1. Construction scheme of DMA

2. FTS anomaly recognition algorithms: DRAS, FLARS and FCARS DRAS (Difference Recognition Algorithm for Signals ) - 2003 FLARS (Fuzzy Logic Algorithm for Recognition of Signals) – 2005 FCARS (Fuzzy Comparison Algorithm for Recognition of Signals) - 2007 realize “smooth” modeling (in fuzzy mathematics sense introduced by L. Zade) of interpreter’s logic, that searches for anomalies on FTS. FTS DRAS,FLARS, FCARS local level Rectification of FTS FTS Anomalies FLARS global level DRAS global level FCARS global level Examples of FTS rectification functionals Length of the fragment, energy of the fragment, difference of the fragment from its regression of order n.

3. Interpreter’s Logic. Illustration Global level - searching the uplifts on rectification Local level - rectification of the record Record

4. DRAS and FLARS: local level - rectification Discrete positive semiaxes  h + ={kh; k=1,2,3,…} Record y={y k =y(kh), k=1,2,3,…} Registration period Y   h + Parameter of local observation Δ=lh, l=1,2,… Fragment of local observation Δ k y={y k-Δ/h,…, y k,…, y k+Δ/h }   Δ  h+1 Definition. A non-negative mapping  defined on the set of fragments  {Δ k y}  2Δ/h+1 we call by a rectifying functional of the given record “y”. We call any function  y  k  Δ k y  by rectification of the record “y”.

5. Examples of rectifications 1 Length of the fragment: 2 Energy of the fragment: 3 Difference of the fragment from its regression of order n: here as usual is an optimal mean squares approximation of order n of the fragment. If n=0 we get the previous functional “energy of the fragment”: 4 Oscillation of the fragment:

6. Illustration of rectification Record Rectification «Energy» Rectification «Length»

7. DRAS: Difference Recognition Algorithm for Signals. Left and Right background measures Record rectification Record fragmentation Potential anomaly on the record Genuine anomaly on the record Record Paris, 3-5 November 2004

8. DRAS: global level. Recognition of potential anomalies. Left and right background measures of silence - β– horizontal level of background Potential anomaly on the record y:  - vertical level of background PA={kh  Y : min((L α Φ y )(k), (R α Φ y )(k)) < β} Regular behavior of the record y: B={kh  Y : min((L α Φ y )(k), (R α Φ y )(k))  β}

9. DRAS: global level. Recognition of genuine anomalies. Potential anomalies PA = UP(i), n=1,2, N. is a union of coherent components DRAS recognizes genuine anomalies A(n) as parts of P(n) by analyzing operator DΦ(k) = LΦ(k) - RΦ(k). The beginning of A(n) is the first positive maximum of DΦ(k) on P(n). Indeed, the difference between “calmness” from the left and anomaly behavior from the right is the biggest in this point. By the same reason, the end of A(n) is in the last negative minimum of DΦ(k).

10. DRAS: recognition of potential anomaly.

11. DRAS: recognition of genuine anomaly. Genuine anomalies on the record y, A = {alternating-sign decreasing segments for (DαΦy)(k)}

12. FLARS: Global level. recognition of genuine anomaly. α  [0,1] – vertical level of how extreme are the measure values Regular behavior/ potential anomaly NA = { kh  Y : μ(k)<α} Genuine anomaly on the record y A = { kh  Y : μ(k)  α}

13. FLARS: global level. Recognition of potential anomaly. We introduce the function that possesses the following properties: One-sided background measures - Θ – the parameter of intermediate observation: Δ<Θ≤Δ. β – horizontal level of background,  (-1,1) Potential anomaly on the record y PA={kh  NA : min((L α Φ y )(k), (R α Φ y )(k)) < β} Regular behavior of the record y B={kh  NA : min((L α Φ y )(k), (R α Φ y )(k))  β}

14. FLARS: anomaly measure μ(k)  - parameter of global observation δ k  k  - model of global observation record at the point k The following sum will be an “argument” for minimality (regularity) of the point “kh” The following sum will be an “argument” for maximality (anomaly) of the point “kh” The measure is a result of the comparison of the “arguments” and

15. FLARS: recognition of anomaly on the record. Anomality measure Rectification Record

16. FLARS: application to the Superconducting Gravimeters data preprocessing (Strasbourg, France)

17. DRAS FLARS DRAS and FLARS recognition comparison

18. FCARS FCARS anomaly recognition

19. What algorithm to apply to FTS data sets? DRAS. Calm and anomaly points are quite well distinguished, but genuine anomalies are not evident. DRAS is useful in searching big anomalies. FLARS. High amplitude anomalies are quite obvious and small anomalies are not so evident on the background of noise. Useful to search very small isolated anomalies. FCARS. Important in searching oscillating anomalies and identification of the beginning and ends of the signals.