A source rod increment optimization layout method for in-service co-60 radiation facilities

Abstract

This invention discloses a source rod incremental optimization layout method for in-service Co-60 radiation facilities, belonging to the technical field of source rod optimization layout, including constructing in-service Co-60 radiation facilities. 60 A basic model for incremental optimization of the radiation field of a radiation facility; a pre-calculated dose coefficient matrix is ​​constructed based on the basic model; based on the pre-calculated dose coefficient matrix, a greedy-backtracking hybrid optimization algorithm is used to optimize the radiation field of the in-service Co facility. 60 The layout scheme of the new source rods for the radiation facility is incrementally searched and iteratively optimized, and the final output is the new Co. 60 The optimal layout scheme for source rods. This invention defines a safe solution space through precise constraint modeling, and achieves a balance between depth exploration and computational efficiency within this constrained space through a greedy-backtracking hybrid algorithm, providing a basis for in-service Co 60 Source rod replenishment engineering for irradiation facilities provides a safe, intelligent, and efficient tool that can scientifically guide the deployment of new resources, enabling precise upgrades to facility performance and optimized resource allocation.

Description

Technical Field

[0001] This invention belongs to the technical field of source rod optimization layout, specifically relating to a source rod incremental optimization layout method for in-service Co-60 radiation facilities. Background Technology

[0002] Irradiation processing technology, as an important component of civilian nuclear technology, primarily utilizes ionizing radiation to trigger chemical or biological reactions, enabling the deep processing and modification of products. According to data from the International Atomic Energy Agency (IAEA), there are approximately 300 gamma-ray irradiation facilities and over 2,500 industrial irradiation electron accelerators globally, including Co... 60 Gamma irradiation technology has played an irreplaceable role in fields such as medical device sterilization, food preservation, and material modification. However, the quality and efficiency of irradiation treatment heavily depend on the uniformity of dose distribution within the radiation field. Uneven dose distribution can lead to decreased product yield and resource waste. The arrangement of the radiation source rods is a key factor determining the uniformity of the radiation field dose distribution. Therefore, developing intelligent source rod arrangement optimization methods to reduce overall dose non-uniformity is of significant engineering value and urgent application for improving technology, ensuring product quality, and achieving economic benefits.

[0003] Current research on source rod arrangement optimization has made some progress, but significant limitations still exist, making these methods unsuitable for practical industrial applications. 60 During long-term operation, the source rods of irradiation facilities experience a decline in activity due to radioactive decay. To ensure that the irradiation dose rate meets process requirements, it is necessary to periodically replenish the source rods to maintain the dose rate. According to data updated in 2020 by the International Atomic Energy Agency (IAEA) Industrial Irradiation Facility Database (DIIF), nearly 300 irradiation facilities worldwide, including gamma irradiators and electron accelerators, typically replenish Co every 3-4 years. 60 Source stick.

[0004] However, existing academic research and engineering practices mainly focus on the "from scratch" global optimization design paradigm. This paradigm assumes that all source rod positions can be freely configured, aiming to find the theoretically optimal arrangement on a completely empty source rack, while neglecting a common and crucial real-world scenario: the replenishment and upgrading of source rods in in-service irradiation facilities—that is, how to optimize the layout of new source rods under the constraint that some existing source rods have fixed positions and activities. If the "from scratch" optimization scheme is mechanically applied in this scenario, the output will inevitably include instructions for rearranging existing source rods, which has significant cost and safety drawbacks in engineering practice.

[0005] In practice, the disassembly, relocation, and reinstallation of a single source rod are costly, ranging from $800 to $1200 according to industry data. For a facility with dozens or even hundreds of source rods, the overall cost of a complete overhaul would be enormous, severely undermining the economic feasibility of technological upgrades. More importantly, once a source rod has undergone initial installation and service, its mechanical structure, such as the welded parts of the encapsulation shell, will weaken due to initial stress release and material fatigue. Any unnecessary movement or operation will significantly increase the potential risk of seal failure and radioactive material leakage. Frequent relocation operations undoubtedly place the facility and operators in unnecessary danger. Therefore, the limitations of existing technologies lie not only in the contradiction between theoretical models and engineering practice, but also in the potential for costly and risky engineering decisions.

[0006] In conclusion, there is an urgent need to invent a highly efficient optimization method tailored to the "modification scenario". This method must be able to intelligently search for the optimal layout of the new source rods while strictly respecting the physical and safety constraints that "the position and activity of the existing source rods are fixed", thereby reducing engineering costs and risks, and improving the uniformity of radiation field dose. Summary of the Invention

[0007] The purpose of this invention is to address the aforementioned shortcomings of the prior art by providing a method for incremental optimization of source rod layout in in-service Co-60 radiation facilities, thereby solving the following technical problems: First, layout optimization is performed under the strict safety and economic constraint of "absolutely fixed position and activity of existing source rods." This requires establishing a new optimization paradigm whose search space automatically excludes any schemes that move fixed source rods, thereby ensuring that all generated schemes have direct engineering feasibility and safety. Second, within this limited solution space, the core challenge lies in finding high-quality new source rod layout schemes that can significantly improve the overall dose field uniformity. This requires overcoming the limitation of simple heuristic methods easily getting trapped in local optima, and using intelligent methods to deeply coordinate the complex interactions between new and old source rods to maximize the benefits of new resources. Finally, it is essential to effectively balance the search depth and computational efficiency in the optimization process. For combinatorial optimization problems with "fixed partial variables," an efficient hybrid strategy must be designed to find a feasible solution close to the global optimum within an acceptable timeframe for engineering decisions.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for incremental optimization of source rod layout for in-service Co-60 radiation facilities, comprising the following steps: S1, Constructing In-Service Co 60 Basic model for incremental optimization of radiation field of radiation facilities; S2. Construct a pre-calculated dose coefficient matrix based on the aforementioned radiation field incremental optimization basic model; S3. Based on the pre-calculated dose coefficient matrix, a greedy-backtracking hybrid optimization algorithm is used to optimize the in-service Co... 60 The layout scheme of new source rods for the radiation facility is incrementally searched and iteratively optimized. The final output is the corresponding increase in Co that minimizes the dose inhomogeneity of the radiation field under the constraints of existing source rod positions and fixed activity. 60 The optimal layout scheme for the source rod.

[0009] Furthermore, step S1 includes the following sub-steps: S11. Define a radiation source plane in the XOZ coordinate system plane, and set a source slot in the radiation source plane to represent the placement position of the source rod. The coordinate set of the source slot is: In the formula, This represents the set of coordinates of the source slot within the radiation source plane; This represents the coordinates of the vertex on the source slot. Let x be the x-coordinate of the vertex on the source slot. Let be the vertical coordinate of the vertex on the source slot. , These represent the number of rows and columns of the source slot, respectively. and These represent the total number of rows and columns of the source slots, respectively. S12. Define a dose reference plane parallel to the radiation source plane. The dose reference plane is located at the vertical coordinate Y=100cm, and its coordinate set is as follows: In the formula, The set of coordinates representing the reference plane; Indicates the coordinates of the reference point. The x-coordinate of the reference point The vertical coordinate of the reference point, The row number of the reference point. The number of columns for the reference point. , These represent the total number of rows and columns of the reference point, respectively. S13. Based on the radiation source plane and dose reference plane, construct Co 60 A three-dimensional parametric geometric model of an irradiation station; S14. In a three-dimensional parametric geometric model, calculate a single root Co. 60 The radiation dose from the radiation source rod to reference point O; S15. Based on the radiation dose calculation results in S14, calculate all Co... 60The total dose of the radiation source rod to a single reference point is calculated, and the dose non-uniformity of the reference plane is calculated. S16. Divide the total set of slots for the radiation facility to obtain the set of slots for fixed source rods and the set of available slots. S17. Construct the global activity vector of the radiation facility, set the activity value of the corresponding position of the fixed source rod slot set as a known constant, and set the activity value of the corresponding position of the available slot set as the variable to be optimized. S18. Construct the system response matrix of the radiation facility, calculate the total dose distribution of the radiation facility based on the system response matrix and the global activity vector, and define a dose non-uniformity evaluation function based on the total dose distribution of the radiation facility. S19. The optimization objective is to minimize the dose nonuniformity evaluation function value, and the optimization objective is formalized as a non-convex optimization problem with structural prior constraints.

[0010] Furthermore, in S14, the calculation of a single Co root 60 The radiation dose from the radiation source rod to reference point O is expressed as: In the formula, For the first Line number The irradiation dose of the source rod to reference point O, The irradiation constant, For source rod activity, This represents the perpendicular distance between any irradiated point in the reference plane and the source rod. Indicates the length of the source rod. This represents the distance from the foot of the perpendicular to the lower vertex of the source rod.

[0011] Furthermore, in S15, all Co are calculated. 60 The total dose from the radiation source rod to a single reference point is expressed as: In the formula, Total dose; Based on the total dose, the dose non-uniformity of the reference plane is calculated, and it is expressed as: In the formula, Dose nonuniformity at the reference plane.

[0012] Furthermore, in S16, the fixed source rod slot set is a set of slots that have been occupied by the source rod and whose position and activity cannot be changed, and it is represented as: In the formula, For a fixed source rod slot set, For the total number of slots; The available slot set is the set of free slots after subtracting the fixed source bar slot set from the total slot set, and it is represented as: In the formula, For the set of available slots, The set difference operator means removing all elements contained in the right set from the set on the left.

[0013] Furthermore, in S18, the system response matrix is ​​defined as follows: The system response matrix Any row of elements represents the unit activity dose response of the corresponding slot to all reference points; The total dose distribution of the radiation facility is calculated based on the system response matrix and the global activity vector, and is expressed as follows: D=C U In the formula, D represents the total dose distribution of the radiation facility; U represents the global activity vector. Define a dose nonuniformity evaluation function based on the total dose distribution of a radiation facility: In the formula, This is a function for evaluating dose nonuniformity. This represents the total dose value at the reference point in the nth row and mth column of the dose reference plane.

[0014] Furthermore, in S19, the optimization objective is to minimize the dose nonuniformity evaluation function value, which is expressed as: In the formula, For dose non-uniformity, This represents the minimum dose nonuniformity obtained under the optimal source rod arrangement scheme.

[0015] Furthermore, step S2 includes the following sub-steps: S21, The pre-calculated dose coefficient matrix is ​​constructed by: taking the irradiation dose in S14... The expression is separated into a geometric influence factor and a source rod activity A, and then a dose contribution matrix B is constructed. The total dose distribution D of the radiation facility is transformed into a matrix multiplication operation of source rod activity A and dose contribution matrix B, that is: ; S22, Dose Contribution Matrix B in Co 60 The radiation source rod arrangement optimization is calculated and stored once before the iteration, and can be repeatedly called in subsequent optimization iterations without recalculating the geometric influence factor, thus eliminating redundant calculation overhead.

[0016] Furthermore, in S21, the geometric influence factor is expressed as: In the formula, For dose contribution matrix The element in represents the slot number. OK The geometric influence factor of the source bar at column n on the reference point plane at row m.

[0017] Furthermore, step S3 includes the following sub-steps: S31. Initialize activity configuration: Construct the spatial layout of the radiation facility and initialize the global activity vector U based on the existing source rod configuration. Assign known activity values ​​to the occupied source cells and initialize unoccupied source cells to zero activity. S32. Pre-calculated dose contribution: The dose contribution of each source cell to the reference point is pre-calculated to form a pre-calculated dose coefficient matrix, which is used to accelerate subsequent dose assessment. S33. Greedy-backtracking hybrid search: First, a locally optimal initial layout of the source bar layout is generated using a greedy strategy. Then, a backtracking mechanism is introduced within the preset maximum search depth to adjust the placement order of the source bars and explore a better layout scheme. S34. Heuristic Pruning Acceleration: Using the dose non-uniformity evaluation function as the objective function, the source bar is placed in the slot with the lowest dose during the search process. Branches that cannot improve uniformity are pruned to improve optimization efficiency.

[0018] The source rod incremental optimization layout method for in-service Co-60 radiation facilities provided by this invention has the following beneficial effects: 1. This invention achieves safety assurance and zero additional engineering costs, ensuring the feasibility of the optimized solution. The core constraint of retrofitting in-service facilities is prohibiting the movement of existing source bars. Existing global optimization algorithms, unable to ignore this constraint, generate "optimal" solutions that harbor significant risks of radioactive leakage and dismantling and reinstallation costs of up to $800-$1200 per bar, making them impractical for engineering. This invention, through its core technology—defining and locking a "fixed source slot subset" during the problem modeling phase—internalizes this safety and economic constraint as the boundary condition for the algorithm's search. Whether subsequent greedy initialization or backtracking search occurs, its operational space is strictly limited to the "available source slot subset." Therefore, every intermediate and final layout scheme disclosed in this invention satisfies the requirement of "not moving the old source," and can be directly and safely used for on-site construction, optimizing the problem of traditional optimization methods where "the results are excellent but unusable," and seamlessly integrating optimization technology with engineering practice.

[0019] 2. This invention significantly improves the optimization quality of dose uniformity within a strongly constrained solution space, achieving synergistic effects between new and old source rods. While existing simple methods (such as pure greedy algorithms or random insertion) are feasible, their optimization capabilities are low. The greedy-backtracking hybrid algorithm (GB) proposed in this invention effectively addresses this problem. The algorithm first quickly locks in a locally optimal initial layout using a greedy strategy, ensuring the basic quality of the solution. More importantly, the constrained backtracking search mechanism gives the algorithm the ability to escape local optima. It systematically explores different placement orders and combinations, performing a depth search within a user-controllable depth (max_depth). As shown in Table 5 below, in the scenario of supplementing 30 source rods, the average dose nonuniformity (μ=1.3449) achieved by the GB algorithm is significantly better than that of the pure greedy strategy (μ=1.44704) and the random strategy (μ=1.5732), and its result is closer to the ideal full optimization benchmark (μ=1.0768). This demonstrates that the GB algorithm can intelligently coordinate the spatial and activity relationships between new source rods and fixed old source rods, maximizing the performance improvement return on new investments. Attached Figure Description

[0020] Figure 1 This is a flowchart of the source rod incremental optimization layout method for in-service Co-60 radiation facilities in the embodiments.

[0021] Figure 2 This is a schematic diagram of the three-dimensional coordinate system of the source plane and the reference plane in the embodiment.

[0022] Figure 3 This is a schematic diagram of the three-dimensional coordinates of the source rod and the reference point in the embodiment.

[0023] Figure 4 This is a flowchart of the hybrid greedy-backtracking algorithm in the embodiment.

[0024] Figure 5 This is a schematic diagram of the source frame modeling in the embodiment. Detailed Implementation

[0025] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0026] This embodiment discloses a method for incremental optimization of source rod layout in in-service Co-60 radiation facilities. Its core lies in disclosing a technical framework of "strictly constrained modeling + greedy-backtracking hybrid search (GB)," aiming to intelligently search for the optimal layout of new source rods within a limited solution space under the rigid constraint of "fixed existing source rod positions," thereby maximizing the improvement of overall radiation field dose uniformity. (Refer to...) Figure 1 Specifically, it includes the following: S1, Constructing In-Service Co 60 The basic model for incremental optimization of the radiation field of a radiation facility includes the following sub-steps: S11. Definition of the source plane; Define a radiation source plane in the XOZ coordinate system, and set a slot (referred to as the source slot) in the radiation source plane to represent the placement position of the source rod. The coordinate set of the source slot is: In the formula, This represents the set of coordinates of the source slot within the radiation source plane; This represents the coordinates of the vertex on the source slot. Let x be the x-coordinate of the vertex on the source slot. Let be the vertical coordinate of the vertex on the source slot. , These represent the number of rows and columns of the source slot, respectively. and These represent the total number of rows and columns of the source slots, respectively. S12. Definition of Dose Reference Plane; Define a dose reference plane parallel to the radiation source plane. The dose reference plane is set at the vertical coordinate Y=100cm, and its coordinate set is as follows: In the formula, The set of coordinates representing the reference plane; Indicates the coordinates of the reference point. The x-coordinate of the reference point The vertical coordinate of the reference point, The row number of the reference point. The number of columns for the reference point. , These represent the total number of rows and columns of the reference point, respectively.

[0027] In one specific embodiment, the reference points are distributed using a u×v uniform grid, covering the effective irradiation area aligned with the projection of the radiation source plane. The dimensions of the two planes are strictly matched, and the reference plane is set at Y = 100cm according to standard recommendations to simulate typical industrial irradiation conditions.

[0028] S13. Based on the radiation source plane and dose reference plane, and according to the standardized requirements for the spatial distribution of the radiation field in "JJG-591-1989 Gamma-ray Radiation Source (for Radiation Processing)," construct Co. 60 The three-dimensional parametric geometric model of the irradiation station, specifically as follows: Figure 2 As shown; S14, Dose field calculation; in the three-dimensional parametric geometric model, Co 60 The activity of the source rod can be considered approximately uniform, and its positional relationship with the irradiation point in a spatial rectangular coordinate system is as follows: Figure 3 As shown. The coordinates of the bottom endpoint of the source rod are (X... i Y i Z i The coordinates of the top endpoint are (X... i Y i Z i +L), based on this, calculate a single root Co 60 The radiation dose from the radiation source rod to the irradiation reference point O is expressed as: In the formula, For the first Line number The radiation dose of the source rod to the irradiation reference point O, This is the irradiation constant, typically taken as 1.48 × 10⁻⁶. -4 Ci - ¹ cm²; Source rod activity, measured in Bq, represents the number of decaying nuclei per unit time; This represents the perpendicular distance between any irradiated point in the reference plane and the source rod. Indicates the length of the source rod. This represents the distance from the foot of the perpendicular to the lower vertex of the source rod; in, Specifically, it is expressed as follows: In the formula, , Let O be the coordinates of the irradiation reference point. , The coordinates of the source rod.

[0029] S15. Based on the radiation dose calculation results in S14, calculate all Co... 60 The total dose of the radiation source rod to a single reference point is calculated, and the dose non-uniformity of the reference plane is calculated. Among them, all Co 60 The total dose from a radiation source rod to a single reference point is a linear superposition of the dose contributions from each source rod, expressed as: In the formula, Total dose; Based on the total dose, the dose non-uniformity of the reference plane is calculated and expressed as: In the formula, Dose nonuniformity at the reference plane.

[0030] S16. Divide the total set of slots for the radiation facility to obtain the set of slots for fixed source rods and the set of available slots. In practical industrial irradiation applications, irradiation systems (radiation facilities) typically have a partially fixed source rod arrangement, the position and activity configuration of which cannot be changed. To improve dose distribution uniformity or extend system lifespan, new source rods are often introduced into remaining empty slots to modify the system and optimize its performance. For combinatorial optimization problems with some known variables, the core challenge lies in determining the optimal spatial configuration of the new source rods to achieve the most uniform dose distribution across the reference point set, while keeping the existing source rod arrangement unchanged.

[0031] Based on this, this embodiment formally defines the optimization problem, assuming the total set of slots is . The total number of slots is Q; The set of fixed source rod slots is defined as the set of slots that are already occupied by the source rod and whose position and activity cannot be changed. It is represented as: In the formula, For a fixed source rod slot set, For the total number of slots; The available slot set is defined as the set of free slots after subtracting the fixed source bar slot set from the total slot set, and is expressed as: In the formula, For the set of available slots, The set difference operator means removing all elements contained in the right set from the set on the left. S17. Construct the global activity vector U of the radiation facility, set the activity values ​​at the corresponding positions of the fixed source rod slot set as known constants, and set the activity values ​​at the corresponding positions of the available slot set as variables to be optimized. Specifically, the global activity vector is ,in: like ,but Let be a known constant; if ,but These are the variables to be optimized.

[0032] S18. Construct the system response matrix of the radiation facility. In this embodiment, the system response matrix is ​​denoted as... System response matrix any row element C i This represents the unit activity dose response of the corresponding slot to all reference points. The total dose distribution of the radiation facility is calculated based on the system response matrix and the global activity vector. A dose non-uniformity evaluation function based on the total dose distribution of the radiation facility is defined. The total dose distribution of the radiation facility is expressed as follows: D=C U In the formula, D represents the total dose distribution of the radiation facility; U represents the global activity vector. To measure uniformity, a dose nonuniformity evaluation function based on the total dose distribution of the radiation facility is introduced: In the formula, This is a function for evaluating dose nonuniformity. The total dose value at the reference point in the nth row and mth column of the dose reference plane, max(D j ) and min(D j ) represent the maximum and minimum dose values ​​in the reference point set, respectively.

[0033] S19. The optimization objective is to minimize the dose nonuniformity evaluation function value. This optimization objective is a non-convex optimization problem with structural prior constraints. Its solution space is jointly restricted by the available slot combinations and the new source rod activity configuration strategy. The final optimization objective is expressed as: In the formula, For dose non-uniformity, This represents the minimum dose nonuniformity obtained under the optimal source rod arrangement scheme.

[0034] S2. To improve optimization efficiency, a pre-calculated dose coefficient matrix (DCM) is constructed based on a fixed geometric structure before the algorithm begins. This includes the following sub-steps: S21. During the algorithm initialization phase, according to Co... 60 The three-dimensional parametric geometric model of the irradiation station is used to construct a pre-calculated dose coefficient matrix, specifically by: [constructing the matrix based on the irradiation dose in S14]. The expression is separated into the geometric influence factor and the source rod activity A, and then the dose contribution matrix B is constructed. The total dose distribution D is then transformed into a matrix multiplication operation between the source rod activity A and the dose contribution matrix B, i.e.: ; The geometric influence factor is expressed as follows: In the formula, For dose contribution matrix The element in represents the slot number. OK The geometric influence factor of the source bar at column n on the reference point plane at row n and column m; the key characteristic of this matrix is ​​that... The calculation of the total dose distribution is entirely determined by the geometric parameters of the source rod (position, length, width) and the position of the reference point, and is independent of the source rod activity A. Therefore, during the optimization process, the activity A can be separated from the dose calculation formula, allowing the total dose distribution D to be calculated in real time using matrix multiplication.

[0035] S22, Dose Contribution Matrix B in Co 60 The radiation source rod arrangement optimization is calculated and stored once before the iteration, and can be repeatedly called in subsequent optimization iterations without recalculating the geometric influence factor, thus eliminating redundant calculation overhead.

[0036] Specifically, this embodiment pre-calculates and stores the dose contribution matrix B. Each arrangement adjustment only requires one matrix multiplication, eliminating the need to repeatedly calculate the geometric influence factor. This reduces the computational complexity of each iteration from O(P×R) to O(R) (where P is the number of source bars and R is the number of reference points), achieving a computational speedup of hundreds of times (experiments verify approximately 500 times). Compared to point-by-point calculation... The computational cost of matrix multiplication is significantly reduced, making it particularly suitable for optimization scenarios of large-scale irradiation stations.

[0037] In addition, matrix elements The method calculates and stores the dose contribution matrix B once before optimization, eliminating the need for repeated calculations in multiple optimization iterations and further reducing redundant computational overhead. This results in highly stable computation and broad applicability. However, this method assumes a static geometric configuration. If the source rod or reference point position changes dynamically, the dose contribution matrix B needs to be updated, potentially increasing computational costs. For large systems, storing the dose contribution matrix B may face memory limitations.

[0038] S3. Incremental optimization design using the Greedy-Backtracking (GB) hybrid optimization algorithm; In irradiation facilities with pre-existing fixed source rod layouts, a key challenge in retrofitting is determining how to effectively incorporate new source rods to improve overall dose field uniformity. Since some source slots are already occupied, the placement space for new source rods is inherently limited. Therefore, the central optimization problem is to select the most suitable slot from the remaining available locations to minimize dose non-uniformity. To address this challenge, this invention proposes a greedy-backtracking (GB) hybrid optimization algorithm designed to efficiently identify the optimal arrangement of new source rods within an acceptable computational timeframe. Based on a pre-computed dose coefficient matrix, the greedy-backtracking hybrid optimization algorithm is used to optimize the arrangement of in-service Co... 60 The layout scheme of new source rods for the radiation facility is incrementally searched and iteratively optimized. The final output is the corresponding increase in Co that minimizes the dose inhomogeneity of the radiation field under the constraints of existing source rod positions and fixed activity. 60 The optimal layout scheme of the source rod; as a preferred embodiment, refer to Figure 4 Specifically, it includes the following sub-steps: S31. Initialize activity configuration: Construct the spatial layout of the radiation facility and initialize the global activity vector U based on the existing source rod configuration. Assign known activity values ​​to the occupied source cells and initialize unoccupied source cells to zero activity. S32. Pre-calculated dose contribution: The dose contribution of each source cell to the reference point is pre-calculated to form a pre-calculated dose coefficient matrix, which is used to accelerate subsequent dose assessment. S33. Greedy-backtracking hybrid search: First, a locally optimal initial layout of the source bar layout is generated using a greedy strategy. Then, a backtracking mechanism is introduced within the preset maximum search depth to adjust the placement order of the source bars and explore a better layout scheme. In one specific embodiment, a greedy strategy is applied to generate the initial layout: at each step, the algorithm selects the available slots that minimize dose inhomogeneity to place the new source rod, thereby achieving a local optimum. However, due to the inherent limitations of the greedy algorithm—namely, its tendency to get trapped in local optima and its limited exploration capability—the system incorporates a backtracking search mechanism. Within the user-defined maximum search depth (max_depth), the algorithm iteratively adjusts the arrangement order through backtracking, explores different layout schemes, and ultimately seeks a more globally optimal solution.

[0039] S34, Heuristic Pruning Acceleration: Reference Figure 4 Using the dose nonuniformity evaluation function as the objective function, the source rod is placed in the slot of the region with the lowest dose during the search process, thereby accelerating the convergence to the optimal solution. If the candidate configuration can improve the uniformity, the search continues along the path; otherwise, the current branch will be pruned in advance to reduce unnecessary computational overhead and improve optimization efficiency.

[0040] S4. Experimental Results and Analysis; To verify the effectiveness of the algorithm proposed in this invention, a Co used in actual production at a research institution was selected. 60 The source code is used as a reference. Figure 5 The source rack adopts a three-layer structure (upper, middle, and lower layers), with each layer containing two sub-racks (left and right), forming a total of six sub-racks, named E, F, H, T, V, and W. Each sub-rack is equipped with 30 source slots, for a total of 180 slots in the entire source rack. Source slot naming follows an XY format, where X represents the sub-rack identifier (E, F, H, T, V, W), and Y defines the slot number (1 to 30) from left to right within each sub-rack. For example, the 13th slot from the left in sub-rack E is labeled E-13. In terms of geometry, the center-to-center distance between adjacent source rods within a sub-rack is 3.5 cm, the center-to-center distance between adjacent vertical source slots is 56 cm, and the center-to-center distance between adjacent horizontal source rods is 11 cm. Commonly used Co... 60 The source rod is 45.14 cm long and 1.11 cm in diameter.

[0041] The verification method of this invention includes the following sub-steps: Performance verification of S41 and GB algorithms in modified scenarios; To verify the effectiveness and practicality of the greedy-backtracking hybrid algorithm (GB) in source rod arrangement optimization, a systematic experiment was conducted in a typical modification scenario. This invention simulates an irradiation station source rack with pre-existing source rods in fixed positions, aiming to optimize the placement of new source rods to enhance the uniformity of the overall dose distribution. The optimization objective is to minimize the ratio of the maximum dose to the minimum dose at each reference point while adhering to physical constraints.

[0042] S42. In the experimental design, three modification scales were set, corresponding to 10, 20, and 30 new source rods, respectively, while the number of old source rods was fixed at 50. The activities of the source rods used in this invention are shown in Tables 1, 2, 3, and 4.

[0043] Table 1 - Information on existing fixed source rods in the source rack Table 2 - Activity data of the 10 new source rods added in the modification plan Table 3 - Activity data of the 20 new source rods added in the modification plan Table 4 - Activity data of the 30 new source rods added in the modification plan All source rod activity data were obtained from the institute's historical records. To comprehensively evaluate the adaptability and robustness of each algorithm, five independent runs were performed for each modification scale, and the optimized dose non-uniformity (defined as the ratio of the maximum dose to the minimum dose) and the algorithm's running time were recorded.

[0044] The comparison algorithms include: (1) Pure greedy strategy (G): Place source rods sequentially based on the current optimal dose insertion position; (2) Greedy-backtracking hybrid algorithm (GB): The greedy-backtracking hybrid optimization algorithm (GB) proposed in this invention; (3) Random insertion strategy (R): Randomly insert source bars as a lower bound reference for algorithm performance; (4) Optimal permutation (O): Theoretically perfect permutation, assuming no constraints from existing source bars, using the traditional simulated annealing algorithm as the ideal baseline generation; S43. Calculate the mean and sample standard deviation of the five runs for each case. The mean and standard deviation of dose nonuniformity and run time for each algorithm under the modification scenarios of adding 10, 20, and 30 source rods are shown in Tables 5 and 6.

[0045] Table 5 - Comparison of Non-uniformity of Algorithms in Modified Scenarios Table 6 - Comparison of runtime of various algorithms in the modified scenario S44. Comparing the test results, it was found that in modification scenarios with a high proportion of newly added source rods, the Greedy-Backtracking (GB) algorithm consistently achieved the lowest dose inhomogeneity in multiple experimental runs compared to the pure greedy strategy and the random insertion strategy. The improvement in average dose inhomogeneity was particularly significant when the number of newly added source rods reached 30. However, the GB algorithm incurs higher computational resource consumption, resulting in a significantly longer running time compared to the pure greedy and random strategies. Balancing optimization quality and computational cost, the GB algorithm is well-suited for source rod placement tasks requiring high dose field uniformity, while the pure greedy strategy is a low-overhead approximation solution suitable for scenarios with rapid online deployment or limited hardware resources. In summary, the GB algorithm has a significant advantage in optimization quality, particularly suitable for source rod placement problems with high accuracy requirements. In scenarios with strict runtime constraints, the pure greedy strategy remains a practical lightweight alternative with considerable engineering applicability.

[0046] This invention constructs an incremental optimization problem-solving framework that conforms to engineering constraints. By explicitly dividing the source slot set into a "fixed source slot subset" (with known activity and location) and a "available source slot subset", and forcibly fixing the state of the former in the mathematical model and algorithm design, it is ensured that all output schemes do not require any modification to existing facilities, reducing safety hazards and unnecessary costs.

[0047] This invention provides a hybrid optimization algorithm that combines depth search and efficient pruning capabilities within a constrained solution space. To achieve this, this invention discloses a Greedy-Back racking (GB) hybrid algorithm to optimize the placement of new source bars while maintaining the fixed positions of existing source bars. This algorithm employs a greedy strategy to quickly generate near-optimal solutions and is enhanced by a backtracking mechanism to address the limitations of local optima. Furthermore, an efficient pruning strategy is used to reduce computational costs. By achieving near-global optimal solutions under acceptable computational constraints, this algorithm effectively reduces the high costs and security risks associated with repositioning existing source bars.

[0048] This invention maximizes the synergistic effect of new and existing source rods. Through a fine-grained search using the aforementioned hybrid algorithm, the ultimate goal is to determine the optimal spatial configuration of the new source rod in the remaining empty slots. This ensures that the dose uniformity (measured by the maximum / minimum dose ratio) of the combined radiation field formed by the new and existing source rods reaches an optimal or near-optimal state under given constraints. Thus, with minimal modifications and lowest risk, a substantial upgrade to the performance of the irradiation device is achieved, extending its effective service life and improving processing quality. By achieving these objectives, this invention aims to effectively optimize the synergistic effect of new and existing source rods in modified environments, and significantly reduces algorithm runtime through pre-computation techniques, resulting in considerable economic benefits and industrial application value.

[0049] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.

Claims

1. A method for incremental optimization of source rod layout in in-service Co-60 radiation facilities, characterized in that, Includes the following steps: S1, Constructing In-Service Co 60 Basic model for incremental optimization of radiation field of radiation facilities; S2. Construct a pre-calculated dose coefficient matrix based on the aforementioned radiation field incremental optimization basic model; S3. Based on the pre-calculated dose coefficient matrix, a greedy-backtracking hybrid optimization algorithm is used to optimize the in-service Co... 60 The layout scheme of new source rods for the radiation facility is incrementally searched and iteratively optimized. The final output is the corresponding increase in Co that minimizes the dose inhomogeneity of the radiation field under the constraints of existing source rod positions and fixed activity. 60 The optimal layout scheme for the source rod.

2. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 1, characterized in that, S1 includes the following sub-steps: S11. Define a radiation source plane in the XOZ coordinate system plane, and set a source slot in the radiation source plane to represent the placement position of the source rod. The coordinate set of the source slot is: In the formula, This represents the set of coordinates of the source slot within the radiation source plane; This represents the coordinates of the vertex on the source slot. Let x be the x-coordinate of the vertex on the source slot. Let be the vertical coordinate of the vertex on the source slot. , These represent the number of rows and columns of the source slot, respectively. and These represent the total number of rows and columns of the source slots, respectively. S12. Define a dose reference plane parallel to the radiation source plane. The dose reference plane is located at the vertical coordinate Y=100cm, and its coordinate set is as follows: In the formula, The set of coordinates representing the reference plane; Indicates the coordinates of the reference point. The x-coordinate of the reference point The vertical coordinate of the reference point, The row number of the reference point. The number of columns for the reference point. , These represent the total number of rows and columns of the reference point, respectively. S13. Based on the radiation source plane and dose reference plane, construct Co 60 A three-dimensional parametric geometric model of an irradiation station; S14. In a three-dimensional parametric geometric model, calculate a single root Co. 60 The radiation dose from the radiation source rod to reference point O; S15. Based on the radiation dose calculation results in S14, calculate all Co... 60 The total dose of the radiation source rod to a single reference point is calculated, and the dose non-uniformity of the reference plane is calculated. S16. Divide the total set of slots for the radiation facility to obtain the set of slots for fixed source rods and the set of available slots. S17. Construct the global activity vector of the radiation facility, set the activity value of the corresponding position of the fixed source rod slot set as a known constant, and set the activity value of the corresponding position of the available slot set as the variable to be optimized. S18. Construct the system response matrix of the radiation facility, calculate the total dose distribution of the radiation facility based on the system response matrix and the global activity vector, and define a dose non-uniformity evaluation function based on the total dose distribution of the radiation facility. S19. The optimization objective is to minimize the dose nonuniformity evaluation function value, and the optimization objective is formalized as a non-convex optimization problem with structural prior constraints.

3. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 2, characterized in that, In S14, the calculation of a single Co root 60 The radiation dose from the radiation source rod to reference point O is expressed as: In the formula, For the first Line number The irradiation dose of the source rod to reference point O, The irradiation constant, For source rod activity, This represents the perpendicular distance between any irradiated point in the reference plane and the source rod. Indicates the length of the source rod. This represents the distance from the foot of the perpendicular to the lower vertex of the source rod.

4. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 3, characterized in that, In S15, all Co are calculated. 60 The total dose from the radiation source rod to a single reference point is expressed as: In the formula, Total dose; Based on the total dose, the dose non-uniformity of the reference plane is calculated, and it is expressed as: In the formula, Dose nonuniformity at the reference plane.

5. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 2, characterized in that, In S16, the fixed source rod slot set is a set of slots that have been occupied by the source rod and whose position and activity cannot be changed, and it is represented as follows: In the formula, For a fixed source rod slot set, For the total number of slots; The available slot set is the set of free slots after subtracting the fixed source bar slot set from the total slot set, and it is represented as: In the formula, For the set of available slots, The set difference operator means removing all elements contained in the right set from the set on the left.

6. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 2, characterized in that, In S18, the system response matrix is ​​defined as follows: The system response matrix Any row of elements represents the unit activity dose response of the corresponding slot to all reference points; The total dose distribution of the radiation facility is calculated based on the system response matrix and the global activity vector, and is expressed as follows: D=C U In the formula, D represents the total dose distribution of the radiation facility; U represents the global activity vector. Define a dose nonuniformity evaluation function based on the total dose distribution of a radiation facility: In the formula, This is a function for evaluating dose nonuniformity. This represents the total dose value at the reference point in the nth row and mth column of the dose reference plane.

7. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 6, characterized in that, In step S19, the optimization objective is to minimize the dose nonuniformity evaluation function value, which is expressed as follows: In the formula, For dose non-uniformity, This represents the minimum dose nonuniformity obtained under the optimal source rod arrangement scheme.

8. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 7, characterized in that, S2 includes the following sub-steps: S21, The pre-calculated dose coefficient matrix is ​​constructed by: taking the irradiation dose in S14... The expression is separated into a geometric influence factor and a source rod activity A, and then a dose contribution matrix B is constructed. The total dose distribution D of the radiation facility is transformed into a matrix multiplication operation of source rod activity A and dose contribution matrix B, that is: ; S22, Dose Contribution Matrix B in Co 60 The radiation source rod arrangement optimization is calculated and stored once before the iteration, and can be repeatedly called in subsequent optimization iterations without recalculating the geometric influence factor, thus eliminating redundant calculation overhead.

9. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 8, characterized in that, In S21, the geometric influence factor is expressed as follows: In the formula, For dose contribution matrix The element in represents the slot number. OK The geometric influence factor of the source bar at column n on the reference point plane at row m.

10. The source rod incremental optimization layout method for in-service Co-60 radiation facilities according to claim 1, characterized in that, S3 includes the following sub-steps: S31. Initialize activity configuration: Construct the spatial layout of the radiation facility and initialize the global activity vector U based on the existing source rod configuration. Assign known activity values ​​to the occupied source cells and initialize unoccupied source cells to zero activity. S32. Pre-calculated dose contribution: The dose contribution of each source cell to the reference point is pre-calculated to form a pre-calculated dose coefficient matrix, which is used to accelerate subsequent dose assessment. S33. Greedy-backtracking hybrid search: First, a locally optimal initial layout of the source bar layout is generated using a greedy strategy. Then, a backtracking mechanism is introduced within the preset maximum search depth to adjust the placement order of the source bars and explore a better layout scheme. S34. Heuristic Pruning Acceleration: Using the dose non-uniformity evaluation function as the objective function, the source bar is placed in the slot with the lowest dose during the search process. Branches that cannot improve uniformity are pruned to improve optimization efficiency.

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