A method using a fast algorithm automated analysis of time series sensor data that can find an optimal clustering value k for k-means analysis by using statistical analysis of the results of clustering for a stated maximal upper value of k.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. In a system comprising a piece of equipment with one or more sensors installed thereon, said one or more sensors capable of obtaining data relevant to the operation of said equipment and capable of forwarding said data to a computing device, said computing device capable of populating a database with said data and of performing calculations on data contained therein, a method comprising the following steps: A1. Obtain multiple data points from the one or more sensors over regular intervals for a fixed period of time, whereby each data point is a value reported by said one or more sensors attached to said equipment; A2. Store data points in said computer readable database; A3. Perform an initial cluster analysis on the set of stored data points to obtain a maximum of N clusters for some N which is larger than an expected optimal number of clusters (designated “k”); A4. Reject false clusters containing only two members when such clusters are identifiable as an anomaly caused by the one or more sensors; A5. Calculate cluster centroids (mean values) for each non-rejected cluster; A6. Store non-rejected clusters and their corresponding centroids in said computer readable database; B1. Build a vector of input values from each of the stored cluster centroids from the set of clusterings, whereby the input is a set of clustering obtained by repeating Steps A1-A4 one or more times; B2. Compute all possible clusterings from 1 to N−1 using said vector of input values and for each said clustering compute a distortion function; B3. Select as k the optimal clustering that produces the largest difference in the distortion function; B4. Store the optimal clustering in the database together with means, standard deviations, number of members, and pre-computed confidence interval values; C1. Take the clustering from Step B4 and test for overlapping confidence intervals and compute the pooled standard deviations, yielding a single clustering that represents a set of operating states for the equipment, said clustering having discrete boundaries given by confidence intervals; C2. Using a series of sensor measurements over time, test each measurement to see which operating state it represents, corresponding to cluster 0 through k, building a chain of operating states over time; C3. Traverse the chain of operating states to yield a set of state transitions as well as the count, mean, and standard deviation of the time spent in each state; C4. Using the set of state transitions, construct a transition matrix that gives the probability of changing to state Y, given any state X; C5. Apply an equipment specific set of criteria based on the state counts and/or duration and the transition probabilities whereby states with low duration and relatively equal transition probabilities indicate the removal of transitional or spurious operating states caused by anomalies of the measurement sensor or known properties of the equipment; and C6. Store the final set of operating states in a database table and use same to provide information to an end-user or to alert the end-user to conditions requiring human attention. 2. The method of claim 1 wherein Step A1 involves one sensor reading per minute. 3. The method of claim 1 wherein Step A3 involves performing the initial cluster analysis over a period of multiple days. 4. The method of claim 1 wherein Step A3 involves performing the initial cluster analysis over a period ranging from 5 days to 90 days. 5. The method of claim 1 wherein Step A3 involves choosing initial cluster seeds from a mean set of previous clusterings. 6. The method of claim 1 wherein Step A3 involves developing initial cluster seeds by applying a k-means++ algorithm. 7. The method of claim 1 wherein Step B1 further involves computing pooled variance when the centroids represent distributions rather than single observations. 8. The method of claim 1 wherein the distortion function computed in Step B2 is the distortion function defined by Sugar and James. 9. The method of claim 1 further comprising the following step: B3A. If the optimal clustering contains only two members, as determined using a threshold test of the coefficient of variability, reject said clustering and repeat Step B3, whereby Step B3A follows Step B3. 10. The method of claim 1 wherein clusters are collapsed in Step C1 if necessary. 11. In a system comprising a piece of equipment with one or more sensors installed thereon, said one or more sensors capable of obtaining data relevant to the operation of said equipment and capable of forwarding said data to a computing device, said computing device capable of populating a database with said data and of performing calculations on data contained therein, a method comprising the following steps: A1. Obtain multiple data points from the one or more sensors over regular intervals for a fixed period of time, whereby each data point is a value reported by said one or more sensors attached to said equipment, with one sensor reading per minute; A2. Store data points in said computer readable database; A3. Perform an initial cluster analysis on the set of stored data points over a period of multiple days ranging from 5 to 90 to obtain a maximum of N clusters for some N which is larger than an expected optimal number of clusters (designated “k”), whereby initial cluster seeds are chosen from the mean set of previous clusterings if such exist, or if previous clusterings do not exist the initial cluster seeds are developed by applying a k-means++ algorithm; A4. Reject false clusters containing only two members when such clusters are identifiable as an anomaly caused by the corresponding sensor; A5. Calculate cluster centroids (mean values) for each non-rejected cluster; A6. Store non-rejected clusters and their corresponding centroids in said computer readable database; B1. Build a vector of input values from each of the stored cluster centroids (mean values) from the set of clusterings, whereby the input is a set of clustering obtained by repeating Steps A1-A4 one or more times, computing pooled variance where necessary; B2. Compute all possible clusterings from 1 to N−1 using said vector of input values and for each said clustering compute a distortion function; B3. Select as k the optimal clustering that produces the largest difference in the distortion function; B4. If the optimal clustering contains only two members, as determined using a threshold test of the coefficient of variability, reject said clustering and repeat Step B3; B5. Store the optimal clustering in the database together with means, standard deviations, number of members, and pre-computed confidence interval values; C1. Take the clustering from Step B5 and test for overlapping confidence intervals, collapsing clusters if necessary, and compute the pooled standard deviations, yielding a single clustering that represents a set of operating states for the equipment, said clustering having discrete boundaries given by confidence intervals; C2. Using a series of sensor measurements over time, test each measurement to see which operating state it represents, corresponding to cluster 0 through k, building a chain of operating states over time; C3. Traverse the chain of operating states to yield a set of state transitions as well as the count, mean, and standard deviation of the time spent in each state; C4. Using the set of state transitions, construct a transition matrix that gives the probability of changing to state Y, given any state X; C5. Apply an equipment specific set of criteria based on the state counts and/or duration and the transition probabilities whereby states with low duration and relatively equal transition probabilities indicate the removal of transitional or spurious operating states caused by anomalies of the measurement sensor or known properties of the equipment; and C6. Store the final set of operating states in a database table and use same to provide information to an end-user or to alert the end-user to conditions requiring human attention. 12. In a system monitoring a number of pieces of equipment with one or more sensors installed thereon, with some of said pieces of equipment of a known type and other of said pieces of equipment of an unknown type, a method for performing operating state analysis to tentatively identify said equipment of unknown types, said method comprising the following steps: A1. Obtain multiple data points from the one or more sensors over regular intervals for a fixed period of time, whereby each data point is a value reported by said one or more sensors attached to said equipment; A2. Store data points in said computer readable database; A3. Perform an initial cluster analysis on the set of stored data points to obtain a maximum of N clusters for some N which is larger than an expected optimal number of clusters (designated “k”); A4. Reject false clusters containing only two members when such clusters are identifiable as an anomaly caused by the one or more sensors; A5. Calculate cluster centroids (mean values) for each non-rejected cluster; A6. Store non-rejected clusters and their corresponding centroids in said computer readable database; B1. Build a vector of input values from each of the stored cluster centroids from the set of clusterings, whereby the input is a set of clustering obtained by repeating Steps A1-A4 one or more times; B2. Compute all possible clusterings from 1 to N−1 using said vector of input values and for each said clustering compute a distortion function; B3. Select as k the optimal clustering that produces the largest difference in the distortion function; B4. Store the optimal clustering in the database together with means, standard deviations, number of members, and pre-computed confidence interval values; C1. Take the clustering from Step B4 and test for overlapping confidence intervals and compute the pooled standard deviations, yielding a single clustering that represents a set of operating states for the equipment, said clustering having discrete boundaries given by confidence intervals; C2. Using a series of sensor measurements over time, test each measurement to see which operating state it represents, corresponding to cluster 0 through k, building a chain of operating states over time; C3. Traverse the chain of operating states to yield a set of state transitions as well as the count, mean, and standard deviation of the time spent in each state; C4. Using the set of state transitions, construct a transition matrix that gives the probability of changing to state Y, given any state X; C5. Apply an equipment specific set of criteria based on the state counts and/or duration and the transition probabilities whereby states with low duration and relatively equal transition probabilities indicate the removal of transitional or spurious operating states caused by anomalies of the measurement sensor or known properties of the equipment; C6. Store the final set of operating states in a database table; D1. Use stored operating state analyses over a period of time for each piece of equipment, performing a four dimensional optimal cluster analysis on the operating state analyses of known equipment with similar sensors, using the following dimensions: number of operating states, mean duration of each operating state, relative amplitude of each operating state, and distance between the state transition matrices; D2. Accept as valid types those clusters that have narrow confidence intervals in each dimension; D3. Compute the Euclidean distance in four dimensions between the operating state analyses of the unknown piece of equipment and the accepted clusters of equipment types; D4. If each dimension falls within the n% confidence intervals of each component of some cluster, then it can be accepted as belonging to that cluster; D5. If some dimensions match and others do not, the overall clustering can be repeated and if nothing changes except the one cluster containing the unknown equipment and that cluster continues to have acceptably narrow confidence intervals, then it can be accepted as belonging to that cluster; and D6. Otherwise the unknown piece of equipment is rejected as a member of any known type.