A method and system for generating a resistance training program based on constrained optimization

Abstract

This invention relates to the field of training plan generation and intelligent optimization technology, and specifically to a method and system for generating endurance training plans based on constraint optimization. The method includes the following steps: S1, acquiring various user data; S2, determining the historical daily training load index sequence and calculating the current physiological equilibrium state; S3, determining the target physiological equilibrium state and risk constraint value at the end of the planning cycle; S4, generating a set of candidate training topologies and performing Boolean pruning on the candidate topologies to obtain a set of feasible training topologies; S5, establishing a continuous load allocation model; S6, performing double-loop constraint optimization on the candidate training topologies; and S7, outputting the target endurance training plan. This invention provides an endurance training plan that ensures the physiological equilibrium state at the end of the planning cycle approaches the target physiological equilibrium state while also considering the safety of training load distribution.

Description

Technical Field

[0001] This invention relates to the field of training plan generation and intelligent optimization technology, and in particular to a method and system for generating endurance training plans based on constraint optimization. Background Technology

[0002] Developing an endurance training plan typically requires considering the user's past training history, current physical condition, and future training goals to determine the training schedule within the planned period. Existing technologies already exist that calculate and predict athletic performance based on historical training information and future training schedules.

[0003] For example, US8533001B2 discloses a sports performance calculation system and method. This technical solution receives information related to target performance, information related to a proposed training schedule, and past training records or past performance records, and calculates and predicts future sports performance based on the training schedule and training stress. The document also discloses that future performance can be modeled and evaluated based on positive and negative training effects.

[0004] As can be seen from the existing technologies described above, their main technical focus lies in predicting or evaluating future athletic performance based on a given target performance and a proposed training schedule, combined with past training information. In other words, this type of approach emphasizes extrapolating future results based on existing or pre-set training arrangements.

[0005] However, in the actual process of developing endurance training plans, in addition to historical training loads, it is usually necessary to consider calendar constraints such as subjective feedback, recovery status, trainable periods, required rest days, and competition days, as well as the training type boundaries and training load boundaries corresponding to different planned days. In this situation, relying solely on existing methods for predicting the proposed training schedule is insufficient to directly achieve: under the premise of satisfying multiple constraints, reverse-engineering the training arrangement within the planning period and ensuring that the state at the end of the planning period approaches the expected target state as closely as possible. This judgment is based on a technical comparison made between the aforementioned closest existing technology disclosure and the requirements for generating training plans.

[0006] The technical problem to be solved by this invention is: how to generate an endurance training plan that makes the physiological equilibrium state at the end of the planning cycle approach the target physiological equilibrium state under the conditions of comprehensive historical training load, subjective feedback, recovery state, calendar constraints and training boundary constraints. Summary of the Invention

[0007] To overcome the aforementioned technical deficiencies, the present invention aims to provide a method and system for generating endurance training plans based on constraint optimization. This invention first quantifies historical training load into the current physiological equilibrium state, then combines subjective feedback, recovery exercise state, and calendar constraints. Through deterministic bounded state mapping, the target physiological equilibrium state and risk constraint values ​​are determined. Furthermore, candidate training topology generation and Boolean pruning, along with double-loop constraint optimization based on the outer loop search and inner loop load allocation of the total weekly change point, are employed to solve the training structure and training load hierarchically. This generates an endurance training plan that ensures the physiological equilibrium state at the end of the planning cycle approaches the target physiological equilibrium state while also considering the safety of the training load distribution.

[0008] This invention discloses a method for generating endurance training plans based on constraint optimization, comprising the following steps:

[0009] S1. Obtain the user's historical training data, subjective feedback data, recovery exercise status data, historical plan execution result data, calendar constraint data, and training boundary data for each planned day within the planning period. Among them, the historical training data includes at least endurance training kinematic data or training load data arranged in chronological order; the subjective feedback data includes at least pain scores and fatigue scores; the calendar constraint data includes at least one of the following: trainable periods, mandatory rest days, competition days, and travel days; and the training boundary data includes at least the training type boundary and training load boundary corresponding to each planned day.

[0010] S2. Determine the historical daily training load index sequence based on historical training data, and calculate the current physiological equilibrium state based on the historical daily training load index sequence. Let the first step be... The historical daily training load index for the day is Acute load is Chronic burden is The current physiological homeostasis is ,but:

[0011]

[0012]

[0013]

[0014] in, This is the acute load recursion coefficient. This is the recursive coefficient for chronic load;

[0015] S3. Based on the current physiological balance state, subjective feedback data, and the recovery movement state data, determine the target physiological balance state and risk constraint value at the end of the planning cycle through deterministic bounded state mapping, wherein the target physiological balance state is located within a preset safety offset range relative to the current physiological balance state.

[0016] S4. Generate a set of candidate training topologies for each planned day within the planning period based on the training type boundary, and perform Boolean pruning on the set of candidate training topologies based on calendar constraint data and training mode constraints to obtain a set of feasible training topologies.

[0017] S5. For each candidate training topology in the feasible training topology set, establish a continuous load allocation model based on the training load boundaries of each planned day, assuming the planning period includes... The planned day, the first The training load for each planned day is Its lower boundary is The upper boundary is Midpoint load is The width of the half interval is The offset is ,but:

[0018]

[0019]

[0020]

[0021] S6. Constructing Weekly Change Points And perform double-loop constraint optimization on the candidate training topology according to the following formula:

[0022]

[0023] Among them, the outer ring represents the point of change in the total week. Perform a bounded scalar search to ensure that the predicted physiological equilibrium state at the end of the planning cycle matches the target physiological equilibrium state. The difference between them decreases; the inner ring satisfies and Under these conditions, the training load for each planned day is allocated;

[0024] S7. Based on the double-cycle constraint optimization, candidate training plans corresponding to each candidate training topology are obtained, and the candidate training plans are scored and sorted according to the convergence degree of physiological equilibrium state, the safety of load distribution and the risk constraint value, and the target endurance training plan is output.

[0025] Preferably, the determination of the historical daily training load index sequence in step S2 includes: mechanical power based on endurance training kinematic data. With critical power Calculate normalized intensity The training load index for a single training session is determined based on the normalization intensity. ,in:

[0026]

[0027]

[0028] in, The duration of a single training session. The intensity weighting parameter is greater than 1.

[0029] Preferably, in step S2, the acute load recursion coefficient and chronic load inversion coefficient Each is determined by the acute time constant. and chronic time constant The parameters are determined and satisfy:

[0030]

[0031]

[0032] in, .

[0033] Preferably, the deterministic bounded state mapping includes: first calculating the reference target state based on subjective feedback data and recovered motion state data. Then, based on the state correction amount Determine the target physiological homeostasis Risk constraint values ​​are determined based on subjective feedback data and recovery movement status data, where:

[0034]

[0035]

[0036] in, and These are the lower and upper limits of the allowed range for the target state, respectively. To integrate input data, For the maximum safe offset, This indicates the interval truncation operation.

[0037] Preferably, the state correction amount and risk constraint value are determined by a machine learning model. The input to the machine learning model includes at least the current physiological equilibrium state, subjective feedback data, recovery movement state features extracted from recovery movement state data, trainable time period features extracted from calendar constraint data, historical training load features extracted from historical training data, and historical plan execution result features extracted from historical plan execution result data.

[0038] Preferably, the step S4 of generating a candidate training topology set includes: marking each planned day within the planning period as one of the training element types of easy run, quality class, long run and rest, and combining and arranging the training element types of each planned day to form a candidate training topology set.

[0039] Preferably, the Boolean pruning based on calendar constraint data and training mode constraints in step S4 includes at least one of the following:

[0040] Candidate training topologies where two adjacent planned days are both quality classes are deemed infeasible.

[0041] Set a minimum interval of days between two consecutive quality assessment sessions;

[0042] The training elements for planned days within a preset number of days before the competition will be limited to reduced training types.

[0043] Designate the planned days corresponding to mandatory rest days as rest days;

[0044] Designate the planned days corresponding to non-training periods as rest days.

[0045] Preferably, the training load boundaries are set separately according to the training element type, wherein the planned rest day for the training element type satisfies:

[0046]

[0047] The planned days for training elements such as easy runs, quality sessions, and long-distance runs each have different training load ranges.

[0048] Preferably, in step S6, the total weekly change points The search boundary is determined by the half-interval width of each planned day, satisfying:

[0049]

[0050]

[0051] The outer loop is based on the objective function To optimize the objective:

[0052]

[0053] in, For the point of change in the weekly report The predicted physiological equilibrium state at the end of the planning cycle is obtained.

[0054] Preferably, the inner loop uses an objective function. The training load for each planned day is allocated as follows:

[0055]

[0056] And satisfy the constraints:

[0057]

[0058] in, The standard deviation of the 3-day rolling average sequence obtained by splicing historical training load sequences and training load sequences for the planning period is... The standard deviation of the training load sequence for the planning period, As an indicator of the alternation of days, and These are the weighting coefficients.

[0059] Preferably, the 3-day rolling average series is determined by the following operator:

[0060]

[0061] in, The first training load sequence after splicing Item load value, The spliced ​​training load sequence is in the first... The 3-day rolling average corresponding to the item.

[0062] Preferably, the daily alternation index g is calculated based on the average absolute difference between non-zero training load days within the planning period, assuming the non-zero training load sequence after removing rest days is... ,but:

[0063] when hour, ;

[0064] when hour, .

[0065] Preferably, the weighting coefficient and Scoring based on the diversity of candidate training topologies Dynamically determined, diversity scoring satisfy:

[0066]

[0067]

[0068]

[0069] in, The set of unique training element types in the candidate training topology. The cardinality of the set of elements of the unique training type. For diversity threshold, and These are the preset maximum weight parameters.

[0070] Preferably, in step S6, double-loop constraint optimization is performed in parallel at the topology granularity for each candidate training topology; when the number of candidate training topologies is less than a preset threshold, local multi-process pool is used for parallel processing; when the number of candidate training topologies is not less than the preset threshold, the candidate training topology tasks are sharded and sent to a remote job queue for parallel processing; and within the scope of a single planning request, memoization caching is performed on the inner loop solution results and the recursive intermediate states of acute load and chronic load.

[0071] In view of this, the present invention also provides an endurance training plan generation system based on constraint optimization, comprising:

[0072] The data acquisition module is used to acquire historical training data, subjective feedback data, recovery motion state data, historical plan execution result data, calendar constraint data, and training boundary data for each planned day within the planning period;

[0073] The state quantification module is used to determine the historical daily training load index sequence based on historical training data, and to calculate the current physiological equilibrium state based on the historical daily training load index sequence.

[0074] The target state determination module is used to determine the target physiological balance state and risk constraint value through deterministic bounded state mapping based on the current physiological balance state, the subjective feedback data, and the recovery movement state data.

[0075] The topology generation and pruning module is used to generate a set of candidate training topologies based on the training type boundary, and to perform Boolean pruning on the set of candidate training topologies based on calendar constraint data and training mode constraints to obtain a set of feasible training topologies.

[0076] The dual-loop constraint optimization module is used to establish a continuous load allocation model for each feasible training topology, construct the total weekly change point, and generate candidate training plans through continuous load allocation with outer loop bounded scalar search and inner loop equality constraints and boundary constraints.

[0077] The scoring, ranking, and output module is used to score and rank each candidate training plan according to the degree of convergence of physiological equilibrium, the safety of load distribution, and the risk constraint value, and output the target endurance training plan.

[0078] Compared with existing technologies, the above technical solution has the following advantages:

[0079] 1. This invention, under the premise of satisfying complex discrete constraints, enables the physiological equilibrium state at the end of the planning cycle to approach the target physiological equilibrium state, thereby significantly improving the target convergence and physiological accuracy of endurance training plan generation. Existing technologies typically focus on predicting the results of a given training arrangement or rely on experience templates to generate training plans, making it difficult to guarantee that the predetermined physiological state will be reached at specified time boundaries such as the weekend, the end of a training block, or a competition week. In contrast, this invention transforms historical training load into a predictable and controllable physiological equilibrium state, and uses the target physiological equilibrium state as the direct objective of constraint optimization. By combining the outer loop search of the total weekly change point and the inner loop optimization of the daily load allocation, it achieves the reverse solution of the training plan to the target state, thus mathematically improving the convergence ability of the training plan to the target state.

[0080] 2. This invention can explicitly suppress rolling training load fluctuations while maintaining the diversity of training stimuli, thereby reducing acute load spikes and improving the safety of training load distribution. This invention does not merely pursue matching the total training volume, but rather, by introducing a rolling average fluctuation term, a training load sequence dispersion term for the planning period, and a daily alternation index into the inner-loop optimization, it controls short-window load fluctuations while ensuring the differentiation of training intensity, thereby reducing acute load peaks associated with injury risk. In other words, this invention can not only generate "trainable" plans, but also generate "safer" plans.

[0081] 3. This invention significantly reduces solution complexity and improves solvability and stability under multi-constraint scenarios by separating the discrete solution of the training structure from the continuous solution of the training load. Specifically, this invention first forms candidate training topologies by combining and arranging training element types. Then, it performs hard pruning on the candidate training topologies using adjacency constraints, interval constraints, pre-match day reduction constraints, mandatory rest day constraints, and trainable time period constraints to obtain a feasible training structure. Subsequently, continuous load allocation optimization is performed based on the feasible training topology. Since infeasible structures are eliminated first, and then continuous optimization is performed, computational resources are avoided on training structures that do not meet the constraints, thereby improving solution efficiency and stability.

[0082] 4. This invention employs a dual-loop optimization architecture that combines a one-dimensional outer loop search centered on the weekly total change point with an inner loop load allocation constrained by equality and boundary constraints. This architecture enables fine-grained control of the training load within a week while ensuring state convergence. Specifically, the outer loop searches for the weekly total change point to converge the physiological equilibrium state at the end of the planning cycle towards the target physiological equilibrium state. The inner loop, under the condition of satisfying the training load boundary and total change point constraints, finely allocates the daily training load to shape a more reasonable intra-weekly load curve. This technical solution considers both overall weekly load control and fine-grained control of daily granular training arrangements, thus possessing high engineering feasibility and interpretability.

[0083] 5. This invention improves the conditional consistency of training load representation by normalizing and state-based processing of the training load, thereby enhancing the stability of the training plan generation results. This invention preferably uses a nonlinear physiological cost mapping between running power and relative critical power to quantify the training load, and uses a dual-memory exponential model to convert historical training loads into acute load, chronic load, and physiological equilibrium states. Compared to simply using indicators such as pace and mileage for empirical estimation, this invention can more stably reflect training stress under conditions of terrain, environment, and speed changes, thus providing a more reliable numerical basis for subsequent target state control and load allocation optimization. Attached Figure Description

[0084] Figure 1 This is a schematic diagram of the overall process of the endurance training plan generation method of the present invention;

[0085] Figure 2 This is a schematic diagram of candidate training topology generation and Boolean pruning in this invention;

[0086] Figure 3 This is a schematic diagram of the double-loop constraint optimization and scoring ranking of the present invention;

[0087] Figure 4 This is a schematic diagram of the relationship between the total weekly change points and the predicted physiological equilibrium state at the end of the planning cycle in this invention.

[0088] Figure 5 This is a schematic diagram of the training load distribution curves of the present invention and the comparative embodiment. Detailed Implementation

[0089] The advantages of the present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments.

[0090] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0091] The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. The singular forms “a,” “the,” and “the” as used in this disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0092] It should be understood that although the terms first, second, third, etc., may be used in this disclosure to describe various information, such information should not be limited to these terms. These terms are used only to distinguish information of the same type from one another. For example, without departing from the scope of this disclosure, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0093] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0094] In the description of this invention, unless otherwise specified and limited, it should be noted that the terms "installation", "connection" and "linking" should be interpreted broadly. For example, they can refer to mechanical or electrical connections, or internal connections between two components. They can be direct connections or indirect connections through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0095] In the following description, suffixes such as "module," "part," or "unit" used to denote elements are used only for the convenience of the description of the invention and have no specific meaning in themselves. Therefore, "module" and "part" can be used interchangeably.

[0096] This embodiment provides a method for generating endurance training plans based on constraint optimization, including the following steps:

[0097] S1. Obtain the user's historical training data, subjective feedback data, recovery exercise status data, historical plan execution result data, calendar constraint data, and training boundary data for each planned day within the planning period. The historical training data must include at least endurance training kinematic data or training load data arranged chronologically; the subjective feedback data must include at least pain and fatigue scores; the calendar constraint data must include at least one of the following: trainable periods, mandatory rest days, competition days, and travel days; and the training boundary data must include at least the training type boundary and training load boundary for each planned day. S2. Determine the historical daily training load index sequence based on the historical training data, and calculate the current physiological equilibrium state based on the historical daily training load index sequence. Let the first... The historical daily training load index for the day is Acute load is Chronic burden is The current physiological homeostasis is ,but: ; ; ;in, This is the acute load recursion coefficient. S3. Based on the current physiological equilibrium state, subjective feedback data, and the recovery exercise state data, determine the target physiological equilibrium state and risk constraint value at the end of the planning period through deterministic bounded state mapping, wherein the target physiological equilibrium state is within a preset safe offset range relative to the current physiological equilibrium state; S4. Generate a candidate training topology set for each planned day within the planning period according to the training type boundary, and perform Boolean pruning on the candidate training topology set based on calendar constraint data and training mode constraints to obtain a feasible training topology set; S5. For each candidate training topology in the feasible training topology set, establish a continuous load allocation model based on the training load boundary of each planned day, assuming the planning period includes... The planned day, the first The training load for each planned day is Its lower boundary is The upper boundary is Midpoint load is The width of the half interval is The offset is ,but: ; ; S6. Constructing Weekly Change Points And perform double-loop constraint optimization on the candidate training topology according to the following formula: Among them, the outer ring represents the point of change in the total weekly cycle. Perform a bounded scalar search to ensure that the predicted physiological equilibrium state at the end of the planning cycle matches the target physiological equilibrium state. The difference between them decreases; the inner ring satisfies and Under the condition of allocation, the training load of each planned day is allocated; S7, based on the double-loop constraint optimization, the candidate training plan corresponding to each candidate training topology is obtained, and the candidate training plan is scored and sorted according to the convergence degree of physiological equilibrium state, the safety of load distribution and the risk constraint value, and the target endurance training plan is output.

[0098] The present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the following specific embodiments are only used to explain the technical solution of the present invention and are not intended to limit the scope of protection of the present invention. The present invention is applicable to the automatic generation of endurance training plans, and is particularly applicable to training plan generation scenarios that require simultaneous integration of historical training load, subjective feedback, recovery exercise state, calendar constraints, and training boundary constraints, and, under the premise of satisfying complex discrete constraints, to make the physiological equilibrium state at the end of the planning period approach the target physiological equilibrium state.

[0099] In this embodiment, the endurance training plan generation system can be deployed on a server, edge device, or cloud platform. The system receives historical training data, subjective feedback data, recovery exercise state data, historical plan execution result data, calendar constraint data, and training boundary data for each planned day within the planning period from the user terminal, and outputs a target endurance training plan arranged by planned day. The target endurance training plan preferably includes daily training element types, daily training load, predicted physiological equilibrium state at the end of the planning period, and necessary training prompts. Unlike existing solutions that only predict results for a given training schedule, the technical focus of this invention is to construct the training plan generation problem as a hierarchical constrained optimization problem that simultaneously includes discrete structure solving and continuous load solving.

[0100] See Figure 1This implementation first organizes the input data. Historical training data includes at least endurance training kinematic data or training load data arranged in chronological order. Endurance training kinematic data preferably includes speed data, incline data, duration data, displacement data, and power data directly measured by the equipment or estimated. Subjective feedback data includes at least pain scores and fatigue scores, and preferably, subjective readiness scores and sleep recovery scores. Recovery exercise status data preferably includes the number of training sessions in the last 7 days, the number of training sessions in the last 14 days, the longest consecutive training days, the duration of the most recent interruption, the number of weeks of return training, and whether the individual is currently in the return training phase. Historical plan execution result data preferably includes the plan completion rate for the most recent weeks, the average training load deviation, the number of delayed executions, the number of early executions, the number of interruptions, and the number of make-up sessions. Calendar constraint data preferably includes trainable periods, mandatory rest days, competition days, business trip days, travel days, and user-defined non-trainable periods. Training boundary data preferably includes the types of training elements allowed on each planned day within the planning period, and the lower and upper boundaries of the training load allowed under each training element type. Through the above-mentioned multi-source input, the present invention can simultaneously handle physiological state constraints, pattern constraints, and calendar constraints.

[0101] During the state quantification phase, the system first determines the sequence of historical daily training load indicators based on historical training data. To improve the conditional invariance of training load quantification, this implementation prefers to use mechanical power as the base quantity, rather than directly using pace or mileage as the sole load base. Let the mechanical power be... The critical power is The normalized strength is ,but:

[0102]

[0103] Among them, mechanical power It can be estimated by combining speed, gradient, and resistance parameters. If the user is at time... The speed is The slope angle is The total resistance is Then the mechanical power can be estimated by the following formula:

[0104]

[0105] Furthermore, the total resistance preferably includes a gravity component, a rolling resistance component, and an air resistance component, namely:

[0106]

[0107] in, Indicates the user's weight. Represents gravitational acceleration. Indicates the rolling resistance coefficient. Indicates air density, This represents the combined parameters related to air resistance. Using the above estimation method, even under different inclines, speeds, and environmental resistance conditions, the system can still characterize the training stimulus with mechanical power that more closely approximates the actual external work requirements.

[0108] To facilitate understanding, the following is an example of mechanical power calculation. Let a user's weight be... Gravitational acceleration Rolling resistance coefficient air density Combined parameters of air resistance Speed ​​at a certain moment The corresponding pace is approximately 3 minutes and 42 seconds per kilometer, and the sine value corresponding to the slope angle is approximately... The cosine value is approximately: The gravitational component is then approximately:

[0109]

[0110] The rolling resistance component is approximately:

[0111]

[0112] The air resistance component is approximately:

[0113]

[0114] Therefore, the total resistance at that moment is approximately:

[0115]

[0116] Therefore, the mechanical power at that moment can be approximately:

[0117]

[0118] That is, the mechanical power at that moment is approximately 117.9W. If the critical power cp = 300W for the same user, then the normalized intensity at that moment is:

[0119]

[0120] This calculation example shows that the present invention does not simply determine training intensity based on pace, but rather converts terrain, resistance and speed factors into mechanical power, and then further converts them into normalized intensity, making subsequent training load indicators more comparable across scenarios.

[0121] After obtaining the normalized intensity, the system maps a single training session to a training load metric. Let the intensity weighting parameter be... The duration of a single training session is The training load index for a single training session is ,but:

[0122]

[0123] Among them, intensity weighted parameters Preferably, the value is a real number greater than 1, and more preferably 1.3 to 1.8. The reason for using superlinear weighting is that the impact of high-intensity training on acute fatigue does not increase linearly; if only linear integrals are used, the physiological cost during high-intensity periods is easily underestimated. For multiple training sessions occurring within the same natural day, the system adds the training load indices of each individual training session to obtain the historical daily training load index for that day. Let the... The historical daily training load index for the day is ,but:

[0124]

[0125] in, Indicates the first The number of training sessions that occur each day Indicates the day's number The training load index for the training session. If the training load index for the training session... Without training, one will be ordered .

[0126] To make the calculation of the above training load index more intuitive, a discrete approximate integral example is given below. Suppose a training session lasts 30 minutes. For ease of calculation, it is divided into three equal phases, each lasting 10 minutes, or 600 seconds. The normalized intensities of the three phases are 0.70, 0.85, and 1.05, respectively, and the intensity weighting parameter is set to k=1.5. Then:

[0127] The intensity items for the first stage are:

[0128]

[0129] The load contribution in the first phase is:

[0130]

[0131] The intensity items for the second stage are:

[0132]

[0133] The load contribution in the second phase is:

[0134]

[0135] The intensity items for the third stage are:

[0136]

[0137] The load contribution in the third stage is:

[0138]

[0139] The training load index for this training session is approximately:

[0140]

[0141] To facilitate unified management of the training system, this value can also be normalized according to a preset scale. For example, if the system specifies dividing the second-level integral value by 20, the normalized single training load index will be approximately:

[0142]

[0143] Therefore, the training load index for this training session can be approximately 73.4. This example demonstrates that when the normalization intensity exceeds 1, its contribution to the training load index is amplified, thus giving higher weight to quality sessions or long-duration, high-intensity training in subsequent state recursion.

[0144] After obtaining the historical daily training load index sequence, the system uses a dual-memory exponential model to calculate the current physiological equilibrium state. Let the first... The acute load of the day is Chronic burden is The current physiological homeostasis is ,but:

[0145]

[0146]

[0147]

[0148] Among them, the acute load progression coefficient and chronic load inversion coefficient Each is determined by the acute time constant. and chronic time constant Parameterization determination:

[0149]

[0150]

[0151] Preferably, the acute time constant Take 5 to 10 days, chronic time constant The time period is 28 to 56 days, more preferably 7 days for acute and 42 days for chronic. Acute load is used to characterize the cumulative effect of short-term training stimuli, while chronic load is used to characterize medium- to long-term training adaptation. The current physiological homeostasis is obtained by subtracting the acute load from the chronic load, and its value reflects the user's overall readiness at the current point in time. The lower the current physiological homeostasis, the higher the short-term fatigue stress; the higher the current physiological homeostasis, the better the recovery or the higher the physiological readiness.

[0152] The following is an example of recursive calculation. Let the acute time constant be... Chronic time constant ,but:

[0153]

[0154]

[0155] therefore,

[0156]

[0157]

[0158] Assume the first Acute load Chronic burden , No. Daily training load index of historical days Then the first The acute load of the day is:

[0159]

[0160]

[0161] No. The chronic load is:

[0162]

[0163]

[0164] Therefore, the first The current physiological balance state is:

[0165]

[0166] That is, the current physiological homeostasis is approximately This example demonstrates that when the daily training load index is high, the acute load increases faster than the chronic load, thus lowering the current physiological equilibrium state and reflecting the suppressive effect of short-term fatigue on the state.

[0167] After obtaining the current physiological equilibrium state, the system begins to determine the target physiological equilibrium state at the end of the planning cycle. To this end, the system first extracts recovery exercise state features based on recovery exercise state data, extracts historical plan execution result features based on historical plan execution result data, and extracts trainable time period features based on calendar constraint data. Simultaneously, the system also explicitly extracts historical training load features based on historical training data. Preferred historical training load features include the average training load over the past 7 days, the average training load over the past 14 days, the acute load change rate over the past 7 days, the number of high-load days over the past 14 days, and the number of days since the most recent high-load training session. Preferred recovery exercise state features include the number of training sessions over the past 7 days, the number of training sessions over the past 14 days, the longest consecutive training days, the number of days of the most recent interruption, and the number of weeks since the return to training. Preferred historical plan execution result features include the plan completion rate over the past few weeks, the average training load deviation, the frequency of delayed execution, and the frequency of make-up training. Preferred trainable time period features include the total trainable time within the future planning cycle, the number of effective time periods available for high-intensity training, the location of necessary rest days, and the number of days remaining before the competition date. Subsequently, the system inputs the current physiological balance state, subjective feedback data, characteristics of recovery exercise state, characteristics of historical plan execution results, characteristics of trainable time periods, and characteristics of historical training load into the machine learning model to obtain the target correction amount and risk constraint value.

[0168] In a preferred implementation, the machine learning model can employ a gradient boosting tree model, a shallow neural network model, or an ensemble of these models. The output of the machine learning model includes a target correction and a risk constraint value. The target correction is used to adjust the basic target, while the risk constraint value reflects the safety pressure of the planned progress under the current state. To ensure continuity and boundary constraints in the determination of the target state, the system preferably uses a combination of a bounded transfer function and a truncation function. Let the lower limit of the allowable interval for the target state be... The upper limit of the allowed range for the target state is The amount of fused input is The reference target state is The target correction amount is The maximum safe offset is The target physiological homeostasis is ,but:

[0169]

[0170]

[0171] in, This indicates interval truncation operation. In this way, the target physiological equilibrium state can reflect the combined effects of subjective feedback and recovery movement, while avoiding excessive inter-cycle jumps relative to the current physiological equilibrium state.

[0172] The following is an example of calculating the target state. Let the lower limit of the allowable interval for the target state be given. The upper limit of the allowed range for the target state , fusion input Target correction amount Current physiological homeostasis Maximum safety offset Then calculate first:

[0173]

[0174] therefore:

[0175]

[0176]

[0177] Therefore, the target state is:

[0178]

[0179]

[0180]

[0181] Recalculate the corrected target value before truncation:

[0182]

[0183] Then calculate the allowed safe interval:

[0184]

[0185]

[0186] Since −0.750 falls within Since it's within the interval, the result after truncation is still:

[0187]

[0188] The calculation result is consistent with the target physiological equilibrium state used in subsequent embodiments. Therefore, the target physiological equilibrium state is not arbitrarily given, but is determined by interval mapping, state correction, and safety truncation.

[0189] See Figure 2After the target physiological equilibrium state is determined, the system enters the candidate training topology generation stage. This invention does not directly search for training structures and training loads simultaneously in a mixed space; instead, it first calculates discrete training structures and then continuous training loads. To this end, the system generates a set of candidate training topologies for each planned day within the planning period based on the training type boundaries. Let the planning period contain N planned days, preferably N=7. For each planned day, the system provides a set of allowed training element types based on the training boundary data. Preferred training element types include easy runs, quality sessions, long-distance runs, and rest days. Easy runs represent low to medium loads, primarily for recovery and maintaining basic capacity; quality sessions represent loads higher than easy runs, aiming to improve thresholds, speed endurance, or tempo endurance; long-distance runs represent training elements with large durations or total loads; and rest days represent planned days without training load. The system combines and arranges the allowed training element types for each planned day to form a set of candidate training topologies.

[0190] After the candidate training topology set is formed, the system performs Boolean pruning on it. Boolean pruning includes at least the following rules: a candidate training topology where two adjacent planned days are both quality sessions is deemed infeasible; if the interval between any two adjacent quality sessions is less than a preset threshold, the candidate training topology is deemed infeasible; if the training element type of a planned day within a preset number of days before the competition date does not meet the reduction rule, the candidate training topology is deemed infeasible; if a planned day corresponding to a mandatory rest day is not a rest day, the candidate training topology is deemed infeasible; if a planned day covered by a non-trainable period is assigned a training element type that requires long-term occupation, the candidate training topology is deemed infeasible.

[0191] In this embodiment, the reduced training type preferably includes at least one of rest, easy runs, and reduced-weight long-distance runs or reduced-weight quality sessions with a training load upper boundary below a preset race week threshold. Preferably, the preset race week threshold can be set according to the user's race distance, race level, and historical training volume. For example, the upper boundary of the training load two days before the race can be limited to 40% to 70% of the upper boundary of the same type of training element in a normal week, so that the "reduced training type" can maintain a basic activity level without introducing excessive training stimulation before the race. Through the above Boolean pruning, the system ultimately retains a set of feasible training topologies that satisfy calendar constraints and pattern constraints. By adopting this hierarchical solution strategy of topology first and load later, the complexity of the search space can be effectively reduced, and the training structure entering the continuous optimization stage can be guaranteed to satisfy the basic hard constraints.

[0192] The following is an example of candidate training topology generation and pruning calculation. Assume the set of allowed training element types for each planned day over the next 7 days is as follows:

[0193] Day 1: Easy run or rest;

[0194] Day 2: Easy run or quality class;

[0195] Day 3: Rest only;

[0196] Day 4: Easy run or quality class;

[0197] Day 5: Easy run or long run;

[0198] Day 6: Rest only;

[0199] Day 7: Easy run or long run.

[0200] The initial number of candidate training topologies is:

[0201]

[0202] Then Boolean pruning is performed. For example, the candidate training topology "easy run - quality class - rest - quality class - easy run - rest - long run" satisfies that both days 2 and 4 are quality classes, and the interval between them is one full rest day. If the system sets the minimum interval requirement for quality classes to be at least one day, then this candidate training topology is retained. However, the candidate training topology "easy run - quality class - quality class - easy run - long run - rest - easy run" is directly determined to be infeasible because days 2 and 3 are adjacent quality classes. If, out of the 32 initial candidate training topologies, 10 are eliminated due to adjacent quality classes, 8 are eliminated due to insufficient interval between quality classes, 4 are eliminated due to conflicts with required rest days, and 4 are eliminated due to conflicts with untrainable time periods, and some of these conflicts overlap, then 6 feasible training topologies remain. This example shows that discrete layer Boolean pruning can significantly shrink the solution space before entering numerical optimization.

[0203] For each feasible training topology, the system establishes a continuous load allocation model. Let the first... The training load for each planned day is The lower boundary of the training load is The upper bound of the training load is Midpoint load is The width of the half interval is The offset is ,but:

[0204]

[0205]

[0206]

[0207] When the training element type is rest, the corresponding planned day satisfies and When the training element type is an easy run, quality session, or long-distance run, the corresponding plan days have different training load boundary intervals. The introduction of midpoint load and half-interval width allows subsequent optimization to be performed within a relatively normalized offset space, rather than directly performing a joint search on training load values ​​at different scales.

[0208] The following is an example of parameterization for a continuous load allocation model. Suppose a feasible training topology is “easy run—quality session—rest—easy run—easy run—rest—long run”, and the training load boundaries for each planned day are set as follows:

[0209] Day 1: 42 to 62;

[0210] Day 2: 80 to 112;

[0211] Day 3: 0 to 0;

[0212] Day 4: 40 to 58;

[0213] Day 5: 38 to 56;

[0214] Day 6: 0 to 0;

[0215] Day 7: 92 to 128.

[0216] The midpoint load and half-interval width for day 1 are as follows:

[0217]

[0218]

[0219] Day 2 includes:

[0220]

[0221]

[0222] Day 7 includes:

[0223]

[0224]

[0225] The remaining planned days can be calculated similarly. The final load vector at the midpoint of the week is:

[0226]

[0227] The half-interval width vector is:

[0228]

[0229] When the offset vector is subsequently obtained as At that time, you can press Get the full week's training load.

[0230] See Figure 3 After establishing the continuous load distribution model, the system performs dual-loop constraint optimization. Dual-loop constraint optimization includes searching for the total weekly change point in the outer loop and optimizing the daily load distribution in the inner loop. Let the total weekly change point be... ,but:

[0231]

[0232] The weekly total change point reflects the overall offset of the weekly training load relative to the midpoint load combination. A positive weekly total change point indicates that the overall weekly training load is higher than the midpoint combination; a negative weekly total change point indicates that the overall weekly training load is lower than the midpoint combination. The feasible boundary of the weekly total change point is jointly determined by the half-interval width of each planned day.

[0233]

[0234]

[0235] The outer ring's goal is within the range The algorithm searches for an optimal point of total change within the week that minimizes the difference between the predicted physiological equilibrium state and the target physiological equilibrium state at the end of the planning cycle. Let the predicted physiological equilibrium state at the end of the planning cycle be... Then the outer loop objective function can be expressed as:

[0236] The following is an example of calculating the outer ring search. Using the aforementioned half-interval width vector... For example, we can obtain:

[0237]

[0238]

[0239] The system in Explore several weekly changes within the interval. For example, examine them separately. , , , The physiological equilibrium state is predicted at the end of the planning cycle. It is assumed that the following results are obtained through inner-loop solution and state recursion simulation:

[0240]

[0241]

[0242]

[0243]

[0244] If the target physiological balance state The corresponding objective function values ​​are as follows:

[0245]

[0246]

[0247]

[0248]

[0249] Therefore, it can be seen that among these probing points, The objective function value is minimized at time t, therefore the optimal point of change in the weekly total will converge to approximately t. The area. Figure 4 The curve shown also intuitively reflects this point, that is, when the total weekly change point increases, the predicted physiological equilibrium state at the end of the planning cycle rises as a whole, while the target physiological equilibrium state is an approximately horizontal reference line, and the area where the two are closest is the outer ring search result.

[0250] Given a total change point for a given week in the outer loop, the system enters the inner loop optimization phase. The task of inner loop optimization is to allocate the training load offset for each planned day while satisfying equality constraints and boundary constraints, balancing load distribution safety and training stimulus variability. Let the inner loop objective function be... ,but:

[0251]

[0252] And satisfy the constraints:

[0253]

[0254] in, The standard deviation of the 3-day rolling average sequence obtained by splicing historical training load sequences and training load sequences for the planning period is... The standard deviation of the training load sequence for the planning period, As an indicator of the alternation of days, and These are the weighting coefficients. The 3-day rolling average series is determined using the following operator:

[0255]

[0256] in, The first training load sequence after splicing The training load value. The daily alternation index is defined as the average absolute difference between days with non-zero training loads after removing rest days. Let the non-zero training load sequence after removing rest days be... ,but:

[0257] when hour, ;

[0258] when hour, .

[0259] Among these factors, a smaller standard deviation of the 3-day rolling average sequence indicates a more stable short-window rolling load; a larger standard deviation of the training load sequence during the planning period indicates a more significant difference in training stimuli within the week; and a larger daily alternation index indicates a more pronounced switch between light and heavy training days. By integrating these factors into the same objective function, the system can maintain a reasonable training polarization structure while reducing injury-related load fluctuations.

[0260] Below is a calculation example for each indicator of the inner loop. Assume the last two days of the historical training load sequence are 86 and 44, and the training load sequence for the planning period is 49.5, 100, 0, 46, 43.5, 0, 107. Then the first few terms of the concatenated sequence are:

[0261]

[0262] Then, starting from the third item, the 3-day rolling average is calculated as follows:

[0263]

[0264]

[0265]

[0266]

[0267]

[0268]

[0269]

[0270] The above rolling average sequence is as follows:

[0271]

[0272] The mean of this sequence is approximately:

[0273]

[0274] Then calculate the standard deviation, and we can get It is approximately 11.0. The smaller this value, the more stable the short window rolling load is.

[0275] Next, let's look at the standard deviation of the training load sequence during the planning period. The training load sequence for the planning period is as follows:

[0276]

[0277] Its mean is approximately:

[0278]

[0279] Subtract the mean from each term, square the result, and then take the average to get the variance. Take the square root of the variance to get the standard deviation. Calculations show that... It is approximately 42.8. This value is relatively large, indicating that there are significant differences in training load within the week, preserving the daily differentiation between light and heavy training.

[0280] Let's look at the day-to-day alternation indicator. The non-zero training load sequence after removing rest days is as follows:

[0281]

[0282] The absolute values ​​of the adjacent differences are as follows:

[0283]

[0284]

[0285]

[0286]

[0287] therefore:

[0288]

[0289] If the non-zero training load sequence of a candidate scheme is closer to the average distribution, for example... If the diurnal alternation index is significantly lower than 42.625, it will not be advantageous in inner-loop optimization. This indicates that the present invention can still encourage appropriate strength variations between adjacent training days while controlling short-window fluctuations.

[0290] To make the inner-loop objective function adaptive to different training structures, the system further introduces a diversity score for candidate training topologies. Let U be the set of unique training element types in the candidate training topologies, H be the diversity threshold, and D be the diversity score, then:

[0291]

[0292] in, Let be the cardinality of the unique training element type set. Let the preset maximum weight parameters be respectively... and The weighting coefficients are then dynamically determined by the following formula:

[0293]

[0294]

[0295] Below is an example of diversity score calculation. For the candidate training topology "Easy Run—Quality Lesson—Rest—Easy Run—Easy Run—Rest—Long Distance Run", its unique set of training element types is:

[0296]

[0297] therefore:

[0298]

[0299] If diversity threshold ,but:

[0300]

[0301] If the maximum weight parameter is preset , ,but:

[0302]

[0303]

[0304] This means that when the training architecture itself is already highly diverse, there is no longer an additional emphasis on enhancing polarization through numerical assignment. For example, if a candidate training topology consists only of "easy run" and "rest," then:

[0305]

[0306] then:

[0307]

[0308] but:

[0309]

[0310]

[0311] At this point, the system will more strongly encourage variations in numerical weight to compensate for insufficient diversity at the structural level. This example illustrates that the diversity scoring mechanism can pass discrete structural information to the continuous optimization layer.

[0312] For multiple feasible training topologies, the system performs the outer and inner loop solutions described above, respectively, to obtain multiple candidate training plans. Subsequently, the system scores and ranks each candidate training plan according to the convergence degree of physiological equilibrium, the safety of load distribution, and risk constraints. The scoring and ranking can be achieved using a weighted comprehensive method or a combination of rule-based selection and machine learning-assisted scoring. A higher score indicates that the corresponding candidate training plan is more suitable as the final output scheme. Finally, the system outputs the target endurance training plan, which includes the training element types and training loads for each planned day within the planning period, and may also include a predicted physiological equilibrium state at the end of the planning period.

[0313] Below is a simple example of ranking calculation. We have two candidate training plans, A and B, with the following key metrics: Candidate Training Plan A: Terminal state bias 0.06, short-window rolling fluctuation standard deviation 10.9, risk constraint value 0.24; Candidate Training Plan B: Terminal state bias 0.42, short-window rolling fluctuation standard deviation 14.5, risk constraint value 0.31.

[0314] If the scoring function takes:

[0315]

[0316] Assuming the normalization method for the short-window rolling fluctuation standard deviation is division by 20, the score of candidate training plan A is:

[0317]

[0318]

[0319] The score for candidate training plan B is:

[0320]

[0321]

[0322] Therefore, due to The system will select candidate training plan A as the final output scheme. This example illustrates that the final output scheme of this invention is not determined by a single metric, but rather by a comprehensive evaluation of multiple metrics related to safety and objective convergence.

[0323] To improve solution efficiency in multi-topology scenarios, the system preferentially performs double-loop constraint optimization in parallel at the candidate training topology granularity. When the number of candidate training topologies is less than a preset threshold, the system preferentially uses a local multi-process pool for parallel processing; when the number of candidate training topologies is not less than the preset threshold, the system preferentially sends candidate training topology tasks in chunks to a remote job queue for parallel processing. Furthermore, within the scope of a single planning request, the system performs memoization caching on the inner loop solution results and the intermediate states of acute and chronic load recursion to reduce the overhead of repeated calculations at similar weekly change points.

[0324] The implementation process of this invention is illustrated below with a specific numerical example. Assume a running user's historical daily training load index sequence for the past 14 days is shown in Table 1. The user's critical power is 300W, the acute time constant is 7 days, and the chronic time constant is 42 days. In subjective feedback, the pain score is 3 points, and the fatigue score is 5 points. Recovery exercise status data shows that the user trained 8 times in the past 14 days, with the longest continuous training period being 3 days, the most recent training interruption lasting 2 days, and is currently in the 3rd week after returning to training. Historical plan execution results data shows that the plan completion rate for the past 4 weeks was 88%, and the average training load deviation was 6.4%. Calendar constraint data shows that the 3rd and 6th days are mandatory rest days, and the morning of the 7th day has a long period available for long-distance training.

[0325] Table 1 Examples of Historical Daily Training Load Indicator Sequences

[0326] Date relative position Historical daily training load indicators Day -14 38 Day -13 0 Day -12 52 Day -11 74 Day -10 46 Day -9 0 Day -8 81 Day -7 55 Day -6 0 Day -5 69 Day -4 48 Day -3 0 Day -2 86 Day -1 44

[0327] Based on the historical daily training load index sequence in Table 1, the system recursively estimates the current acute load to be approximately 54.7 and the current chronic load to be approximately 51.9, therefore the current physiological equilibrium state is approximately −2.8. Simultaneously, the system further extracts historical training load characteristics. For example, the average historical training load over the past 7 days is approximately:

[0328]

[0329] The average training load over the past 14 days is approximately:

[0330]

[0331] If training days with a load greater than 70 are defined as high-load days, then the number of high-load days in the past 14 days is 3, namely day -11, day -8, and day -2. The above historical training load characteristics, along with recovery exercise state characteristics, historical plan execution result characteristics, and trainable time period characteristics, are input into the machine learning model. Assume the machine learning model output target correction is 0, and the risk constraint value is 0.24. Further assuming the lower limit of the target state allowable interval is -6.0, the upper limit of the target state allowable interval is 2.5, the maximum safety offset is 4.0, and the fusion input is 0.48, then the reference target state can be calculated to be approximately -0.75, and the final target physiological equilibrium state is approximately -0.75.

[0332] During the user's 7-day planning period, the system generates a set of candidate training topologies based on training type boundaries. Assume Day 1 allows easy running or rest, Day 2 allows easy running or quality training, Day 3 allows only rest, Day 4 allows easy running or quality training, Day 5 allows easy running or long-distance running, Day 6 allows only rest, and Day 7 allows long-distance running or easy running. Initial permutation expansion generates 32 candidate training topologies. After Boolean pruning based on adjacent quality training constraints, minimum interval constraints for quality training, and mandatory rest day constraints, 6 feasible training topologies remain. The feasible training topology with superior features is "easy run—quality training—rest—easy run—easy run—rest—long-distance run".

[0333] For this feasible training topology, the training load boundaries and parameterization results for each planned day are shown in Table 2.

[0334] Table 2 Training load boundaries and parameterization results for each planned day

[0335] Planned Day Training element type Training load lower boundary Upper boundary of training load Midpoint load Half-interval width Day 1 Easy Run 42 62 52 10 Day 2 Quality Class 80 112 96 16 Day 3 rest 0 0 0 0 Day 4 Easy Run 40 58 49 9 Day 5 Easy Run 38 56 47 9 Day 6 rest 0 0 0 0 Day 7 Long distance running 92 128 110 18

[0336] Table 2 shows that the search boundary for the total weekly change point is between -62 and 62. Within this interval, the system performs an outer-loop bounded scalar search, obtaining an optimal total weekly change point of approximately -8.0 that best approximates the predicted physiological equilibrium state at the end of the planning cycle. Under this optimal total weekly change point condition, the offset vector obtained by the inner loop is: Based on this, the training load sequences for the planning cycle were obtained as follows: 49.5, 100, 0, 46, 43.5, 0, 107. After incorporating this training load sequence into the historical daily training load index sequence for simulation, the predicted physiological equilibrium state at the end of the planning cycle was approximately -0.81, and the absolute deviation from the target physiological equilibrium state of -0.75 was approximately 0.06, which met the preset convergence requirements.

[0337] To more intuitively illustrate the technical effects of the present invention, a comparative embodiment is further provided. The comparative embodiment adopts a processing approach closer to the prior art, namely, first giving a proposed training schedule and then predicting the results, instead of using candidate training topology Boolean pruning, weekly change point outer loop search, and inner loop constraint optimization. The comparative embodiment uses a fixed training structure of "easy run—quality lesson—rest—quality lesson—easy run—rest—long run," and directly provides the empirical training load sequence: 55, 92, 0, 88, 50, 0, 115. Because this scheme does not perform Boolean pruning on the training topology, nor does it design convergence of the final state of the planning cycle towards the target state, its simulation results differ significantly from those of the present invention.

[0338] The comparison results between the present invention and the comparative embodiments are shown in Table 3.

[0339] Table 3 Comparative test results of the present invention and comparative embodiments

[0340] Comparison items Comparative Examples Invention Solution Predicting physiological homeostasis at the end of the planning cycle 1.48 -0.81 absolute deviation from the target physiological homeostasis 2.23 0.06 3-day rolling average series standard deviation 19.6 10.9 Standard deviation of training load sequence during planning period 40.2 42.8 Daytime Alternation Indicator 16.0 29.2 Calendar constraint violation count 0 0 Number of adjacent high-quality training conflicts 1 0

[0341] As shown in Table 3, the absolute deviation between the proposed solution and the target physiological equilibrium state under the same input conditions is significantly smaller than that of the comparative embodiment, indicating that the proposed solution can achieve state convergence at the end of the planning cycle. Simultaneously, the standard deviation of the 3-day rolling average sequence of the proposed solution is significantly lower, indicating that the proposed solution can more effectively reduce short-window rolling load fluctuations. While maintaining a high standard deviation of the training load sequence and a high daily alternation index, the proposed solution can also avoid conflicts between adjacent high-quality training sessions, indicating that the proposed solution does not achieve smoothness by simply distributing the load evenly, but rather balances the differences in training stimuli and the safety of load distribution while satisfying constraints. (See also...) Figure 5 The training load distribution curves of the present invention and the comparative embodiment intuitively reflect this difference. That is, the present invention has a more reasonable load progression and isolation structure in the arrangement of quality lessons and long-distance runs, while the comparative embodiment has the problem of high-load training being too concentrated.

[0342] In another preferred embodiment, if the user is in a significant retraining phase, such as having trained less than 4 times in the past 14 days or having experienced a training interruption of more than 10 days, the recovery of motion state characteristics will significantly reduce the fusion input, and the target correction amount output by the machine learning model will also tend to be conservative, thus causing the target physiological equilibrium state to lean towards the recovery range. In this case, even if there are large upper boundaries of training load on certain planned days, the system will still use a lower optimal weekly total change point and a more conservative inner loop allocation scheme to make the output training plan present a recovery-oriented structure. This shows that the present invention is applicable not only to the training advancement phase but also to the retraining and recovery phases.

[0343] In another preferred embodiment, if the planning period is a match week, the pre-match reduction constraint will automatically narrow the range of training element types and training load boundaries that can be used on several planned days before the match, so that the output training plan exhibits pre-match reduction characteristics. Simultaneously, the match day can also be incorporated into the terminal state prediction as a special high-stress event, thus making the optimal weekly total change point given by the outer loop search more consistent with the state requirements of the match week. This demonstrates that the present invention can adapt to the training rhythms of different season stages, rather than being limited to ordinary training weeks.

[0344] In summary, this invention first quantifies historical training load into the current physiological equilibrium state, then combines subjective feedback, recovery exercise state, and calendar constraints to determine the target physiological equilibrium state. It then employs candidate training topology generation and Boolean pruning, along with dual-loop constraint optimization based on the outer loop search and inner loop load allocation of weekly total change points, to hierarchically solve the training structure and training load. This generates an endurance training plan that ensures the physiological equilibrium state at the end of the planning cycle approaches the target physiological equilibrium state while also considering the safety of the training load distribution. This implementation adds numerical examples to each key calculation step, including examples of mechanical power calculation, integral approximation of training load indicators, recursive examples of acute and chronic load, calculation of the target physiological equilibrium state, calculation of the number of candidate training topologies generated, parameterization of training load boundaries, outer loop search of weekly total change points, calculation of inner loop rolling average and daily alternation indicators, calculation of diversity scoring and dynamic weights, and ranking of candidate plans.

[0345] Furthermore, the endurance training plan generation system of the present invention includes a data acquisition module, a state quantification module, a machine learning target determination module, a topology generation and pruning module, a double-loop constraint optimization module, and a scoring, ranking, and output module. The data acquisition module is used to acquire historical training data, subjective feedback data, recovery exercise state data, historical plan execution result data, calendar constraint data, and training boundary data; the state quantification module is used to calculate the historical daily training load index sequence, acute load, chronic load, and current physiological equilibrium state based on historical training data; the target state determination module is used to determine the target physiological equilibrium state and risk constraint value based on the current physiological equilibrium state, subjective feedback data, and recovery exercise state data through deterministic bounded state mapping. In an optional embodiment, the target state determination module further includes a machine learning sub-module for determining the state correction amount and risk constraint value; the topology generation and pruning module is used to generate a candidate training topology set and perform Boolean pruning based on calendar constraints and training mode constraints; the double-loop constraint optimization module is used to establish a continuous load allocation model and perform weekly total change point outer loop search and daily load allocation inner loop optimization; the scoring, ranking, and output module is used to score and rank multiple candidate training plans and output the target endurance training plan.

[0346] It should be noted that the embodiments of the present invention have better implementability and are not intended to limit the present invention in any way. Any person skilled in the art may use the above-disclosed technical content to change or modify it into equivalent effective embodiments. However, any modifications or equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for generating endurance training plans based on constraint optimization, characterized in that, Includes the following steps: S1. Obtain the user's historical training data, subjective feedback data, recovery exercise status data, historical plan execution result data, calendar constraint data, and training boundary data for each planned day within the planning period. The historical training data includes at least endurance training kinematic data or training load data arranged in chronological order. The subjective feedback data includes at least pain scores and fatigue scores. The calendar constraint data includes at least one of the following: trainable periods, mandatory rest days, competition days, and travel days. The training boundary data includes at least the training type boundary and training load boundary corresponding to each planned day. S2. Determine the historical daily training load index sequence based on the historical training data, and calculate the current physiological equilibrium state based on the historical daily training load index sequence. Let the first... The historical daily training load index for the day is Acute load is Chronic burden is The current physiological homeostasis is ,but: in, This is the acute load recursion coefficient. This is the recursive coefficient for chronic load; S3. Based on the current physiological balance state, the subjective feedback data, and the recovery movement state data, determine the target physiological balance state and risk constraint value at the end of the planning cycle through deterministic bounded state mapping, wherein the target physiological balance state is located within a preset safety offset range relative to the current physiological balance state. S4. Generate a set of candidate training topologies for each planned day within the planning period based on the training type boundary, and perform Boolean pruning on the set of candidate training topologies based on the calendar constraint data and training mode constraints to obtain a set of feasible training topologies. S5. For each candidate training topology in the feasible training topology set, establish a continuous load allocation model based on the training load boundary of each planned day, assuming the planning period includes... The planned day, the first The training load for each planned day is Its lower boundary is The upper boundary is Midpoint load is The width of the half interval is The offset is ,but: S6. Constructing Weekly Change Points And perform double-loop constraint optimization on the candidate training topology according to the following formula: Among them, the outer ring corresponds to the total change point of the circumference. A bounded scalar search is performed to reduce the difference between the predicted physiological equilibrium state and the target physiological equilibrium state at the end of the planning cycle; the inner loop satisfies... and Under these conditions, the training load for each planned day is allocated; S7. Based on the dual-cycle constraint optimization, candidate training plans corresponding to each candidate training topology are obtained, and the candidate training plans are scored and sorted according to the convergence degree of physiological equilibrium state, the safety of load distribution and the risk constraint value, and the target endurance training plan is output.

2. The endurance training plan generation method based on constraint optimization according to claim 1, characterized in that, The step S2, which determines the historical daily training load index sequence, includes: mechanical power based on the endurance training kinematic data. With critical power Calculate normalized intensity The training load index for a single training session is determined based on the normalization intensity. ,in: in, The duration of a single training session. The intensity weighting parameter is greater than 1.

3. The endurance training plan generation method based on constraint optimization according to claim 1, characterized in that, In step S2, the acute load recursion coefficient and the chronic load recursion coefficient Each is determined by the acute time constant. and chronic time constant The parameters are determined and satisfy: in, .

4. The endurance training plan generation method based on constraint optimization according to claim 1, characterized in that, The deterministic bounded state mapping includes: first calculating a reference target state based on the subjective feedback data and the recovered motion state data. Then, based on the state correction amount Determine the target physiological homeostasis The risk constraint value is determined based on the subjective feedback data and the recovery motion state data, wherein: in, and These are the lower and upper limits of the allowed range for the target state, respectively. To integrate input data, For the maximum safe offset, This indicates the interval truncation operation.

5. The endurance training plan generation method based on constraint optimization according to claim 4, characterized in that, The state correction amount and the risk constraint value are determined by a machine learning model. The input of the machine learning model includes at least the current physiological balance state, the subjective feedback data, the recovery movement state features extracted from the recovery movement state data, the trainable time period features extracted from the calendar constraint data, the historical training load features extracted from the historical training data, and the historical plan execution result features extracted from the historical plan execution result data.

6. The endurance training plan generation method based on constraint optimization according to claim 1, characterized in that, The step S4 of generating a candidate training topology set includes: marking each planned day within the planning period as one of the training element types of easy run, quality class, long distance run and rest, and combining and arranging the training element types of each planned day to form the candidate training topology set.

7. The endurance training plan generation method based on constraint optimization according to claim 6, characterized in that, Step S4, which involves Boolean pruning based on the calendar constraint data and training mode constraints, includes at least one of the following: Candidate training topologies where two adjacent planned days are both quality classes are deemed infeasible. Set a minimum interval of days between two consecutive quality assessment sessions; The training elements for planned days within a preset number of days before the competition will be limited to reduced training types. The planned days corresponding to the aforementioned mandatory rest days shall be designated as rest days; Designate the planned days corresponding to non-training periods as rest days.

8. The endurance training plan generation method based on constraint optimization according to claim 1, characterized in that, The training load boundaries are set separately according to the training element type, wherein the planned rest day for the training element type satisfies: The planned days for training elements such as easy runs, quality sessions, and long-distance runs each have different training load ranges.

9. The endurance training plan generation method based on constraint optimization according to claim 1, characterized in that, In step S6, the total weekly change points The search boundary is determined by the half-interval width of each planned day, satisfying: The outer loop is based on the objective function To optimize the objective: in, For the point of change in the weekly report The predicted physiological equilibrium state at the end of the planning cycle is obtained.

10. A system for generating endurance training plans based on constraint optimization, characterized in that, include: The data acquisition module is used to acquire historical training data, subjective feedback data, recovery motion state data, historical plan execution result data, calendar constraint data, and training boundary data for each planned day within the planning period; The state quantification module is used to determine the historical daily training load index sequence based on the historical training data, and to calculate the current physiological equilibrium state based on the historical daily training load index sequence. The target state determination module is used to determine the target physiological balance state and risk constraint value through deterministic bounded state mapping based on the current physiological balance state, the subjective feedback data, and the recovery movement state data. The topology generation and pruning module is used to generate a set of candidate training topologies based on the training type boundary, and to perform Boolean pruning on the set of candidate training topologies based on the calendar constraint data and training mode constraints to obtain a set of feasible training topologies. The dual-loop constraint optimization module is used to establish a continuous load allocation model for each feasible training topology, construct the total weekly change point, and generate candidate training plans through continuous load allocation with outer loop bounded scalar search and inner loop equality constraints and boundary constraints. The scoring, ranking, and output module is used to score and rank each candidate training plan according to the degree of convergence of physiological equilibrium state, the safety of load distribution, and the risk constraint value, and output the target endurance training plan.

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