the UHV equipment, and the service support layer receives an operation instruction transmitted from the application service layer, accesses an infrastructure service layer, and performs corresponding business logic processing to generate a processing result in response to the operation instruction; and the service support layer comprises fault diagnosis module and a state monitoring module, and the fault diagnosis module comprises a dimensionality reduction unit which utilizes a non-linear manifold learning algorithm to directly extract low-dimensionality manifold in an original high-dimensional data space and a diagnostic unit for fault diagnosis based on a hybrid hidden Markov model.

The invention belongs to the field of computer technique recommending methods, and relates to a song recommending method based on nonlinear manifold learning. The song recommending method mainly comprises the following steps of establishing a relationship model between a user and a song; performing classifying and dimensional reduction on the song; according to the relationship model obtained after dimensional reduction, recommending by the song recommending method. The song recommending method has the beneficial effect that compared with the traditional synergistic filtering algorithm, more accuracy is obtained, and a recommending plan is more reasonable.

The invention discloses a complex equipment fault prediction method and system based on an LPP-HMM method, belongs to the field of complex equipment fault prediction, introduces nonlinear manifold learning into complex equipment fault diagnosis, and provides a fault diagnosis method using LPP and HMM.According to the method, original high-dimensional fault data are directly learned; the complex high-dimensional space is converted into a low-dimensional feature space to achieve dimensionality reduction, and extracting intrinsic low-dimensional manifold features of the data. Simulation experiments show that the method can well reserve the overall structure information in the fault data, and is beneficial to fault identification. The LPP algorithm can be used for analog circuit nonlinear fault feature reduction, and the effect is better than that of PCA and other linear dimension reduction methods.

The invention relates to the technical field of control, and provides a process disturbance-oriented bidirectional anti-interference control system and method, and the system comprises the steps: receiving an external disturbance signal and controlled object state monitoring data in parallel through a process sensing module, generating a disturbance feature vector through frequency band decomposition, and processing the state monitoring data through a nonlinear manifold learning algorithm, deep recognition of response features is realized; the disturbance coupling module takes the feedforward control pre-estimated quantity and the feedback control compensation quantity as optimization variables and takes the disturbance suppression ratio and the response recovery time as revenue functions to construct a differential game model, and the revenue functions are optimized through a gradient iterative algorithm; the bidirectional fusion module realizes dynamic weighting of two types of control quantities based on the coupling weight matrix; and the intelligent control module obtains a control deviation integral and response recovery time in real time, and dynamically adjusts parameters of the revenue function and parameters of weighted fusion through the reward function.

The invention discloses a method and device for abnormity detection of sparse data. The method comprises the steps that characteristic processing is conducted to original data of different types, so the original data of the different types is converted into the sparse data with a uniform format; a factorization machine is used for modeling of the sparse data, so a nonlinear manifold model is obtained; according to the nonlinear manifold model, abnormal value scores of data objects are computed; and according to abnormal value scores of the data objects, whether the data objects are abnormal data is judged.

The invention provides a lithium ion battery thermal process space-time modeling method based on dual-scale manifold learning, which comprises the following steps: constructing a group of nonlinear space basis functions for time / space separation according to a manifold learning method; truncating the nonlinear space basis function by adopting a Galerkin method to obtain a time model based on physics; carrying out evaluation learning on unknown model structures and parameters existing in the time model by utilizing an extreme learning machine; and reconstructing an LIBs space-time model by using a space-time synthesis method based on the nonlinear space basis function and the time model. According to the lithium ion battery thermal process space-time modeling method based on dual-scale manifold learning provided by the invention, local and global nonlinear manifold structure information is considered at the same time through a BFs learning method, so that the method is superior to a modeling method based on local linear embedding (LLE) and isometric mapping (ISOMAP); and the method is suitable for space-time dynamic modeling of a distributed parameter system DPS.

A method and an apparatus can include a system processor control and a system controller. The system controller can retrieve data from at least one database, the data including information associated with at least one of subscribers, multimedia content, and customer premises equipment. The system processor can formulate an input dataset from the retrieved data, perform nonlinear manifold clustering on the input dataset to formulate clusters, and determine a recommendation of multimedia content, the recommendation of multimedia content being based on a metric distance between a subscriber and a multimedia content. The system controller can transmit, to a customer premises equipment of the subscriber, the recommendation of multimedia content.

The invention discloses a vehicle intrusion detection method and device. The method comprises the steps: collecting high-dimensional CAN data on a vehicle-mounted CAN bus in the vehicle running process; clustering the high-dimensional CAN data based on a spectral clustering algorithm of a manifold distance kernel; obtaining a detection data low-dimensional manifold of each data cluster by adoptinga nonlinear manifold learning method; collecting CAN data in a simulated normal driving environment, constructing a normal data set and performing training to obtain a standard low-dimensional manifold; according to vehicle characteristics, comparing the detection data low-dimensional manifold with a standard low-dimensional manifold in a three-dimensional space, and judging whether an intrusionevent occurs in the vehicle or not. Intrusion detection is carried out based on the geometrical shape of the CAN data, the detection speed is high, continuous delivery of CAN messages in the vehicle driving process is met, and the vehicle can be detected in real time.

The invention relates to a surge monitoring method based on incremental nonlinear manifold learning, high-dimensional characteristic information is constructed according to multipath dynamic characteristics expressed in the operating process of a compressor, a one-dimensional main manifold is extracted by utilizing a local tangent space algorithm, the one-dimensional main manifold is updated in real time by an incremental manifold learning method, and whether a surge occurs or not under the varying duty condition of the compressor is judged by monitoring the change of a geometrical structure of a main manifold time sequence. The monitoring method extracts a concealed nonlinear change rule from complete high-dimensional characteristic data in the self operation of compressor equipment, thereby avoiding a phenomenon of missing report; meanwhile, the main manifold has the characteristic of enlarging diversity, and on the basis of ensuring real-time performance, an incremental algorithm simplifies the setting of a warning line and achieves low false alarm rate, and lays a foundation for effectively realizing surge early warning.

A fault diagnosis method based on OLPP feature reduction in rotary machine fault diagnosis field includes that a vibration signal is performed with EMD to construct Shannon entropy to obtain high-dimensional feature vectors, and then OLPP is adopted reduce the high-dimensional vectors to low-dimensional feature vectors which are inputted to a Morlet MWSVM for fault recognition. The OLPP preserving local and overall structure retains the low-dimensional internal features of the nonlinear manifold structure, and the MWSVM has self-adaptive decisive power and can be used as a terminal classifier. The invention sufficiently excels the advantages of EMD, OLPP and MWSVM respectively in fault feature extraction, information compression and pattern recognition, not only realizes the full automatic process from fault feature extraction to fault diagnosis, but also has high fault diagnosis accuracy and self-adaptive diagnosis capacity.

The invention relates to the technical field of power system equipment monitoring, in particular to a substation equipment state monitoring embedded edge analysis system, which comprises a monitoring front-end module for acquiring and transmitting substation equipment operation state data; the edge processing module comprises a multi-scale wavelet transform unit, a topology continuity analysis unit and a manifold learning unit, wherein the multi-scale wavelet transform unit decomposes data and separates signals and noise through a self-adaptive threshold mechanism; the topological persistence analysis unit maps the de-noised signal to a high-dimensional feature space, calculates a persistent coherence group, and extracts a topological feature vector; and the manifold learning unit constructs a nonlinear manifold structure, calculates a geodesic distance, and executes discharge type identification and anomaly evaluation, and the FPGA and ARM heterogeneous calculation architecture is adopted, and through the synergistic effect of multi-scale wavelet transform, topology persistence analysis and manifold learning, high-precision extraction of weak discharge signals and accurate identification of fault modes are realized.

The invention discloses an image super-resolution reconstruction method based on maximum linear block neighborhood embedding, the main steps of which include: constructing a training sample set, clustering by using a hierarchical splitting clustering method, and approximately dividing the nonlinear manifold into multiple The largest linear block, after clustering, uses medium and high frequency features to construct the largest linear block; classifies low-resolution test images into edge blocks and non-edge blocks, and uses two different neighborhood selection methods to reconstruct the results more accurately ; Neighborhood selection; Neighborhood embedding; Image reconstruction, deblurring the initial reconstructed image to obtain a complete and clear high-resolution reconstructed image. The present invention approximates a plurality of maximum linear block structures from the nonlinear manifold of training samples through a clustering method, combines feature representation and neighborhood selection to realize local linear neighborhood embedding, reconstructs more accurate high-frequency information, and greatly reduces The time complexity is reduced, and the super-resolution reconstruction of natural images can restore clearer edge details.

The invention relates to an electromechanical device nonlinear failure prediction method, comprising the following steps: 1, obtain data which can represent the running state of a device and select a section continuous vibration signal which has a long course and is sensitive to the failure to analyze; 2, respectively carry out exceptional value elimination and missing data filling to the vibration data by a 3 sigma method and an interpolation method; 3, carry out noise reduction to the vibration signal by a lifting wavelet method; 4, decompose the vibration signal after the noise reduction to corresponding characteristic bandwidths; 5, obtain a low dimension manifold character by utilizing a typical predicted characteristic bandwidth and adopting a nonlinear manifold learning method through decoupling of topological mapping and non-failure energy information; 6, carry out intelligent failure prediction with long course trend in a time domain by utilizing a recurrent neural network which has the dynamic self-adaptive characteristic and a first dimension of the low dimension manifold character as a neural network input. The lifting wavelet method is adopted in the invention, the algorithm is simple, the arithmetic speed is high, and the used memory is less, thereby being suitable for the characteristic bandwidth abstraction of failure character. The electromechanical device nonlinear failure prediction method can be widely applied to the failure prediction of all kinds of electromechanical devices.

The invention opens a identification method of human motion data based on integrated hidden Markov model learning method. This method extracts two-dimensional geometric features for capturing data from human motion, and then effectively reducts the dimensionality of movement features data by the introduction of dimension reduction methods of non-linear flow pattern learning, and finally learns the movement of sports database by adoption of Hidden Markov integrated learning based on self-adaptive advance algorithm for achieving fast retrieval of conventional movement. Two-dimensional geometric features extracted by the method well expresses the essential attribute of movement, dimensionality reduction methods of the expansion of nonlinear manifold will successfully map features of high-dimensional movement to low-dimensional space that can reflect the inherent links between data, thus greatly eliminates data redundancy. While this invention can study through drop dimensional data used by methods of integrated Hidden Markov Model learning, makes movement automatically identificate and classificate on the basis of high-precision.

The present invention discloses a method for synthesizing three-dimensional human body movement based on non-linearity manifold study, so as to make three-dimensional human body movement animations, characterized in that firstly a set of sparse three-dimensional human body movement samples is mapped in movement semantic parameter space builded on a low-dimentsion manifold; then implementing uniformly distributed coarctation resample to the low dimensional movement semantic parameter space, and applying resample coefficient set to movement samples distributed in an original movement space sparsely to obtain dense and well distributed movement samples of a high dimensional space; then remapping the newly sampled high dimensional movement samples to obtain a final low dimensional movement semantic parameter space; finally, by means of interacting the movement semantic parameters synthezed selectively in the low dimensional semantic parameter space by users, the system maps the movement semantic parameter to a high dimensional movement space to obtain a new movement sequence. The invention is not only capable of controlling precisively movement physical parameters, e.g. movement position, physical movement characteristics of special arthrosis, and also used to synthesize novel movement data having high-rise movement semantion such as movement styles.

The invention provides a nuclear power plant fault diagnosis method based on local linear embedding and K-nearest neighbor classifier. (1) Obtain the operating data of nuclear power plants in steady state operation and typical accident conditions as training data; (2) Use the mean-variance standardization method to perform dimensionless standardization on the training data to obtain high-dimensional sample data; (3) Use the local linear embedding algorithm to extract the low-dimensional manifold structure of high-dimensional sample data, and obtain the low-dimensional feature vector; (4) input the low-dimensional feature vector into the K-nearest neighbor classifier for classification training; (5) obtain the nuclear power plant Run the data in real time, repeat (2), (3); (6) use the trained K-nearest neighbor classifier to classify the feature vectors. The invention utilizes the advantages of the nonlinear manifold learning method in feature dimension reduction and extraction, is suitable for fault diagnosis of nonlinear and high-dimensional data systems, and has high fault diagnosis accuracy.

The invention discloses a sparse self-representation subspace clustering algorithm for self-adaptive local structure embedding. The invention belongs to the technical field of information. According to the invention, the optimal subspace and the most distinct clustering structure in the low-dimensional space can be identified at the same time, and the invention is superior to other two-stage subspace clustering methods; in addition, a nonlinear manifold regularizer is introduced, so that the learning trade-off between an original space and a subspace can be dynamically utilized; a local structure in an original space is encoded into a dictionary by a sparse self-representation method, and adaptive learning can be carried out in a clustering process. According to the invention, the non-square l2, 1-norm is adopted to minimize the residual error, and different from other methods based on the square l2-norm, the SSS can realize stable performance because the model based on the square l2,1-norm has robustness to abnormal values and noise; experimental results on an actual benchmark data set show that the method can provide more interpretable clustering results, and the performance ofthe method is superior to that of other alternative schemes.