An old-age home key care resource estimation method based on time-varying gray level prediction information

Abstract

The present application relates to a kind of based on time-varying grey level prediction information's old-age homes key care resource estimation method, including the construction of old-age homes key care resource estimation's hierarchical architecture and clear its each level's composition content, establish double time-varying parameter dynamic grey prediction model and carry out parameter solution, the hierarchical architecture of old-age homes key care resource estimation constructed with double time-varying parameter dynamic grey prediction model is combined, constructs demand level estimation framework, obtains the estimation result of old-age homes key care resource layer by layer.The present application accurately depicts the dynamic change law of different levels of old-age homes key care resource demand, clear the demand trend of each type of care resource and level difference, realize the high-precision estimation of old-age homes key care resource.

Description

Technical Field

[0001] This invention relates to the field of elderly care service management system technology, and in particular to a method for estimating critical care resources in elderly care institutions based on time-varying gray hierarchy prediction information. Background Technology

[0002] Population aging is profoundly changing the operational logic of the elderly care service system. As the proportion of the elderly population continues to grow, estimating the critical care resource needs of elderly care institutions has become an increasingly important research area. On the one hand, different elderly individuals have varying requirements for care intensity and resource input levels, leading to a complex and diverse hierarchical structure in the care needs of elderly care institutions. The operation of elderly care institutions can essentially be viewed as a resource allocation system driven by heterogeneous care needs, with significantly different resource demand structures at different levels of need. On the other hand, care needs are not static; the evolution of the elderly's health status makes the transfer between different care levels a common occurrence. Allocating resources without considering the hierarchical structure of needs and its dynamic characteristics often leads to a mismatch between care resources and actual needs.

[0003] Regarding methods for predicting the demand for care resources in elderly care institutions, some scholars have conducted quantitative estimation studies. For example, by characterizing the heterogeneity of elderly care service demand, they estimate the manpower and service capacity requirements of elderly care institutions under different scenarios. By modeling the duration and intensity of care for the elderly in institutions, they quantitatively estimate the burden on care resources such as beds in elderly care institutions. On the other hand, a multi-category prediction method system integrating statistical modeling and intelligent prediction has gradually formed. In terms of statistical methods, some studies utilize survey data and employ statistical models such as regression analysis and state transition models to predict the level of care demand corresponding to health status and functional limitations. Statistical risk prediction methods based on regression are used to predict the probability of care placement-related outcomes for elderly patients and estimate the likelihood of individuals entering elderly care institutions. In terms of intelligent prediction, machine models are used to predict the probability of high-intensity care risks and the care service demand of high-care-demand groups. Deep learning models are used to predict all-cause mortality, home care demand, and the risk of admission to elderly care institutions among the elderly in Spain.

[0004] While existing research examines critical care needs in elderly care institutions from multiple perspectives, it largely focuses on analysis within each individual level, emphasizing single-level demand forecasting. However, the formation of care resource demand is not a result of a single level, but rather stems from overall demand, considering various factors at different levels, such as price positioning and group characteristics. Current research lacks sufficient connection between these levels and has not systematically addressed how to translate the forecasts of critical care needs at different levels into actionable resource allocation decisions at the institutional level. Therefore, it is necessary to distinguish the mechanisms of action at different levels during the demand forecasting process, thereby constructing a multi-level framework for forecasting critical care resource needs in elderly care institutions. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for estimating critical care resources in elderly care institutions based on time-varying grey hierarchical prediction information. This method overcomes the limitations of traditional methods in terms of the insufficient connection between different levels and the lack of a systematic solution for translating the predicted results of critical care needs at different levels into actionable resource allocation decisions at the institutional level. This invention deconstructs the hierarchical structure of care resource needs in elderly care institutions and explores dynamic prediction methods to assess future needs for multi-level elderly care resources. This allows for the reconstruction of the true demand structure within elderly care institutions under limited data conditions, providing a quantitative basis for resource allocation decisions and ensuring that the elderly population receives necessary support and services.

[0006] To achieve the above technical objectives, the present invention provides the following technical solution: a method for estimating critical care resources in elderly care institutions based on time-varying gray hierarchy prediction information, comprising the following steps: Construct a hierarchical framework for estimating critical care resources in elderly care institutions, and clarify the composition of each level; Data on the composition of each level of the hierarchical structure for estimating critical care resources in elderly care institutions was collected and preprocessed to obtain the care resource sequence of each level of the hierarchical structure for estimating critical care resources in elderly care institutions. A dual time-varying parameter dynamic grey prediction model is established; the dual time-varying parameter dynamic grey prediction model takes the original sequence as input and outputs the predicted value of the original sequence at any time point. Using the sequence of care resources at each level as the original sequence, the parameters to be solved in the dynamic grey prediction model with dual time-varying parameters for each level of the hierarchical structure for estimating key care resources in elderly care institutions are calculated; the parameters to be solved include fixed parameters and dynamic parameters. By utilizing a dynamic grey prediction model with dual time-varying parameters and the hierarchical framework for estimating critical care resources in elderly care institutions, the estimation results of critical care resources in elderly care institutions at each level are obtained by progressively obtaining the estimation results at the prediction time points.

[0007] Optionally, the hierarchical structure for estimating key care resources in elderly care institutions is a three-layer structure; the first layer describes the total scale of care resource demand for elderly people entering elderly care institutions; the second layer, under the total scale of care resource demand in the first layer, classifies care costs to obtain various care cost categories; the third layer, under the various care cost categories in the second layer, further classifies the disability status of the elderly to obtain various disability status categories.

[0008] Optionally, the care cost categories include three categories: low cost, medium cost, and high cost; The disability categories include four types: no disability, mild disability, moderate disability, and severe disability.

[0009] Optionally, the data on the composition of each level of the hierarchical structure for estimating critical care resources in elderly care institutions is collected and preprocessed to obtain the care resource sequence for each level of the hierarchical structure for estimating critical care resources in elderly care institutions, including: Collect the total scale data of care resource demand for the first layer. The total scale data of care resource demand is a single time series at continuous time points, which serves as the care resource sequence for the first layer. The second layer of care cost category data and the third layer of disability status category data are collected, wherein the care cost category data and the disability status category data are component data at discrete time points; The care cost category data and the disability status category data are interpolated to obtain a continuous sequence of the total number of care resource demand at the same time point as the total scale data of care resource demand, which is used as the component sequence of the second and third layers. The component sequences of the second and third layers are mapped to modeling sequences through a central logarithmic transformation, serving as care resource sequences for the third layer. This process is mathematically represented as follows: ; in, Represents the central logarithmic transformation. Represented by natural base Calculate the logarithm of the base; Indicates the component index; Indicates the number of components; Indicates a point-in-time index. , Indicates the total number of points in time; Indicates the first element in the component sequence Class components in the first Time-series values; Indicating the first step in the modeling sequence Class components in the first Time-series values; Indicates to exist Values ​​from 1 to Cumulative multiplication within a range; This represents the index for cumulative multiplication operations; its physical meaning is a component index. .

[0010] Optionally, the expression for the dual time-varying parameter dynamic grey prediction model is as follows: ; in, Indicates a point-in-time index. , Indicates the total number of points in time; The order of the operator applied to the original sequence; Indicates the original sequence after After the first-order cumulative generation, the second-order... The sequence values ​​at time points; let , For state coefficient functions, , It is a time trend function; , These are the exponent parameters of the power function terms in the state coefficient function and the time trend function, respectively; , , , These are dynamic parameters; This represents the coefficient of the constant term in the state coefficient function; This represents the coefficient of the first-order time term in the state coefficient function; This represents the coefficient of the power function term in the state coefficient function; This represents the coefficient of the constant term in the time trend function; This represents the coefficient of the first-order time term in the time trend function; This represents the coefficient of the power function term in the time trend function; , , , , , For fixed parameters; The dual time-varying parameter dynamic grey prediction model, original sequence of Rank sequence The definition satisfies the following form: ; in, Indicates the original sequence after After the first-order cumulative generation, the second-order... Time-series values; The index for the summation operation is physically a time point index; Represents the gamma function; Indicates the original sequence at the th Time-series values; Original sequence of The recurrence relation of the order sequence satisfies the following form: ; in, The index for the summation operation is physically a time point index; The dual time-varying parameter dynamic grey prediction model, combined with the solved parameters, calculates the cumulative sequence prediction value of the original sequence at any time point using a time response formula, and then restores the cumulative sequence prediction value to the original sequence prediction value using a cumulative subtraction restoration formula. This process is mathematically represented as follows: ; ; in, Indicates the first Accumulated sequence prediction values ​​at time points; , Indicates to exist Values ​​from 2 to Multiplication within a range; This is the index for cumulative multiplication operations; its physical meaning is a time point index. The index for the summation operation is physically a time point index; , , All of these are auxiliary functions related to time points introduced during the solution process of the dual time-varying parameter dynamic grey prediction model, used to simplify the formula expression. Indicates by The intermediate function obtained from the cumulative multiplication operation; Indicates the first The predicted values ​​of the original sequence at each time point.

[0011] Optionally, the step of using the care resource sequences at each level as the original sequences to solve for the parameters to be solved in the dual time-varying parameter dynamic grey prediction model at each level includes: The fixed parameters are solved using the least squares method; The particle swarm optimization algorithm is used to globally optimize the dynamic parameters, including: constructing an objective function that minimizes the global average relative simulation error, and solving for the optimal values ​​of the dynamic parameters; the objective function is mathematically represented as follows: ; in Indicates minimization. Indicates based on , A function for calculating the global average relative simulation error; This indicates the operation of calculating the absolute value.

[0012] Optionally, during the calculation of the parameters to be solved, a three-dimensional evaluation system is constructed using three indicators: average relative percentage error, standard deviation of relative percentage error, and average absolute scale error, to evaluate the performance of the dynamic grey prediction model with dual time-varying parameters.

[0013] Optionally, the mean relative percentage error, the standard deviation of the relative percentage error, and the mean absolute scale error are used to treat the care resource sequence of the first layer as the number of components. The component sequences are used in the calculation; The average relative percentage error is calculated as follows: ; in, Indicates the average relative percentage error; Indicates the component index; Indicates the number of components; This represents the index of a time point in the original sequence. , This represents the total number of time points in the original sequence; express The relative error; This indicates the absolute value operation; Indicates the original sequence number 1 Class components in the first Time-series values; Indicates the first Class components in the first Original sequence predictions at specific time points; The standard deviation of the relative percentage error is calculated as follows: , ; in, The standard deviation represents the relative percentage error. Indicates the first The average relative error of the class components; The average absolute scale error is calculated as follows: .

[0014] Optionally, the estimated results of critical care resources in elderly care institutions at each level of the dual time-varying parameter dynamic grey prediction model and the resulting hierarchical structure for estimating critical care resources in elderly care institutions are obtained level by level, including: Using a dual time-varying parameter dynamic grey prediction model, combined with the parameters to be solved in the first layer, the original sequence prediction values ​​of the prediction time points are generated using the care resource sequence of the first layer as the original sequence, which serve as the estimation results of the key care resources of elderly care institutions at the prediction time points of the first layer. Using a dual time-varying parameter dynamic grey prediction model, combined with the parameters to be solved in the second and third layers, the original sequence prediction values ​​of the prediction time points are generated using the care resource sequences of the second and third layers as the original sequences, respectively. Then, the component data ratio prediction values ​​of the prediction time points of the second and third layers are generated by using the inverse central logarithmic transformation. Multiply the estimated results of critical care resources for elderly care institutions at the first-level prediction time point by the predicted values ​​of component data proportions at the second-level prediction time point to obtain the estimated results of critical care resources for elderly care institutions at the second-level prediction time point. Multiply the estimated critical care resources of elderly care institutions at the second-level prediction time point by the predicted component data proportions at the third-level prediction time point to obtain the estimated critical care resources of elderly care institutions at the third-level prediction time point.

[0015] Optionally, the method of using a dual-time-varying parameter dynamic grey prediction model, combined with the parameters to be solved in the second and third layers, generates original sequence prediction values ​​for the prediction time points using the care resource sequences of the second and third layers as the original sequences, and then uses inverse central logarithmic transformation to generate component data ratio prediction values ​​for the prediction time points of the second and third layers, includes: The predicted values ​​of the original sequences generated by the dual time-varying parameter dynamic grey prediction model in the second and third layers are used as preliminary predicted values. An inverse central logarithmic transformation is performed on the preliminary predicted values ​​to obtain the component data proportion predicted values, which are mathematically represented as follows: ; in, Indicates the first Class components in the first The predicted proportion of component data at a given time point is used as the predicted proportion of component data. Indicates the first Class components in the first Original sequence prediction values ​​at time points, Represents the natural base.

[0016] By employing the above technical solution, the present invention provides a method for estimating critical care resources in elderly care institutions based on time-varying gray hierarchy prediction information, which has at least the following beneficial effects: (1) In terms of problem modeling, this invention characterizes the key care needs of elderly care institutions as structural problems with hierarchical and dynamic evolutionary features. It breaks through the traditional analysis perspective that focuses on total scale or single-level needs, and can more accurately reflect the multi-level structural characteristics and changing patterns of care needs of elderly care institutions. (2) At the method level, this invention constructs a demand hierarchy estimation framework that integrates a dynamic gray prediction model with dual time-varying parameters, which can realize the systematic estimation of implicit hierarchical care demand and effectively address the modeling problem under the conditions of limited data and complex hierarchy in the process of the evolution of elderly care service demand. (3) At the application level, this invention uses the constructed demand hierarchy estimation framework and dual time-varying parameter dynamic grey prediction model to characterize the evolution trend of the demand hierarchy of key care resources in elderly care institutions, and finally forms dynamic evolution curves of different care levels. This solves the decision-making problem of difficulty in accurately identifying the changing trend of hierarchical care demand in the resource allocation of elderly care institutions, and improves the scientificity and foresight of the resource allocation and operation management of elderly care institutions. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a method for estimating critical care resources in elderly care institutions based on time-varying gray hierarchy prediction information, according to the present invention. Figure 2 This is a schematic diagram of the critical care resource estimation process for elderly care institutions in an embodiment of the present invention; Figure 3 This is a schematic diagram showing the changes in the proportion of low-cost, medium-cost, and high-cost Level 2 nursing home bed care resource demand of the dual time-varying parameter dynamic grey prediction model constructed in this embodiment of the invention and the existing grey model over the years. Figure 4 This is a schematic diagram showing the changes in the proportion of low-cost, medium-cost, and high-cost nursing home bed care resource demand Level 2 of the dual time-varying parameter dynamic grey prediction model constructed in this embodiment of the invention and the existing non-grey model over the years. Figure 5 This is a schematic diagram illustrating the estimated demand for elderly care facility beds in different years in an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the estimated proportion of bed care costs in elderly care institutions in different years in an embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0019] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0020] Please refer to Figures 1-6 This illustration shows a specific implementation of the present embodiment. This embodiment constructs a hierarchical architecture for estimating critical care resources in elderly care institutions and clarifies the composition of each level. It establishes a dynamic grey prediction model with dual time-varying parameters and solves for the parameters. The constructed hierarchical architecture for estimating critical care resources in elderly care institutions is combined with the dynamic grey prediction model with dual time-varying parameters to construct a demand-level estimation framework. The estimation results of critical care resources in elderly care institutions are obtained level by level, accurately depicting the dynamic changes in the demand for critical care resources at different levels of elderly care institutions, clarifying the demand trends and hierarchical differences of various care resources, and achieving high-precision estimation of critical care resources in elderly care institutions.

[0021] Please refer to Figure 1 This embodiment proposes a method for estimating critical care resources in elderly care institutions based on time-varying grey level prediction information. The method includes the following steps:

[0022] S1. Construct a hierarchical framework for estimating critical care resources in elderly care institutions, and clarify the composition of each level.

[0023] As a preferred embodiment of step S1, it specifically includes:

[0024] The hierarchical structure for estimating critical care resources in elderly care institutions is a three-tier structure.

[0025] Level 1 depicts the total scale of care resource demand for elderly people residing in nursing homes, corresponding to the total demand for a certain type of care resource for elderly people residing in nursing homes, reflecting the scale of service demand.

[0026] Level 2, based on the total scale of care resource demand in Level 1, categorizes care costs into different cost classes. These cost classes include low-cost, medium-cost, and high-cost categories, represented as follows: , , This is to reflect the differences in the total demand structure under different cost constraints. Different fees correspond to different service configuration levels, and the elderly can make their choice of different institutions based on their own ability to pay and their needs.

[0027] Level 3 further categorizes the disability status of the elderly under the care cost categories of Level 2, resulting in four disability status categories: no disability, mild disability, moderate disability, and severe disability, denoted as Category 1, 2, 3, and 4, respectively. Based on this, Level 3 can construct combinations for specific elderly groups at different price points, such as... This represents low-cost, non-disabled elderly individuals, reflecting the actual care needs based on different care costs and different categories of elderly people, thus forming a hierarchical structure for estimating the critical care resource needs of elderly care institutions in three tiers: "overall – cost – disability".

[0028] At the problem modeling level, this invention characterizes the key care needs of elderly care institutions as a structural problem with hierarchical and dynamic evolutionary features. It breaks through the traditional analytical perspective that focuses on total scale or single-level needs, and can more accurately reflect the multi-level structural characteristics and changing patterns of bed care needs in elderly care institutions.

[0029] S2. Collect the component data of each level of the hierarchical structure for estimating critical care resources in elderly care institutions, and preprocess the data to obtain the care resource sequence of each level of the hierarchical structure for estimating critical care resources in elderly care institutions.

[0030] As a preferred embodiment of step S2, it specifically includes:

[0031] S21. Collect the total scale data of care resource demand in the first layer. The total scale data of care resource demand is a single time series at continuous time points, which serves as the care resource sequence of the first layer.

[0032] S22. Collect the care cost category data of the second layer and the disability status category data of the third layer. The care cost category data and the disability status category data are component data at discrete time points and are extracted from the database.

[0033] S23. The care cost category data and the disability status category data are interpolated to obtain a continuous sequence of the total number of care resource demand at the same time point as the total scale data, which is used as the component sequence of the second and third layers.

[0034] S24. The component sequences of the second and third layers are mapped to modeling sequences through central logarithmic transformation (CLR) as care resource sequences of the third and third layers.

[0035] Let the component sequence be represented as The modeling sequence is represented as The mathematical representation of the central logarithmic transformation process is as follows: ; in, Represents the central logarithmic transformation. Represented by natural base Calculate the logarithm of the base; Indicates the component index in the component sequence; Indicates the number of components in the component sequence; This represents the time point index in the care resource sequence (i.e., the time point index in the component sequence and subsequent modeling sequence). , This represents the total number of time points in the care resource sequence (i.e., the total number of time points in the component sequence and subsequent modeling sequence). Indicates the first element in the component sequence Class components in the first Time-series values; Indicating the first step in the modeling sequence Class components in the first Time-series values; Indicates to exist Values ​​from 1 to Cumulative multiplication within a range; This represents the index for cumulative multiplication operations; its physical meaning is a component index. Used for the first component in the component sequence Class components in the first Time-series values Perform cumulative multiplication.

[0036] This step uses the central logarithmic transformation as a technical means to map the original structural data to a modelable space. Its parameters reflect the systematic drift of the care resource structure around the equilibrium state, without changing the structural generation and evolution mechanism depicted by the model.

[0037] S3. Establish a dual time-varying parameter dynamic grey prediction model; the dual time-varying parameter dynamic grey prediction model takes the original sequence as input and outputs the predicted value of the original sequence at any time point.

[0038] The hierarchical architecture for estimating critical care resources in elderly care institutions constructed in step S1 features top-level data with high update frequency, strong timeliness, and relatively stable caliber. In contrast, subdivided-level data are typically presented in the form of "component data," exhibiting problems such as low update frequency and delayed publication, and are characterized by small sample size and incomplete information. Therefore, this invention constructs a dual-time-varying parameter dynamic grey prediction model suitable for estimating the demand for critical care resources with small samples and multiple levels. The dual-time-varying parameter dynamic grey prediction model constructs development coefficients by selecting a combination structure of linear terms and power function terms. Gray input The dual time-varying parameters aim to structurally characterize the nonlinear time evolution features of the system under small sample conditions, while intelligently optimizing the order. Double exponential parameters , .

[0039] As a preferred embodiment of step S3, the dual time-varying parameter dynamic grey prediction model is expressed as follows:

[0040] ;

[0041] in, Indicates a point-in-time index. , Indicates the total number of points in time; The order of the operator applied to the original sequence is used to avoid excessive smoothing or noise amplification of the needs for elderly care resources due to an excessively large order. Limited to Within the range; Indicates the original sequence after After the first-order cumulative generation, the second-order... The sequence values ​​at time points; let , This is a state coefficient function used to determine the coefficients of the accumulated sequence value from the previous time point at the current time point; , This is a time trend function used to determine the time trend in the model. Independent functions that change at specific points in time; , These are the exponent parameters of the power function terms in the state coefficient function and the time trend function, respectively, used to adjust the model's response to nonlinear changes. To ensure the model's stability and extrapolation rationality under small sample conditions, these parameters are... , All are limited to Within the range; , , , These are dynamic parameters. This represents the coefficient of the constant term in the state coefficient function; This represents the coefficient of the first-order time term in the state coefficient function; This represents the coefficient of the power function term in the state coefficient function; This represents the coefficient of the constant term in the time trend function; This represents the coefficient of the first-order time term in the time trend function; This represents the coefficient of the power function term in the time trend function; , , , , , These are fixed parameters.

[0042] The dual time-varying parameter dynamic grey prediction model, original sequence of Rank sequence The definition satisfies the following form: ; in, Indicates the original sequence after After the first-order cumulative generation, the second-order... Time-series values; The index for the summation operation is physically a time point index; Represents the gamma function; Indicates the original sequence at the th Time-series values;

[0043] Original sequence of The recurrence relation of the order sequence satisfies the following form: ; in, The index for the summation operation is physically a time point index;

[0044] The dual time-varying parameter dynamic grey prediction model, combined with the solved parameters, calculates the cumulative sequence prediction value of the original sequence at any time point using a time response formula, and then restores the cumulative sequence prediction value to the original sequence prediction value using a cumulative subtraction restoration formula. This process is mathematically represented as follows: ;

[0045] in, Indicates the first Accumulated sequence prediction values ​​at time points; , Indicates to exist Values ​​from 2 to Multiplication within a range; This is the index for cumulative multiplication operations; its physical meaning is a time point index. The index for the summation operation is physically a time point index; , , All of these are auxiliary functions related to time points introduced during the solution process of the dual time-varying parameter dynamic grey prediction model, used to simplify the formula expression. Indicates by The intermediate function obtained from the cumulative multiplication operation; Indicates the first The predicted values ​​of the original sequence at each time point.

[0046] S4. Using the care resource sequence at each level as the original sequence, calculate the parameters to be solved for each level of the hierarchical structure for estimating key care resources in elderly care institutions using a dynamic grey prediction model with dual time-varying parameters; the parameters to be solved include fixed parameters and dynamic parameters.

[0047] As a preferred embodiment of step S4, it specifically includes:

[0048] S41. Solve for the fixed parameters using the least squares method.

[0049] Specifically, , , , , , Constructed as a parameter matrix column , recorded as ,satisfy , This indicates the transpose operation. Representation matrix The inverse matrix, where, The response vector is composed of the adjacent differences of the sequence generated by accumulating the original sequence. This represents the parameter identification matrix, which consists of sequence terms, time terms, and nonlinear power terms generated by accumulating the original sequence. and The definition is as follows: ; .

[0050] S42. Utilizing the particle swarm optimization algorithm to globally optimize the dynamic parameters includes: constructing an objective function aimed at minimizing the global average relative simulation error, and solving for the optimal values ​​of the dynamic parameters; the objective function is mathematically represented as follows: ; in Indicates minimization. Indicates based on , A function for calculating the global average relative simulation error; This indicates the operation of calculating the absolute value.

[0051] More specifically, during the calculation of the parameters to be solved, a three-dimensional evaluation system is constructed using three indicators: average relative percentage error, standard deviation of relative percentage error, and average absolute scale error, to evaluate the performance of the dynamic grey prediction model with dual time-varying parameters.

[0052] The average relative percentage error is calculated as follows: ; in, Indicates the average relative percentage error; Indicates the component index; Indicates the number of components; This represents the index of a time point in the original sequence. , This represents the total number of time points in the original sequence; express The relative error; This indicates the absolute value operation; Indicates the original sequence number 1 Class components in the first Time-series values; Indicates the first Class components in the first The predicted values ​​of the original sequence at each time point.

[0053] The standard deviation of the relative percentage error is calculated as follows: , ; in, The standard deviation represents the relative percentage error. Indicates the first The average relative error of the class components.

[0054] The average absolute scale error is calculated as follows: .

[0055] This invention considers the first-layer care resource sequence as the number of components. The component sequences were used in the evaluation.

[0056] S5. Using the dual time-varying parameter dynamic grey prediction model and the hierarchical structure of the estimation of critical care resources in elderly care institutions obtained by solving, the estimation results of critical care resources in elderly care institutions at each level are obtained step by step.

[0057] As a preferred embodiment of step S5, it specifically includes:

[0058] S51. Using a dual time-varying parameter dynamic grey prediction model, combined with the parameters to be solved in the first layer, the original sequence prediction value of the prediction time point is generated using the care resource sequence of the first layer as the original sequence, and used as the estimation result of the key care resources of the elderly care institution at the prediction time point of the first layer.

[0059] S52. Using a dual time-varying parameter dynamic grey prediction model, combined with the parameters to be solved in the second and third layers, the original sequence prediction values ​​for the prediction time points are generated using the care resource sequences of the second and third layers as the original sequences, respectively. Then, the component data ratio prediction values ​​for the prediction time points of the second and third layers are generated by using the inverse central logarithmic transformation.

[0060] More specifically, as a preferred embodiment of step S52, it specifically includes:

[0061] The predicted values ​​of the original sequences generated by the dual time-varying parameter dynamic grey prediction model in the second and third layers are used as preliminary predicted values. An inverse central logarithmic transformation is performed on the preliminary predicted values ​​to obtain the component data proportion predicted values, which are mathematically represented as follows: ; in, Indicates the first Class components in the first The predicted proportion of component data at a given time point is used as the predicted proportion of component data. Indicates the first Class components in the first Original sequence prediction values ​​at time points, Represents the natural base.

[0062] S53. Multiply the estimated results of critical care resources in the first-tier elderly care institutions by the predicted proportion of component data in the second-tier institutions to obtain the estimated results of critical care resources in the second-tier elderly care institutions.

[0063] S54. Multiply the estimated results of critical care resources in the second-tier elderly care institutions by the predicted proportion of the component data in the third-tier to obtain the estimated results of critical care resources in the third-tier elderly care institutions.

[0064] The critical care resource estimation process for elderly care institutions in this embodiment can be referred to... Figure 2First, raw data is collected and processed. Then, Level 1 is predicted, followed by Level 2 and Level 3 predictions, thereby estimating the actual resource quantity at each level. Finally, the model is validated using three indicators: Mean Relative Percentage Error (MAPE), Mean Absolute Scale Error (MASE), and Standard Deviation of Relative Percentage Error (STD). In predicting Level 2 and Level 3, based on the construction of a dual-time-varying parameter dynamic grey prediction model similar to that used in predicting Level 1, a central logarithmic transformation is introduced to transform the component data. The construction process of the dual-time-varying parameter dynamic grey prediction model involves four steps: modeling sequence grouping, model definition, parameter solving, and model solving. Finally, an inverse central logarithmic transformation is performed on the obtained preliminary prediction values.

[0065] At the methodological level, this invention constructs a demand hierarchy estimation framework that integrates a dual-time-varying parameter dynamic grey prediction model. This framework enables a systematic estimation of implicit hierarchical care needs and effectively addresses modeling challenges arising from limited data and complex hierarchical structures in the evolution of elderly care service demand. At the application level, this invention, through the constructed demand hierarchy estimation framework and the dual-time-varying parameter dynamic grey prediction model, characterizes the evolutionary trends of hierarchical demand for key care resources in elderly care institutions. Ultimately, it generates dynamic evolution curves for different care levels, solving the decision-making problem of accurately identifying the changing trends of tiered care needs in the resource allocation of elderly care institutions. This improves the scientific rigor and foresight of resource allocation and operational management in elderly care institutions.

[0066] In this embodiment, based on the CLHLS database, the bed care resource needs of all elderly people entering elderly care institutions through the CLHLS database are selected and processed as the research object. Simultaneously, based on the CLHLS database data, three care cost categories—low cost, medium cost, and high cost—are derived according to different fee classifications of elderly care institutions, and four disability categories—non-disabled, mildly disabled, moderately disabled, and severely disabled—are derived from the degree of disability under each care cost category. To compare the advantages of the proposed dual time-varying parameter dynamic grey prediction model (abbreviated as ABSitadgm), several advanced grey models were selected for comparison: the GM(1,1) model optimized by order and background value (abbreviated as GM), the fractional-order DGM(1,1) model (abbreviated as DGM), the TDGM(1,1) model optimized by order and background value (abbreviated as TDGM), and the Verhulst model optimized by order and background value (abbreviated as Verhulst). Simultaneously, non-grey models, including the exponential nonlinear regression model (abbreviated as NLREG), the support vector regression model (abbreviated as SVR), and the weighted linear regression model (abbreviated as WLR), were selected for modeling and prediction.

[0067] According to the hierarchical structure set in step S1, the constituent content data is obtained. 85% of the constituent content data at each level is used as the training set to train the constructed dual time-varying parameter dynamic grey prediction model. The remaining 15% is used as the test set to test the prediction performance. Through simulation, the proportions of low-cost, medium-cost, and high-cost Level 2 of the elderly care institution bed care resource demand constructed in this invention and the existing grey models change with the year as follows: Figure 3 As shown, the proportions of low-cost, medium-cost, and high-cost elderly care resources in Level 2 of the existing non-grey model change with the years as follows: Figure 4 As shown. Figure 3 , Figure 4 The simulation results within the simulated prediction interval are presented as dashed lines.

[0068] The performance evaluation of each model (based on the three-dimensional evaluation system) is shown in Table 1.

[0069] Table 1. Performance evaluation results of Level 2 of the ABSitadgm constructed in this invention compared with existing grey and non-grey models for the demand for nursing home bed care resources.

[0070] The results show that, across different levels and data types, only in the Level 2 cost category does the MAPE-based evaluation slightly outperform the SVR model. However, numerically, the error of the ABsitadgm model in this invention is 1.956%, while that of SVR is 1.875%, both being low errors with minimal difference. In summary, although it does not achieve optimal performance on every individual metric, the ABsitadgm model proposed in this paper exhibits the lowest overall MAPE, overall MASE, and overall STD, demonstrating excellent performance and superior stability. The highest overall MAPE value is below 5%, belonging to Level 1 accuracy (>95%), reflecting the effectiveness and rationality of the proposed method.

[0071] The estimation results of the demand for beds in elderly care institutions in different years in this embodiment can be referred to Figure 5 The bed demand (in ten thousand beds) is categorized into three cost categories: low-cost, medium-cost, and high-cost care, and four disability categories: non-disabled, mildly disabled, moderately disabled, and severely disabled.

[0072] The estimated percentage of bed care costs in elderly care facilities for different years in this embodiment can be referenced. Figure 6 It includes the proportion of components in four disability categories—non-disabled, mildly disabled, moderately disabled, and severely disabled—under three care cost categories: low cost, medium cost, and high cost.

[0073] In summary, the method proposed in this invention constructs a novel grey prediction model targeting the specific needs of key care resources at different levels in elderly care institutions. Based on small sample data, the constructed model effectively captures the trends of different data structure sequences at each level and achieves high prediction accuracy. Furthermore, based on the time-varying grey prediction model, the evolution and demand estimates of key care resources at each level in elderly care institutions are obtained. This provides a new technical path and specific quantitative analysis results for modeling and calculating the allocation of care resources in elderly care institutions. It can provide a basis for optimizing the allocation of human, equipment, and service resources under different levels of care needs, thereby improving the accuracy of elderly care service supply and the efficiency of resource utilization.

[0074] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0075] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0076] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for estimating critical care resources in elderly care institutions based on time-varying grey hierarchy prediction information, characterized in that, include: Construct a hierarchical framework for estimating critical care resources in elderly care institutions, and clarify the composition of each level; Data on the composition of each level of the hierarchical structure for estimating critical care resources in elderly care institutions was collected and preprocessed to obtain the care resource sequence of each level of the hierarchical structure for estimating critical care resources in elderly care institutions. A dual time-varying parameter dynamic grey prediction model is established; the dual time-varying parameter dynamic grey prediction model takes the original sequence as input and outputs the predicted value of the original sequence at any time point. Using the sequence of care resources at each level as the original sequence, the parameters to be solved in the dynamic grey prediction model with dual time-varying parameters for each level of the hierarchical structure for estimating key care resources in elderly care institutions are calculated; the parameters to be solved include fixed parameters and dynamic parameters. By utilizing a dynamic grey prediction model with dual time-varying parameters and the hierarchical framework for estimating critical care resources in elderly care institutions, the estimation results of critical care resources in elderly care institutions at each level are obtained by progressively obtaining the estimation results at the prediction time points.

2. The method for estimating critical care resources in elderly care institutions based on time-varying grey level prediction information according to claim 1, characterized in that: The hierarchical structure for estimating key care resources in elderly care institutions is a three-layer structure. The first layer describes the total scale of care resource demand for elderly people entering elderly care institutions. The second layer, under the total scale of care resource demand in the first layer, classifies care costs to obtain various care cost categories. The third layer, under the care cost categories in the second layer, further classifies the disability status of the elderly to obtain various disability status categories.

3. The method for estimating critical care resources in elderly care institutions based on time-varying grey hierarchy prediction information according to claim 2, characterized in that: The care cost categories include three categories: low cost, medium cost, and high cost; The disability categories include four types: no disability, mild disability, moderate disability, and severe disability.

4. The method for estimating critical care resources in elderly care institutions based on time-varying grey level prediction information according to claim 2, characterized in that: The process involves collecting and preprocessing the data to determine the composition of each level of the hierarchical structure for estimating critical care resources in elderly care institutions. This yields a sequence of care resources for each level of the hierarchical structure, including: Collect the total scale data of care resource demand for the first layer. The total scale data of care resource demand is a single time series at continuous time points, which serves as the care resource sequence for the first layer. The second layer of care cost category data and the third layer of disability status category data are collected, wherein the care cost category data and the disability status category data are component data at discrete time points; The care cost category data and the disability status category data are interpolated to obtain a continuous sequence of the total number of care resource demand at the same time point as the total scale data of care resource demand, which is used as the component sequence of the second and third layers. The component sequences of the second and third layers are mapped to modeling sequences through a central logarithmic transformation, serving as care resource sequences for the third layer. This process is mathematically represented as follows: ； in, Represents the central logarithmic transformation. Represented by natural base Calculate the logarithm of the base; Indicates the component index; Indicates the number of components; Indicates a point-in-time index. , Indicates the total number of points in time; Indicates the first element in the component sequence Class components in the first Time-series values; Indicating the first step in the modeling sequence Class components in the first Time-series values; Indicates to exist Values ​​from 1 to Cumulative multiplication within a range; This represents the index for cumulative multiplication operations; its physical meaning is a component index. .

5. The method for estimating critical care resources in elderly care institutions based on time-varying grey level prediction information according to claim 1, characterized in that: The expression for the dual time-varying parameter dynamic grey prediction model is as follows: ； in, Indicates a point-in-time index. , Indicates the total number of points in time; The order of the operator applied to the original sequence; Indicates the original sequence after After the first-order cumulative generation, the second-order... The sequence values ​​at time points; let , For state coefficient functions, , It is a time trend function; , These are the exponent parameters of the power function terms in the state coefficient function and the time trend function, respectively; , , , These are dynamic parameters; This represents the coefficient of the constant term in the state coefficient function; This represents the coefficient of the first-order time term in the state coefficient function; This represents the coefficient of the power function term in the state coefficient function; This represents the coefficient of the constant term in the time trend function; This represents the coefficient of the first-order time term in the time trend function; This represents the coefficient of the power function term in the time trend function; , , , , , For fixed parameters; The dual time-varying parameter dynamic grey prediction model, original sequence of Rank sequence The definition satisfies the following form: ； in, Indicates the original sequence after After the first-order cumulative generation, the second-order... Time-series values; The index for the summation operation is physically a time point index; Represents the gamma function; Indicates the original sequence at the th Time-series values; Original sequence of The order sequence recurrence relation satisfies the following form: ； in, The index for the summation operation is physically a time point index; The dual time-varying parameter dynamic grey prediction model, combined with the solved parameters, calculates the cumulative sequence prediction value of the original sequence at any time point using a time response formula, and then restores the cumulative sequence prediction value to the original sequence prediction value using a cumulative subtraction restoration formula. This process is mathematically represented as follows: ； ； in, Indicates the first Accumulated sequence prediction values ​​at time points; , Indicates to exist Values ​​from 2 to Multiplication within a range; This is the index for cumulative multiplication operations; its physical meaning is a time point index. The index for the summation operation is physically a time point index; , , All of these are auxiliary functions related to time points introduced during the solution process of the dual time-varying parameter dynamic grey prediction model, used to simplify the formula expression. Indicates by An intermediate function obtained from cumulative multiplication; Indicates the first The predicted values ​​of the original sequence at each time point.

6. The method for estimating critical care resources in elderly care institutions based on time-varying grey level prediction information according to claim 5, characterized in that: The process of using the care resource sequences at each level as the original sequence to solve for the parameters to be solved in the dual time-varying parameter dynamic grey prediction model at each level includes: The fixed parameters are solved using the least squares method; The particle swarm optimization algorithm is used to globally optimize the dynamic parameters, including: constructing an objective function that minimizes the global average relative simulation error, and solving for the optimal values ​​of the dynamic parameters; the objective function is mathematically represented as follows: ； in Indicates minimization. Indicates based on , A function for calculating the global average relative simulation error; This indicates the operation of calculating the absolute value.

7. The method for estimating critical care resources in elderly care institutions based on time-varying grey level prediction information according to claim 4, characterized in that: In the process of solving the parameters to be solved, a three-dimensional evaluation system is constructed using three indicators: average relative percentage error, standard deviation of relative percentage error, and average absolute scale error, to evaluate the performance of the dynamic grey prediction model with dual time-varying parameters.

8. The method for estimating critical care resources in elderly care institutions based on time-varying grey hierarchy prediction information according to claim 7, characterized in that: The mean relative percentage error, the standard deviation of the relative percentage error, and the mean absolute scale error are used to treat the first-level care resource sequence as the number of components. The component sequences are used in the calculation; The average relative percentage error is calculated as follows: ； in, Indicates the average relative percentage error; Indicates the component index; Indicates the number of components; This represents the index of a time point in the original sequence. , This represents the total number of time points in the original sequence; express The relative error; This indicates the absolute value operation; Indicates the original sequence number 1 Class components in the first Time-series values; Indicates the first Class components in the first Original sequence predictions at specific time points; The standard deviation of the relative percentage error is calculated as follows: ， ； in, The standard deviation represents the relative percentage error. Indicates the first The average relative error of the class components; The average absolute scale error is calculated as follows: 。 9. The method for estimating critical care resources in elderly care institutions based on time-varying grey hierarchy prediction information according to claim 4, characterized in that: The dual time-varying parameter dynamic grey prediction model and the hierarchical structure of the estimation of critical care resources in elderly care institutions obtained by solving it are used to obtain the estimation results of critical care resources in elderly care institutions at each prediction time point level by level, including: Using a dual time-varying parameter dynamic grey prediction model, combined with the parameters to be solved in the first layer, the original sequence prediction values ​​of the prediction time points are generated using the care resource sequence of the first layer as the original sequence, which serve as the estimation results of the key care resources of elderly care institutions at the prediction time points of the first layer. Using a dual time-varying parameter dynamic grey prediction model, combined with the parameters to be solved in the second and third layers, the original sequence prediction values ​​of the prediction time points are generated using the care resource sequences of the second and third layers as the original sequences, respectively. Then, the component data ratio prediction values ​​of the prediction time points of the second and third layers are generated by using the inverse central logarithmic transformation. Multiply the estimated results of critical care resources for elderly care institutions at the first-level prediction time point by the predicted values ​​of component data proportions at the second-level prediction time point to obtain the estimated results of critical care resources for elderly care institutions at the second-level prediction time point. Multiply the estimated critical care resources of elderly care institutions at the second-level prediction time point by the predicted component data proportions at the third-level prediction time point to obtain the estimated critical care resources of elderly care institutions at the third-level prediction time point.

10. The method for estimating critical care resources in elderly care institutions based on time-varying grey hierarchy prediction information according to claim 9, characterized in that: The method utilizes a dual-time-varying parameter dynamic grey prediction model, combining the parameters to be solved in the second and third layers, to generate original sequence prediction values ​​for the prediction time points using the care resource sequences of the second and third layers as the original sequences, respectively. Then, it uses an inverse central logarithmic transformation to generate component data ratio prediction values ​​for the prediction time points of the second and third layers, including: The predicted values ​​of the original sequences generated by the dual time-varying parameter dynamic grey prediction model in the second and third layers are used as preliminary predicted values. An inverse central logarithmic transformation is performed on the preliminary predicted values ​​to obtain the component data proportion predicted values, which are mathematically represented as follows: ； in, Indicates the first Class components in the first The predicted proportion of component data at a given time point is used as the predicted proportion of component data. Indicates the first Class components in the first Original sequence prediction values ​​at time points, Represents the natural base.

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