An online dimensionality reduction method and system based on stacked fourier kernel recursive width learning autoencoder

Abstract

The application discloses an online dimension reduction method based on a stacked Fourier kernel recursive width learning self-encoder, which comprises the following steps: constructing a multi-layer stacked Fourier kernel recursive width learning self-encoder architecture, wherein the self-encoder architecture is stacked from top to bottom by P-layer Fourier kernel recursive width learning self-encoder units, and P is an integer greater than or equal to 2; the self-encoder architecture is used for receiving high-dimensional space-time temperature data collected by a sensor in real time, and the high-dimensional space-time temperature data is compressed to a low-dimensional hidden space through progressive nonlinear mapping, so that space-time decoupling is realized; in each layer network of the stacked self-encoder architecture, two-stage nonlinear mapping is performed by using a Fourier KAN activation function, the encoding output of the pth layer is the initial dimension reduction result, and initial nonlinear dimension reduction is completed. While the dimension is greatly compressed, the core original temperature field core space topological information is reserved, and the accuracy of a traditional dimension reduction method is broken through from the system framework.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to an online dimensionality reduction method and system based on a stacked Fourier kernel recursive width learning autoencoder. Background Technology

[0002] The thermal process of a lithium-ion battery is a typical parabolic distributed parameter system, where the temperature field evolves simultaneously with time and spatial location, exhibiting inherent characteristics of spatiotemporal coupling, infinite dimension, and strong nonlinearity. Due to hardware resource limitations, onboard BMS can only acquire local temperatures through a finite number of discrete sensors, and cannot directly obtain the temperature distribution across the entire surface. Furthermore, the infinite-dimensional spatiotemporal coupled data cannot be directly used in conventional timing control algorithms. Therefore, spatiotemporal dimensionality reduction is an essential prerequisite for battery thermal process modeling and control.

[0003] The core function of spatiotemporal dimensionality reduction is to map high-dimensional spatiotemporally coupled temperature data into low-dimensional pure time-series feature coefficients, achieving "spatial dimension compression + spatiotemporal decoupling," thus transforming an infinite-dimensional distributed parameter system problem into a finite-dimensional time-series system problem. The accuracy, efficiency, and adaptability of the dimensionality reduction process directly determine the performance ceiling of the entire thermal modeling scheme.

[0004] There are currently three main dimensionality reduction schemes: 1. A linear dimensionality reduction method based on Karhunen-Loève decomposition (KLD): Principle and function: This method extracts a set of orthogonal spatial basis functions from historical temperature data through orthogonal eigenvalue decomposition. High-dimensional temperature data is projected onto these basis functions to obtain low-dimensional time-series coefficients, making it the most widely used spatiotemporal dimensionality reduction scheme in industry. Its core function is to achieve spatiotemporal decoupling through linear orthogonal transformation, significantly reducing the computational complexity of subsequent modeling. This method is simple in principle, has clear physical meaning, and fast initial calculation speed; however, it is essentially a linear transformation, only able to capture the linear correlation of temperature spatial distribution, and cannot fit the strongly nonlinear spatiotemporal coupling characteristics of battery thermal processes. The loss of dimensionality reduction information is significant, and the accuracy of subsequent modeling has a natural upper limit. To achieve online updating of basis functions, matrix eigenvalue decomposition needs to be repeatedly performed, and the computational complexity increases cubically with the number of sensors, resulting in extremely poor real-time performance. Therefore, most solutions adopt an offline fixed basis function mode, which cannot adapt to the time-varying drift of battery thermal characteristics.

[0005] 2. Nonlinear Dimensionality Reduction Method Based on Kernel Extreme Learning Machine Principle and Function: This method maps the original data to a high-dimensional feature space through a kernel function, and then combines it with an extreme learning machine to achieve nonlinear dimensionality reduction. Some multi-layer schemes further enhance the nonlinear expressive power through stacking structures. Its core function is to break through the accuracy limit of linear dimensionality reduction and realize feature extraction of complex nonlinear spatiotemporal data. This method has better nonlinear expressive power than linear KLD and higher dimensionality reduction fidelity; however, the kernel method requires storing support vectors. As online data accumulates, the number of support vectors continues to grow, and memory consumption and computational complexity increase linearly, making long-term resource consumption uncontrollable; moreover, most schemes are offline training modes with imperfect online update mechanisms, making it difficult to run stably for a long time on resource-constrained automotive embedded devices.

[0006] 3. Feature extraction and dimensionality reduction techniques based on breadth learning (BLS) Principle and Function: Width learning achieves nonlinear feature transformation through randomly generated feature nodes and augmentation nodes. The output weights are solved in one step through ridge regression, resulting in a training speed far faster than deep learning. Existing Recursive Width Learning (R-BLS) further introduces recursive least squares to achieve incremental online updates of output weights, mainly used for general classification and regression tasks. Its core function is to significantly improve training and update efficiency while ensuring nonlinear expressive power. This method has high computational efficiency and fast update speed; however, existing schemes are mostly single-layer structures, which lack nonlinear expressive power when used for spatiotemporal dimensionality reduction and cannot capture complex hierarchical spatiotemporal coupling features; they generally use traditional activation functions such as sigmoid and tanh, which have weak fitting ability for the periodic and high-frequency nonlinear features of battery thermal processes; and they are mostly cumulative recursive updates without a forgetting mechanism, resulting in poor adaptability to time-varying systems; currently, there is no online spatiotemporal dimensionality reduction scheme that combines recursive width learning with stacked autoencoders specifically for distributed parameter systems, and it cannot directly adapt to the dimensionality reduction requirements of battery thermal processes.

[0007] Existing dimensionality reduction techniques suffer from gradual distortion of fixed dimensionality reduction mappings as the thermal characteristics of batteries slowly shift throughout their lifecycle, resulting in a continuous decline in long-term accuracy. Therefore, developing a spatiotemporal dimensionality reduction method with high-precision nonlinear expression capabilities, low computational overhead, and online adaptive adjustment is a core technical problem urgently needing to be solved in this field. Summary of the Invention

[0008] To address the aforementioned shortcomings, the present invention aims to propose an online dimensionality reduction method and system based on a stacked Fourier kernel recursive width learning autoencoder.

[0009] To achieve this objective, the present invention employs the following technical solution: an online dimensionality reduction method based on a stacked Fourier kernel recursive width learning autoencoder, comprising: A multi-layer stacked Fourier kernel recursive width learning autoencoder architecture is constructed, wherein the autoencoder architecture is composed of P layers of Fourier kernel recursive width learning autoencoder units stacked from top to bottom, where P is an integer greater than or equal to 2; The self-encoder architecture is used to receive high-dimensional spatiotemporal temperature data collected in real time by the sensor. Through a layer-by-layer progressive nonlinear mapping, the high-dimensional spatial temperature data is compressed into a low-dimensional hidden space to achieve spatiotemporal decoupling. Within each layer of the stacked autoencoder architecture, a two-stage nonlinear mapping is performed using the Fourier KAN activation function, with the encoded output of the p-th layer serving as the initial dimensionality reduction result, thus completing the initial nonlinear dimensionality reduction.

[0010] Preferably, in the autoencoder architecture, the encoded feature output of the previous autoencoder is directly used as the input of the next autoencoder, and the dimension is compressed layer by layer from top to bottom. The original input is a spatial temperature vector, and after P-layer nonlinear transformation, the final output is a low-dimensional time series coefficient.

[0011] Preferably, the step of performing a two-stage nonlinear mapping using the Fourier KAN activation function is as follows: Step S21: Use Fourier KAN activation function Instead of traditional sigmoid / tanh activation, the Fourier KAN activation function is used to process the input of this layer structure to obtain preliminary features; The Fourier KAN activation function is as follows: ; Where gridsize is the frequency order of the Fourier basis, controlling the frequency coverage range of the nonlinear expression. , respectively, are the cosine and sine coefficients of the k-th Fourier basis, x is the input, and bias is the global bias term; Step S22: Perform a first-level random nonlinear transformation on the preliminary features to extract feature nodes; The first-order stochastic nonlinear transformation is expressed as follows: ; Let be the random weight matrix of the i-th group of feature nodes. The corresponding bias vectors are randomly generated and then permanently fixed, and do not participate in training. X is the matrix of preliminary features output by the Fourier KAN activation function, and n is the number of feature node groups. Step S23: Perform a second-level random nonlinear mapping on the feature nodes to extract enhanced nodes; The second-order stochastic nonlinear mapping is expressed as follows: ; m is the number of independent groups of the augmented node. Let J be the random weight matrix of the j-th group of augmenting nodes. The corresponding bias vector is randomly generated and then permanently fixed, and Z is the matrix of feature nodes; Step S24: Concatenate the feature nodes and enhancement nodes; Obtain the total features ; Step S25: With the goal of reconstructing the input of this layer, calculate the weight matrix of each layer using the analytical solution of ridge regression; The expression for the weights is as follows: ; The initial total features during initial training. Here, I is the regularization coefficient, l is the variance matrix, and l is the number of layers. Step S26: Multiply the weight matrix by the total feature, and use the total feature as the output of this layer.

[0012] Preferably, step A is also included; Obtain the covariance matrix of each layer, and invert the covariance matrix to obtain the first parameter; The old output weight matrix retained from the previous time step The current new feature matrix is ​​predicted and reconstructed, and the deviation between it and the true new input is calculated as the second parameter. The weight matrix is ​​updated using the first and second parameters.

[0013] The formula for obtaining the first parameter is as follows: ; in Forgetting factor, Let be the covariance matrix of the l-th layer at time n. The total features of the l-th layer at time n; The formula for obtaining the second parameter is as follows: ; in This is the input of layer l-1 at time n+1. The total features of layer l-1 at time n+1. Let n be the weight matrix of the l-th layer at time n; The formula for updating the weight matrix is ​​as follows: .

[0014] An online dimensionality reduction system based on stacked Fourier kernel recursive width learning autoencoder, using the aforementioned online dimensionality reduction method based on stacked Fourier kernel recursive width learning autoencoder, includes a construction module and a hierarchy setting module; The building module is used to construct a multi-layer stacked Fourier kernel recursive width learning autoencoder architecture, which is composed of P-layer Fourier kernel recursive width learning autoencoder units stacked from top to bottom. The layer setting module is used to perform two-level nonlinear mapping using the Fourier KAN activation function within each layer of the stacked autoencoder architecture, with the encoding output of the p-th layer as the initial dimensionality reduction result, thus completing the initial nonlinear prior dimensionality reduction.

[0015] Preferably, in the building module, the encoded feature output of the previous layer autoencoder is directly used as the input of the next layer autoencoder, and the dimension is compressed layer by layer from top to bottom; The original input is a spatial temperature vector, and after P-layer nonlinear transformation, the final output is a low-dimensional time series coefficient.

[0016] Preferably, the building module includes a first submodule, a second submodule, a third submodule, a fourth submodule, a fifth submodule, and a sixth submodule; The first submodule is used to employ the Fourier KAN activation function. Instead of traditional sigmoid / tanh activation, the Fourier KAN activation function is used to process the input of this layer structure to obtain preliminary features; The second submodule is used to perform a first-level random nonlinear transformation on the preliminary features to extract feature nodes; The third submodule is used to perform a second-level random nonlinear mapping on the feature nodes to extract enhanced nodes; The fourth submodule is used to concatenate the feature nodes and enhancement nodes; Obtain the total features ; The fifth submodule is used to calculate the weight matrix of each layer by means of ridge regression analytical solution with the goal of reconstructing the input of this layer; The sixth submodule is used to multiply the weight matrix by the total feature, and use the total feature as the output of this layer.

[0017] Preferably, it also includes a weight update module; The weight update module is used to obtain the covariance matrix of each layer and to invert the covariance matrix to obtain the first parameter; The old output weight matrix retained from the previous time step is used to predict and reconstruct the current new feature matrix, and the deviation between it and the true new input is calculated as the second parameter. The weight matrix is ​​updated using the first and second parameters.

[0018] One of the above technical solutions has the following advantages or beneficial effects: This invention employs a deep autoencoder architecture composed of P-layer Fourier kernel recursive width learning (FK-RBLS) units stacked from top to bottom. It changes the traditional global backpropagation mode, adopting a layer-by-layer independent self-supervised reconstruction mechanism to achieve progressive feature compression. This architecture successfully decouples high-dimensional spatial temperature field data smoothly into extremely low-dimensional pure temporal features, greatly compressing dimensionality while preserving the core original temperature field spatial topology information, thus breaking through the accuracy limitations of traditional dimensionality reduction methods in terms of system framework. Attached Figure Description

[0019] Figure 1 This is a flowchart of one embodiment of the method of the present invention.

[0020] Figure 2 This is a schematic diagram of the structure of one embodiment of the system of the present invention. Detailed Implementation

[0021] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0022] In the description of embodiments of the present invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0023] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0024] like Figures 1-2 As shown, an online dimensionality reduction method based on a stacked Fourier kernel recursive width learning autoencoder includes: A multi-layer stacked Fourier kernel recursive width learning autoencoder architecture is constructed, wherein the autoencoder architecture is composed of P layers of Fourier kernel recursive width learning autoencoder units stacked from top to bottom, where P is an integer greater than or equal to 2; The self-encoder architecture is used to receive high-dimensional spatiotemporal temperature data collected in real time by the sensor. Through a layer-by-layer progressive nonlinear mapping, the high-dimensional spatial temperature data is compressed into a low-dimensional hidden space to achieve spatiotemporal decoupling. Within each layer of the stacked autoencoder architecture, a two-stage nonlinear mapping is performed using the Fourier KAN activation function, with the encoded output of the p-th layer serving as the initial dimensionality reduction result, thus completing the initial nonlinear dimensionality reduction.

[0025] This invention presents a deep autoencoder architecture composed of P-layer Fourier kernel recursive width learning (FK-RBLS) units stacked from top to bottom. Its core technical logic lies in changing the traditional global backpropagation mode and employing a layer-by-layer independent self-supervised reconstruction mechanism to achieve progressive feature compression. This architecture successfully decouples high-dimensional spatial temperature field data into extremely low-dimensional pure temporal features, greatly compressing dimensionality while preserving the core original spatial topological information of the temperature field, thus breaking through the accuracy limitations of traditional dimensionality reduction methods at the system framework level. Furthermore, this invention innovatively introduces a Fourier Kolmogorov-Arnold network (Fourier KAN) containing multi-order sine and cosine bases within each single-layer autoencoder unit. The input data sequentially passes through two levels of Fourier KAN mapping, generating "feature nodes" for extracting the basic spatial distribution and "enhancement nodes" for capturing high-order dynamic features. The periodic oscillation characteristics of the Fourier basis functions achieve a high degree of mechanistic matching with the periodic heat transfer law caused by battery charging and discharging, significantly improving the model's ability to express nonlinear dynamic boundaries and its noise robustness at the operator level.

[0026] Preferably, in the autoencoder architecture, the encoded feature output of the previous autoencoder is directly used as the input of the next autoencoder, and the dimension is compressed layer by layer from top to bottom. The original input is a spatial temperature vector, and after P-layer nonlinear transformation, the final output is a low-dimensional time series coefficient.

[0027] Preferably, the step of performing a two-stage nonlinear mapping using the Fourier KAN activation function is as follows: Step S21: Use Fourier KAN activation function Instead of traditional sigmoid / tanh activation, the Fourier KAN activation function is used to process the input of this layer structure to obtain preliminary features; Addressing the technical weakness of existing wide-range learning networks and most deep neural networks, which rely heavily on traditional fixed-form nonlinear activation functions such as sigmoid, tanh, or ReLU, resulting in poor representation of the complex periodic heat generation patterns and high-frequency nonlinear temperature jumps exhibited by batteries during charge-discharge cycles, this paper abandons traditional static activation functions by starting from the underlying mathematical operators of neural networks. Within each basic computational unit of the stacked autoencoder architecture, it introduces activation functions with different frequency orders. Fourier Kolmogorov-Arnold Network (Fourier KAN) is used for feature mapping.

[0028] The Fourier KAN activation function is as follows: ; Where gridsize is the frequency order of the Fourier basis, controlling the frequency coverage range of the nonlinear expression. , respectively, are the cosine and sine coefficients of the k-th Fourier basis, x is the input, and bias is the global bias term; Step S22: Perform a first-level random nonlinear transformation on the preliminary features to extract feature nodes; The first-order stochastic nonlinear transformation is expressed as follows: ; Let be the random weight matrix of the i-th group of feature nodes. The corresponding bias vectors are randomly generated and then permanently fixed, and do not participate in training. X is the matrix of preliminary features output by the Fourier KAN activation function, and n is the number of feature node groups. Step S23: Perform a second-level random nonlinear mapping on the feature nodes to extract enhanced nodes; The second-order stochastic nonlinear mapping is expressed as follows: ; m is the number of independent groups of the augmented node. Let J be the random weight matrix of the j-th group of augmenting nodes. The corresponding bias vector is randomly generated and then permanently fixed, and Z is the matrix of feature nodes; A second-level random nonlinear mapping is performed on all the obtained feature nodes to extract enhancement nodes. The enhancement nodes further capture residual nonlinear information based on the feature nodes, thereby greatly enriching the feature representation capability. After completing the two-level random mapping, step S24 is executed to horizontally concatenate all feature nodes and all enhancement nodes in the feature dimension. The total feature contains information from both the basic random mapping and the deep residual mapping, providing a sufficient and high-quality feature basis for subsequent linear mapping.

[0029] Step S24: Concatenate the feature nodes and enhancement nodes; Obtain the total features ; Step S25: With the goal of reconstructing the input of this layer, calculate the weight matrix of each layer using the analytical solution of ridge regression; The expression for the weights is as follows: ; The initial total features during initial training. Here, I is the regularization coefficient, l is the variance matrix, and l is the number of layers. Step S26: Multiply the weight matrix by the total feature, and use the total feature as the output of this layer.

[0030] Preferably, step A is also included; Obtain the covariance matrix of each layer, and invert the covariance matrix to obtain the first parameter; The old output weight matrix retained from the previous time step The current new feature matrix is ​​predicted and reconstructed, and the deviation between it and the true new input is calculated as the second parameter. The weight matrix is ​​updated using the first and second parameters.

[0031] Preferably, to address the issue that historical data has a continuous cumulative effect during recursive updates, and that when battery aging or operating conditions change significantly, the model becomes overly reliant on historical information, making it difficult to adjust the current weight matrix in a timely manner and resulting in insufficient adaptability of the dimensionality reduction model to dynamic changes, this invention introduces a forgetting factor mechanism into the recursive width learning framework. By assigning different weights to data collected at different time stages, this reduces the impact of early historical data on the current model update, while enhancing the role of the latest operating status data in the weight matrix update process.

[0032] covariance matrix It is the core carrier of historical data characteristics. Utilizing the matrix inversion lemma, traditional high-dimensional matrix inversion operations are transformed into matrix multiplication with extremely low computational complexity, and an adjustable forgetting factor is creatively embedded. The covariance matrix of fixed dimensions is recursively updated.

[0033] The formula for obtaining the first parameter is as follows: ; in Forgetting factor, Let be the covariance matrix of the l-th layer at time n. The total features of the l-th layer at time n; Mathematically, this formula is equivalent to applying an exponential decay penalty to historical covariance data from a long period of time, thereby reducing the weight of old thermal characteristic data. Since the formula only involves simple matrix multiplication and addition operations, its computational complexity is significantly lower than that of traditional offline pseudo-inverses. Descending to This ensures that memory usage and single-step time remain constant throughout long-term operation.

[0034] The formula for obtaining the second parameter is as follows: ; in This is the input of layer l-1 at time n+1. The total features of layer l-1 at time n+1. Let n be the weight matrix of the l-th layer at time n; Second parameter Physically, this represents new information in the newly arrived temperature data that has not yet been captured by the old dimensionality reduction mapping rules. If the battery thermal characteristics do not drift, this error will approach zero; however, if sudden changes in operating conditions or battery aging cause changes in the heating pattern, this error will increase significantly, thus triggering the weight matrix correction in subsequent steps.

[0035] The formula for updating the weight matrix is ​​as follows: .

[0036] This formula forms a feedback closed loop. Gain matrix. This determines the step size and direction of parameter updates. By assigning higher learning weights to the latest acquired temperature error data, the model is forcibly pulled back to the latest health state and dynamic characteristics of the battery. It then evolves and self-corrects in real time based on the physical time-varying characteristics.

[0037] An online dimensionality reduction system based on stacked Fourier kernel recursive width learning autoencoder, using the aforementioned online dimensionality reduction method based on stacked Fourier kernel recursive width learning autoencoder, includes a construction module and a hierarchy setting module; The building module is used to construct a multi-layer stacked Fourier kernel recursive width learning autoencoder architecture, which is composed of P-layer Fourier kernel recursive width learning autoencoder units stacked from top to bottom. The layer setting module is used to perform two-level nonlinear mapping using the Fourier KAN activation function within each layer of the stacked autoencoder architecture, with the encoding output of the p-th layer as the initial dimensionality reduction result, thus completing the initial nonlinear prior dimensionality reduction.

[0038] Preferably, in the building module, the encoded feature output of the previous layer autoencoder is directly used as the input of the next layer autoencoder, and the dimension is compressed layer by layer from top to bottom; The original input is a spatial temperature vector, and after P-layer nonlinear transformation, the final output is a low-dimensional time series coefficient.

[0039] Preferably, the building module includes a first submodule, a second submodule, a third submodule, a fourth submodule, a fifth submodule, and a sixth submodule; The first submodule is used to employ the Fourier KAN activation function. Instead of traditional sigmoid / tanh activation, the Fourier KAN activation function is used to process the input of this layer structure to obtain preliminary features; The second submodule is used to perform a first-level random nonlinear transformation on the preliminary features to extract feature nodes; The third submodule is used to perform a second-level random nonlinear mapping on the feature nodes to extract enhanced nodes; The fourth submodule is used to concatenate the feature nodes and enhancement nodes; Obtain the total features ; The fifth submodule is used to calculate the weight matrix of each layer by means of ridge regression analytical solution with the goal of reconstructing the input of this layer; The sixth submodule is used to multiply the weight matrix by the total feature, and use the total feature as the output of this layer.

[0040] Preferably, it also includes a weight update module; The weight update module is used to obtain the covariance matrix of each layer and to invert the covariance matrix to obtain the first parameter; The old output weight matrix retained from the previous time step is used to predict and reconstruct the current new feature matrix, and the deviation between it and the true new input is calculated as the second parameter. The weight matrix is ​​updated using the first and second parameters.

[0041] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0042] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. An online dimensionality reduction method based on a stacked Fourier kernel recursive width learning autoencoder, characterized in that, include: A multi-layer stacked Fourier kernel recursive width learning autoencoder architecture is constructed, wherein the autoencoder architecture is composed of P layers of Fourier kernel recursive width learning autoencoder units stacked from top to bottom, where P is an integer greater than or equal to 2; The self-encoder architecture is used to receive high-dimensional spatiotemporal temperature data collected in real time by the sensor. Through a layer-by-layer progressive nonlinear mapping, the high-dimensional spatial temperature data is compressed into a low-dimensional hidden space to achieve spatiotemporal decoupling. Within each layer of the stacked autoencoder architecture, a two-stage nonlinear mapping is performed using the Fourier KAN activation function, with the encoded output of the p-th layer serving as the initial dimensionality reduction result, thus completing the initial nonlinear prior dimensionality reduction.

2. The online dimensionality reduction method based on a stacked Fourier kernel recursive width learning autoencoder according to claim 1, characterized in that, In the autoencoder architecture, the encoded feature output of the previous autoencoder is directly used as the input of the next autoencoder, and the dimension is compressed layer by layer from top to bottom. The original input is a spatial temperature vector, and after P-layer nonlinear transformation, the final output is a low-dimensional time series coefficient.

3. The online dimensionality reduction method based on a stacked Fourier kernel recursive width learning autoencoder according to claim 2, characterized in that, The steps for performing a two-level nonlinear mapping using the Fourier KAN activation function are as follows: Step S21: Use Fourier KAN activation function Instead of traditional sigmoid / tanh activation, the Fourier KAN activation function is used to process the input of this layer structure to obtain preliminary features; The Fourier KAN activation function is as follows: ； Where gridsize is the frequency order of the Fourier basis, controlling the frequency coverage range of the nonlinear expression. , respectively, are the cosine and sine coefficients of the k-th Fourier basis, x is the input, and bias is the global bias term; Step S22: Perform a first-level random nonlinear transformation on the preliminary features to extract feature nodes; The first-order stochastic nonlinear transformation is expressed as follows: ； Let be the random weight matrix of the i-th group of feature nodes. The corresponding bias vectors are randomly generated and then permanently fixed, and do not participate in training. X is the matrix of preliminary features output by the Fourier KAN activation function, and n is the number of feature node groups. Step S23: Perform a second-level random nonlinear mapping on the feature nodes to extract enhanced nodes; The second-order stochastic nonlinear mapping is expressed as follows: ； m is the number of independent groups of the augmented node. Let J be the random weight matrix of the j-th group of augmenting nodes. The corresponding bias vector is randomly generated and then permanently fixed, and Z is the matrix of feature nodes; Step S24: Concatenate the feature nodes and enhancement nodes; Obtain the total features ; Step S25: With the goal of reconstructing the input of this layer, calculate the weight matrix of each layer using the analytical solution of ridge regression; The expression for the weights is as follows: ； The initial total features during initial training. Here, I is the regularization coefficient, l is the variance matrix, and l is the number of layers. Step S26: Multiply the weight matrix by the total feature, and use the total feature as the output of this layer.

4. The online dimensionality reduction method based on a stacked Fourier kernel recursive width learning autoencoder according to claim 1, characterized in that, It also includes step A; Obtain the covariance matrix of each layer, and invert the covariance matrix to obtain the first parameter; The old output weight matrix retained from the previous time step The current new feature matrix is ​​predicted and reconstructed, and the deviation between it and the true new input is calculated as the second parameter. The weight matrix is ​​updated using the first and second parameters.

5. The online dimensionality reduction method based on a stacked Fourier kernel recursive width learning autoencoder according to claim 4, characterized in that, The formula for obtaining the first parameter is as follows: ； in Forgetting factor, Let be the covariance matrix of the l-th layer at time n. The total features of the l-th layer at time n; The formula for obtaining the second parameter is as follows: ； in This is the input of layer l-1 at time n+1. The total features of layer l-1 at time n+1. Let n be the weight matrix of the l-th layer at time n; The formula for updating the weight matrix is ​​as follows: 。 6. An online dimensionality reduction system based on a stacked Fourier kernel recursive width learning autoencoder, characterized in that, The online dimensionality reduction method based on stacked Fourier kernel recursive width learning autoencoder according to any one of claims 1 to 5 includes a construction module and a hierarchy setting module; The building module is used to construct a multi-layer stacked Fourier kernel recursive width learning autoencoder architecture, which is composed of P-layer Fourier kernel recursive width learning autoencoder units stacked from top to bottom. The layer setting module is used to perform two-level nonlinear mapping using the Fourier KAN activation function within each layer of the stacked autoencoder architecture, with the encoding output of the p-th layer as the initial dimensionality reduction result, thus completing the initial nonlinear prior dimensionality reduction.

7. The online dimensionality reduction system based on a stacked Fourier kernel recursive width learning autoencoder according to claim 6, characterized in that, In the aforementioned building module, the encoded feature output of the previous layer autoencoder is directly used as the input of the next layer autoencoder, and the dimension is compressed layer by layer from top to bottom. The original input is a spatial temperature vector, and after P-layer nonlinear transformation, the final output is a low-dimensional time series coefficient.

8. The online dimensionality reduction system based on a stacked Fourier kernel recursive width learning autoencoder according to claim 7, characterized in that, The building module includes a first submodule, a second submodule, a third submodule, a fourth submodule, a fifth submodule, and a sixth submodule; The first submodule is used to employ the Fourier KAN activation function. Instead of traditional sigmoid / tanh activation, the Fourier KAN activation function is used to process the input of this layer structure to obtain preliminary features; The second submodule is used to perform a first-level random nonlinear transformation on the preliminary features to extract feature nodes; The third submodule is used to perform a second-level random nonlinear mapping on the feature nodes to extract enhanced nodes; The fourth submodule is used to concatenate the feature nodes and enhancement nodes; Obtain the total features ; The fifth submodule is used to calculate the weight matrix of each layer by means of ridge regression analytical solution with the goal of reconstructing the input of this layer; The sixth submodule is used to multiply the weight matrix by the total feature, and use the total feature as the output of this layer.

9. The online dimensionality reduction system based on a stacked Fourier kernel recursive width learning autoencoder according to claim 6, characterized in that, It also includes a weight update module; The weight update module is used to obtain the covariance matrix of each layer and to invert the covariance matrix to obtain the first parameter; The old output weight matrix retained from the previous time step is used to predict and reconstruct the current new feature matrix, and the deviation between it and the true new input is calculated as the second parameter. The weight matrix is ​​updated using the first and second parameters.

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