Engineering cost anomaly identification and early warning method based on machine learning

Abstract

The invention discloses an engineering cost anomaly identification and early warning method based on machine learning. The method comprises the following steps: collecting engineering data, and processing the engineering data to generate a state vector sequence; constructing a state diagram, and generating a topological complex; performing continuous homology analysis on the topological complex, calculating topological characteristics, and generating a target engineering topological fingerprint sequence; generating a historical topological fingerprint sequence, performing vectorization embedding, and determining a normal behavior baseline region; carrying out vectorization embedding on the topological fingerprint sequence of the target project, and comparing with a normal behavior baseline region to generate a topological anomaly score; and executing power bifurcation detection processing, and generating a cost early warning signal when a bifurcation sign occurs or the topology anomaly score exceeds an identification threshold. According to the method, topology coherence analysis and power bifurcation identification are fused, accurate early warning of engineering cost evolution abnormity is realized, and the method has the advantages of early identification, high stability and strong applicability.

Description

Technical Field

[0001] This invention relates to the field of engineering cost anomaly detection technology, and in particular to a method for identifying and warning of engineering cost anomalies based on machine learning. Background Technology

[0002] Existing technologies for identifying and warning of anomalies in engineering costs largely rely on empirical rules, statistical thresholds, or traditional machine learning models. They identify risks by performing linear analysis or single-dimensional comparisons of bills of quantities, cost data, and schedule information. However, these methods struggle to extract high-dimensional structural relationships from multi-source engineering data, fail to characterize the complex coupling constraints between cost, schedule, and pricing rules, and cannot reflect the overall changing trends of engineering behavior over time. When data exhibits multi-scale structural changes, structural disturbances, or nonlinear evolution characteristics, traditional methods often fail to identify potential anomalies in a timely manner, leading to delayed warnings or increased misjudgment rates.

[0003] Furthermore, existing technologies generally lack the ability to analyze the stability of engineering data topology, cannot utilize high-dimensional topological features to characterize engineering behavior patterns, and cannot judge potential systemic changes through data evolution characteristics. The lack of a unified topological baseline model for normal engineering behavior makes it difficult to compare consistency between different projects. Simultaneously, existing technologies do not incorporate dynamic system bifurcation theory, making it impossible to detect sudden changes in engineering costs based on the dynamic evolution of topological fingerprints, and thus difficult to provide reliable early warnings. Therefore, there is an urgent need for a method for identifying and warning of engineering cost anomalies that integrates topological structure analysis, temporal evolution characteristics, and abnormal trend recognition. Summary of the Invention

[0004] One objective of this invention is to propose a machine learning-based method for identifying and warning of engineering cost anomalies. This invention integrates topological homology analysis and dynamic bifurcation identification to achieve accurate early warning of engineering cost evolution anomalies, and has the advantages of early identification, high stability and strong applicability.

[0005] A method for identifying and warning of engineering cost anomalies based on machine learning according to an embodiment of the present invention includes the following steps:

[0006] Collect bill of quantities, cost, schedule and pricing rule data, clean and encode them, combine them into state vectors under each time index, and generate a state vector sequence.

[0007] A state graph is constructed based on the state vector sequence. The state vectors are set as graph nodes and edges are connected according to time sequence and similarity threshold. A topological complex representing the relationship between cost, schedule and pricing rule constraints is generated on the state graph.

[0008] Perform continuous homology analysis on the topological complex under different scale parameters, calculate topological features, and generate a topological fingerprint sequence of the target project in time index order;

[0009] Data from multiple historical normal projects are processed to generate historical topological fingerprint sequences. These historical topological fingerprint sequences are then vectorized and embedded to determine the baseline region for normal behavior within the embedding space.

[0010] The target engineering topological fingerprint sequence is vectorized and embedded, and compared with the normal behavior baseline region in the topological attention neural network to generate a topological anomaly score;

[0011] Based on the topological fingerprint sequence of the target project, dynamic bifurcation detection processing is performed to construct a bifurcation feature sequence that characterizes the evolution trend of the topological fingerprint. When the bifurcation feature sequence shows signs of bifurcation such as eigenvalue sign reversal, eigenvalue real part crossing zero, or eigenvalue changing from real pair to conjugate complex pair, or when the topological anomaly score exceeds the recognition threshold, a cost warning signal is generated.

[0012] Optionally, the generation of the state vector sequence specifically includes:

[0013] Collect bill of quantities, cost, schedule and pricing rules data, and record the data in a structured manner according to the bill of quantities item code, cost item, schedule time index and rule identifier;

[0014] Perform missing item correction, data consistency verification, and outlier removal on structured records; perform time alignment on data with different time indexes; and generate multi-source engineering data.

[0015] Perform normalization processing on numerical fields in multi-source engineering data, perform encoding processing on category fields, and generate bill of quantities features, cost features, schedule features, and pricing rule features;

[0016] The four types of features corresponding to each time index are extracted, combined in a preset order to form a state vector, and then arranged in the order of time index to generate a state vector sequence.

[0017] Optionally, the generation of the topological complex specifically includes:

[0018] Based on the time index in the state vector sequence, each state vector is set as a graph node in chronological order, and a graph node set is generated in the set order.

[0019] Temporal constraints are applied to the state vectors based on the time index, time connections are established between state vectors with adjacent time indices, and time connections are established between state vectors whose time index difference is within a preset range in chronological order.

[0020] Calculate the feature difference degree for any two state vectors, filter state vector pairs whose feature difference degree does not exceed a preset threshold, and establish similarity edges for the filtered state vector pairs.

[0021] A graph edge set is formed by time-connected edges and similarity-connected edges, which is combined with a graph node set to generate a state graph.

[0022] On the state graph, graph nodes are used as zero-dimensional units and graph edges are used as one-dimensional units. High-dimensional units are generated according to the construction rules based on node connectivity. The topological complex is composed of all zero-dimensional units, one-dimensional units and their high-dimensional units.

[0023] Optionally, the generation of the target project topology fingerprint sequence specifically includes:

[0024] Apply scale changes sequentially to the topological complex under multiple preset scale parameters to generate the topological complex shape at the corresponding scale;

[0025] Topological features are extracted from the topological complex morphology at various scales to generate a set of topological features composed of topological features at different scales;

[0026] Arrange the topological feature sets in chronological order according to the time index to generate a topological feature sequence;

[0027] The topological feature sequence is fingerprinted and arranged in time index order to generate the target project topological fingerprint sequence.

[0028] Optionally, determining the baseline region for normal behavior specifically includes:

[0029] Data from multiple historical normal projects are collected and preprocessed, and each historical normal project is generated into a corresponding historical state vector sequence according to the time index.

[0030] A historical state graph is constructed based on each historical state vector sequence, and the corresponding historical topological complex is generated.

[0031] Continuous homology analysis is performed on each historical topological complex under multiple preset scale parameters to extract topological features at different scales and generate a set of historical topological features for each historical project.

[0032] Based on the time index, each set of historical topological features is arranged in chronological order to generate a sequence of historical topological features for each historical project.

[0033] The historical topological feature sequence is fingerprinted to generate the corresponding historical topological fingerprint sequence.

[0034] Multiple historical topological fingerprint sequences are vectorized and embedded to generate a set of historical topological fingerprint vectors;

[0035] Based on the distribution structure of historical topological fingerprint vector sets in the embedding space, the baseline region for normal behavior is determined.

[0036] Optionally, the generation of the topology anomaly score specifically includes:

[0037] The topological fingerprint sequence of the target project is organized, and the topological fingerprints corresponding to each time index are generated into a topological fingerprint input sequence in a set order;

[0038] The topological fingerprint input sequence is vectorized to generate a topological fingerprint vector sequence arranged by time index;

[0039] The topological fingerprint vector sequence is input into the topological attention neural network to extract attention features from the topological fingerprint vector sequence;

[0040] The extracted attention features are compared with the baseline region of normal behavior to generate topological association features;

[0041] A topological anomaly score is generated based on topological association features.

[0042] Optionally, the generation of the cost warning signal specifically includes:

[0043] Perform change calculations on the topological fingerprints corresponding to adjacent time indices in the topological fingerprint sequence of the target project to generate a change sequence;

[0044] Local change features are generated for each item in the change sequence, resulting in a local change feature sequence.

[0045] For the local change feature sequence, perform symbol recording and symbol comparison, write the time index of the positive and negative flip of the symbol into the symbol flip record, perform real part recording and zero-point crossing detection, write the time index of the real part crossing the zero point into the zero-point crossing record, perform complex value form recording and form change judgment, and write the time index of the real value form changing into the paired complex value form into the conjugate change record.

[0046] The sign flip record, zero-point crossing record, and conjugate change record are written into the same structure in time index order to generate a bifurcation feature sequence;

[0047] Read the topology anomaly score, and generate a cost warning signal when any record exists in the bifurcation feature sequence or the topology anomaly score exceeds the identification threshold.

[0048] The beneficial effects of this invention are:

[0049] This invention constructs a state vector sequence based on multi-source engineering data, and generates a topological complex that can characterize the coupling relationship between cost, schedule, and pricing rules. This achieves a high-dimensional structured expression of complex engineering behavior, breaking through the limitations of existing methods that rely on single features or linear correlation analysis. By performing continuous cohomology analysis at different scales, stable and discriminative topological features are extracted and a topological fingerprint sequence is generated. This clearly presents the overall trend and local changes of engineering behavior over time, effectively improving the structural sensitivity and robustness of cost anomaly identification.

[0050] This invention further vectorizes and embeds the topological fingerprint sequences of multiple historical projects into a unified space to form a normal behavior baseline region. This allows the behavior patterns of different projects to be compared under a unified standard, overcoming the problem of poor cross-project consistency in traditional methods. Based on this, this invention uses a topological attention neural network to extract features from the topological fingerprint sequence of the target project and correlates it with the normal behavior baseline region. This can accurately quantify the degree of deviation of project behavior, improve the accuracy and reliability of anomaly identification, and avoid the subjective bias caused by relying on manual rule setting.

[0051] This invention introduces a dynamic bifurcation detection mechanism into the field of engineering cost anomaly identification. By identifying bifurcation signs such as sign flipping, zero-point crossing, and changes in complex value forms, it constructs a bifurcation feature sequence, enabling the capture of potential risks before critical changes occur in engineering data evolution, thus achieving early warning of engineering costs. This invention forms a dual discrimination mechanism combining topological anomaly detection and evolutionary trend mutation identification, making anomaly identification more comprehensive, sensitive, and accurate. Overall, this invention has significant technical effects such as early identification, accurate judgment, strong robustness, and high cross-engineering applicability, providing a novel, structured, high-dimensional, and intelligent early warning method for engineering cost risk monitoring. Attached Figure Description

[0052] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0053] Figure 1 This is a flowchart of a machine learning-based method for identifying and warning of engineering cost anomalies proposed in this invention.

[0054] Figure 2 This is a flowchart illustrating the generation of target engineering topological fingerprint sequences based on multi-scale continuous homology analysis, a method for identifying and warning of engineering cost anomalies based on machine learning proposed in this invention. Detailed Implementation

[0055] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0056] refer to Figures 1-2 A machine learning-based method for identifying and warning of engineering cost anomalies includes the following steps:

[0057] Collect bill of quantities, cost, schedule and pricing rule data, clean and encode them, combine them into state vectors under each time index, and generate a state vector sequence.

[0058] A state graph is constructed based on the state vector sequence. The state vectors are set as graph nodes and edges are connected according to time sequence and similarity threshold. A topological complex representing the relationship between cost, schedule and pricing rule constraints is generated on the state graph.

[0059] Perform continuous homology analysis on the topological complex under different scale parameters, calculate topological features, and generate a topological fingerprint sequence of the target project in time index order;

[0060] Data from multiple historical normal projects are processed to generate historical topological fingerprint sequences. These historical topological fingerprint sequences are then vectorized and embedded to determine the baseline region for normal behavior within the embedding space.

[0061] The target engineering topological fingerprint sequence is vectorized and embedded, and compared with the normal behavior baseline region in the topological attention neural network to generate a topological anomaly score;

[0062] Based on the topological fingerprint sequence of the target project, dynamic bifurcation detection processing is performed to construct a bifurcation feature sequence that characterizes the evolution trend of the topological fingerprint. When the bifurcation feature sequence shows signs of bifurcation such as eigenvalue sign reversal, eigenvalue real part crossing zero, or eigenvalue changing from real pair to conjugate complex pair, or when the topological anomaly score exceeds the recognition threshold, a cost warning signal is generated.

[0063] In this embodiment, the generation of the state vector sequence specifically includes:

[0064] Collect bill of quantities, cost, schedule and pricing rules data, and record the data in a structured manner according to the bill of quantities item code, cost item, schedule time index and rule identifier;

[0065] The structured record specifically includes:

[0066] Read the bill of quantities item codes and quantity fields from the bill of quantities data and write them into the corresponding fields of the structured record; read the cost items and cost amounts from the cost data and write them into the corresponding fields of the structured record; read the progress time index and completion percentage from the progress data and write them into the corresponding fields of the structured record; read the rule identifier and rule parameters from the pricing rule data and write them into the corresponding fields of the structured record; merge the four types of fields according to the bill of quantities item codes, cost items, progress time indexes, and rule identifiers and write them into the same structured record to generate a structured record;

[0067] Perform missing item correction, data consistency verification, and outlier removal on structured records; perform time alignment on data with different time indexes; and generate multi-source engineering data.

[0068] The generation of the multi-source engineering data specifically includes:

[0069] For missing quantity, cost, schedule, or pricing rule fields in structured records, the system searches backwards for the most recent record with the same bill of quantities item code, cost item, and rule identifier, and writes the found field values ​​into the current record. For structured records after missing items have been corrected, the system compares the ratio of the cost field to the quantity field under adjacent time indices by grouping by bill of quantities item code, cost item, and rule identifier, and deletes records with ratio differences exceeding a preset range. For the remaining records, the system determines the time index range within each group, and copies the field values ​​under adjacent time indices to form a complete time index sequence for records with missing time indices. Finally, the system sorts all the completed records by bill of quantities item code, cost item, rule identifier, and time index to generate multi-source project data.

[0070] Perform normalization processing on numerical fields in multi-source engineering data, perform encoding processing on category fields, and generate bill of quantities features, cost features, schedule features, and pricing rule features;

[0071] The generation of the bill of quantities features, cost features, schedule features, and pricing rule features specifically includes:

[0072] For numerical fields related to the bill of quantities, cost, schedule, and pricing rules, obtain the maximum and minimum values, truncate values ​​exceeding the range, and scale them using a uniform scaling factor to obtain regular integer value fields; assign a unique number to each value for the bill of quantities item code, cost item, schedule-related category identifier, and rule identifier, and write it into the corresponding field; under the same time index, concatenate the regularized quantity fields with the bill of quantities item code number according to the bill of quantities item code order to generate the bill of quantities feature; concatenate the regularized cost fields with the cost item number according to the cost item order to generate the cost feature; concatenate the regularized schedule fields with the schedule category number according to the schedule time index order to generate the schedule feature; concatenate the regularized rule fields with the rule identifier number according to the rule identifier order to generate the pricing rule feature;

[0073] Extract the four types of features corresponding to each time index, combine them in a preset order to form a state vector, and arrange the state vectors in the order of time index to generate a state vector sequence.

[0074] The generation of the state vector sequence specifically includes:

[0075] Determine all time indices in the multi-source engineering data and arrange them in ascending order; for each time index, read the bill of quantities features, cost features, schedule features, and pricing rule features under the corresponding time index, and concatenate the four types of features in a preset order to form the state vector of the current time index; arrange all state vectors in the order of time index to generate a state vector sequence.

[0076] In this embodiment, the generation of the topological complex specifically includes:

[0077] Based on the time index in the state vector sequence, each state vector is set as a graph node in chronological order, and a graph node set is generated in the set order.

[0078] The generation of the graph node set specifically includes:

[0079] Read the state vectors one by one from the state vector sequence, and read the time index of each state vector; sort all the time indices in ascending order, and read the corresponding state vectors in that order; create a graph node for each state vector and write the state vector into the data field of the graph node; add all the graph nodes to the same set in chronological order to generate a graph node set.

[0080] Temporal constraints are applied to the state vectors based on the time index, time connections are established between state vectors with adjacent time indices, and time connections are established between state vectors whose time index difference is within a preset range in chronological order.

[0081] The establishment of time-based edges specifically includes:

[0082] Read two graph nodes with adjacent time indices from the graph node set, compare their time indices, and create a time connection when the time index difference is one; read any two graph nodes whose time index difference is within a preset range from the graph node set, determine their time relationship, and create time connections in chronological order.

[0083] Calculate the feature difference degree for any two state vectors, filter state vector pairs whose feature difference degree does not exceed a preset threshold, and establish similarity edges for the filtered state vector pairs.

[0084] The establishment of similarity-based edges specifically includes:

[0085] Select any two graph nodes from the graph node set and read all the numerical fields of their corresponding state vectors; calculate the difference of field values ​​for the same field and sum all field differences to generate a feature difference score; compare the feature difference score with a preset threshold, and create a similarity edge for the two graph nodes when the feature difference score does not exceed the threshold.

[0086] A graph edge set is formed by time-connected edges and similarity-connected edges, which is combined with a graph node set to generate a state graph.

[0087] The generation of the state diagram specifically includes:

[0088] Set the graph node set as the node set of the state graph; merge the time-related edges and similarity-related edges into a graph edge set and mark it as the edge set of the state graph; write the node set and edge set into the same structure to generate the state graph;

[0089] On the state graph, graph nodes are used as zero-dimensional units and graph edges are used as one-dimensional units. High-dimensional units are generated according to the construction rules based on node connectivity. The topological complex is composed of all zero-dimensional units, one-dimensional units and their high-dimensional units.

[0090] The generation of the topological complex specifically includes:

[0091] Read all graph nodes from the state diagram, label each node as a zero-dimensional unit and write it into the zero-dimensional unit set; read all graph edges from the state diagram, label each edge as a one-dimensional unit and write it into the one-dimensional unit set; traverse the combinations of units that satisfy continuous connectivity in the zero-dimensional unit set and the one-dimensional unit set, and when there is a complete connected path between several units, create the corresponding high-dimensional unit and write it into the high-dimensional unit set; write the zero-dimensional unit set, the one-dimensional unit set, and the high-dimensional unit set into the same structure to generate a topological complex.

[0092] In this embodiment, the generation of the target project topology fingerprint sequence specifically includes:

[0093] Apply scale changes sequentially to the topological complex under multiple preset scale parameters to generate the topological complex shape at the corresponding scale;

[0094] The generation of the topological complex shape at the corresponding scale specifically includes:

[0095] Read zero-dimensional, one-dimensional, and high-dimensional units one by one from the topological complex and write the read units into the unit list; read the current scale parameter sequentially from the preset scale parameter set and write the scale parameter into the connection condition field of each unit in the unit list; compare the connection conditions of any two units in the unit list, and when the connection conditions meet the preset merging conditions, write the two units into the same unit combination structure; add all unit combination structures formed under the corresponding scale parameter into the same set in sequence to generate the topological complex shape of the corresponding scale;

[0096] Topological features are extracted from the topological complex morphology at various scales to generate a set of topological features composed of topological features at different scales;

[0097] The generation of the topological feature set specifically includes:

[0098] Read zero-dimensional units one by one from the topological complex shape at the current scale, record the existence state of the zero-dimensional units at the current scale, and write them into the zero-dimensional feature record; read one-dimensional units one by one from the same topological complex shape, record the existence state of the one-dimensional units at the current scale, and write them into the one-dimensional feature record; read high-dimensional units one by one from the same topological complex shape, record the existence state of the high-dimensional units at the current scale, and write them into the high-dimensional feature record; add the zero-dimensional feature record, one-dimensional feature record, and high-dimensional feature record to the same set in sequence to generate the topological feature set at the current scale; add the topological feature sets corresponding to all scales to the same set to generate the topological feature set;

[0099] Arrange the topological feature sets in chronological order according to the time index to generate a topological feature sequence;

[0100] The generation of the topological feature sequence specifically includes:

[0101] Read all time indices from the time index records of the target project and write them into the time index sequence in ascending order; for each time index in the time index sequence, read the topology feature set corresponding to that time index and write it into the corresponding position in the topology feature sequence; add the topology feature sets under all time indices into the same sequence structure in chronological order to generate the topology feature sequence;

[0102] The topological feature sequence is fingerprinted and arranged in time index order to generate the target project topological fingerprint sequence.

[0103] The generation of the target project topology fingerprint sequence specifically includes:

[0104] Read the topological feature set corresponding to each time index sequentially from the topological feature sequence; write the zero-dimensional feature record, one-dimensional feature record, and high-dimensional feature record in the topological feature set into the fingerprint vector field in sequence to generate the topological fingerprint of the current time index; add the topological fingerprints corresponding to each time index into the same sequence structure in chronological order to generate the target project topological fingerprint sequence.

[0105] In this embodiment, the determination of the normal behavior baseline region specifically includes:

[0106] Data from multiple historical normal projects are collected and preprocessed, and each historical normal project is generated into a corresponding historical state vector sequence according to the time index.

[0107] The corresponding historical state vector sequence includes:

[0108] The system sequentially reads the bill of quantities, cost, schedule, and pricing rule data for each historical normal project under each time index; performs missing item completion and field value consistency checks on each of the four types of data, and writes the checked data into the data entries of the same time index; under each time index, the checked bill of quantities, cost, schedule, and pricing rule fields are written into the status vector field in a fixed order to generate the historical status vector for the corresponding time index; all historical status vectors are written into the same sequence one by one in ascending order of time index to generate a historical status vector sequence.

[0109] A historical state graph is constructed based on each historical state vector sequence, and the corresponding historical topological complex is generated.

[0110] The generation of the corresponding historical topological complex specifically includes:

[0111] Read state vectors sequentially from the historical state vector sequence and write them into the graph node set. Create time edges between two nodes with adjacent time indices in the graph node set and write them into the time edge set. Calculate the field difference between any two state vectors in the graph node set, sum them to obtain the feature difference score. When the feature difference score does not exceed a preset threshold, create corresponding similarity edges and write them into the similarity edge set. Write the time edge set and the similarity edge set into the graph edge set, and then write the graph node set and the graph edge set into the state graph structure. In the state graph, label each graph node as a zero-dimensional unit and each graph edge as a one-dimensional unit. Sequentially judge the combinations of zero-dimensional units and one-dimensional units that satisfy the connectivity relationship. When the complete connectivity relationship is satisfied, create the corresponding high-dimensional unit and write it into the high-dimensional unit set. Write all zero-dimensional units, one-dimensional units, and high-dimensional units into a unified structure to generate a historical topological complex.

[0112] Continuous homology analysis is performed on each historical topological complex under multiple preset scale parameters to extract topological features at different scales and generate a set of historical topological features for each historical project.

[0113] The generation of the historical topological feature set for each historical project specifically includes:

[0114] For each historical project, its corresponding historical topological complex is read. Zero-dimensional, one-dimensional, and high-dimensional units are sequentially read from the historical topological complex and written into the unit set of the project. Current-scale parameters are read one by one from a preset scale parameter set and written into the connection condition field of all units in the unit set. The existence state of zero-dimensional, one-dimensional, and high-dimensional units at the current scale is determined based on the connection condition field, and the determination results are written into the corresponding zero-dimensional feature field, one-dimensional feature field, and high-dimensional feature field at the current scale, respectively. The three feature fields are written into the same structure to form the historical topological feature item corresponding to the project at the current scale. The historical topological feature items corresponding to all scales of the project are added to the same set to generate the historical topological feature set of the project. The historical topological feature sets corresponding to all historical projects are written into the same structure to generate the historical topological feature set of each historical project.

[0115] Based on the time index, each set of historical topological features is arranged in chronological order to generate a sequence of historical topological features for each historical project.

[0116] The generation of the historical topological feature sequences of each historical project specifically includes:

[0117] For each historical project, its historical topology feature set is read sequentially, and all time indices are extracted from the set and written into a time index list. The time index list is sorted in ascending order, and the sorted time indices are written into a time index sequence. The historical topology feature items of the historical project under the corresponding time index are read sequentially according to the order of the time index sequence, and each historical topology feature item is written into the corresponding position of the topology feature sequence of the historical project. The topology feature sequences generated by each historical project are written into the same structure to form the historical topology feature sequence of each historical project.

[0118] The historical topological feature sequence is fingerprinted to generate the corresponding historical topological fingerprint sequence.

[0119] The generation of the historical topological fingerprint sequence specifically includes:

[0120] Read each historical topological feature set sequentially from the historical topological feature sequence in chronological order; write the zero-dimensional feature field, one-dimensional feature field, and high-dimensional feature field in the set into the fingerprint field in a set order to generate the current historical topological fingerprint; write the historical topological fingerprints corresponding to all time indices into the same sequence in chronological order to generate the corresponding historical topological fingerprint sequence.

[0121] Multiple historical topological fingerprint sequences are vectorized and embedded to generate a set of historical topological fingerprint vectors;

[0122] The generation of the historical topological fingerprint vector set specifically includes:

[0123] For each historical topological fingerprint sequence, read the historical topological fingerprint one by one, write the fingerprint field into the vector field to generate the corresponding historical topological fingerprint vector; write all historical topological fingerprint vectors into the same set to generate a historical topological fingerprint vector set.

[0124] Based on the distribution structure of historical topological fingerprint vector sets in the embedding space, the baseline region for normal behavior is determined;

[0125] The determination of the baseline region for normal behavior includes:

[0126] Write the set of historical topological fingerprint vectors one by one into the coordinate structure of the embedding space; perform pairwise distance comparisons on all coordinates in the embedding space to identify continuous intervals with significant clustering density; write each clustering interval into the region field and merge them into a unified structure to generate the baseline region for normal behavior.

[0127] In this embodiment, the generation of the topological anomaly score specifically includes:

[0128] The topological fingerprint sequence of the target project is organized, and the topological fingerprints corresponding to each time index are generated into a topological fingerprint input sequence in a set order;

[0129] The generation of the topological fingerprint input sequence specifically includes:

[0130] Read the topological fingerprints in the target project topological fingerprint sequence in the order of time index; write the read topological fingerprints into the sequence structure in the order of the set fields; continue writing until the topological fingerprints corresponding to all time indices have been recorded, and generate the topological fingerprint input sequence;

[0131] The topological fingerprint input sequence is vectorized to generate a topological fingerprint vector sequence arranged by time index;

[0132] The generation of the topological fingerprint vector sequence specifically includes:

[0133] Read the topological fingerprints from the topological fingerprint input sequence sequentially; write all fields of the topological fingerprint into the vector field to generate a topological fingerprint vector; write all the topological fingerprint vectors into the same structure in time index order to generate a topological fingerprint vector sequence;

[0134] The topological fingerprint vector sequence is input into the topological attention neural network to extract attention features from the topological fingerprint vector sequence;

[0135] The topological attention neural network adopts an existing attention network structure and receives a sequence of topological fingerprint vectors as input;

[0136] The attention feature extraction specifically includes:

[0137] The topological fingerprint vector sequence is input into the topological attention neural network in chronological order; attention weights are calculated for each input vector; the attention weights are combined with the corresponding input vectors and written into the attention feature field to generate attention features.

[0138] The extracted attention features are compared with the baseline region of normal behavior to generate topological association features;

[0139] The generation of the topological association features specifically includes:

[0140] Read the corresponding feature fields from the attention features by time index; read the corresponding region fields from the normal behavior baseline region; perform a distance comparison between the two and write the comparison result into the association field to generate topological association features;

[0141] Generate topological anomaly scores based on topological association features;

[0142] The generation of the topology anomaly score specifically includes:

[0143] Read the association field from the topological association features; write the association field into the scoring input field; perform statistical operations on the scoring input field and write the statistical results into the scoring field to generate a topological anomaly score.

[0144] In this embodiment, the generation of the cost warning signal specifically includes:

[0145] Perform change calculations on the topological fingerprints corresponding to adjacent time indices in the topological fingerprint sequence of the target project to generate a change sequence;

[0146] Local change features are generated for each item in the change sequence, resulting in a local change feature sequence.

[0147] The generation of the local change feature sequence specifically includes:

[0148] For each variable in the change sequence, the direction of numerical change is determined according to the time index, and the direction information under the corresponding time index is generated; for each variable in the change sequence, the magnitude of numerical change is determined, and the magnitude information under the corresponding time index is generated; the direction information and magnitude information under the same time index are combined to form local change features, and a local change feature sequence is generated according to the time index.

[0149] For the local change feature sequence, perform symbol recording and symbol comparison, write the time index of the positive and negative flip of the symbol into the symbol flip record, perform real part recording and zero-point crossing detection, write the time index of the real part crossing the zero point into the zero-point crossing record, perform complex value form recording and form change judgment, and write the time index of the real value form changing into the paired complex value form into the conjugate change record.

[0150] The generation of the symbol flip record, zero-point crossing record, and conjugate change record specifically includes:

[0151] For each local change feature in the local change feature sequence, sign recognition processing is performed. The sign features are compared in time index order, and the time index of the sign flipping is written into the sign flip record. For the local change features, real part value processing is performed. The real part values ​​are compared in time index order, and the time index of the real part crossing the zero point is written into the zero point crossing record. For the local change features, numerical form recognition processing is performed. The time index of the numerical form changing from real value form to paired complex value form is written into the conjugate change record.

[0152] The sign flip record, zero-point crossing record, and conjugate change record are written into the same structure in time index order to generate a bifurcation feature sequence;

[0153] Read the topology anomaly score, and generate a cost warning signal when any record exists in the bifurcation feature sequence or the topology anomaly score exceeds the identification threshold.

[0154] Example 1:

[0155] To verify the feasibility of this invention in practice, it was applied to the whole-process cost management scenario of a municipal infrastructure construction project. This construction project is large in scale, has a long construction period, and involves many participating units. The labor costs, material costs, and equipment costs involved fluctuate significantly over time. Moreover, the construction procedures and pricing rules need to be adjusted multiple times during the construction period, resulting in dynamic changes in the relationship between cost, schedule, and rule constraints. In this scenario, traditional methods that rely on static thresholds, fixed rules, or manual experience to identify anomalies often fail to detect potential cost deviation trends in a timely manner, and are prone to delayed warnings or ignoring structural changes. Therefore, the anomaly identification and early warning method based on topology analysis and bifurcation detection proposed in this invention is very suitable.

[0156] In the practical application of this construction project, the bill of quantities, various cost data, construction progress information, and corresponding pricing rules are first collected on a daily basis. As construction progresses, these data exhibit different combination characteristics at different points in time. For example, cost data at the same time needs to be matched with progress data at the corresponding time, and cost changes at the same stage need to meet the constraints of pricing rules. At the same time, to ensure the consistency of data use, it is necessary to correct missing records and fill in errors, and align content from different sources according to a unified time index so that they can be analyzed and processed under the same time benchmark.

[0157] After obtaining the data, the engineering quantity features, cost features, schedule features, and pricing rule features corresponding to each time index are combined and recorded as state vectors according to the steps of this invention, forming a state vector sequence covering the entire construction cycle. In this sequence, different time indices not only reflect changes in cost and schedule, but also record the constraint changes brought about by rule adjustments. On this basis, a state diagram is constructed according to the time sequence and feature difference relationship, where the time index determines the time connection relationship and the feature difference degree determines the similarity connection relationship. The state diagram is further used to generate a topological complex, which expresses the relationship of multi-source data in a high-dimensional unit structure, so that the construction project presents a topological form with structural meaning at different time periods.

[0158] Subsequently, based on multiple preset scale parameters, continuous cohomology analysis is performed on the topological complex to extract stable topological features and generate a topological fingerprint sequence to characterize the trend of the construction project's cost behavior over time. In order to achieve deviation judgment, multiple historical construction data with normal construction behavior are used to generate historical topological fingerprint sequences in the same way, and vectorized embedding is used to combine them to form a normal behavior baseline region, making it an important reference for judging whether the construction project has experienced structural deviation.

[0159] In practical use, whenever new daily data is written into the state vector sequence, a new topological fingerprint sequence can be generated synchronously and input into the topological attention neural network to extract attention features. Then, it is compared with the normal behavior baseline area. The comparison results can clarify whether the current evolution trend of the construction project deviates from the normal behavior range and whether the degree of deviation is within an acceptable range. When the gap between the attention features extracted by the topological attention neural network and the normal behavior baseline area gradually widens, it indicates that there is a potential cost deviation risk.

[0160] To further capture early structural changes, this invention introduces a dynamic bifurcation detection mechanism in actual engineering operations. Based on the topological fingerprint sequence, by calculating the change in adjacent time indices and further generating local change features, it can identify bifurcation signs such as sign reversal, real part crossing zero, and numerical form changing from real value to paired complex value. If the above changes occur, it indicates that the cost evolution trend may have a critical turning point and is about to enter the risk range of cost runaway. Such signs often appear before the actual cost deviation has manifested, providing a more early judgment basis for risk management.

[0161] To further verify the reliability of this method, the present invention conducted a follow-up analysis during a phased plan adjustment. During this period, due to adjustments in construction content and the reallocation of some resources, the constraints of cost, schedule, and pricing rules changed simultaneously. Traditional methods failed to identify the potential impact at that time, and the risk only became apparent when subsequent costs were significantly higher. However, the present invention showed a structural change trend in the topological fingerprint sequence and continuous sign flipping and zero-point crossing signs in the bifurcation feature sequence, indicating a possible risk of abrupt cost structure changes. Furthermore, it showed a trend of deviating from the normal behavior baseline area in the topological anomaly score. The management personnel then adjusted the resource allocation rhythm and prioritized checking the resource occupancy content based on the bifurcation signs, ultimately avoiding a potential cost runaway. This process fully reflects the early warning sensitivity of the present invention in the evolution of complex construction behavior.

[0162] Furthermore, another practical application scenario of this invention occurred during a period when continuous rainfall caused changes in construction progress and resource scheduling plans. Although various costs did not increase significantly at that time, the topological fingerprint sequence showed a subtle structural drift trend. Through dynamic bifurcation detection, this invention identified multiple sign changes in local change features and formed a slight deviation outside the normal behavior baseline area, indicating the risk of indirect cost increases caused by progress delays. Managers optimized the process and scheduled personnel in advance, avoiding the risk of cumulative cost increases, demonstrating the invention's ability to identify hidden risks in advance.

[0163] Table 1. Comparison of the overall performance of the method of the present invention and the traditional method.

[0164]

[0165] As shown in Table 1, the method of this invention significantly improves the anomaly identification performance compared to both traditional rule-based thresholding and traditional statistical monitoring methods. The accuracy of the traditional rule-based thresholding method is only 81.2%, and that of the traditional statistical monitoring method is improved to 84.5%, but it is still insufficient to fully capture the complex changes in engineering cost behavior. The method of this invention, through topological complex modeling, multi-scale continuous homology analysis, and topological fingerprint sequence generation, preserves high-dimensional structural relationships and achieves a more comprehensive behavioral description. Therefore, the accuracy reaches 89.6%, which is significantly better than the two traditional methods. In terms of recall, the method of this invention reaches 86.4%, which is an improvement compared to 74.3% of the traditional rule-based thresholding method and 78.1% of the traditional statistical monitoring method. This indicates that the invention can identify more potential anomalies, especially when structural changes have not yet fully manifested. Early risks can be captured through bifurcation signs and topological shifts. The improvement in precision and F1-score further proves that the method of this invention improves the identification ability while reducing false positives. This is due to the topological attention neural network's capture of complex structural features and the unified constraint of the normal behavior baseline region, which makes the judgment of abnormal behavior more accurate.

[0166] In terms of early warning lead time, the method of this invention has achieved significant advantages. The average early warning time of the traditional rule threshold method is only 0.8 days, and that of the traditional statistical monitoring method is 1.6 days, while the method of this invention reaches 3.9 days, which is several times higher than that of the traditional method. The core reason for this significant difference is that the method of this invention not only relies on changes in data results, but also captures potential risks in advance through topological evolution trends and dynamic bifurcation signs. The topological fingerprint sequence can sensitively reflect slight shifts in structural morphology, while the bifurcation feature sequence can identify key signs such as sign flipping and zero-point crossing before the system reaches its critical point, thereby achieving a more significant early warning lead time than the traditional method.

[0167] In terms of stability, the advantages of the method of this invention can be further demonstrated by the fluctuation sensitivity. The traditional rule threshold method is extremely sensitive to data fluctuations, with a fluctuation sensitivity as high as 0.41. The traditional statistical monitoring method has improved this to 0.35, but it is still easily affected by noise interference and may lead to false judgments of fluctuations. The fluctuation sensitivity of the method of this invention is reduced to 0.23, and the stability is significantly improved. This is mainly due to the strong noise resistance of the topological features themselves, and the continuous homology analysis can suppress the influence of local disturbances, making the method of this invention insensitive to short-term fluctuations, thereby maintaining the continuity and consistency of identification.

[0168] In terms of false alarm capability, the false alarm rate of the method of this invention is 6.7%, which is significantly lower than the 12.3% of the traditional rule threshold method and the 10.4% of the traditional statistical monitoring method. Traditional methods are prone to false alarms when the data fluctuates slightly due to the use of fixed thresholds or statistical deviation features. However, this invention uses vectorized modeling of the normal behavior baseline region to enable quantitative comparison of behavior at each moment in a high-dimensional topological space. Only when the behavior deviates from the normal behavior structure will an early warning be triggered, which fundamentally reduces false alarms. The introduction of the topological attention neural network also makes feature extraction more targeted, further reducing the false alarm rate.

[0169] In summary, all the indicators in the table demonstrate that the method of this invention is superior to traditional methods in terms of accuracy, lead time, stability, and false alarm rate. This improvement is not only due to the high-dimensional structural representation capabilities provided by topological complexes and continuous cohomology for engineering behavior, but also to the sensitive capture of trend critical points by bifurcation detection and the intelligent identification of abnormal offsets by topological attention neural networks. This enables the method of this invention to achieve more comprehensive, reliable, and lead time cost anomaly warnings in complex engineering scenarios.

[0170] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for identifying and warning of engineering cost anomalies based on machine learning, characterized in that, Includes the following steps: Collect bill of quantities, cost, schedule and pricing rule data, clean and encode them, combine them into state vectors under each time index, and generate a state vector sequence. A state graph is constructed based on the state vector sequence. The state vectors are set as graph nodes and edges are connected according to time sequence and similarity threshold. A topological complex representing the relationship between cost, schedule and pricing rule constraints is generated on the state graph. Perform continuous homology analysis on the topological complex under different scale parameters, calculate topological features, and generate a topological fingerprint sequence of the target project in time index order; Data from multiple historical normal projects are processed to generate historical topological fingerprint sequences. These historical topological fingerprint sequences are then vectorized and embedded to determine the baseline region for normal behavior within the embedding space. The target engineering topological fingerprint sequence is vectorized and embedded, and compared with the normal behavior baseline region in the topological attention neural network to generate a topological anomaly score; Based on the topological fingerprint sequence of the target project, dynamic bifurcation detection processing is performed to construct a bifurcation feature sequence that characterizes the evolution trend of the topological fingerprint. When the bifurcation feature sequence shows signs of bifurcation such as eigenvalue sign reversal, eigenvalue real part crossing zero, or eigenvalue changing from real pair to conjugate complex pair, or when the topological anomaly score exceeds the recognition threshold, a cost warning signal is generated.

2. The method for identifying and warning of engineering cost anomalies based on machine learning according to claim 1, characterized in that, The generation of the state vector sequence specifically includes: Collect bill of quantities, cost, schedule and pricing rules data, and record the data in a structured manner according to the bill of quantities item code, cost item, schedule time index and rule identifier; Perform missing item correction, data consistency verification, and outlier removal on structured records; perform time alignment on data with different time indexes; and generate multi-source engineering data. Perform normalization processing on numerical fields in multi-source engineering data, perform encoding processing on category fields, and generate bill of quantities features, cost features, schedule features, and pricing rule features; The four types of features corresponding to each time index are extracted, combined in a preset order to form a state vector, and then arranged in the order of time index to generate a state vector sequence.

3. The method for identifying and warning of engineering cost anomalies based on machine learning according to claim 1, characterized in that, The generation of the topological complex specifically includes: Based on the time index in the state vector sequence, each state vector is set as a graph node in chronological order, and a graph node set is generated in the set order. Temporal constraints are applied to the state vectors based on the time index, time connections are established between state vectors with adjacent time indices, and time connections are established between state vectors whose time index difference is within a preset range in chronological order. Calculate the feature difference degree for any two state vectors, filter state vector pairs whose feature difference degree does not exceed a preset threshold, and establish similarity edges for the filtered state vector pairs. A graph edge set is formed by time-connected edges and similarity-connected edges, which is combined with a graph node set to generate a state graph. On the state graph, graph nodes are used as zero-dimensional units and graph edges are used as one-dimensional units. High-dimensional units are generated according to the construction rules based on node connectivity. The topological complex is composed of all zero-dimensional units, one-dimensional units and their high-dimensional units.

4. The method for identifying and warning of engineering cost anomalies based on machine learning according to claim 1, characterized in that, The generation of the target project topology fingerprint sequence specifically includes: Apply scale changes sequentially to the topological complex under multiple preset scale parameters to generate the topological complex shape at the corresponding scale; Topological features are extracted from the topological complex morphology at various scales to generate a set of topological features composed of topological features at different scales; Arrange the topological feature sets in chronological order according to the time index to generate a topological feature sequence; The topological feature sequence is fingerprinted and arranged in time index order to generate the target project topological fingerprint sequence.

5. The method for identifying and warning of engineering cost anomalies based on machine learning according to claim 1, characterized in that, The determination of the baseline region for normal behavior specifically includes: Data from multiple historical normal projects are collected and preprocessed, and each historical normal project is generated into a corresponding historical state vector sequence according to the time index. A historical state graph is constructed based on each historical state vector sequence, and the corresponding historical topological complex is generated. Continuous homology analysis is performed on each historical topological complex under multiple preset scale parameters to extract topological features at different scales and generate a set of historical topological features for each historical project. Based on the time index, each set of historical topological features is arranged in chronological order to generate a sequence of historical topological features for each historical project. The historical topological feature sequence is fingerprinted to generate the corresponding historical topological fingerprint sequence. Multiple historical topological fingerprint sequences are vectorized and embedded to generate a set of historical topological fingerprint vectors; Based on the distribution structure of historical topological fingerprint vector sets in the embedding space, the baseline region for normal behavior is determined.

6. The method for identifying and warning of engineering cost anomalies based on machine learning according to claim 1, characterized in that, The generation of the topology anomaly score specifically includes: The topological fingerprint sequence of the target project is organized, and the topological fingerprints corresponding to each time index are generated into a topological fingerprint input sequence in a set order; The topological fingerprint input sequence is vectorized to generate a topological fingerprint vector sequence arranged by time index; The topological fingerprint vector sequence is input into the topological attention neural network to extract attention features from the topological fingerprint vector sequence; The extracted attention features are compared with the baseline region of normal behavior to generate topological association features; A topological anomaly score is generated based on topological association features.

7. The method for identifying and warning of engineering cost anomalies based on machine learning according to claim 1, characterized in that, The generation of the cost warning signal specifically includes: Perform change calculations on the topological fingerprints corresponding to adjacent time indices in the topological fingerprint sequence of the target project to generate a change sequence; Local change features are generated for each item in the change sequence, resulting in a local change feature sequence. For the local change feature sequence, perform symbol recording and symbol comparison, write the time index of the positive and negative flip of the symbol into the symbol flip record, perform real part recording and zero-point crossing detection, write the time index of the real part crossing the zero point into the zero-point crossing record, perform complex value form recording and form change judgment, and write the time index of the real value form changing into the paired complex value form into the conjugate change record. The sign flip record, zero-point crossing record, and conjugate change record are written into the same structure in time index order to generate a bifurcation feature sequence; Read the topology anomaly score, and generate a cost warning signal when any record exists in the bifurcation feature sequence or the topology anomaly score exceeds the identification threshold.

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