Method for formulating road maintenance strategy based on Markov process

Abstract

The invention discloses a method for formulating a road maintenance strategy based on a Markov process. The method comprises the following specific operation steps: (1) generating a state matrix: in formulating a road maintenance strategy, a maintenance mode and a shelf life are two states, a set composed of the states is the state matrix, and the state matrix has Markov property; (2) generating a state chain matrix: extending and arranging the state matrix of each year according to rows or columns to obtain the state chain matrix; (3) generating a unique identification number of the state chain matrix; (4) searching a state chain matrix; (5) generating a position matrix; (6) calculating a scheduling matrix: multiplying the state chain matrix and the position matrix according to a matrix multiplication to calculate the scheduling matrix; and (7) scheduling the combination of calculation rules, and calculating the required condition and result. The method has the beneficial effects that the method is applied to a complex decision-making process (different from a simple calculation process), and the efficiency of a decision-making algorithm is greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field related to highway maintenance decision-making, and in particular to a method for formulating a road maintenance strategy based on a Markov process. Background Art

[0002] In the field of highway maintenance, we want to analyze changes in the technical condition and maintenance costs of roads over the next several years, given the selection of different maintenance methods. This change is characterized by the fact that decisions and outcomes for the next year are influenced by those made in the previous year. Sometimes, we also want to change a decision made in a particular year and then analyze the performance in subsequent years. The current common practice is to calculate the performance of decisions over multiple years, year by year, using a set of rules (consisting of multiple technical rules). When a change occurs in a particular year, this continuous process is repeated from the year in which the change occurred. This approach has several drawbacks: First, while most cases only allow for a single future year, we have to calculate the performance for multiple consecutive years, as future years are influenced by the previous year. Second, if a change is made in a single year during a multi-year period, all subsequent years must be recalculated, especially if the change occurred earlier. These two issues significantly impact the efficiency of the decision-making algorithm.

[0003] In related fields, there are examples of Markov methods, such as "CN112632677B - Bridge Lifecycle Maintenance Strategy Optimization Method Based on a Semi-Markov Decision Process" and "CN110852610A - Road, Bridge, and Tunnel Health Status and Maintenance Cost Calculation Method Based on a Markov Model." However, these patents differ in that: first, they use Markov methods to calculate a specific indicator (such as funding or health); second, they use Markov processes to determine the final decision, relying on probability. Summary of the Invention

[0004] The present invention aims to overcome the above-mentioned deficiencies in the prior art and provides a method for formulating road maintenance strategies based on a Markov process that can improve the efficiency of decision-making algorithms.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions: A method for formulating road maintenance strategies based on Markov processes. The specific steps are as follows: (1) Generating a state matrix: All categories of calculation rules specify a specific calculation rule item. There are as many different calculation rules as there are types of states. The set of states is the state matrix, which has Markov properties. In formulating road maintenance strategies, the state values ​​of road maintenance-related states in the previous year only depend on the state values ​​of road maintenance-related states in the previous year. (2) Generate a state chain matrix: For multiple consecutive road maintenance decisions, the state matrix of each year is extended and arranged in rows or columns according to the order of years to obtain a state chain matrix; (3) Generate a unique identification number for the state chain matrix: Generate a unique identification number for the state chain matrix using any symmetric or asymmetric encryption, binary, or UUID method; (4) Searching for the state chain matrix: Save the state matrices of several future years by year and state, then search for the unique identification number according to the conditions to obtain the state chain matrix that meets the conditions; (5) Generate position matrix: a state matrix used to extract the multi-year state values ​​corresponding to the calculation rules from the state chain matrix; (6) Calculate the scheduling matrix: The scheduling matrix is ​​calculated by multiplying the state chain matrix and the position matrix according to matrix multiplication; (7) Use the scheduling matrix to select the required calculation rules from the set of calculation rules corresponding to various states, and then calculate the required results.

[0006] The key features of this method are: first, it relies on a state matrix to drive the computational rules; second, it pre-stores all possible state chain matrices; and third, it transforms "multiple consecutive decision computations" into "query plus a single decision computation." The technical benefits of this method are: first, it relies on a Markov process to generate a state matrix (intermediate result) rather than a final indicator; and second, it uses the state matrix generated by the Markov process to optimize the scheduling of computational rules rather than making final decisions. In summary, this method applies the Markov process to complex decision-making processes (as distinct from simple computational processes), significantly improving the efficiency of the decision-making algorithm.

[0007] Preferably, in step (1), specifically: the state refers to the state of the calculation rules corresponding to different calculation intervals in different categories, there are as many types of states as there are different calculation rules, and there are as many value changes of the state corresponding to the number of interval groups of a certain type of calculation rules; the state matrix has a Markov property, that is, the state matrix of the next decision only depends on the state matrix of the previous decision; and the maintenance method and shelf life both contain several state values, and the state value of the maintenance method and the state value of the shelf life constitute the state matrix.

[0008] Preferably, the states or intervals are finite, that is, the number of states or intervals is not infinite; the calculation rules are long-range, that is, any specified calculation rule can be effective for any one of multiple consecutive decisions within a certain state.

[0009] Preferably, in step (5), the position matrix is ​​a matrix containing two states of "yes" or "no". If a state corresponding to a certain calculation rule needs to be calculated and obtained, the corresponding position is 1, otherwise it is 0. Specifically, each type of state in the state matrix uses a calculation rule to predict the value of the future year. If this type of state is to be predicted during the prediction, the corresponding position of the position matrix is ​​1; otherwise, the corresponding position of the position matrix is ​​0.

[0010] Preferably, in step (7), the specific scheduling method is: if the corresponding position of the scheduling matrix is ​​0, there is no need to calculate the state; if the corresponding position of the scheduling matrix is ​​not 0, the calculation rule of the corresponding state under the corresponding non-zero value is selected to participate in the calculation.

[0011] As a preference, in step (7), specifically: use the state matrix to store all finite states and finite calculation rule labels, when a certain decision situation and result is needed, find the corresponding state chain matrix, and then use the scheduling matrix to unify the scheduling calculation rules to calculate the corresponding decision situation and result; wherein, the state in the state matrix refers to when a certain road maintenance indicator in a certain year in the future changes in a certain form, and the state is used to indicate this form. Since the state is not the road maintenance indicator itself, the obtained state cannot be used directly, so a calculation rule is required: this calculation rule takes the road maintenance indicator of the initial year and the state chain matrix of the previous forecast years as conditions, and uses the calculation rule of the scheduling matrix to calculate the road maintenance indicator value of the target forecast year.

[0012] The advantages of this invention are: first, it relies on a Markov process to generate a state matrix (an intermediate result) rather than a final indicator; second, it uses the state matrix generated by the Markov process to optimize the scheduling of calculation rules rather than making final decisions. In summary, this method applies the Markov process to complex decision-making processes (as opposed to simple calculation processes), significantly improving the efficiency of the decision-making algorithm. DETAILED DESCRIPTION

[0013] The following specific embodiments further describe the present invention.

[0014] A method for formulating road maintenance strategies based on Markov processes. The specific steps are as follows: (1) Generating a state matrix: All categories of calculation rules specify a specific calculation rule item. There are as many types of states as there are different calculation rules. The set of states is the state matrix, which has Markov properties. In formulating road maintenance strategies, the state values ​​of road maintenance-related states (including but not limited to maintenance methods and shelf life) in the next year only depend on the state values ​​of road maintenance-related states in the previous year. Specifically, the states described above refer to the states of calculation rules corresponding to different calculation intervals in different categories. There are as many different types of states as there are different calculation rules, and there are as many value variations for the states corresponding to a given category of calculation rules as there are interval groups. The state matrix exhibits Markov properties, meaning that the state matrix for the next decision depends solely on the state matrix for the previous decision. The format of the state matrix includes any data stored in memory that performs the function. Both the maintenance method and the shelf life contain several state values, and the state values ​​for the maintenance method and the shelf life constitute the state matrix. The states or intervals described above are finite, meaning that the number of states or intervals is not infinite. The calculation rules exhibit long-range properties, meaning that any given calculation rule, within a given state, can be effective for any one of multiple consecutive decisions.

[0015] (2) Generate a state chain matrix: For multiple consecutive road maintenance decisions, the state matrix of each year is extended and arranged in rows or columns according to the order of years to obtain a state chain matrix; the format of the state chain matrix includes any data stored in the memory to perform the function.

[0016] (3) Generate a unique identification number for the state chain matrix: Generate a unique identification number for the state chain matrix, including but not limited to using any symmetric and asymmetric encryption, binary, UUID, etc.; the format of the unique identification number includes any data stored in the memory that performs the function.

[0017] (4) Searching the state chain matrix: Save the state matrices of several future years by year and state, and then search the unique identification number according to the conditions to obtain the state chain matrix that meets the conditions; the search method includes but is not limited to loop, hash, hash, B+ tree, inverted, etc.

[0018] (5) Generate a position matrix: A state matrix used to extract the multi-year state values ​​corresponding to the calculation rule from the state chain matrix; the format of the position matrix includes any data stored in the memory to perform this function. The position matrix is ​​a matrix containing two states: "yes" (usually represented by 1, but including but not limited to other methods) or "no" (usually represented by 0, but including but not limited to other methods). If a state corresponding to a certain calculation rule needs to be calculated and obtained, the corresponding position is 1, otherwise it is 0.

[0019] Specifically: each type of state in the state matrix uses a calculation rule to predict the value of the future year. If this type of state is to be predicted during the prediction, the corresponding position in the position matrix is ​​1; otherwise, the corresponding position in the position matrix is ​​0.

[0020] (6) Calculate the scheduling matrix: The scheduling matrix is ​​calculated by multiplying the state chain matrix and the position matrix according to matrix multiplication; (7) Use the scheduling matrix to select the required calculation rules from the set of calculation rules corresponding to various states, and then calculate the required results. The specific scheduling method is: if the corresponding position of the scheduling matrix is ​​0, then there is no need to calculate the state; if the corresponding position of the scheduling matrix is ​​not 0, then the calculation rule of the corresponding state under the corresponding non-zero value is selected to participate in the calculation. Specifically: use the state matrix to store all finite states and finite calculation rule marks. When a certain decision situation and result are needed, find the corresponding state chain matrix, and then use the scheduling matrix to unify the scheduling calculation rules to calculate the corresponding decision situation and result; Among them, the state in the state matrix refers to when a certain road maintenance indicator in a certain year in the future changes in a certain form, and use the state to indicate this form. Since the state is not the road maintenance indicator itself, the state cannot be used directly, so a calculation rule is needed: this calculation rule takes the road maintenance indicator of the initial year and the state chain matrix of the previous forecast years as conditions, and uses the calculation rule of the scheduling matrix to calculate the road maintenance indicator value of the target forecast year.

[0021] The specific implementation examples are as follows: Examples of applications in road maintenance decision-making, where the decision is made annually for many consecutive years: 1) Generate a state matrix: Maintenance mode is a state that is used to drive the rule for improving the effect of road condition indicators. Maintenance modes are divided into no maintenance, daily maintenance, preventive maintenance, performance repair maintenance, and structural repair maintenance, which can correspond to five states: 0, 1, 2, 3, and 4 respectively (the maintenance mode can be represented by a numerical value, including but not limited to this mode); the shelf life is a state that is used to drive the rule for attenuation of road condition indicators. The shelf life is an integer and a finite number of years. If the shelf life is N years, it is represented by N; if there are other states, they are similar; it contains positive integers between 0 and 8, for a total of 9 states. Therefore, if a certain year is preventive maintenance and the shelf life is 3 years, the state matrix is ​​[1 3] (or [1 3] T ).

[0022] The next year's maintenance method status value and shelf life status value depend only on the previous year's maintenance method status value and shelf life status value. The specific rules are as follows: If the previous year's maintenance method status value is 0, it is considered no maintenance. In that year, any maintenance method status (0-4) can be assigned, and the shelf life status value is the standard value of the corresponding maintenance method status (for example, if the maintenance method status is 0, 1, 2, 3, or 4, the standard shelf life values ​​are 0, 3, 5, 8, or 3, respectively). If the previous year's maintenance method status value is not 0, its shelf life status value is compared with the standard shelf life value. If it is greater than the standard shelf life value, any maintenance method status (0-4) can be assigned in that year, and the shelf life status is the standard value of the corresponding maintenance method status. If it is less than or equal to the standard shelf life value, the maintenance method status is 0, and the shelf life status is the previous year's shelf life status value plus 1.

[0023] The mathematical form of the state matrix for each year can be written as [1 3] (or [1 3] T ), stored in memory in a corresponding data format (e.g., a one-dimensional list). For mathematical simplicity, the state matrix is ​​typically a single row or column in practice, but storage is not limited to a single row or column.

[0024] 2) Generate state chain matrix: The state matrix of each year can be arranged into multiple rows (or columns) to form a state chain matrix. Its mathematical form is as follows , stored in the memory in the corresponding data form (such as a two-dimensional list).

[0025] The state matrix of each year is extended and arranged in rows or columns according to the order of years to obtain the state chain matrix; the state chain matrix is ​​generally multi-row and multi-column. Of course, if the algorithm state is only one-dimensional, the state chain matrix is ​​also a single row and single column.

[0026] Because the decision-making system includes predictive capabilities, if the year is in the future—for example, the current year is 2025, and the current year is 2030—then, depending on the algorithm model group invoked by the final scheduling matrix, multiple state matrices for 2030 may be generated, leading to multiple calculation results for decision-making. However, if the current year is now or in the past, history is generally certain, and only one state matrix will remain to describe it. For example, if it is now 2031, then only one state matrix will be calculated for 2030. In short, there is only one initial state matrix used for calculation in the steps, while there are multiple state matrices for each year of the decision.

[0027] 3) Generate a unique identification number for the state chain matrix: A one-dimensional method can be used to generate a unique identification number. For the state chain matrix in step 2), the one-dimensional unique identification number is 1302.

[0028] 4) Finding the Status Chain Matrix: If we want to find a specific situation in year N, we can use a slice query to find it. The unique identification number corresponding to year N is the 2N-1 and 2N positions. For example, to find a situation where no maintenance was performed in the second year, we can find the unique identification number where the third position is 0. This will determine the unique identification number that meets the conditions and, in turn, the status chain matrix that meets the conditions. (Assuming that the status chain matrix is ​​retrieved from step 2)) The state matrix in the state chain matrix that meets the conditions does not refer to the initial state matrix, but rather the predicted state matrix for each year. For example, the state matrices for several future years can be stored in a table by year and state, and then retrieved based on the conditions. For example, for the years 2025 to 2030, there are several state matrices for each year, stored in the database with each year as a row and each state as a column. Then, when searching, you can search based on the conditions.

[0029] 5) Generate position matrix: The position matrix is ​​allowed to be the unit matrix or 1 (that is, the state chain matrix is ​​allowed to be retained as it is). Each type of state in the state matrix can use a calculation rule to predict the value of the future year. For the state corresponding to the calculation rule that is not needed, the value of the corresponding position is 0, otherwise it is 1; for a certain plan that is not needed, the value of the corresponding position is 0, otherwise it is 1. Specifically: if this type of state is to be predicted when we predict, the corresponding position of the position matrix is ​​1; otherwise, the corresponding position of the position matrix is ​​0. Because when making decisions, not all states must be predicted, and only some states of future years may be predicted, thereby drawing partial conclusions. If the state chain matrix in step 2) is taken out, if it is required to calculate the improvement of the indicator effect in the second year, and not calculate other cases, the corresponding position matrix is ​​[1 0] T .

[0030] 6) Calculate the scheduling matrix: Multiply the state chain matrix in step 2) and the position matrix in step 5) by matrix multiplication to obtain the scheduling matrix. According to the above example, the obtained scheduling matrix is ​​[1 0] T .

[0031] 7) Use the scheduling matrix from step 6) to schedule the corresponding calculation rules: In the first year, if the maintenance status is 1, schedule the corresponding effect improvement rule. In the second year, if the maintenance value is 0, there is no effect improvement, and the effect can be reduced by a specified value. The state in the state matrix refers to when a road maintenance indicator changes in some form in a future year. This change is indicated by the state. These states can be represented by numbers or letters, though numbers are more convenient for mathematical calculations. Since the status is not the road maintenance indicator itself, the obtained status cannot be used directly. Therefore, a calculation rule is required: this calculation rule can use the road maintenance indicator for the initial year and the state chain matrix of the previous forecast years as conditions, and use the calculation rules of the scheduling matrix to calculate the road maintenance indicator value for the target forecast year. Effect improvement rules and specified value reduction rules are examples of this calculation rule.

[0032] The key features of this method are: first, it relies on a state matrix to drive the computational rules; second, it pre-stores all possible state chain matrices; and third, it transforms "multiple consecutive decision computations" into "query plus a single decision computation." The technical benefits of this method are: first, it relies on a Markov process to generate a state matrix (intermediate result) rather than a final indicator; and second, it uses the state matrix generated by the Markov process to optimize the scheduling of computational rules rather than making final decisions. In summary, this method applies the Markov process to complex decision-making processes (as distinct from simple computational processes), significantly improving the efficiency of the decision-making algorithm.

Claims

1. A method for formulating road maintenance strategies based on Markov processes, characterized by: The specific steps are as follows: (1) Generating a state matrix: All categories of calculation rules specify a specific calculation rule item. There are as many different calculation rules as there are types of states. The set of states is the state matrix, which has Markov properties. In formulating road maintenance strategies, the state values ​​of road maintenance-related states in the previous year only depend on the state values ​​of road maintenance-related states in the previous year. (2) Generate a state chain matrix: For multiple consecutive road maintenance decisions, the state matrix of each year is extended and arranged in rows or columns according to the order of years to obtain a state chain matrix; (3) Generate a unique identification number for the state chain matrix: Generate a unique identification number for the state chain matrix using any symmetric or asymmetric encryption, binary, or UUID method; (4) Searching for the state chain matrix: Save the state matrices of several future years by year and state, then search for the unique identification number according to the conditions to obtain the state chain matrix that meets the conditions; (5) Generate position matrix: a state matrix used to extract the multi-year state values ​​corresponding to the calculation rules from the state chain matrix; (6) Calculate the scheduling matrix: The scheduling matrix is ​​calculated by multiplying the state chain matrix and the position matrix according to matrix multiplication; (7) Use the scheduling matrix to select the required calculation rules from the set of calculation rules corresponding to various states, and then calculate the required results.

2. The method for formulating a road maintenance strategy based on a Markov process according to claim 1, wherein In step (1), specifically: the state refers to the state of the calculation rules corresponding to different calculation intervals in different categories. There are as many types of states as there are different calculation rules, and there are as many value changes as there are interval groups for a certain type of calculation rules. The state matrix has a Markov property, that is, the state matrix of the next decision only depends on the state matrix of the previous decision. The maintenance method and the shelf life both contain several state values, and the state value of the maintenance method and the state value of the shelf life constitute the state matrix.

3. The method for formulating a road maintenance strategy based on a Markov process according to claim 2, wherein: The states or intervals are finite, that is, the number of states or intervals is not infinite; the calculation rules are long-range, that is, any specified calculation rule can be effective for any one of multiple consecutive decisions within a certain state.

4. The method for formulating a road maintenance strategy based on a Markov process according to claim 1, wherein: In step (5), the position matrix is ​​a matrix containing two states, "yes" or "no". If a state corresponding to a certain calculation rule needs to be calculated and obtained, the corresponding position is 1, otherwise it is 0. Specifically, each type of state in the state matrix uses a calculation rule to predict the value of the future year. If this type of state is to be predicted during the prediction, the corresponding position in the position matrix is ​​1. Otherwise, the corresponding position in the position matrix is ​​0.

5. The method for formulating a road maintenance strategy based on a Markov process according to claim 1, wherein: In step (7), the specific scheduling method is: if the corresponding position of the scheduling matrix is ​​0, there is no need to calculate the state; if the corresponding position of the scheduling matrix is ​​not 0, the calculation rule of the corresponding state under the corresponding non-zero value is selected to participate in the calculation.

6. A method for formulating a road maintenance strategy based on a Markov process according to claim 1 or 4, characterized in that: In step (7), specifically: use the state matrix to store all finite states and finite calculation rule labels, when a certain decision situation and result is needed, find the corresponding state chain matrix, and then use the scheduling matrix to unify the scheduling calculation rules to calculate the corresponding decision situation and result; wherein, the state in the state matrix refers to when a certain road maintenance indicator in a certain year in the future changes in a certain form, and the state is used to indicate this form. Since the state is not the road maintenance indicator itself, the obtained state cannot be used directly, so a calculation rule is needed: this calculation rule takes the road maintenance indicator of the initial year and the state chain matrix of the previous forecast years as conditions, and uses the calculation rule of the scheduling matrix to calculate the road maintenance indicator value of the target forecast year.