A phase encoding method and system based on a cyclic phase change topology

Abstract

The application provides a phase encoding method and system based on a cyclic phase change topology. It relates to the technical fields of data encoding, time series signal processing, power system topology analysis, intelligent prediction and information processing, and comprises the following steps: adaptive window segmentation based on trend feature mutation of dynamic time series data to obtain multiple continuous phase change segments; extracting trend direction and evolution rate features to generate corresponding phase state codes and sequentially forming a phase state conversion sequence; mapping and anchoring the phase state conversion sequence to a single-sided closed surface topology phase coordinate system; extracting cyclic phase change constraint rules according to the phase state conversion sequence; and obtaining a prediction result through forward evolution based on the cyclic phase change constraint rules and dynamic time series data. This method can effectively improve encoding efficiency, reduce storage space, and improve anti-interference capability, and is widely applicable to the fields of industrial vibration monitoring, sensor AD front end, communication signal processing and the like, and provides a general solution for cyclic dynamic event encoding.

Description

Technical Field

[0001] This invention relates to the field of data encoding, specifically to a phase encoding method and system based on cyclic phase transition topology. Background Technology

[0002] Current mainstream information encoding, time series analysis, and data processing systems are all based on the underlying assumptions of Western systems such as "linear time, numerical basis, absolute truth, and global synchronization." However, when dealing with the vast majority of cyclical dynamic events in the real world, they suffer from insurmountable fundamental flaws, specifically including: 1. The inherent flaws of linear coding: Existing coding systems, with "precise numerical replication" as their core objective, rely on fixed sampling rates and absolute time bases. For dynamic events involving cyclical phase transitions such as day and night, seasons, mechanical vibrations, life cycles, and economic cycles, they suffer from severe structural information loss and data redundancy. To ensure numerical accuracy, the sampling rate and computational overhead must be significantly increased. Simultaneously, the problem of sequence positioning and synchronization—where "loss of control occurs without an external absolute time base"—remains unresolved. This flaw is particularly prominent in scenarios such as sensor AD front-end sampling, communication signal transmission, and multi-core computer synchronization.

[0003] 2. Underlying limitations of time series analysis systems: Existing time series analysis methods (ARIMA, wavelet transform, LSTM, etc.) are all based on linear numerical statistics and fitting. The core is the probabilistic extrapolation of numerical sequences. They cannot capture the essential cyclic phase transition structure behind the time series, resulting in poor interpretability, weak anti-interference ability, and low prediction accuracy for long periods. Furthermore, they cannot achieve self-synchronization and self-localization of sequences without external benchmarks, and are difficult to adapt to complex nonlinear scenarios such as nested cycles and chaotic transition states.

[0004] 3. Insufficient adaptability to complex nonlinear scenarios: Existing coding schemes can only process ideal periodic signals. When faced with nonlinear time-series data with noise, abrupt changes, and bifurcation points in the real world, they are prone to coding distortion and system instability. They cannot effectively encode and parse nested loops and chaotic transition states. Their adaptability is extremely poor in scenarios such as industrial monitoring with strong noise and communication transmission in complex electromagnetic environments.

[0005] 4. Inherent bottlenecks of formal systems: Existing coding systems are all based on formal systems that include Peano arithmetic, which cannot achieve self-consistency proof within the system. They also have self-reference traps. When faced with complex cyclical scenarios such as chaos and fractals, they are prone to system collapse and logical contradictions, making it difficult to build a stable, scalable, and universal coding system.

[0006] While existing technologies have made some progress in the field of phase coding, such as introducing deep learning into time-series prediction and designing modulation schemes by combining the concept of cyclic codes in radar signals, they have not broken away from the underlying framework of linear coding and cannot fundamentally solve the above-mentioned defects. In the face of emerging technology requirements such as the lack of crystal oscillator synchronization in sensor AD front-ends, self-alignment of communication signals, and asynchronous scheduling of multi-core computers at the underlying level, there are obvious research gaps and technical bottlenecks. Summary of the Invention

[0007] To overcome the existing technical problems, this invention provides a phase encoding method and system based on cyclic phase transition topology.

[0008] The present invention adopts the following technical solution.

[0009] A phase encoding method based on cyclic phase transition topology includes the following steps: S1. Acquire dynamic time series data, and perform adaptive window segmentation based on the trend feature abrupt changes of the dynamic time series data to obtain multiple continuous phase transition segments; S2. Extract the trend direction and evolution rate characteristics of each phase transition segment, generate the corresponding phase state code, and arrange the phase state codes of all phase transition segments into a phase state transition sequence in order. S3. Map and anchor the phase state transition sequence to the topological phase coordinate system of a one-sided closed surface; S4. Extract cyclic phase transition constraint rules based on the phase state transition sequence; S5. Based on the cyclic phase transition constraint rules and dynamic time series data, perform forward evolution to generate the future phase state transition sequence, and obtain the prediction result based on the phase amplitude mapping relationship.

[0010] As a further improvement of the present invention, the specific steps for adaptive window segmentation based on the abrupt changes in trend features of dynamic time-series data include: The slope abrupt change feature is used to segment the line segments in dynamic time series data; The curve segments in the dynamic time series data are divided into six equal-length phase steps as the segmentation unit and the local tangent coordinate system as the reference.

[0011] As a further improvement of the present invention, S1 also includes the step of: If a sudden change point with discontinuous trend characteristics is identified in dynamic time series data and a preset multi-scale nested loop configuration is found, the corresponding sudden change point is marked as a chaotic transition state and the phase encoding method is in multi-order encoding mode; otherwise, the phase encoding method is in single-order encoding mode. If at least three consecutive phase steps fail to match the pre-trained cyclic constraint rules or the system signal-to-noise ratio is lower than a preset threshold, then switch to the traditional linear coding mode. In the traditional linear encoding mode, when the dynamic time series data matches the cyclic constraint rule for three consecutive phase steps, adaptive window segmentation is performed based on the abrupt change in the trend characteristics of the dynamic time series data to obtain multiple continuous phase transition segments.

[0012] As a further improvement of the present invention, the six phase steps correspond to a six-dimensional phase encoding unit. The six-dimensional phase encoding unit includes a three-dimensional position phase unit corresponding to the start point, peak point and end point of the phase transition segment, and a three-dimensional momentum phase unit corresponding to the slope change rate, acceleration and direction change of the phase transition segment. The specific steps of S2 include: if in single-order coding mode, take the local tangent coordinate system of each phase step as the reference, if the trajectory of the current phase step deviates upward relative to the X-axis of the local tangent coordinate system, it is considered a positive feature; otherwise, it is considered a negative feature. Combine the positive features and / or negative features of the six phase steps to obtain the phase state code, and arrange the phase state codes of all phase transition segments into a phase state transition sequence in order. If in a multi-level coding mode, the six-dimensional phase coding unit is expanded into an N-dimensional coding system, N=6·K, where K is the total order obtained by multi-scale nested loop configuration. Each nested loop corresponds to a set of independent six-dimensional phase coding units. Taking the local tangent coordinate system of each phase step as the reference, if the trajectory of the current phase step deviates upward relative to the X-axis of the local tangent coordinate system, it is considered a positive feature; otherwise, it is considered a negative feature. The positive features and / or negative features of the six phase steps are combined to obtain the phase state code. All phase state codes corresponding to the same level are arranged in order to form the phase state transition sequence of the corresponding level.

[0013] As a further improvement of the present invention, the single-sided closed surface topological phase coordinate system is the Möbius topological phase coordinate system corresponding to the Möbius strip; The specific steps of S3 include: if in single-order coding mode, mapping the three-dimensional position phase unit to the two-dimensional plane of the Möbius ring to achieve unique phase position calibration, calculating the phase state of the phase state code in the loop direction and temporal position on the Möbius ring using the three-dimensional momentum phase unit information to complete the loop counting, taking the sampling point as the dynamic origin O, the distance between two dynamic origins O as the corresponding Möbius ring phase difference, and constraining all phase steps within the preset topological boundary of the Möbius ring; If in multi-order coding mode, the phase state transition sequence is sorted from largest to smallest according to the order, and mapped sequentially to a Möbius strip distributed from the outer layer to the inner layer. The three-dimensional position phase unit is mapped to the two-dimensional plane of the Möbius strip to achieve unique phase position calibration. The phase state of the phase state code is calculated from the three-dimensional momentum phase unit information to determine the loop direction and temporal position on the Möbius strip to complete the loop counting. The sampling point dynamic origin O of the corresponding scale level is used, and the distance between the two dynamic origins O is the phase difference of the Möbius strip of the corresponding order.

[0014] As a further improvement of the present invention, S4 also includes step S41: reconstructing the phase state transition sequence and the phase amplitude mapping relationship to obtain reconstructed timing data, and calculating the coding accuracy based on the reconstructed timing data and the dynamic timing data; The specific steps of reconstruction include: providing amplitude base anchor points based on three-dimensional position phase units, recovering the dynamic change process of amplitude based on three-dimensional momentum phase units, and recovering the original data point by point through reverse decoding and topological constraints to obtain reconstructed time series data; Methods for calculating coding accuracy include one or both of the root mean square error and the correlation coefficient.

[0015] As a further improvement of the present invention, each phase status code has a corresponding phase state; In S4, the specific steps for extracting cyclic phase transition constraint rules based on the phase state transition sequence include: A graph-theory-based state transition network and a machine learning-based pattern recognition algorithm are used to construct the state transition network and construct the pattern recognition algorithm. The phase state corresponding to the phase state code is regarded as a node and the state transition of adjacent phase state codes is regarded as an edge. All legal paths of phase state transition and the probability distribution of the corresponding legal paths are extracted. Combined with the preset topological boundary constraints, the cyclic phase transition constraint rules are obtained.

[0016] As a further improvement of the present invention, the specific steps of S5 include: generating a future phase state transition sequence based on the phase state of the current phase state code, and the set of legal paths and probability distributions for phase state transitions in the cyclic phase transition constraint rules; reconstructing the future phase state transition sequence and the phase amplitude mapping relationship to obtain future time series data; generating multiple evolution paths through Monte Carlo simulation and multi-scale fusion strategy and calculating a weighted average based on the probability distribution set; and outputting a prediction result with confidence intervals.

[0017] As a further improvement of the present invention, S5 also includes the step of: if the state transition is not in the set of legal paths for phase state transition in the cyclic phase transition constraint rule, then trigger an abnormal warning.

[0018] This invention also proposes a phase coding system based on cyclic phase transition topology, employing the phase coding method based on cyclic phase transition topology as described above, including: The time series preprocessing module is used to acquire dynamic time series data and perform adaptive window segmentation based on the abrupt changes in the trend characteristics of the dynamic time series data to obtain multiple continuous phase transition segments. Phase encoding module: used to extract the position and momentum features of each phase transition segment, generate the corresponding phase state code, and assemble the phase state codes of all phase transition segments into a phase state transition sequence in sequence; Phase anchoring module: used to map and anchor the phase state transition sequence to the topological phase coordinate system of a one-sided closed surface through geometric algebra and topological homeomorphism transformation algorithms; Self-consistency verification and rule extraction module: used to reconstruct the time series data based on the phase state transition sequence and the phase amplitude mapping relationship, calculate the coding accuracy based on the reconstructed time series data and dynamic time series data, and extract cyclic phase transition constraint rules based on the phase state transition sequence. Cyclic Evolution Prediction Module: This module is used to perform forward evolution based on cyclic phase transition constraint rules and dynamic time series data, generate future phase state transition sequences, and obtain prediction results based on phase amplitude mapping relationships.

[0019] The beneficial effects of this invention are as follows: 1. A disruptive breakthrough in underlying logic, constructing a universal coding system: A brand-new coding system based on cyclic phase transition topology has been established, with structural features as the core of coding, fundamentally solving the inherent defects of linear coding such as structural loss, data redundancy, and dependence on external benchmarks; This universal coding system, as a universal coding framework parallel to linear coding, can cover all application areas of linear coding, such as sensor AD front-end, communication, and computer underlying layer, realizing the underlying reconstruction of the coding system.

[0020] 2. Perfect unity of mathematical rigor and self-consistency: It deeply integrates cyclic phase transitions with dynamical systems, topology, Hamiltonian phase space theory, and Lie group representation theory. Combined with core theories such as local tangent coordinate systems and topological boundaries, it constructs a self-consistent system that does not rely on Peano arithmetic. Utilizing the property that the Euler characteristic of the Möbius ring is 0, the system can achieve self-stability and self-expansion, and has solid mathematical theoretical support.

[0021] 3. The scientific nature of minimal complete coding, balancing accuracy and efficiency: Minimal complete coding of cyclic phase transition events is achieved through a six-dimensional phase coding unit. Dimensions below six lead to phase aliasing, failing to fully describe the position and momentum characteristics of the cyclic system; dimensions above six introduce redundant degrees of freedom, triggering the curse of dimensionality and leading to chaotic and uncontrollable systems. Six dimensions represent the minimum descriptive length for complex cyclic systems, corresponding to six equal-length phase steps, representing the unique balance between mathematical necessity and engineering optimality, achieving effective control over information entropy minimization and coding redundancy.

[0022] 4. Significant engineering and technical benefits, high coding efficiency and strong anti-interference ability: Actual tests have verified that, under the same signal-to-noise ratio, the coding efficiency of this invention is about 40% higher than that of traditional binary numerical coding, and the required storage space can be reduced by more than 75%. In industrial vibration signal processing, the data compression rate can be increased to more than twice that of traditional methods. At the same time, it has extremely strong anti-noise and anti-interference capabilities. Even in a strong noise environment with a signal-to-noise ratio of 20dB, it can still maintain more than 95% structural reconstruction overlap, which is far superior to traditional methods. It can be adapted to harsh application scenarios such as strong noise and complex electromagnetic environments.

[0023] 5. Universal cross-domain adaptability covering core needs across multiple fields: This invention does not rely on specific scenarios, fixed sampling rates, or external time bases. The structural semantics of the cyclic phase have cross-scenario uniformity, perfectly adapting to all cyclic dynamic scenarios from industrial predictive maintenance, low-power IoT, meteorological cycle analysis, economic cycle forecasting to sensor AD front-end sampling, communication signal transmission, and computer underlying architecture optimization. It can realize practical engineering needs such as sensor sampling without a reference, crystal oscillator replacement, communication signal self-alignment, and asynchronous synchronization of computer multi-core processors, demonstrating significant cross-domain adaptability and practicality.

[0024] 6. Modular system design, easy to implement and scalable: The system adopts a modular architecture design, with each functional module being independent and efficiently coupled. It can be implemented in software and integrated in hardware, adapting to the deployment requirements of different application scenarios. The six-dimensional phase encoding unit can be expanded into an N-dimensional multi-level encoding system. The system supports online updates and dynamic expansion, and can optimize model parameters and constraint rules according to new scenarios and new data, possessing good scalability and engineering feasibility. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the steps of the present invention.

[0027] Figure 2 These are comparison diagrams showing the effects of the motor bearing in Embodiment 1 of the present invention; Figure 3 This is a module architecture diagram of the phase encoding system of the present invention; Figure 4 This is a schematic diagram of the local tangent coordinate system and phase step structure of the six-dimensional phase encoding unit of the present invention. Detailed Implementation

[0028] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. To better illustrate this embodiment, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions of the product.

[0029] It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings. The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0030] To facilitate understanding of the technical solution of this invention, some of the terminology used in this invention will be explained: 1. Cyclic Phase Transition: Assume a dynamic system<X,T> Where X is an n-dimensional state space, and T is a state space satisfying the semigroup property T(t+s)=T(t). An evolution operator for T(s) (t, s ≥ 0); if there exists a non-empty closed subset A Let X be a region of attraction of a closed orbital O(x) = {T(t)x|t≥0} such that for any x∈A, the closure of the orbital O(x) = {T(t)x|t≥0} contains a closed orbital with a minimum period of t0 (i.e., there exists t0>0 such that T(t0)x = x), and A is the region of attraction of this closed orbital (the ω-limit set ω(x) for any x∈A). If the system has a closed orbit, then it is said that the system has undergone a cyclic phase transition on A.

[0031] 2. Six-dimensional phase coding unit (the smallest complete and optimal unit of this invention): This is the smallest complete and optimal unit for describing cyclic phase transition events. The first three bits are position phase units, used to anchor the phase position of the event within the cyclic phase transition cycle (corresponding to 3D position coordinates in Hamiltonian phase space); the last three bits are momentum phase units, used to anchor the evolution trend and rate of the event (corresponding to 3D momentum coordinates in Hamiltonian phase space). Its completeness can be proven by Lie group representation theory, and its optimality is reflected in the minimization of information entropy and effective control of coding redundancy. Specifically, the six-dimensional phase coding unit corresponds to six equal-length phase steps. Taking the local tangent of the curve as the dynamic reference, the deviation direction of each step relative to the tangent (upward deviation corresponds to positive features, downward deviation corresponds to negative features; positive features can also be called yang features, and negative features can also be called yin features, used to characterize the deviation direction of the phase step relative to the tangent) constitutes the core feature of the momentum phase unit (note that the momentum phase unit is not the phase state code; the phase state code is obtained by the deviation direction of each of the six phase steps relative to the tangent). The six steps combine to form 2 2 2 2 2 With 2 = 64 uniquely corresponding structural forms, this achieves non-aliasing and non-redundant structural encoding. This six-dimensional phase encoding unit solves the technical problems of low-dimensional phase aliasing and high-dimensional dimensionality curse in existing technologies, realizes minimal complete encoding of cyclic events, and significantly reduces sampling computing power overhead and data redundancy. Furthermore, this invention provides a dimension adaptability demonstration for six dimensions, clarifying the insufficient coverage problem of a 5-phase step size (below 6 dimensions) and the redundancy problem of an 8-phase step size (above 6 dimensions), thereby strengthening the uniqueness and optimality of six dimensions: (1) 5-phase step size (less than 6 dimensions): Insufficient coverage, unable to achieve complete encoding of cyclic phase transitions. The complete evolution process of cyclic phase transitions includes 6 core phases: initiation, initial rise, pre-peak, peak, decline, and regression. These correspond to the dual feature requirements of 3D position + 3D momentum in Hamiltonian phase space. A 5-phase step size can only divide 5 equal-length phase intervals, which cannot fully cover the 6 core phases and cannot simultaneously take into account the 3D feature characterization of position and momentum. This inevitably leads to phase aliasing—that is, structural features of different cyclic stages are misjudged as the same phase state, resulting in encoding distortion. It is impossible to construct a stable cyclic attractor structure and cannot achieve accurate description and reconstruction of cyclic events. For example, in industrial vibration monitoring scenarios, a 5-phase step size cannot distinguish between the two key phases of "peak" and "decline," resulting in the inability to capture abnormal trends of equipment in a timely manner and losing the core practical value of encoding.

[0032] (2) 8-bit phase step (higher than 6 dimensions): Redundancy exists, triggering the curse of dimensionality and causing system chaos. Encoding units with more than 6 dimensions will introduce redundant degrees of freedom. On the one hand, for every additional phase step, the computational complexity of the encoding will increase exponentially (i.e., the curse of dimensionality), resulting in a significant increase in computing power and making it unsuitable for low-power, high-real-time engineering scenarios such as sensor AD front-ends and communication chips. On the other hand, in physical hardware implementation (such as relaxor oscillator arrays and ring registers), the extra 2-dimensional phase step will introduce unavoidable circuit coupling noise, destroying the constraints of the topological boundary of this invention (fixed slope ratio X / Y=6, the value here is the nominal value, and the actual value is the adaptive dynamic range), causing the phase step to deviate from the range out of control, triggering system chaos—that is, disordered phase state transitions, inability to achieve self-synchronization and self-positioning, and complete loss of encoding stability and reliability. Meanwhile, the information entropy of an 8-bit phase step is much higher than that of a 6-dimensional one, introducing a large amount of redundant information and increasing data storage overhead, which contradicts the engineering requirements of "low redundancy and high efficiency". Moreover, the extra 2 dimensions cannot improve the structural fidelity of the encoding and are therefore invalid redundancy with no practical engineering value.

[0033] In summary, the six-dimensional phase coding unit represents the only balance between mathematical necessity and engineering optimality: dimensions below six cannot achieve complete coding and phase aliasing occurs; dimensions above six trigger dimensionality disasters and system chaos, introducing ineffective redundancy. Only six dimensions can achieve the dual goals of "minimum completeness + optimal efficiency," perfectly adapting to the structural characteristics of cyclic phase transitions and the requirements for engineering implementation.

[0034] 3. N-Dimensional Multi-Level Phase Coding System (Multi-Level Coding Mode): For complex dynamic events containing nested cycles, a six-dimensional phase coding unit can be extended to an N-dimensional coding system, where N = 6 × K, and K represents the number of nested cycle levels (in meteorological forecasting, the number of levels can be daily, monthly, and annual cycles). Each nested cycle corresponds to a set of independent six-dimensional phase coding units. Coding units at different levels are coupled through hierarchical association rules, allowing for flexible adaptation to multi-scale cycle scenarios. This coding system solves the problem of independent processing capabilities for multi-layered nesting under complex dynamics.

[0035] 4. Phase State Transition Sequence: A sequence composed of multiple six-dimensional phase coding units (or N-dimensional multi-level coding units) arranged in phase order, corresponding to the complete evolution process of cyclic phase transition events. It is the core data carrier for realizing time series reconstruction, rule extraction, and trend prediction. This phase state transition solves the problem of sequentially recorded coding states, ensuring the integrity of structured information.

[0036] 5. Möbius Phase Anchoring: A Möbius single-sided closed surface topology with an Euler characteristic of 0 is used as the phase carrier for cyclic phase transitions. The phase state transition sequence is mapped onto the Möbius ring, binding a unique phase position and loop count to the sequence, achieving phase self-synchronization and self-positioning without external reference. The embedding dimension of the Möbius ring is 3, naturally corresponding to the six-dimensional phase encoding unit. Its single-sided characteristic ensures continuous phase connection between the beginning and end of the sequence, avoiding periodic boundary problems. Specifically, the mapping process uses sampling points on the curve as the dynamic origin O. The distance between two O points corresponds to the phase difference on the Möbius ring, used to distinguish cyclic segments of different nesting levels. This anchoring method solves the core implementation of self-synchronization.

[0037] 6. Cyclic Phase Transition Constraint Rules: These are the sets of legal phase state transition paths extracted from the phase state transition sequence. They correspond to the topological invariants and evolutionary constraints of closed orbits in the dynamical system. These rules can be extracted using graph theory modeling and machine learning algorithms, revealing the essential evolutionary laws of cyclic phase transitions. The constraint rules also include topological boundary constraints (see reference...). Figure 4 The two symmetrical arcs in the tangent coordinate system are the topological boundary constraints. This ensures that the deviation changes of all phase steps are limited to a fixed slope ratio (e.g., X / Y=6, where the value is nominal but the actual adaptive dynamic range), preventing trend overflow and divergence. This rule solves the problem of unknown boundaries and allows for the setting of specific rules to make the boundaries interpretable.

[0038] 7. Singularity (Bifurcation Point): A point in dynamic time-series data where trend characteristics are discontinuously abruptly changed. Corresponding to a bifurcation point in a cyclic trajectory within a dynamic system, it serves as a transition node between nested cycles at different scales and can trigger multi-stage phase encoding mechanisms and chaotic transition state marking. The system can automatically switch back to the traditional linear encoding mode through a fallback mechanism until the cyclic structure is restored. This approach solves the identification rules and methods for abrupt changes and achieves compatible reconstruction through a fallback mechanism. The triggering condition for automatically switching to the traditional linear encoding mode is: three or more consecutive phase steps fail to match the cyclic phase transition constraint rules (mainly topological boundary constraints in the constraint rules), or the system signal-to-noise ratio is lower than a preset threshold. When the system re-identifies a stable cyclic structure and three consecutive phase steps match the constraint rules, it automatically switches back to the phase encoding mode of this invention.

[0039] 8. Local tangent coordinate system: (refer to) Figure 4 A dynamic local coordinate system is established with any sampling point O on the curve as the origin, the X-axis coinciding with the tangent direction of the curve at that point, and the Y-axis perpendicular to the X-axis (tangent direction). This coordinate system is independent of the global absolute coordinates and time, and is only used to determine the deviation direction of each phase step relative to the tangent of the curve, providing a reference for phase encoding and phase anchoring. This coordinate system solves the problem of structured calculation anchor points for real-time processing of trend patterns. 9. Topological Boundary: A trend constraint range determined by a fixed slope ratio (example: X / Y=6, where the value is nominal but the actual adaptive dynamic range). Based on the X-axis (tangent direction) of the local tangent coordinate system, two symmetrical boundary lines are formed (see reference). Figure 4 All deviations at sampling points and phase steps are contained within this boundary to ensure the stability of phase encoding and fitting, and to filter out abnormal deviations caused by noise. The slope ratio of the topological boundary can be adaptively and dynamically adjusted according to the system signal-to-noise ratio or sampling accuracy. A fixed slope ratio X / Y=6 (this value is a nominal value, but the actual value is the adaptive dynamic range) corresponds to the number of step sizes in the six-dimensional phase encoding unit, ensuring that all deviations at the six phase steps are constrained within the boundary. This slope ratio can be adaptively adjusted according to the system signal-to-noise ratio. The lower the signal-to-noise ratio, the larger the slope ratio should be to improve anti-interference capability; the higher the signal-to-noise ratio, the smaller the slope ratio should be to improve coding accuracy through parameterization.

[0040] The technical solution of this invention relates to the fields of data encoding, time-series signal processing, dynamic system topology analysis, intelligent prediction and information processing. The core technology of this invention can be further extended to phase sampling encoding of sensor AD front-end, crystal-free distributed cyclic synchronization, phase self-alignment and encoding of communication signals, cyclic phase encoding of computer bottom layer and multi-core asynchronous self-synchronization, etc. It provides a general solution that is free from linear time reference for various fields that rely on the synchronization and encoding of cyclic / periodic dynamic events, and can be widely adapted to the technical needs of multiple scenarios such as industry, communication, Internet of Things, and computer hardware.

[0041] The core concept of this invention originates from the cyclic phase sampling requirements of sensor AD front-ends and the distributed synchronization requirements to replace crystal oscillators. Based on this core concept, it can be naturally extended to fields such as communication signal alignment and computer underlying synchronization. A rigorous mathematical support system has been established, with high-fidelity, low-redundancy, and strong anti-interference capabilities. It can be widely adapted to all cyclic dynamic events such as industrial vibration monitoring, meteorological cycle analysis, economic cycle forecasting, sensor AD front-end design, communication signal processing, and computer underlying architecture optimization, providing a universal coding solution parallel to linear coding systems for related fields.

[0042] Furthermore, this invention defines "no crystal oscillator," "no crystal oscillator synchronization," and "no external reference" as follows: These refer to clock distribution modes that do not rely on traditional quartz crystal oscillators as a globally unified time reference and do not employ a single crystal oscillator central timing mode, rather than prohibiting the use of any oscillating elements or resonant units. The timing and phase synchronization of this invention are autonomously generated by a cyclic phase-change topology, Möbius phase anchoring, and a multi-unit coupling self-synchronization mechanism. It belongs to a topology-driven system with self-synchronization, self-positioning, and self-reference, which differs from the principle of traditional crystal oscillator clock systems. Including but not limited to: RC relaxor oscillators, 555 timers, operational amplifiers, comparators, ceramic resonators, MEMS resonators, and quartz crystal resonators (including quartz crystal oscillators) are all equivalent implementations of this patent and fall within the scope of protection of this patent.

[0043] Reference Figures 1 to 4 A phase encoding method based on cyclic phase transition topology includes the following steps: S1. Acquire dynamic time series data, and perform adaptive window segmentation based on the trend feature abrupt changes of the dynamic time series data to obtain multiple continuous phase transition segments; When acquiring dynamic time-series data, the data is filtered and denoised. Since preprocessing techniques such as filtering and denoising are common, they will not be elaborated upon further in this invention. The sampling frequency of the dynamic time-series data can be dynamically adjusted according to the application scenario to avoid oversampling redundancy or undersampling information loss.

[0044] Reference Figure 4 As a further improvement of the present invention, the specific steps for adaptive window segmentation based on the abrupt changes in trend features of dynamic time-series data include: The slope abrupt change feature is used to segment the line segments in dynamic time series data; The curve segments in the dynamic time-series data are divided into six equal-length phase steps as the unit of segmentation, based on the local tangent coordinate system. This ensures that the segmentation accurately captures the local structural features of the curve, avoiding the loss of structural information or coarse segmentation.

[0045] It should be further noted that abrupt changes in trend characteristics can be changes in slope, variance, or mean, as described above. Figure 4 This refers to the segmentation of the curve segment. The figure shows two sampling points, O and O1, and their corresponding local tangent coordinate systems. The radius of the circle in the figure is the phase step.

[0046] Each phase transition segment corresponds to a sub-evolution process within the cyclic phase transition cycle. Adaptive window segmentation does not require a fixed sampling rate or a preset window length; it is triggered only by the trend reversal of the cyclic phase transition.

[0047] As a further improvement of the present invention, S1 also includes the step of: If a sudden change point with discontinuous trend characteristics is identified in dynamic time series data and a preset multi-scale nested loop configuration is found, the corresponding sudden change point is marked as a chaotic transition state and the phase encoding method is in multi-order encoding mode; otherwise, the phase encoding method is in single-order encoding mode. If at least three consecutive phase steps fail to match the pre-trained cyclic constraint rules or the system signal-to-noise ratio is lower than a preset threshold, then switch to the traditional linear coding mode. In the traditional linear encoding mode, when the dynamic time series data matches the cyclic constraint rule for three consecutive phase steps, adaptive window segmentation is performed based on the abrupt change in the trend characteristics of the dynamic time series data to obtain multiple continuous phase transition segments.

[0048] When abrupt changes indicating discontinuities in trend characteristics are detected—that is, singularities or bifurcation points—a multi-stage phase encoding mechanism is triggered. The chaotic transition state corresponds to a bifurcation point in the cyclic trajectory of a dynamic system, serving as a transition node in nested cycles at different scales. For meteorological time-series data, the multi-scale nested cycle configuration (nested cycles at different scales) includes a three-level nested cycle structure: year, month, and day. Specifically, the determination of abrupt changes can involve exceeding topological boundaries; refer to [reference needed]. Figure 4 The two symmetrical arcs in the tangent coordinate system are the topological boundary constraints.

[0049] S2. Extract the trend direction and evolution rate characteristics of each phase transition segment, generate the corresponding phase state code, and arrange the phase state codes of all phase transition segments into a phase state transition sequence in order. As a further improvement of the present invention, the six phase steps correspond to a six-dimensional phase encoding unit. The six-dimensional phase encoding unit includes a three-dimensional position phase unit corresponding to the start point, peak point and end point of the phase transition segment, and a three-dimensional momentum phase unit corresponding to the slope change rate, acceleration and direction change of the phase transition segment. The specific steps of S2 include: if in single-order coding mode, take the local tangent coordinate system of each phase step as the reference, if the trajectory of the current phase step deviates upward relative to the X-axis of the local tangent coordinate system, it is considered a positive feature; otherwise, it is considered a negative feature. Combine the positive features and / or negative features of the six phase steps to obtain the phase state code, and arrange the phase state codes of all phase transition segments into a phase state transition sequence in order. If in a multi-level coding mode, the six-dimensional phase coding unit is expanded into an N-dimensional coding system, N=6·K, where K is the total order obtained by multi-scale nested loop configuration. Each nested loop corresponds to a set of independent six-dimensional phase coding units. Taking the local tangent coordinate system of each phase step as the reference, if the trajectory of the current phase step deviates upward relative to the X-axis of the local tangent coordinate system, it is considered a positive feature; otherwise, it is considered a negative feature. The positive features and / or negative features of the six phase steps are combined to obtain the phase state code. All phase state codes corresponding to the same level are arranged in order to form the phase state transition sequence of the corresponding level.

[0050] The reason for encoding based on six-dimensional phase coding units is that the three-dimensional position phase unit is used to anchor the relative position of the phase transition segment within the cyclic phase transition cycle (corresponding to the six core phases of initiation, initial rise, pre-peak, peak, decline, and regression). A three-dimensional position coordinate system is constructed through the initiation point, peak point, and end point of the phase transition segment. The three-dimensional momentum phase unit anchors the evolution trend and rate of the phase transition segment. A three-dimensional momentum coordinate system is constructed through the slope change rate, acceleration, and direction change, realizing the holographic expression of the position and momentum dual features of the cyclic phase transition.

[0051] A six-dimensional phase coding unit corresponds to six equal-length phase steps. Each step's upward deviation from the tangent corresponds to a positive feature, and its downward deviation corresponds to a negative feature. The combination of these six features generates a unique six-dimensional phase status code. An example phase status code could be 111000, 2... 2 2 2 2 2 = 64, corresponding to 64 unique structural forms.

[0052] The semantics of the phase state code are endogenous to the cyclic phase transition structure: positive symbols correspond to the rising phase of the cycle, negative symbols correspond to the falling phase of the cycle, and phase state transitions correspond to the turning points of the cyclic phase transitions, without the need for an external dictionary to bind the semantics; without cyclic phase transition constraint rules, all phase state transition possibilities are in a superposition state; after the cyclic phase transition constraint rules take effect, the phase state transition possibilities collapse into legal paths and illegal paths; the self-consistency of the system is reflected in the self-consistency of phase changes, without the need to prove its consistency within the system, and a self-consistent system in an engineering sense is constructed under topological constraints.

[0053] For complex events involving nested loops, the six-dimensional phase coding unit is extended to an N-dimensional multi-level phase coding system (N=6×K) to encode nested loops at different scales in six dimensions. The large-scale loop coding unit focuses on long-term trends and macro structure, while the small-scale loop coding unit focuses on short-term fluctuations and detailed features. The robustness and adaptability of the coding are improved through information interaction between levels.

[0054] S3. Map and anchor the phase state transition sequence to the topological phase coordinate system of a one-sided closed surface; As a further improvement of the present invention, the single-sided closed surface topological phase coordinate system is the Möbius topological phase coordinate system corresponding to the Möbius strip; The specific steps of S3 include: if in single-order coding mode, mapping the three-dimensional position phase unit to the two-dimensional plane of the Möbius ring to achieve unique phase position calibration, calculating the phase state of the phase state code in the loop direction and temporal position on the Möbius ring using the three-dimensional momentum phase unit information to complete the loop counting, taking the sampling point as the dynamic origin O, the distance between two dynamic origins O as the corresponding Möbius ring phase difference, and constraining all phase steps within the preset topological boundary of the Möbius ring; If in multi-order coding mode, the phase state transition sequence is sorted from largest to smallest according to the order, and mapped sequentially to a Möbius strip distributed from the outer layer to the inner layer. The three-dimensional position phase unit is mapped to the two-dimensional plane of the Möbius strip to achieve unique phase position calibration. The phase state of the phase state code is calculated from the three-dimensional momentum phase unit information to determine the loop direction and temporal position on the Möbius strip to complete the loop counting. The sampling point dynamic origin O of the corresponding scale level is used, and the distance between the two dynamic origins O is the phase difference of the Möbius strip of the corresponding order.

[0055] By employing geometric algebra and topological homeomorphism transformation algorithms, the phase state transition sequence is mapped and anchored to a one-sided closed surface topological phase coordinate system, preferably a Möbius strip topology. This achieves precise mapping and positioning of the phase state transition sequence, binding a unique phase position and loop count to the sequence. The Möbius strip topological phase coordinate system has an Euler characteristic of 0 and an embedding dimension of 3, forming a natural correspondence with the six-dimensional phase encoding unit. The loop count of the Möbius strip is a phase marker of the cycle depth, rather than a nonlinear counter. Re-matching of broken sequences and calibration of cycle depth can be achieved through phase position, eliminating overflow and loss problems. In hardware implementation, the Möbius strip topological phase coordinate system includes, but is not limited to, physical hardware circuit mapping and software logic algorithm mapping. It can be concretized as a delay line circuit with anti-phase coupling at both ends or the odd-bit flip logic of a ring register. Through the one-sided characteristic of this topology, continuous connection of the first and last phases of the sequence is achieved, completing phase self-synchronization and self-positioning without the need for an external absolute time reference. Furthermore, when a local perturbation occurs in the phase state transition sequence, the topological properties of the Möbius strip can automatically adjust the phase position and the loop count to ensure global consistency of the sequence.

[0056] Additional details regarding the mapping and anchoring: Using the sampling point as the dynamic origin O, six equal-length phase steps are distributed along the Möbius strip surface. All phase steps are constrained within the topological boundary (example: fixed slope ratio X / Y=6, where the value is nominal but actually the adaptive dynamic range). The spacing between two O points corresponds to the phase difference on the Möbius strip, used to distinguish different nested levels of loop segments, achieving accurate anchoring and self-synchronization of multi-scale loops.

[0057] For abrupt change points (singular points) marked as chaotic transition states, the system is automatically classified into new phases of the corresponding scale cycle through constraint rule matching of multi-order nested loops, thereby realizing the dynamic expansion of the system.

[0058] S4. Extract cyclic phase transition constraint rules based on the phase state transition sequence; Reference Figure 2 As a further improvement of the present invention, S4 also includes step S41: reconstructing the phase state transition sequence and the phase amplitude mapping relationship to obtain reconstructed timing data, and calculating the coding accuracy based on the reconstructed timing data and the dynamic timing data; The specific steps of reconstruction include: providing amplitude base anchor points based on three-dimensional position phase units, recovering the dynamic change process of amplitude based on three-dimensional momentum phase units, and recovering the original data point by point through reverse decoding and topological constraints to obtain reconstructed time series data; Methods for calculating coding accuracy include one or both of the root mean square error and the correlation coefficient.

[0059] The core objective of reconstruction is structural fidelity, i.e., the consistency of the trend direction between the fitted curve and the original curve, rather than the precise numerical replication of the original curve function. Since reconstruction based on six-dimensional phase coding units is a conventional technique, it will not be elaborated upon further in this invention.

[0060] As a further improvement of the present invention, each phase status code has a corresponding phase state; In S4, the specific steps for extracting cyclic phase transition constraint rules based on the phase state transition sequence include: A graph-theory-based state transition network and a machine learning-based pattern recognition algorithm are used to construct the state transition network and construct the pattern recognition algorithm. The phase state corresponding to the phase state code is regarded as a node and the state transition of adjacent phase state codes is regarded as an edge. All legal paths of phase state transition and the probability distribution of the corresponding legal paths are extracted. Combined with the preset topological boundary constraints, the cyclic phase transition constraint rules are obtained.

[0061] Cyclic phase transition constraint rules provide a theoretical basis for cyclic evolution extrapolation. These rules also include topological boundary constraints, ensuring that the phase steps in subsequent evolution extrapolation do not exceed the fixed slope ratio range. It is important to note that the legal path for phase state transitions here is analogous to the normal state transition path of equipment, environment, and economic laws under non-sudden circumstances, thus enabling subsequent extrapolation to proceed along legal paths.

[0062] Phase state transitions correspond to the turning points of cyclic phase transitions, without the need for external dictionary binding semantics; without cyclic phase transition constraint rules, all phase state transition possibilities are in a superposition state; after the cyclic phase transition constraint rules take effect, the phase state transition possibilities collapse into legal and illegal paths; the self-consistency of the system is reflected in the self-consistency of phase changes, without the need to prove its consistency within the system, and a self-consistent system in an engineering sense is constructed under topological constraints.

[0063] S5. Based on the cyclic phase transition constraint rules and dynamic time series data, perform forward evolution to generate the future phase state transition sequence, and obtain the prediction result based on the phase amplitude mapping relationship.

[0064] As a further improvement of the present invention, the specific steps of S5 include: generating a future phase state transition sequence based on the phase state of the current phase state code, and the set of legal paths and probability distributions for phase state transitions in the cyclic phase transition constraint rules; reconstructing the future phase state transition sequence and the phase amplitude mapping relationship to obtain future time series data; generating multiple evolution paths through Monte Carlo simulation and multi-scale fusion strategy and calculating a weighted average based on the probability distribution set; and outputting a prediction result with confidence intervals.

[0065] Based on the Markov chain state transition model, the extrapolation core relies on the topological evolution of cyclic phase transition structures rather than numerical statistical fitting. It supports an online update mechanism, dynamically adjusting model parameters based on new observation data to adapt to complex time-varying environments. Simultaneously, an uncertainty quantification mechanism is introduced to assess the reliability of prediction results, providing a scientific basis for decision-making. It should be noted that the multi-scale fusion strategy is used for multi-order coding patterns.

[0066] As a further improvement of the present invention, S5 also includes the step of: if the state transition is not in the set of legal paths for phase state transition in the cyclic phase transition constraint rule, then trigger an abnormal warning.

[0067] For ease of understanding, the present invention provides two embodiments: Example 1 (Single-order coding mode): Industrial Vibration Time Series Analysis and Anomaly Early Warning System Based on the Method of this Invention (Single-Order Encoding Mode): This embodiment illustrates a typical software application scenario of the method of the present invention, used for encoding, reconstructing, and anomaly warning of motor bearing vibration timing, verifying the application effect of the present invention in the field of industrial predictive maintenance. The specific implementation steps are as follows: 1. Data Acquisition: Deploy high-precision accelerometers to collect time-series data of motor bearing vibration, obtain 90 points of normalized time-series data, and sample at a frequency of 1kHz; perform preliminary denoising processing on the dynamic time-series data to filter high-frequency noise interference and ensure that the signal quality meets the encoding requirements.

[0068] 2. Adaptive Window Segmentation: Based on the slope abrupt change characteristics and curve structure characteristics of dynamic time series data, the slope abrupt change segmentation of the broken line segment of the vibration curve is adopted through sliding window analysis and dynamic threshold adjustment algorithm. For the smooth curve segment, 6 equal-length phase steps are used as the natural segmentation unit. The 90-point time series data is divided into 21 continuous phase transition segments. Each segment corresponds to a cyclic phase transition subprocess. There is no fixed window length, which perfectly matches the trend turning point and structural characteristics of the time series, effectively reducing data complexity and redundancy.

[0069] 3.6D Phase Encoding: For each phase transition segment, the trend direction and evolution rate features are extracted based on the local tangent coordinate system. Six equal-length phase steps correspond to a 6D encoding unit. The upward deviation from the tangent at each step is recorded as a positive feature and the downward deviation as a negative feature. A position phase coordinate system is constructed through the starting point / peak point / end point. A momentum phase coordinate system is constructed through the slope change rate / acceleration / direction change (upward deviation corresponds to positive features and downward deviation corresponds to negative features). The three-dimensional position phase unit and the three-dimensional momentum phase unit are combined to obtain a six-dimensional phase encoding unit. For example, for a phase transition segment of "uniform ascent - plateau - uniform descent", phase state code 110000 can be generated; for a phase transition segment of "accelerated ascent - decelerated ascent - turning descent", phase state code 111000 can be generated. These are different phase states. When the two segments appear consecutively in the time sequence, a phase state transition process of 110000→111000 is formed, clearly reflecting the state transition relationship. This process is the legal path for phase state transition. This generates multiple one-to-one corresponding 6-bit phase state codes. The 21 segments form a complete phase state transition sequence, achieving minimal complete encoding of the vibration signal.

[0070] 4. Möbius Phase Anchoring: The phase state transition sequence is mapped to the Möbius topological phase coordinate system. The sampling point on the curve is taken as the dynamic origin O. The distance between two O points corresponds to the phase difference on the loop. The optimal phase alignment parameter is calculated to be 6.4577 through geometric algebra and topological homeomorphism transformation algorithm. All phase steps are constrained within the topological boundary of a fixed slope ratio (example: X / Y=6, where the value is nominal and the actual value is the adaptive dynamic range). The phase position binding and loop counting of the sequence are completed, realizing phase self-synchronization and self-positioning, and determining that the current sequence closed loop state is not closed.

[0071] 5. Sequence Reconstruction and Rule Extraction: Based on the anchored phase state transition sequence, the original time series is reconstructed through the phase-amplitude mapping relationship. The reconstructed time series data (refer to...) Figure 2 The reconstructed sequence (with structural fidelity as its core objective) achieves a structural overlap of over 99% with the dynamic time-series data (original sequence), as verified by RMSE and R... 2 Verify the high fidelity of the encoding; at the same time, adopt graph theory modeling method to extract the cyclic phase transition constraint rules of bearing vibration from the sequence, that is, the set of legal paths for phase state transition under normal working conditions, including topological boundary constraints.

[0072] 6. Verification of Technical Effectiveness: The actual test used 16-bit PCM pulse code modulation, commonly used in the industrial field, as the benchmark. The test object was the vibration periodic signal of a motor bearing at 1500 rpm (period T = 40 ms), and the test environment had a signal-to-noise ratio of 20 dB. Traditional PCM encoding requires at least 2T sampling points (80 sampling points) to completely reconstruct the waveform structure. This invention only requires T / 2 phase status codes (20 six-dimensional phase coding units) to achieve lossless reconstruction of the cyclic structure. Therefore, the storage space is reduced by (80-20) / 80 = 75%, and the encoding efficiency is improved by more than 40% compared with traditional PCM encoding. Under a signal-to-noise ratio of 20 dB, the structural overlap between the reconstructed time-series data (reconstructed sequence) and the dynamic time-series data (original sequence) of this solution is maintained at more than 95%, while the structural overlap of traditional PCM encoding is only 72% under the same signal-to-noise ratio.

[0073] 7. Trend Extrapolation and Anomaly Warning: Based on the extracted constraint rules, the time series trend prediction results for the next 30 points are extrapolated through Monte Carlo simulation and multi-scale fusion strategy. At the same time, the phase state of the input dynamic time series data is monitored in real time. When the path of phase state transition exceeds the set of legal paths or the phase step breaks through the topological boundary, an anomaly warning is triggered immediately with a response delay of <10ms, which significantly improves the predictive maintenance capability of industrial equipment.

[0074] It should be noted that the technical solution of the present invention has a training stage and an application stage. The example of the present invention is the application stage. The technical solution covers the contents of both the training stage and the application stage. For example, the generation of the set of legal paths for phase state transition is in the training stage; the immediate triggering of anomaly warning when the phase step breaks through the topological boundary is in the application stage.

[0075] Example 2 (Multi-level coding mode): Meteorological nested cyclic time-series coding and trend prediction based on the method of this invention (multi-level coding mode): This embodiment is used to verify the adaptability of the present invention to complex nested cycle scenarios. It takes meteorological time-series data containing nested annual, monthly, and daily cycles as the processing object. The specific implementation steps are as follows: 1. Data Acquisition: Acquire meteorological time-series data (including indicators such as temperature, precipitation, and air pressure) collected by satellite remote sensing and ground observation stations. The data includes a three-level nested cyclic structure of year, month, and day. Filter and denoise the dynamic time-series data, dynamically adjust the sampling frequency, and adapt to the multi-scale cyclic time characteristics.

[0076] 2. Multi-level adaptive window segmentation: Based on the multi-scale trend turning characteristics of time series, hierarchical adaptive window segmentation is performed. Seasonal changes are used as the basis for annual cycle segmentation, significant fluctuations in temperature / precipitation are used as the basis for monthly cycle segmentation, and diurnal temperature difference is used as the basis for daily cycle segmentation. The smooth curve segments at each scale are segmented with 6 equal-length phase steps, decomposing the time series data into large loop segments and nested small loop segments, accurately capturing the start and end positions of each level of loop, and avoiding the loss of structural information.

[0077] 3. Multi-level phase encoding: Based on the 6-dimensional basic unit, an N=18-dimensional encoding system is extended (K=3, corresponding to three levels of nesting: year, month, and day). The large-cycle segment and the small-cycle segment are respectively encoded in 6-dimensional phase. Each 6-dimensional unit corresponds to 6 equal-length phase steps. The deviation direction is determined based on the local tangent coordinate system (upward deviation corresponds to positive features, and downward deviation corresponds to negative features), generating a multi-level phase state transition sequence, corresponding to the topological structure of the nested cycle. The three sets of 6-dimensional encoding units correspond to the phase description of the daily cycle, monthly cycle, and annual cycle, respectively, realizing the dual feature encoding of position and momentum of the multi-scale cycle.

[0078] 4. Multi-scale phase anchoring: Through the multi-layer nested topology of the Möbius strip, phase synchronization and anchoring of multi-scale cycles are achieved. The annual cycle sequence is mapped to the outer layer of the Möbius strip, the monthly cycle to the middle layer, and the daily cycle to the inner layer. The sampling point of each scale cycle is used as the dynamic origin O, and the distance between two O points is the phase difference of the corresponding level. Each scale sequence is bound to a unique phase position and loop count. Phase alignment of multiple cycles of year, month, and day can be completed without an external time reference. All phase steps are constrained by the topological boundary.

[0079] Multi-scale rule extraction and prediction: Using machine learning pattern recognition algorithms, cyclic phase transition constraint rules at each scale are extracted from multi-stage phase state transition sequences to complete time series reconstruction and multi-scale trend prediction. The reconstructed sequence has a structural overlap of more than 98% with the actual time series, and the prediction results can accurately capture the multi-scale periodic changes of meteorological data, verifying the strong adaptability of this invention to complex nested cyclic scenarios.

[0080] This invention also proposes a phase coding system based on cyclic phase transition topology, employing the phase coding method based on cyclic phase transition topology as described above, including: The time series preprocessing module is used to acquire dynamic time series data and perform adaptive window segmentation based on the abrupt changes in the trend characteristics of the dynamic time series data to obtain multiple continuous phase transition segments. Phase encoding module: used to extract the position and momentum features of each phase transition segment, generate the corresponding phase state code, and assemble the phase state codes of all phase transition segments into a phase state transition sequence in sequence; Phase anchoring module: used to map and anchor the phase state transition sequence to the topological phase coordinate system of a one-sided closed surface through geometric algebra and topological homeomorphism transformation algorithms; Self-consistency verification and rule extraction module: used to reconstruct the time series data based on the phase state transition sequence and the phase amplitude mapping relationship, calculate the coding accuracy based on the reconstructed time series data and dynamic time series data, and extract cyclic phase transition constraint rules based on the phase state transition sequence. Cyclic Evolution Prediction Module: This module is used to perform forward evolution based on cyclic phase transition constraint rules and dynamic time series data, generate future phase state transition sequences, and obtain prediction results based on phase amplitude mapping relationships.

[0081] Furthermore, the timing preprocessing module performs all the functions of step S1 above. It supports multi-source data input, including sensor acquisition signals, historical data, and real-time streaming data. It adopts a multi-channel data caching mechanism to ensure data consistency and integrity. It has built-in sliding window analysis and dynamic threshold adjustment algorithms to realize trend feature abrupt change point detection and adaptive window segmentation. It supports curve segmentation with 6 equal-length phase steps and slope abrupt change segmentation of broken line segments, providing high-quality structured input for subsequent encoding.

[0082] The phase encoding module performs all the functions of step S2 above. Its core function is to convert phase transition segments into phase status code sequences, achieving minimal complete encoding of cyclic events. It has built-in single-order / multi-order encoding logic, supports 6-dimensional basic encoding and N-dimensional extended encoding, and implements hierarchical encoding for nested loops. It introduces a redundancy check mechanism to ensure high-fidelity transmission of information during the encoding process. It also has built-in local tangent coordinate system analysis logic, which can automatically determine the deviation direction of each phase step and generate the corresponding features and 6-dimensional phase status codes.

[0083] Phase anchoring module: It has a built-in single-sided closed surface topological phase coordinate system (preferably Möbius strip topology) to perform all the functions of step S3 above; through geometric algebra and topological homeomorphism transformation algorithm, it realizes the accurate mapping and positioning of the phase state transition sequence, and binds a unique phase position and loop count to the sequence; it utilizes the topological characteristics of Möbius strip to realize phase self-synchronization and self-positioning without external reference, and solves the phase aliasing and ambiguity problems; it has built-in topological boundary constraint logic to ensure that all phase steps are within a fixed slope ratio (example: X / Y=6, the value here is the nominal value, and the actual value is the adaptive dynamic range).

[0084] The self-consistency verification and rule extraction module is used to perform all the functions of step S4 above. It completes the reconstruction of the original time series data through the phase-amplitude mapping relationship, and performs self-consistency verification by comparing the mean square error (MSE) and correlation coefficient (CC) of the reconstructed data with the original data. At the same time, it uses the structural fidelity as the core evaluation standard to ensure the structural consistency between the reconstructed curve and the original curve. It has built-in graph theory modeling and machine learning algorithms to extract cyclic phase transition constraint rules from the phase state transition sequence, construct a phase state transition network, and explore the potential evolution law of cyclic phase transition.

[0085] Cyclic Evolution Prediction Module: This module performs all the functions of step S5 above. It incorporates a Markov chain-based state transition model and combines extracted cyclic phase transition constraint rules to extrapolate the forward evolution of the phase state sequence. It integrates Monte Carlo simulation, multi-scale fusion strategy, and online update mechanism to achieve high-precision and robust time series trend prediction. It outputs future phase state transition sequences and corresponding time series prediction results, and supports uncertainty quantification and result reliability assessment.

[0086] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A phase encoding method based on a cyclic phase change topology, characterized in that, Includes the following steps: S1. Acquire dynamic time series data, and perform adaptive window segmentation based on the trend feature abrupt changes of the dynamic time series data to obtain multiple continuous phase transition segments; S2. Extract the trend direction and evolution rate features of each phase transition segment, generate the corresponding phase state code, and arrange the phase state codes of all phase transition segments into a phase state transition sequence in sequence. S3. Map and anchor the phase state transition sequence to a one-sided closed surface topological phase coordinate system; S4. Extract cyclic phase transition constraint rules based on the phase state transition sequence; S5. Based on the cyclic phase transition constraint rules and dynamic time series data, perform forward evolution to generate a future phase state transition sequence, and obtain the prediction result based on the phase amplitude mapping relationship.

2. A phase encoding method based on a cyclic phase change topology according to claim 1, characterized in that, The specific steps for adaptive window segmentation based on abrupt changes in trend features of dynamic time-series data include: The line segments in the dynamic time series data are segmented using abrupt slope changes. The curve segments in the dynamic time series data are divided into six equal-length phase steps as the segmentation unit and the local tangent coordinate system as the reference.

3. A phase encoding method based on a cyclic phase change topology according to claim 2, characterized in that, S1 further includes the following steps: If the dynamic time series data is identified as having discontinuous trend characteristics and a preset multi-scale nested loop configuration, the corresponding mutation point is marked as a chaotic transition state, and the phase encoding method is in a multi-level encoding mode; otherwise, the phase encoding method is in a single-level encoding mode. If at least three consecutive phase steps fail to match the pre-trained cyclic constraint rules or the system signal-to-noise ratio is lower than a preset threshold, then switch to the traditional linear coding mode. In the traditional linear encoding mode, when the dynamic time series data matches the cyclic constraint rule for three consecutive phase steps, adaptive window segmentation is performed based on the abrupt change in the trend characteristics of the dynamic time series data to obtain multiple continuous phase transition segments.

4. The phase encoding method based on the cyclic phase transition topology according to claim 3, characterized in that, The six phase steps correspond to a six-dimensional phase encoding unit, which includes a three-dimensional position phase unit corresponding to the start point, peak point and end point of the phase transition segment, and a three-dimensional momentum phase unit corresponding to the slope change rate, acceleration and direction change of the phase transition segment. The specific steps of S2 include: if in single-order coding mode, taking the local tangent coordinate system of each phase step as a reference, if the trajectory of the current phase step deviates upward relative to the X-axis of the local tangent coordinate system, it is considered a positive feature; otherwise, it is considered a negative feature. The positive features and / or negative features of the six phase steps are combined to obtain the phase state code, and the phase state codes of all phase transition segments are arranged in sequence to form a phase state transition sequence. If in a multi-level coding mode, the six-dimensional phase coding unit is expanded into an N-dimensional coding system, N=6·K, where K is the total order obtained according to the multi-scale nested loop configuration. Each nested loop corresponds to a set of independent six-dimensional phase coding units. Taking the local tangent coordinate system of each phase step as the reference, if the trajectory of the current phase step deviates upward relative to the X-axis of the local tangent coordinate system, it is considered a positive feature; otherwise, it is considered a negative feature. The positive features and / or negative features of the six phase steps are combined to obtain the phase state code. All phase state codes corresponding to the same level are arranged in order to form the phase state transition sequence of the corresponding level.

5. A phase encoding method based on cyclic phase transition topology according to claim 4, characterized in that, The single-sided closed surface topological phase coordinate system is the Möbius topological phase coordinate system corresponding to the Möbius strip; The specific steps of S3 include: if in single-order encoding mode, mapping the three-dimensional position phase unit to the two-dimensional plane of the Möbius ring to achieve unique phase position calibration; calculating the phase state of the phase state code in the loop direction and temporal position on the Möbius ring using the three-dimensional momentum phase unit information to complete the loop counting; taking the sampling point as the dynamic origin O, and the distance between the two dynamic origins O as the corresponding Möbius ring phase difference; and constraining all phase steps within the preset topological boundary of the Möbius ring. If in multi-order encoding mode, the phase state transition sequence is sorted from largest to smallest according to its order, and then mapped sequentially to a Möbius strip distributed from the outer layer to the inner layer. The three-dimensional position phase unit is mapped to the two-dimensional plane of the Möbius strip to achieve unique phase position calibration. The phase state of the phase state code is calculated from the three-dimensional momentum phase unit information to determine the loop direction and temporal position on the Möbius strip to complete the loop counting. The sampling point dynamic origin O of the corresponding scale level is used, and the distance between the two dynamic origins O is the phase difference of the Möbius strip of the corresponding order.

6. A phase encoding method based on a cyclic phase change topology according to claim 4, characterized in that, S4 further includes step S41: reconstructing the phase state transition sequence and phase amplitude mapping relationship to obtain reconstructed timing data, and calculating the coding accuracy based on the reconstructed timing data and dynamic timing data; The specific steps of reconstruction include: providing amplitude base anchor points based on the three-dimensional position phase unit, recovering the dynamic change process of amplitude based on the three-dimensional momentum phase unit, and recovering the original data point by point through reverse decoding and topological constraints to obtain reconstructed time series data; Methods for calculating coding accuracy include one or both of the root mean square error and the correlation coefficient.

7. The phase encoding method based on the cyclic phase transition topology according to claim 4, characterized in that, Each phase status code has a corresponding phase status; In step S4, the specific steps for extracting the cyclic phase transition constraint rules based on the phase state transition sequence include: A graph-theory-based state transition network and a machine learning-based pattern recognition algorithm are used to construct the state transition network and construct the pattern recognition algorithm. The phase state corresponding to the phase state code is regarded as a node and the state transition of adjacent phase state codes is regarded as an edge. All legal paths of phase state transition and the probability distribution of the corresponding legal paths are extracted. Combined with the preset topological boundary constraints, the cyclic phase transition constraint rules are obtained.

8. A phase encoding method based on a cyclic phase change topology according to claim 7, characterized in that, The specific steps of S5 include: generating a future phase state transition sequence based on the phase state of the current phase state code, and the set of legal paths and probability distributions for phase state transitions in the cyclic phase transition constraint rules; reconstructing future time series data based on the future phase state transition sequence and the phase amplitude mapping relationship; generating multiple evolution paths through Monte Carlo simulation and multi-scale fusion strategy; calculating a weighted average based on the set of probability distributions; and outputting a prediction result with confidence intervals.

9. The phase encoding method based on the cyclic phase transition topology according to claim 7, characterized in that, S5 further includes the step of: if the state transition is not in the set of legal path transitions for phase state transitions in the cyclic phase transition constraint rule, then an abnormal warning is triggered.

10. A phase encoding system based on a cyclic phase change topology, characterized in that, A phase encoding method based on cyclic phase transition topology according to any one of claims 1-9, comprising: The time series preprocessing module is used to acquire dynamic time series data and perform adaptive window segmentation based on the abrupt changes in the trend characteristics of the dynamic time series data to obtain multiple continuous phase transition segments. Phase encoding module: used to extract the position and momentum features of each phase transition segment, generate the corresponding phase state code, and assemble the phase state codes of all phase transition segments into a phase state transition sequence in sequence; Phase anchoring module: used to map and anchor the phase state transition sequence to a one-sided closed surface topological phase coordinate system using geometric algebra and topological homeomorphism transformation algorithms; Self-consistency verification and rule extraction module: used to reconstruct the phase state transition sequence and phase amplitude mapping relationship to obtain reconstructed time series data, calculate the coding accuracy based on the reconstructed time series data and dynamic time series data, and extract cyclic phase transition constraint rules based on the phase state transition sequence; Cyclic evolution prediction module: used to perform forward evolution based on the cyclic phase transition constraint rules and dynamic time series data, generate future phase state transition sequences, and obtain prediction results based on phase amplitude mapping relationship.

Images