Marketing activity effect prediction method based on marketing volume index probability density distribution

Abstract

The invention discloses a catering marketing activity effect prediction method based on marketing volume index probability distribution, and the method comprises the steps: constructing a prediction model which fuses a parameterized drift function representing a marketing volume index deterministic evolution trend, a parameterized spread function representing random fluctuation intensity, and a function describing probability density distribution, the three are fused through a Foke-Planck equation; receiving a parameter vector of the new marketing scheme; determining initial probability density distribution; generating an exclusive drift field function and an exclusive diffusion field function, and substituting the exclusive drift field function and the exclusive diffusion field function into the model for solving to obtain marketing volume index probability density distribution of future target time nodes; and carrying out visual display. The method breaks through the limitation of a traditional model, realizes total probability prediction, provides a multi-dimensional decision basis for catering enterprises, and improves the rationality of budget planning and the accuracy of risk control.

Description

Technical Field

[0001] This invention relates to the catering industry, and in particular to a method for predicting the effectiveness of marketing activities based on the probability density distribution of marketing volume index. Background Technology

[0002] In today's increasingly competitive catering industry, catering companies generally attract customers and increase sales through marketing activities such as new product launches, limited-time discounts, and cross-brand collaborations. Accurately predicting the effectiveness of catering marketing activities in advance has become a core need for companies to plan budgets and control risks.

[0003] In the past, the industry has primarily used "sales volume" as the core predictive indicator for the effectiveness of restaurant marketing activities, employing traditional statistical and econometric models such as Time Series Analysis (ARIMA), exponential smoothing, and multiple linear regression. These models rely on historical sales data, inferring future sales volume by fitting trends and seasonal patterns. However, they have significant limitations: the models can only handle linear relationships, cannot adapt to the complex relationship between restaurant marketing activities and market feedback, and are entirely dependent on structured historical data, essentially representing a lagging replication of "past patterns," unable to cope with the changing drivers of restaurant marketing effectiveness in the internet age.

[0004] In the internet age, data for restaurant marketing campaigns includes two core dimensions: "campaign data" and "user engagement data." "Event data" refers to the execution details of a restaurant marketing event plan, including specific parameters such as discount level (e.g., discount percentage, single item discount price), advertising budget (e.g., total online advertising investment, amount allocated to each channel), channel combination information (e.g., whether social media and local life platforms are covered), and event duration (e.g., number of days the event lasts, daily promotion periods). "User voice data" refers to unstructured user feedback data related to restaurant marketing activities on publicly available internet platforms. Specifically, this includes user-generated content (such as comments and reviews) related to the activity posted by users on social media platforms and restaurant review websites, as well as user interaction data (total likes, total comments, and total shares) corresponding to this content. User voice data directly reflects the market's attention to and word-of-mouth sentiment surrounding restaurant marketing activities, and is a key driver influencing the final conversion rate of the activity—positive word-of-mouth can quickly increase the activity's popularity, while the spread of negative reviews can lead to customer loss.

[0005] However, traditional statistical and econometric models have not incorporated user voice data into their prediction framework, nor have they realized the need to transform it into a mathematically modelable "marketing voice index." The marketing voice index is obtained by collecting user-generated content related to the target restaurant marketing campaign from public internet platforms, analyzing text sentiment through natural language processing, combining it with user interaction behavior data, and calculating it through weighted fusion. This can transform unstructured user voice data into a modelable scalar indicator that directly reflects the market's overall feedback to restaurant marketing campaigns.

[0006] More importantly, traditional forecasting models can only output a single "deterministic predicted value" (such as the predicted increase in sales), and cannot quantify the uncertainty of the effectiveness of restaurant marketing activities (such as the probability that the effect will not meet expectations). In fact, the core indicator for predicting the effectiveness of restaurant marketing activities should be the "probability density distribution of marketing volume index"—this distribution is a mathematical tool that describes all possible values ​​of the marketing volume index at a future moment and their corresponding probabilities. It can reflect both the "deterministic evolution trend" of the marketing volume index driven by the restaurant marketing activity plan (such as discount level, advertising budget) and the "intensity of random fluctuations" brought about by factors such as word-of-mouth dissemination and accidental interactive events in user voice data. Based on this distribution, companies can obtain key information such as expected volume and risk variance to comprehensively evaluate the benefits and risks of the activity.

[0007] Existing technologies lack an understanding of the marketing volume index and its probability density distribution, making it impossible to meet the demand for accurate and comprehensive prediction of the effects of catering marketing activities in the Internet era. There is an urgent need for a new prediction technology based on the probability density distribution of the marketing volume index. Summary of the Invention

[0008] The purpose of this invention is to provide a marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index, which can meet the needs of accurate and comprehensive catering marketing campaign effectiveness prediction in the Internet era, addressing the aforementioned problems.

[0009] The technical solution adopted in this invention is as follows:

[0010] This invention discloses a method for predicting the effectiveness of marketing campaigns based on the probability density distribution of marketing volume index. The method includes the following steps: Step 1: Construct a prediction model, which includes a parameterized drift function A(x(t),M) to characterize the deterministic evolution trend of the marketing volume index x(t), a parameterized diffusion function B(x(t),M) to characterize the intensity of the random fluctuations of the marketing volume index x(t), and a marketing volume index probability density distribution function P(x(t),t) to describe the probability density distribution of the marketing volume index over time; wherein, the drift function A(x(t),M) and the diffusion function B(x(t),M) are connected by the Falk-Planck equation and The marketing volume index probability density distribution function P(x(t),t) is fused to form the prediction model. Here, x(t) is the marketing volume index, which is obtained by collecting user-generated content related to the target catering marketing campaign from publicly available Internet platforms, analyzing text sentiment through natural language processing, and combining it with user interaction behavior data through weighted fusion calculation. M is the marketing parameter vector, which is a set of parameters obtained by extracting the core parameters that affect the effect of the catering marketing campaign, and integrating them after data format unification and dimension standardization. Step 2: Receive the new restaurant marketing campaign plan to be predicted and obtain the new marketing parameter vector M. new ; Step 3: Determine the initial probability density distribution P(x(t),t0), where the initial probability density distribution P(x(t),t0) is the probability density distribution of the marketing volume index of the new catering marketing campaign plan at the prediction start time t0; Step 4: Based on the new marketing parameter vector M of the new catering marketing campaign plan new By calling the parameterized drift function A(x(t),M) and the diffusion function B(x(t),M), a custom drift field function A(x(t),M) adapted to the new catering marketing campaign plan is generated. new ) and the specific diffusion field function B(x(t),M new Then, the specific drift field function A(x(t),M new ), and the dedicated diffusion field function B(x(t),M new Substituting the initial probability density distribution P(x(t), t0) into the prediction model, we obtain the future target time node t. f The probability density distribution of the marketing volume index P(x(t),t) f ); Step 5: Calculate the probability density distribution of the marketing volume index P(x(t),t) f (This will be used to visualize the presentation.)

[0011] Furthermore, the specific implementation process of step 1 is as follows: Step 1.1: Collect activity data and user voice data from multiple catering marketing campaigns, and extract the marketing parameter vector M corresponding to each catering marketing campaign based on the activity data; Step 1.2: Based on user voice volume data, calculate the impact of each catering marketing campaign at each discrete time point t. k Marketing volume observation x(t) k ), and set each discrete time point t k Marketing volume observation x(t) k Aggregate data chronologically to generate a time series of marketing volume observations for each catering marketing campaign plan; the discrete time point t k This refers to the observed value of marketing volume x(t) k The discrete time points used for statistical calculations are k, where k is the index of the discrete time point and represents the specific observation sample of the continuous time variable t. The marketing volume observation time series refers to the same catering marketing campaign plan across all discrete time points t. k Marketing volume observation x(t) k A data sequence arranged in chronological order; Step 1.3: Based on the time series of marketing volume observation values ​​for each catering marketing campaign plan, calculate the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)) at different marketing volume index x(t) levels through the steps of dividing the volume value range interval and classifying data points, calculating interval statistical estimates, and establishing functional relationships. Step 1.4: Construct a training dataset, which includes the marketing parameter vector M corresponding to each catering marketing activity plan, the marketing volume index x(t) of the catering marketing activity corresponding to the plan, the experience drift coefficient A(x(t)) and the experience diffusion coefficient B(x(t)), and the parameterized drift function A(x(t),M) and the parameterized diffusion function B(x(t),M) are trained using machine learning algorithms; Step 1.5: The parameterized drift function A(x(t),M) and parameterized diffusion function B(x(t),M) are fused with the probability density distribution function P(x(t),t) of the marketing volume index through the Falk-Planck equation to form a complete prediction model.

[0012] Furthermore, the specific process of extracting the marketing parameter vector M corresponding to each catering marketing activity plan in step 1.1 is as follows: extract the core parameters affecting the effectiveness of the catering marketing activities from the activity data of the catering marketing activity plan. The core parameters include at least one of the following: discount level, advertising budget, channel combination information, and activity duration; perform data format unification processing on the extracted core parameters; perform dimensional standardization processing on the core parameters after unification; and integrate the standardized core parameters to form the marketing parameter vector M corresponding to the catering marketing activity plan.

[0013] Furthermore, in step 1.2, the marketing volume observation value x(t) is calculated. k The specific process of generating a time series of marketing volume observations is as follows: collect user-generated content related to the target restaurant marketing campaign plan from publicly available internet platforms; Natural language processing is performed on the collected user-generated content to extract the sentiment score S for each text. i The emotional score S i The value range of is [-1, 1]; Statistical analysis at each discrete time point t k User interaction behavior data, the interaction behavior data including the discrete time point t k The total number of likes (t) of all relevant user-generated content within the app. k ), total number of comments (t) k ) and total number of shares (t) k The total number of likes (t) k ) refers to the discrete time point t k The total number of likes and comments received by all relevant user-generated content. k ) refers to the discrete time point t k The total number of comments received by all relevant user-generated content, and the total number of shares (t) k ) refers to the discrete time point t k The total number of reposts and shares received by all relevant user-generated content within the platform; The text sentiment score and user interaction behavior data are weighted and fused to obtain the discrete time point t. k Marketing volume observation x(t) k The specific formula is: ; Wherein, N(t) k ) represents time node t k The total number of user-generated content related to the target restaurant marketing campaign collected internally; For time node t k The average sentiment score of all relevant user-generated content within the platform; For time node t k The weighted total interaction volume of all relevant user-generated content within the platform; , These are preset weighting coefficients; the same restaurant marketing campaign plan will be weighted at all discrete time points t. k Marketing volume observation x(t) kArrange the data in chronological order to generate a time series of marketing volume observations for this catering marketing campaign plan; It is represented as {x(t0), x(t1), x(t2), ..., x(t)} n )}, where t0, t1, t2, ..., t n Discrete time points t arranged in chronological order k .

[0014] Furthermore, the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)) in step 1.3 are determined according to the following steps: Step 1.3.1: Sequence Difference Calculation: For each catering marketing campaign plan, calculate the time series of marketing volume observations {x(t0), x(t1), x(t2), ..., x(t...}}. n )}, traverse all consecutive discrete time points t in the sequence. k Calculate the difference Δx between the observed marketing volume values ​​at adjacent discrete time points. k =x(t k+1 )-x(t k ), and the time interval Δt between adjacent discrete time points. k =t k+1 -t k This forms a group of multiple sets (x(t) k ),Δx k ,Δt k The basic dataset consists of ) Step 1.3.2: Based on the marketing volume observation value x(t) of the catering marketing campaign plan. k The overall value range of the marketing volume index x(t) is divided into multiple continuous and non-overlapping numerical intervals using an equal-interval method. For each numerical interval, all marketing volume observations x(t) are selected from the basic dataset. k The data points whose values ​​fall within this numerical range, and the index of the data point and the discrete time point t k The index k is consistent; integrate the index k corresponding to all the selected data points to form a data point index set S specific to this numerical range; Step 1.3.3: Interval Statistical Estimation Calculation: For each numerical interval, count the total number N of data points in the corresponding data point index set S. S Then, the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)) of the marketing volume index x(t) within this interval are calculated using the following formulas: ; ; Where, N SThe total number of data points N in the data point index set S S Δx k Δt represents the difference in marketing volume observations between adjacent discrete time points. k The time interval between adjacent discrete time points; Step 1.3.4: Establishing the functional relationship: By executing steps 1.3.2 and 1.3.3, establish the mapping relationship between the value of the marketing volume index x(t) and the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)), thereby converting the discrete marketing volume observation time series data into a continuous function estimate of the marketing volume index x(t).

[0015] Furthermore, in step 1.5, the constructed prediction model is as follows: ; in, The partial derivative of the probability density distribution function of the marketing volume index with respect to time represents the rate of change of the probability density distribution over time. The partial derivative of the drift term with respect to the marketing volume index is used to characterize the directional evolution trend of the marketing volume index. is the second partial derivative of the diffusion term with respect to the marketing volume index; used to characterize the random fluctuation characteristics of the marketing volume index.

[0016] Furthermore, the specific process of determining the initial probability density distribution P(x(t),t0) in step 3 is as follows: determine the execution status of the new catering marketing campaign plan; if the plan has not been started, set the initial probability density distribution P(x(t),t0) to a narrow-peak Gaussian distribution centered on the marketing volume index x(t)=0; if the plan has been started, collect user volume data from the start of the plan to the predicted start time t0 in real time, calculate the observed value of the marketing volume index x(t0) at that time, and set the initial probability density distribution P(x(t),t0) to a narrow-peak Gaussian distribution centered on the observed value of the marketing volume x(t0).

[0017] Furthermore, in step 4, the future target time node t is obtained. f The probability density distribution of the marketing volume index P(x(t),t) f The specific process is as follows: The specific drift field function A(x(t),M new ), and the dedicated diffusion field function B(x(t),M new Substituting the initial probability density distribution P(x(t),t0) into the Fock-Planck equation, The specific form of the Fock-Planck equation is as follows: ; The initial condition is P(x(t), t0). This equation is solved using the finite difference method or Monte Carlo simulation method to obtain the future target time node t. f The probability density distribution of the marketing volume index P(x(t),t) f ).

[0018] Furthermore, the visualization method in step 5 includes generating one or more of the following: probability distribution curves, probability interval statistical charts, and cumulative probability distribution charts; simultaneously, based on the probability density distribution P(x(t),t) of the marketing voice index. f Calculate and output key metrics, which include one or more of expected volume, risk variance, and success probability.

[0019] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: This invention constructs a predictive model that integrates a parameterized drift function, a parameterized diffusion function, and a probability density distribution function of the marketing volume index. By leveraging the Falk-Planck equation to combine the deterministic evolutionary trend and stochastic fluctuation intensity of restaurant marketing activities, and using the marketing volume index as the core predictive indicator, it comprehensively captures the core driving factors of restaurant marketing activities in the internet age. Breaking through the limitations of traditional models that rely solely on historical sales data, this invention achieves full probability prediction of the effectiveness of restaurant marketing activities. It not only outputs the complete probability distribution of the future marketing volume index but also provides enterprises with multi-dimensional decision-making support, effectively improving the rationality of budget planning and the accuracy of risk control. This solves the core problem of existing technologies' inability to quantify the uncertainty of marketing activities. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0022] This invention discloses a method for predicting the effectiveness of marketing campaigns based on the probability density distribution of marketing volume index. The method includes the following steps: Step 1: Construct a prediction model, which includes a parameterized drift function A(x(t),M) for characterizing the deterministic evolution trend of the marketing volume index x(t), a parameterized diffusion function B(x(t),M) for characterizing the intensity of random fluctuations in the marketing volume index x(t), and a marketing volume index probability density distribution function P(x(t),t) for describing the probability density distribution of the marketing volume index over time. The drift function A(x(t),M) and the diffusion function B(x(t),M) are fused with the marketing volume index probability density distribution function P(x(t),t) through the Falk-Planck equation to jointly constitute the prediction model. The Falk-Planck equation is a partial differential equation describing the probability density evolution of a stochastic process, used to integrate the influence of deterministic evolution trend and random fluctuation intensity on the probability distribution of the marketing volume index. Here, x(t) represents the marketing volume index probability distribution. The Marketing Volume Index (MVI) is a scalar indicator calculated by collecting user-generated content related to the target restaurant marketing campaign from publicly available internet platforms, analyzing text sentiment through natural language processing, and combining it with user interaction data. It is used to intuitively reflect the overall strength of market feedback and the direction of word-of-mouth regarding the restaurant marketing campaign. `t` is a continuous time variable used to describe the continuous evolution of the Marketing Volume Index `x(t)` over time. `M` is a marketing parameter vector, a set of parameters obtained by extracting core parameters affecting the campaign's effectiveness from the restaurant marketing campaign plan, and integrating them after standardizing data format and dimensions. These core parameters originate from the campaign data of the restaurant marketing campaign plan. The campaign data refers to the execution details of the restaurant marketing campaign plan, including discount levels, advertising budgets, channel combination information, campaign duration, and other parameter data used to define the core content of the restaurant marketing campaign plan. Step 2: Receive the new restaurant marketing campaign plan to be predicted and obtain the new marketing parameter vector M. new The new marketing parameter vector Mnew is the marketing parameter vector corresponding to the new catering marketing activity plan to be predicted, and its construction method is consistent with that of the marketing parameter vector M. Step 3: Determine the initial probability density distribution P(x(t), t0), where P(x(t), t0) is the probability density distribution of the marketing volume index of the new catering marketing campaign plan at the prediction start time t0; the prediction start time t0 refers to the starting time point for predicting the effect of the catering marketing campaign, which is a discrete time point t. k The scope of the marketing volume index probability density distribution is a mathematical tool that describes all possible values ​​of the marketing volume index at a certain moment and their corresponding probabilities. Step 4: Based on the new marketing parameter vector M of the new catering marketing campaign plan newBy calling the parameterized drift function A(x(t),M) and the diffusion function B(x(t),M), a custom drift field function A(x(t),M) adapted to the new catering marketing campaign plan is generated. new ) and the specific diffusion field function B(x(t),M new The specific drift field function A(x(t),M) new ) is a parameterized drift function adapted to the new catering marketing campaign plan, used to characterize the deterministic evolution trend of the marketing volume index driven by the new catering marketing campaign plan; the exclusive diffusion field function B(x(t),M new ) is a parameterized diffusion function adapted to new catering marketing campaign plans, used to characterize the random fluctuation intensity of the marketing volume index under the new catering marketing campaign plan scenario; then the exclusive drift field function A(x(t),M new ), and the dedicated diffusion field function B(x(t),M new Substituting the initial probability density distribution P(x(t), t0) into the prediction model, we obtain the future target time node t. f The probability density distribution of the marketing volume index P(x(t),t) f The future target time node t f This refers to a future point in time where the effectiveness of a restaurant marketing campaign needs to be predicted; it belongs to the discrete time point t. k The scope; Step 5: Calculate the probability density distribution of the marketing volume index P(x(t),t) f (This will be used to visualize the presentation.)

[0023] By employing the aforementioned methods, this invention constructs a predictive model that integrates a parameterized drift function, a parameterized diffusion function, and a probability density distribution function of the marketing volume index. It leverages the Falk-Planck equation to combine the deterministic evolutionary trend and stochastic fluctuation intensity of restaurant marketing activities, using the marketing volume index as the core predictive indicator to comprehensively capture the core driving factors of restaurant marketing activities in the internet age. Breaking through the limitations of traditional models that rely solely on historical sales data, this invention achieves full probability prediction of the effectiveness of restaurant marketing activities. It not only outputs the complete probability distribution of the future marketing volume index but also provides enterprises with multi-dimensional decision-making support, effectively improving the rationality of budget planning and the accuracy of risk control. This solves the core problem of existing technologies' inability to quantify the uncertainty of marketing activities.

[0024] Furthermore, the specific implementation process of step 1 is as follows: Step 1.1: Collect activity data and user engagement data for multiple restaurant marketing campaigns, and extract the marketing parameter vector M corresponding to each campaign based on the activity data. The user engagement data refers to unstructured user feedback data related to restaurant marketing activities on publicly available internet platforms, specifically including user-generated content (such as comments and reviews) related to the campaigns posted by users on social media platforms and restaurant review websites, as well as user interaction data (total likes, total comments, and total shares) corresponding to this user-generated content. User-generated content refers to text information related to restaurant marketing campaigns published independently by internet users, and user interaction data refers to data generated by users interacting with user-generated content. Step 1.2: Based on user voice volume data, calculate the impact of each catering marketing campaign at each discrete time point t. k Marketing volume observation x(t) k ), and set each discrete time point t k Marketing volume observation x(t) k Aggregate data chronologically to generate a time series of marketing volume observations for each catering marketing campaign; the discrete time point t k This refers to the observed value of marketing volume x(t) k The discrete time points used for statistical calculations are k, where k is the index of the discrete time point (e.g., t1 corresponds to the first discrete time point, t2 corresponds to the second discrete time point), and k is the specific observation sample of the continuous time variable t. The marketing volume observation value time series refers to the same catering marketing activity plan at all discrete time points t. k Marketing volume observation x(t) k A data sequence arranged in chronological order; Step 1.3: Based on the time series of marketing volume observation values ​​for each catering marketing campaign plan, calculate the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)) at different marketing volume index x(t) levels through the steps of dividing the volume value range interval and classifying data points, calculating interval statistical estimates, and establishing functional relationships. Step 1.4: Construct a training dataset, which includes the marketing parameter vector M corresponding to each catering marketing activity plan, the marketing volume index x(t) of the catering marketing activity corresponding to the plan, the experience drift coefficient A(x(t)) and the experience diffusion coefficient B(x(t)), and the parameterized drift function A(x(t),M) and the parameterized diffusion function B(x(t),M) are trained using machine learning algorithms; Step 1.5: The parameterized drift function A(x(t),M) and parameterized diffusion function B(x(t),M) are fused with the probability density distribution function P(x(t),t) of the marketing volume index through the Falk-Planck equation to form a complete prediction model.

[0025] This invention constructs a universally applicable predictive model by collecting historical marketing activity data and user voice data for the catering industry. This model can learn the intrinsic relationship between marketing parameters and voice evolution from historical data, ensuring that the predictive model has strong generalization ability and can be adapted to different types of catering marketing activity plans. This avoids the problem of prediction failure due to lack of historical data. At the same time, the standardized modeling process improves the standardization and efficiency of model construction, providing reliable model support for subsequent accurate predictions.

[0026] Furthermore, the specific process of extracting the marketing parameter vector M corresponding to each catering marketing activity plan in step 1.1 is as follows: The activity data is the execution details of each catering marketing activity plan, including parameter data such as discount level, advertising budget, channel combination information, and activity duration used to define the core content of the catering marketing activity plan; Extract core parameters that affect the effectiveness of restaurant marketing campaigns from the campaign data of the campaign plan. The core parameters include at least one of the following: discount level (such as the percentage of discounts for purchases over a certain amount, the discount price of a single item), advertising budget (such as the total investment in online advertising, the amount allocated to each channel), channel combination information (such as whether social media and local life platforms are covered), and campaign duration (such as the number of days the campaign lasts, the daily promotion period). The extracted core parameters are processed to unify their data format. The data format unification processing refers to the operation of converting the core parameters of different formats into a unified data format. The core parameters after the unified format are subjected to dimensional standardization; the dimensional standardization refers to the operation of eliminating the differences in the dimensions of different core parameters and mapping the parameter values ​​to a unified numerical range; the standardized core parameters are integrated to form the marketing parameter vector M corresponding to the catering marketing activity plan.

[0027] This invention explicitly extracts core parameters from activity data of catering marketing campaigns and eliminates interference caused by parameter differences through data format standardization and dimensional standardization, ensuring that the marketing parameter vector accurately represents the core features of the marketing campaign. This makes the construction of the marketing parameter vector more scientific and consistent, avoiding model training bias caused by inconsistent parameter formats or dimensions, improving the training accuracy of the parameterized drift function and diffusion function, and laying the foundation for subsequent accurate generation of dedicated field functions and improved prediction accuracy.

[0028] Furthermore, in step 1.2, the marketing volume observation value x(t) is calculated. k The specific process of generating a time series of marketing volume observations is as follows: The user volume data includes user-generated content and corresponding user interaction behavior data related to various catering marketing campaigns on publicly available internet platforms; collect user-generated content related to the target catering marketing campaigns on publicly available internet platforms. Natural language processing is performed on the collected user-generated content to extract the sentiment score S for each text. i The emotional score S i The value range of is [-1, 1]; Statistical analysis at each discrete time point t k User interaction behavior data, the interaction behavior data including the discrete time point t k The total number of likes (t) of all relevant user-generated content within the app. k ), total number of comments (t) k ) and total number of shares (t) k The total number of likes (t) k ) refers to the discrete time point t k The total number of likes and comments received by all relevant user-generated content. k ) refers to the discrete time point t k The total number of comments received by all relevant user-generated content, and the total number of shares (t) k ) refers to the discrete time point t k The total number of reposts and shares received by all relevant user-generated content within the platform; The text sentiment score and user interaction behavior data are weighted and fused to obtain the discrete time point t. k Marketing volume observation x(t) k The specific formula is: ; Wherein, N(t) k ) represents time node t k The total number of user-generated content related to the target restaurant marketing campaign collected internally; For time node t k The average sentiment score of all relevant user-generated content within the platform; For time node t k The weighted total interaction volume of all relevant user-generated content within the platform; , These are preset weighting coefficients; the same restaurant marketing campaign plan will be weighted at all discrete time points t. k Marketing volume observation x(t)k Arrange the data in chronological order to generate a time series of marketing volume observations for this catering marketing campaign plan; It is represented as {x(t0), x(t1), x(t2), ..., x(t)} n )}, where t0, t1, t2, ..., t n Discrete time points t arranged in chronological order k .

[0029] This invention transforms unstructured user voice volume data into a modelable marketing voice volume index through natural language processing, interactive data statistics, and weighted fusion calculation, generating a time series that fully preserves the temporal evolution characteristics of user voice volume. It achieves standardized quantification of user voice volume data, making previously unusable unstructured data a core basis for prediction. Simultaneously, by fully presenting the patterns of voice volume changes through time series analysis, it provides high-quality data for empirical coefficient calculation and model training, ensuring that the predictive model accurately reflects the dynamic feedback of the market to catering marketing activities.

[0030] Furthermore, the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)) in step 1.3 are determined according to the following steps: Step 1.3.1: Sequence Difference Calculation: For each catering marketing campaign plan, calculate the time series of marketing volume observations {x(t0), x(t1), x(t2), ..., x(t...}}. n )}, traverse all consecutive discrete time points t in the sequence. k (k=0,1,2,…,n, k is the discrete time point t) k index, t k This represents the k-th specific observation time point, including the predicted start time point t0 (corresponding to k=0) and the future target time point t. f (At key discrete moments), calculate the difference Δx between marketing volume observations at adjacent discrete time points. k =x(t k+1 )-x(t k ), and the time interval Δt between adjacent discrete time points. k =t k+1 -t k This forms a group of multiple sets (x(t) k ),Δx k ,Δt k The basic dataset consists of ) Step 1.3.2: Based on the marketing volume observation value x(t) of the catering marketing campaign plan. kThe overall value range of the marketing volume index x(t) is divided into multiple continuous and non-overlapping numerical intervals using an equal-interval method. For each numerical interval, all marketing volume observations x(t) are selected from the basic dataset. k The data points whose values ​​fall within this numerical range, and the index of the data point and the discrete time point t k The index k is consistent; integrate the index k corresponding to all the selected data points to form a data point index set S specific to this numerical range; Step 1.3.3: Interval Statistical Estimation Calculation: For each numerical interval, count the total number N of data points in the corresponding data point index set S. S Then, the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)) of the marketing volume index x(t) within this interval are calculated using the following formulas: ; ; Where, N S The total number of data points N in the data point index set S S Δx k Δt represents the difference in marketing volume observations between adjacent discrete time points. k t represents the time interval between adjacent discrete time points; A(x(t)) is used to characterize the average evolution trend of the marketing volume index x(t) within this interval, and B(x(t)) is used to characterize the average fluctuation intensity of the marketing volume index x(t) within this interval; here t is a continuous time variable, and the marketing volume index x(t) is a general variable symbol, referring to the volume index at any continuous time point, and its value range covers all divided numerical intervals; Step 1.3.4: Establishing the functional relationship: By executing steps 1.3.2 and 1.3.3, establish the mapping relationship between the value of the marketing volume index x(t) and the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)), thereby converting the discrete marketing volume observation time series data into a continuous function estimate of the marketing volume index x(t).

[0031] This invention, based on statistical analysis methods, accurately extracts empirical drift and diffusion coefficients at different volume levels from the time series of marketing volume observations of catering marketing campaigns. This is achieved through sequence differencing, value range classification, interval statistical estimation, and functional relationship establishment. The invention quantifies the average evolution trend and fluctuation intensity of the marketing campaign's volume, constructing a mapping relationship between volume values ​​and empirical coefficients. This provides high-quality foundational data for training parameterized drift and diffusion functions, enabling the subsequently trained functions to accurately characterize the evolutionary patterns at different marketing volume index levels. It effectively captures the deterministic trends and random fluctuations of catering marketing campaigns at different volume stages, significantly improving the adaptability of parameterized functions to actual marketing scenarios. This lays a crucial foundation for the prediction model to accurately simulate the volume evolution process and improve the reliability of the final prediction results.

[0032] Furthermore, in step 1.5, the constructed prediction model is as follows: ; in, The partial derivative of the probability density distribution function of the marketing volume index with respect to time represents the rate of change of the probability density distribution over time. The partial derivative of the drift term with respect to the marketing volume index is used to characterize the directional evolution trend of the marketing volume index. is the second partial derivative of the diffusion term with respect to the marketing volume index; used to characterize the random fluctuation characteristics of the marketing volume index.

[0033] This invention integrates the parameterized drift function with the diffusion function and the probability density distribution function of the marketing volume index using the Falk-Planck equation. Leveraging the equation's precise ability to describe the probability density evolution of stochastic processes, a complete predictive model is constructed. This model enables the prediction model to simulate the evolution of the marketing volume index from a mechanistic perspective, simultaneously considering both the deterministic driving force of marketing campaigns and the random fluctuations of the market. Compared to traditional models, it better reflects the actual evolutionary logic of restaurant marketing activities, significantly improving the scientific rigor and accuracy of the predictions.

[0034] Furthermore, the specific process for determining the initial probability density distribution P(x(t),t0) in step 3 is as follows: Determine the execution status of the new restaurant marketing campaign plan; the execution status includes "not started" and "started". "Not started" means that the new restaurant marketing campaign plan has not yet started implementation, and "started" means that the new restaurant marketing campaign plan has started implementation and is in progress. If the campaign is not initiated, the initial probability density distribution P(x(t), t0) is set as a narrow-peak Gaussian distribution centered at the marketing volume index x(t) = 0. The narrow-peak Gaussian distribution refers to a Gaussian distribution with minimal variance and probability density concentrated near the central value, representing a neutral and minimally fluctuating initial volume corresponding to the uninitiated catering marketing campaign. t0 is the prediction start time point, belonging to the discrete time point t. k The category (corresponding to k=0); If the plan has been launched, real-time data on user engagement (including user-generated content and corresponding user interaction data related to the new catering marketing campaign plan on publicly available internet platforms during that period) will be collected from the launch of the plan to the predicted start time node t0. Natural language processing is performed on the collected user-generated content to extract the sentiment score S for each text. i Statistically predict user interaction behavior data (including total likes(t0), total comments(t0), and total shares(t0)) corresponding to the starting time node t0. Then, the marketing volume index observation value x(t0) at this time point is obtained through weighted fusion calculation. The specific calculation formula is as follows: ; Wherein, N(t0) is the total number of user-generated content related to the new catering marketing campaign plan collected within the time range corresponding to the prediction start time node t0; , The weighting coefficients are preset; the marketing volume index observation value x(t0) is the actual value of the marketing volume index calculated based on the actual user volume data at the predicted start time node t0; finally, the initial probability density distribution P(x(t),t0) is set as a narrow-peak Gaussian distribution centered on x(t0).

[0035] This invention sets reasonable initial probability density distributions based on the execution status of a new catering marketing campaign (not started / started). When not started, a neutral volume is used as the center; when started, an initial volume index is calculated based on real-time collected user volume data, ensuring a high degree of match between the initial conditions and the actual scenario. This avoids the blind setting of initial conditions, making the input of the prediction model more closely aligned with reality. Whether predicting a brand-new campaign in advance or a rolling prediction of an ongoing campaign, it improves the accuracy of the prediction results, providing more targeted support for marketing decisions at different stages.

[0036] Furthermore, in step 4, the future target time node t is obtained. f The probability density distribution of the marketing volume index P(x(t),t) f The specific process is as follows: The specific drift field function A(x(t),M new ), and the dedicated diffusion field function B(x(t),M new Substituting the initial probability density distribution P(x(t),t0) into the Falk-Planck equation, the specific form of the Falk-Planck equation is as follows: ; The initial condition is P(x(t),t0), where t0 is the prediction start time node (corresponding to k=0), and t f Both the target future time point (corresponding to k=f, where f is an integer greater than 0) and the target future time point t belong to discrete time points. k Within this scope, the equation is solved using the finite difference method or Monte Carlo simulation method to obtain the future target time node t. f The probability density distribution of the marketing volume index P(x(t),t) f Furthermore, the visualization method in step 5 includes generating one or more of the following: probability distribution curves, probability interval statistical charts, and cumulative probability distribution charts; simultaneously, based on the probability density distribution P(x(t),t) of the marketing voice index. f Calculate and output key indicators, including one or more of expected volume, risk variance, and success probability; the expected volume refers to the mathematical expectation of the probability density distribution of the marketing volume index, representing the average expected level of the catering marketing activity's effect; the risk variance refers to the variance of the probability density distribution of the marketing volume index, representing the degree of uncertainty and fluctuation in the effect of the catering marketing activity; the success probability refers to the probability that the marketing volume index reaches a preset target threshold, representing the possibility that the catering marketing activity will achieve the expected effect.

[0037] This invention presents the probability distribution of marketing voice index through various visualization methods, and calculates key indicators such as expected voice volume, risk variance, and success probability based on this distribution, transforming the abstract probability distribution into intuitive decision-making information. This lowers the barrier for businesses to understand the prediction results, enabling decision-makers to clearly grasp the probability range and risk level of the effects of catering marketing activities. It not only clarifies the average expected effect of the activity but also allows for the early prediction of potential risks and returns, significantly improving the scientific rigor and foresight of marketing decisions.

[0038] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index, characterized by: The method includes the following steps: Step 1: Construct a prediction model, which includes a parameterized drift function A(x(t),M) to characterize the deterministic evolution trend of the marketing volume index x(t), a parameterized diffusion function B(x(t),M) to characterize the intensity of the random fluctuations of the marketing volume index x(t), and a marketing volume index probability density distribution function P(x(t),t) to describe the probability density distribution of the marketing volume index over time; wherein, the drift function A(x(t),M) and the diffusion function B(x(t),M) are connected by the Falk-Planck equation and The marketing volume index probability density distribution function P(x(t),t) is fused to form the prediction model. Here, x(t) is the marketing volume index, which is obtained by collecting user-generated content related to the target catering marketing campaign from publicly available Internet platforms, analyzing text sentiment through natural language processing, and combining it with user interaction behavior data through weighted fusion calculation. M is the marketing parameter vector, which is a set of parameters obtained by extracting the core parameters that affect the effect of the catering marketing campaign, and integrating them after data format unification and dimension standardization. Step 2: Receive the new restaurant marketing campaign plan to be predicted and obtain the new marketing parameter vector M. new ; Step 3: Determine the initial probability density distribution P(x(t),t0), where the initial probability density distribution P(x(t),t0) is the probability density distribution of the marketing volume index of the new catering marketing campaign plan at the prediction start time t0; Step 4: Based on the new marketing parameter vector M of the new catering marketing campaign plan new By calling the parameterized drift function A(x(t),M) and the diffusion function B(x(t),M), a custom drift field function A(x(t),M) adapted to the new catering marketing campaign plan is generated. new ) and the specific diffusion field function B(x(t),M new Then, the specific drift field function A(x(t),M new ), and the dedicated diffusion field function B(x(t),M new Substituting the initial probability density distribution P(x(t), t0) into the prediction model, we obtain the future target time node t. f The probability density distribution of the marketing volume index P(x(t),t) f ); Step 5: Calculate the probability density distribution of the marketing volume index P(x(t),t) f (This will be used to visualize the presentation.) 2. The marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index according to claim 1, characterized in that, The specific implementation process of step 1 is as follows: Step 1.1: Collect activity data and user voice data from multiple catering marketing campaigns, and extract the marketing parameter vector M corresponding to each catering marketing campaign based on the activity data; Step 1.2: Based on user voice volume data, calculate the impact of each catering marketing campaign at each discrete time point t. k Marketing volume observation x(t) k ), and set each discrete time point t k Marketing volume observation x(t) k Aggregate data chronologically to generate a time series of marketing volume observations for each catering marketing campaign plan; the discrete time point t k This refers to the observed value of marketing volume x(t) k The discrete time points used for statistical calculations are k, where k is the index of the discrete time point and represents the specific observation sample of the continuous time variable t. The marketing volume observation time series refers to the same catering marketing campaign plan across all discrete time points t. k Marketing volume observation x(t) k A data sequence arranged in chronological order; Step 1.3: Based on the time series of marketing volume observation values ​​for each catering marketing campaign plan, calculate the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)) at different marketing volume index x(t) levels through the steps of dividing the volume value range interval and classifying data points, calculating interval statistical estimates, and establishing functional relationships. Step 1.4: Construct a training dataset, which includes the marketing parameter vector M corresponding to each catering marketing activity plan, the marketing volume index x(t) of the catering marketing activity corresponding to the plan, the experience drift coefficient A(x(t)) and the experience diffusion coefficient B(x(t)), and the parameterized drift function A(x(t),M) and the parameterized diffusion function B(x(t),M) are trained using machine learning algorithms; Step 1.5: The parameterized drift function A(x(t),M) and parameterized diffusion function B(x(t),M) are fused with the probability density distribution function P(x(t),t) of the marketing volume index through the Falk-Planck equation to form a complete prediction model.

3. The marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index according to claim 2, characterized in that, The specific process of extracting the marketing parameter vector M corresponding to each catering marketing activity plan in step 1.1 is as follows: Extract core parameters that influence the effectiveness of restaurant marketing campaigns from the campaign data of the campaign plan. The core parameters include at least one of the following: discount level, advertising budget, channel combination information, and campaign duration. The extracted core parameters are processed to unify their data format. Standardize the dimensions of the core parameters after they have been formatted into a unified format. The standardized core parameters are integrated to form the marketing parameter vector M corresponding to this catering marketing campaign plan.

4. The marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index according to claim 2, characterized in that, In step 1.2, the marketing volume observation value x(t) is calculated. k The specific process of generating time series of marketing volume observations is as follows: Collect user-generated content related to the target restaurant marketing campaign from publicly available internet platforms; Natural language processing is performed on the collected user-generated content to extract the sentiment score S for each text. i The emotional score S i The value range of is [-1, 1]; Statistical analysis at each discrete time point t k User interaction behavior data, the interaction behavior data including the discrete time point t k The total number of likes (t) of all relevant user-generated content within the app. k ), total number of comments (t) k ) and total number of shares (t) k The total number of likes (t) k ) refers to the discrete time point t k The total number of likes and comments received by all relevant user-generated content. k ) refers to the discrete time point t k The total number of comments received by all relevant user-generated content, and the total number of shares (t) k ) refers to the discrete time point t k The total number of reposts and shares received by all relevant user-generated content within the platform; The text sentiment score and user interaction behavior data are weighted and fused to obtain the discrete time point t. k Marketing volume observation x(t) k The specific formula is: ； Wherein, N(t) k ) represents time node t k The total number of user-generated content related to the target restaurant marketing campaign collected internally; For time node t k The average sentiment score of all relevant user-generated content within the platform; For time node t k The weighted total interaction volume of all relevant user-generated content within the platform; , These are preset weighting coefficients; the same restaurant marketing campaign plan will be weighted at all discrete time points t. k Marketing volume observation x(t) k Arrange the data in chronological order to generate a time series of marketing volume observations for this catering marketing campaign plan; It is represented as {x(t0), x(t1), x(t2), ..., x(t)} n )}, where t0, t1, t2, ..., t n Discrete time points t arranged in chronological order k .

5. The marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index according to claim 2, characterized in that, In step 1.3, the empirical drift coefficient A(x(t)) and the empirical diffusion coefficient B(x(t)) are determined according to the following formulas: Step 1.3.1: Sequence Difference Calculation: For each catering marketing campaign plan, calculate the time series of marketing volume observations {x(t0), x(t1), x(t2), ..., x(t...}}. n )}, traverse all consecutive discrete time points t in the sequence. k Calculate the difference Δx between the observed marketing volume values ​​at adjacent discrete time points. k =x(t k+1 )-x(t k ), and the time interval Δt between adjacent discrete time points. k =t k+1 -t k This forms a group of multiple sets (x(t) k ),Δx k ,Δt k The basic dataset consists of ) Step 1.3.2: Based on the marketing volume observation value x(t) of the catering marketing campaign plan. k The overall value range is divided into multiple continuous and non-overlapping numerical intervals by using an equal interval division method to divide the effective value range of the marketing voice index x(t). For each numerical interval, select all marketing volume observations x(t) from the basic dataset. k The data points whose values ​​fall within this numerical range, and the index of the data point and the discrete time point t k The index k is consistent; integrate the index k corresponding to all the selected data points to form a data point index set S specific to this numerical range; Step 1.3.3: Interval Statistical Estimation Calculation: For each numerical interval, count the total number N of data points in the corresponding data point index set S. S Then, the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)) of the marketing volume index x(t) within this interval are calculated using the following formulas: ； ； Where, N S The total number of data points N in the data point index set S S Δx k Δt represents the difference in marketing volume observations between adjacent discrete time points. k The time interval between adjacent discrete time points; Step 1.3.4: Establishing the functional relationship: By executing steps 1.3.2 and 1.3.3, establish the mapping relationship between the value of the marketing volume index x(t) and the empirical drift coefficient A(x(t)) and empirical diffusion coefficient B(x(t)), thereby converting the discrete marketing volume observation time series data into a continuous function estimate of the marketing volume index x(t).

6. The marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index according to claim 2, characterized in that... In step 1.5, the resulting prediction model is as follows: ； in, The partial derivative of the probability density distribution function of the marketing volume index with respect to time represents the rate of change of the probability density distribution over time. The partial derivative of the drift term with respect to the marketing volume index is used to characterize the directional evolution trend of the marketing volume index. is the second partial derivative of the diffusion term with respect to the marketing volume index; used to characterize the random fluctuation characteristics of the marketing volume index.

7. The marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index according to claim 1, characterized in that, The specific process for determining the initial probability density distribution P(x(t),t0) in step 3 is as follows: Assess the implementation status of the new restaurant marketing campaign plan; If the plan is not initiated, the initial probability density distribution P(x(t),t0) will be set as a narrow-peak Gaussian distribution centered on the marketing volume index x(t)=0; If the plan has been launched, real-time user voice volume data is collected from the launch of the plan to the prediction start time t0, and the marketing voice volume index observation value x(t0) at that time is calculated. The initial probability density distribution P(x(t),t0) is set as a narrow-peak Gaussian distribution centered on the marketing voice volume observation value x(t0).

8. The marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index according to claim 1, characterized in that, In step 4, the future target time node t is obtained. f The probability density distribution of the marketing volume index P(x(t),t) f The specific process is as follows: The specific drift field function A(x(t),M new ), and the dedicated diffusion field function B(x(t),M new Substituting the initial probability density distribution P(x(t),t0) into the Falk-Planck equation, the specific form of the Falk-Planck equation is as follows: ； The initial condition is P(x(t), t0). This equation is solved using the finite difference method or Monte Carlo simulation method to obtain the future target time node t. f The probability density distribution of the marketing volume index P(x(t),t) f ).

9. The marketing campaign effectiveness prediction method based on the probability density distribution of marketing volume index according to claim 1, characterized in that, The visualization method in step 5 includes generating one or more of the following: probability distribution curves, probability interval statistical charts, and cumulative probability distribution charts; simultaneously, it is based on the probability density distribution P(x(t),t) of the marketing volume index. f Calculate and output key metrics, which include one or more of expected volume, risk variance, and success probability.

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